[ Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_refl2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_refl"
    , taskConjecture = TermSymbol
        ( SymbolPredicate
            ( PredicateSymbol "Cong" )
        )
        [ TermVar
            ( NamedVar "a" )
        , TermVar
            ( NamedVar "b" )
        , TermVar
            ( NamedVar "a" )
        , TermVar
            ( NamedVar "b" )
        ]
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "cong_refl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_sym1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateSymbol "Cong" )
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "b" )
                , TermVar
                    ( NamedVar "c" )
                , TermVar
                    ( NamedVar "d" )
                ]
            )
        ,
            ( Marker "cong_sym2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "d" )
                ]
            )
        ,
            ( Marker "cong_sym3"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "c" )
                ]
            )
        ,
            ( Marker "cong_sym4"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_sym5"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_sym"
    , taskConjecture = TermSymbol
        ( SymbolPredicate
            ( PredicateSymbol "Cong" )
        )
        [ TermVar
            ( NamedVar "c" )
        , TermVar
            ( NamedVar "d" )
        , TermVar
            ( NamedVar "a" )
        , TermVar
            ( NamedVar "b" )
        ]
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "cong_sym"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "a" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "b" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "d" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_transitive1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "f" )
                ]
            )
        ,
            ( Marker "cong_transitive2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "e" )
                ]
            )
        ,
            ( Marker "cong_transitive3"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "d" )
                ]
            )
        ,
            ( Marker "cong_transitive4"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "c" )
                ]
            )
        ,
            ( Marker "cong_transitive5"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_transitive6"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_transitive"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateSymbol "Cong" )
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "b" )
                , TermVar
                    ( NamedVar "c" )
                , TermVar
                    ( NamedVar "d" )
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateSymbol "Cong" )
                )
                [ TermVar
                    ( NamedVar "c" )
                , TermVar
                    ( NamedVar "d" )
                , TermVar
                    ( NamedVar "e" )
                , TermVar
                    ( NamedVar "f" )
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateSymbol "Cong" )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "b" )
            , TermVar
                ( NamedVar "e" )
            , TermVar
                ( NamedVar "f" )
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "cong_transitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "c" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "d" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_sym"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "a" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "b" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "d" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_shuffle_left1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "d" )
                ]
            )
        ,
            ( Marker "cong_shuffle_left2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "c" )
                ]
            )
        ,
            ( Marker "cong_shuffle_left3"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_shuffle_left4"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_shuffle_left"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateSymbol "Cong" )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "b" )
            , TermVar
                ( NamedVar "c" )
            , TermVar
                ( NamedVar "d" )
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateSymbol "Cong" )
            )
            [ TermVar
                ( NamedVar "b" )
            , TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "c" )
            , TermVar
                ( NamedVar "d" )
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "cong_shuffle_left"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_transitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "c" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "d" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_sym"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "a" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "b" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "d" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_shuffle_right1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "d" )
                ]
            )
        ,
            ( Marker "cong_shuffle_right2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "c" )
                ]
            )
        ,
            ( Marker "cong_shuffle_right3"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_shuffle_right4"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_shuffle_right"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateSymbol "Cong" )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "b" )
            , TermVar
                ( NamedVar "c" )
            , TermVar
                ( NamedVar "d" )
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateSymbol "Cong" )
            )
            [ TermVar
                ( NamedVar "b" )
            , TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "d" )
            , TermVar
                ( NamedVar "c" )
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "cong_shuffle_right"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_shuffle_left"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_transitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "c" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "d" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_sym"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "a" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "b" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "d" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "upperdim"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "x" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "y" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "z" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "y" )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Cong" )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateRelation
                                                    ( Command "neq" )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            , TermVar
                                                ( B
                                                    ( NamedVar "v" )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateAdj
                                        [ Just
                                            ( Word "collinear" )
                                        , Just
                                            ( Word "with" )
                                        , Nothing
                                        , Just
                                            ( Word "and" )
                                        , Nothing
                                        ]
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "innerpasch"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "x" )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "y" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "z" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "u" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "x" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "u" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Betw" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "y" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "v" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "z" )
                                        )
                                    ]
                                )
                            )
                            ( Quantified Existentially
                                ( Scope
                                    ( Connected Conjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "w" )
                                                )
                                            ]
                                        )
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( B
                                                        ( NamedVar "w" )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "betw_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Betw" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "five_segment"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "a" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "b" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "aprime" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "bprime" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "OFS" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "aprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "bprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "cprime" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "dprime" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Command "neq" )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "cprime" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "dprime" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "ofs"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateNoun
                                                                ( SgPl
                                                                    { sg =
                                                                        [ Just
                                                                            ( Word "point" )
                                                                        ]
                                                                    , pl =
                                                                        [ Just
                                                                            ( Word "points" )
                                                                        ]
                                                                    }
                                                                )
                                                            )
                                                        )
                                                        [ TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateNoun
                                                            ( SgPl
                                                                { sg =
                                                                    [ Just
                                                                        ( Word "point" )
                                                                    ]
                                                                , pl =
                                                                    [ Just
                                                                        ( Word "points" )
                                                                    ]
                                                                }
                                                            )
                                                        )
                                                    )
                                                    [ TermVar
                                                        ( B
                                                            ( NamedVar "z" )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateNoun
                                                        ( SgPl
                                                            { sg =
                                                                [ Just
                                                                    ( Word "point" )
                                                                ]
                                                            , pl =
                                                                [ Just
                                                                    ( Word "points" )
                                                                ]
                                                            }
                                                        )
                                                    )
                                                )
                                                [ TermVar
                                                    ( B
                                                        ( NamedVar "r" )
                                                    )
                                                ]
                                            )
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateNoun
                                                    ( SgPl
                                                        { sg =
                                                            [ Just
                                                                ( Word "point" )
                                                            ]
                                                        , pl =
                                                            [ Just
                                                                ( Word "points" )
                                                            ]
                                                        }
                                                    )
                                                )
                                            )
                                            [ TermVar
                                                ( B
                                                    ( NamedVar "u" )
                                                )
                                            ]
                                        )
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "v" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "w" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                        )
                        ( Connected Equivalence
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "OFS" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "x" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "y" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "r" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "u" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "v" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "w" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "p" )
                                    )
                                ]
                            )
                            ( Quantified Universally
                                ( Scope
                                    ( Connected Conjunction
                                        ( Connected Conjunction
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "x" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "z" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Betw" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "u" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "w" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                        ( Connected Conjunction
                                            ( Connected Conjunction
                                                ( Connected Conjunction
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "x" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "u" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                    ( TermSymbol
                                                        ( SymbolPredicate
                                                            ( PredicateSymbol "Cong" )
                                                        )
                                                        [ TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "y" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "z" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "v" )
                                                                    )
                                                                )
                                                            )
                                                        , TermVar
                                                            ( F
                                                                ( TermVar
                                                                    ( B
                                                                        ( NamedVar "w" )
                                                                    )
                                                                )
                                                            )
                                                        ]
                                                    )
                                                )
                                                ( TermSymbol
                                                    ( SymbolPredicate
                                                        ( PredicateSymbol "Cong" )
                                                    )
                                                    [ TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "x" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "r" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "u" )
                                                                )
                                                            )
                                                        )
                                                    , TermVar
                                                        ( F
                                                            ( TermVar
                                                                ( B
                                                                    ( NamedVar "p" )
                                                                )
                                                            )
                                                        )
                                                    ]
                                                )
                                            )
                                            ( TermSymbol
                                                ( SymbolPredicate
                                                    ( PredicateSymbol "Cong" )
                                                )
                                                [ TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "y" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "r" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "v" )
                                                            )
                                                        )
                                                    )
                                                , TermVar
                                                    ( F
                                                        ( TermVar
                                                            ( B
                                                                ( NamedVar "p" )
                                                            )
                                                        )
                                                    )
                                                ]
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "segment_construction"
            , Quantified Universally
                ( Scope
                    ( Quantified Existentially
                        ( Scope
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Cong" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( B
                                                ( NamedVar "c" )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "d" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "e" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_id"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Symbol "=" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_pseudotransitive"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( Connected Conjunction
                                ( Connected Conjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "a" )
                                            )
                                        ]
                                    )
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateNoun
                                                ( SgPl
                                                    { sg =
                                                        [ Just
                                                            ( Word "point" )
                                                        ]
                                                    , pl =
                                                        [ Just
                                                            ( Word "points" )
                                                        ]
                                                    }
                                                )
                                            )
                                        )
                                        [ TermVar
                                            ( B
                                                ( NamedVar "b" )
                                            )
                                        ]
                                    )
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateNoun
                                            ( SgPl
                                                { sg =
                                                    [ Just
                                                        ( Word "point" )
                                                    ]
                                                , pl =
                                                    [ Just
                                                        ( Word "points" )
                                                    ]
                                                }
                                            )
                                        )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "d" )
                                    )
                                ]
                            )
                        )
                        ( Connected Implication
                            ( Connected Conjunction
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                )
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateSymbol "Cong" )
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "d" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "e" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "f" )
                                        )
                                    ]
                                )
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateSymbol "Cong" )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "e" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "f" )
                                    )
                                ]
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_refl_swap"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateNoun
                                        ( SgPl
                                            { sg =
                                                [ Just
                                                    ( Word "point" )
                                                ]
                                            , pl =
                                                [ Just
                                                    ( Word "points" )
                                                ]
                                            }
                                        )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "b" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateSymbol "Cong" )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "collinear"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "collinear" )
                                    , Just
                                        ( Word "with" )
                                    , Nothing
                                    , Just
                                        ( Word "and" )
                                    , Nothing
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "b" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "c" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( Connected Disjunction
                                    ( TermSymbol
                                        ( SymbolPredicate
                                            ( PredicateSymbol "Betw" )
                                        )
                                        [ TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "a" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "b" )
                                                    )
                                                )
                                            )
                                        , TermVar
                                            ( F
                                                ( TermVar
                                                    ( B
                                                        ( NamedVar "c" )
                                                    )
                                                )
                                            )
                                        ]
                                    )
                                    ( Connected Disjunction
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                        ( TermSymbol
                                            ( SymbolPredicate
                                                ( PredicateSymbol "Betw" )
                                            )
                                            [ TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "c" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "a" )
                                                        )
                                                    )
                                                )
                                            , TermVar
                                                ( F
                                                    ( TermVar
                                                        ( B
                                                            ( NamedVar "b" )
                                                        )
                                                    )
                                                )
                                            ]
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "cong_zero1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "b" )
                ]
            )
        ,
            ( Marker "cong_zero2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "point" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "points" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "cong_zero"
    , taskConjecture = TermSymbol
        ( SymbolPredicate
            ( PredicateSymbol "Cong" )
        )
        [ TermVar
            ( NamedVar "a" )
        , TermVar
            ( NamedVar "a" )
        , TermVar
            ( NamedVar "b" )
        , TermVar
            ( NamedVar "b" )
        ]
    }
]