[ Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "relation"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateNoun
                                    ( SgPl
                                        { sg =
                                            [ Just
                                                ( Word "relation" )
                                            ]
                                        , pl =
                                            [ Just
                                                ( Word "relations" )
                                            ]
                                        }
                                    )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "f" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "f" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "f" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "rightunique"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateAdj
                                    [ Just
                                        ( Word "right-unique" )
                                    ]
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "f" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "f" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "f" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "dom"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "dom" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "f" )
                                )
                            ]
                        , TermVar
                            ( B
                                ( NamedVar "f" )
                            )
                        ]
                    )
                )
            )
        ,
            ( Marker "apply"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "apply" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "f" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "x" )
                                )
                            ]
                        , TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        ]
                    )
                )
            )
        ,
            ( Marker "definefunctiontest1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateNoun
                        ( SgPl
                            { sg =
                                [ Just
                                    ( Word "relation" )
                                ]
                            , pl =
                                [ Just
                                    ( Word "relations" )
                                ]
                            }
                        )
                    )
                )
                [ TermVar
                    ( NamedVar "f" )
                ]
            )
        ,
            ( Marker "definefunctiontest2"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateAdj
                        [ Just
                            ( Word "right-unique" )
                        ]
                    )
                )
                [ TermVar
                    ( NamedVar "f" )
                ]
            )
        ,
            ( Marker "definefunctiontest3"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "z" )
                                )
                            , TermVar
                                ( F
                                    ( TermVar
                                        ( NamedVar "x" )
                                    )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Symbol "=" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "apply" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "f" )
                                        )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "z" )
                                    )
                                ]
                            , TermVar
                                ( B
                                    ( NamedVar "z" )
                                )
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "definefunctiontest4"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Symbol "=" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "dom" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "f" )
                    ]
                , TermVar
                    ( NamedVar "x" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "definefunctiontest"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "x" )
            , TermVar
                ( NamedVar "y" )
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "x" )
            , TermVar
                ( NamedVar "y" )
            ]
        )
    }
]