[ Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "fin"
    , taskConjecture = TermSymbol
        ( SymbolPredicate
            ( PredicateRelation
                ( Command "in" )
            )
        )
        [ TermSymbol
            ( SymbolMixfix
                [ Just
                    ( Command "emptyset" )
                ]
            ) []
        , TermSymbol
            ( SymbolMixfix
                [ Just
                    ( Command "pow" )
                , Just InvisibleBraceL
                , Nothing
                , Just InvisibleBraceR
                ]
            )
            [ TermVar
                ( NamedVar "A" )
            ]
        ]
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "fin"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "A" )
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermVar
                    ( NamedVar "B" )
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pow" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "A" )
                    ]
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "cons" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "B" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pow" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "A" )
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ,
            ( Marker "fin_mono1"
            , TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "subseteq" )
                    )
                )
                [ TermVar
                    ( NamedVar "A" )
                , TermVar
                    ( NamedVar "B" )
                ]
            )
        ]
    , taskConjectureLabel = Marker "fin_mono"
    , taskConjecture = TermSymbol
        ( SymbolPredicate
            ( PredicateRelation
                ( Command "subseteq" )
            )
        )
        [ TermSymbol
            ( SymbolMixfix
                [ Just
                    ( Command "fin" )
                , Just InvisibleBraceL
                , Nothing
                , Just InvisibleBraceR
                ]
            )
            [ TermVar
                ( NamedVar "A" )
            ]
        , TermSymbol
            ( SymbolMixfix
                [ Just
                    ( Command "fin" )
                , Just InvisibleBraceL
                , Nothing
                , Just InvisibleBraceR
                ]
            )
            [ TermVar
                ( NamedVar "B" )
            ]
        ]
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "tracl"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "w" )
            , TermVar
                ( NamedVar "R" )
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "w" )
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "tracl"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "a" )
                    , TermVar
                        ( NamedVar "b" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "times" )
                        , Nothing
                        ]
                    )
                    [ TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "fld" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "R" )
                        ]
                    , TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "fld" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "R" )
                        ]
                    ]
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "b" )
                    , TermVar
                        ( NamedVar "c" )
                    ]
                , TermVar
                    ( NamedVar "R" )
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pair" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "c" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "quasirefltracl"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "fld" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "R" )
                ]
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pair" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "a" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "quasirefltracl"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "a" )
                    , TermVar
                        ( NamedVar "b" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "times" )
                        , Nothing
                        ]
                    )
                    [ TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "fld" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "R" )
                        ]
                    , TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "fld" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "R" )
                        ]
                    ]
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "b" )
                    , TermVar
                        ( NamedVar "c" )
                    ]
                , TermVar
                    ( NamedVar "R" )
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pair" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "c" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "qrefltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "qrefltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "refltracl"
    , taskConjecture = Connected Implication
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermVar
                ( NamedVar "A" )
            ]
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pair" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "a" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermVar
                    ( NamedVar "A" )
                , TermVar
                    ( NamedVar "A" )
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "qrefltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "qrefltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "refltracl"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "a" )
                    , TermVar
                        ( NamedVar "b" )
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "times" )
                        , Nothing
                        ]
                    )
                    [ TermVar
                        ( NamedVar "A" )
                    , TermVar
                        ( NamedVar "A" )
                    ]
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pair" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "b" )
                    , TermVar
                        ( NamedVar "c" )
                    ]
                , TermVar
                    ( NamedVar "R" )
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "pair" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermVar
                    ( NamedVar "c" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "times" )
                    , Nothing
                    ]
                )
                [ TermVar
                    ( NamedVar "A" )
                , TermVar
                    ( NamedVar "A" )
                ]
            ]
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "refltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "refltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "refltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "refltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "qrefltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "qrefltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "acc"
    , taskConjecture = Quantified Universally
        ( Scope
            ( Connected Implication
                ( TermSymbol
                    ( SymbolPredicate
                        ( PredicateRelation
                            ( Command "subseteq" )
                        )
                    )
                    [ TermVar
                        ( B
                            ( NamedVar "xa" )
                        )
                    , TermVar
                        ( B
                            ( NamedVar "xb" )
                        )
                    ]
                )
                ( TermSymbol
                    ( SymbolPredicate
                        ( PredicateRelation
                            ( Command "subseteq" )
                        )
                    )
                    [ TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "pow" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "xa" )
                            )
                        ]
                    , TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "pow" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "xb" )
                            )
                        ]
                    ]
                )
            )
        )
    }
, Task
    { taskDirectness = Direct
    , taskHypotheses =
        [
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "refltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "refltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "refltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "refltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "refltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "qrefltracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "qrefltracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "quasirefltracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "qrefltracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "a" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    ]
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "tracl" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "R" )
                                        )
                                    ]
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "pair" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "b" )
                                        )
                                    , TermVar
                                        ( B
                                            ( NamedVar "c" )
                                        )
                                    ]
                                , TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "pair" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "c" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "w" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "tracl" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "tracl"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "tracl" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fld" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "R" )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin_mono"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( Connected Conjunction
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            )
                            ( TermSymbol
                                ( SymbolPredicate
                                    ( PredicateRelation
                                        ( Command "in" )
                                    )
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Just
                                            ( Command "fin" )
                                        , Just InvisibleBraceL
                                        , Nothing
                                        , Just InvisibleBraceR
                                        ]
                                    )
                                    [ TermVar
                                        ( B
                                            ( NamedVar "A" )
                                        )
                                    ]
                                ]
                            )
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "cons" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "a" )
                                    )
                                , TermVar
                                    ( B
                                        ( NamedVar "B" )
                                    )
                                ]
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Just
                                        ( Command "fin" )
                                    , Just InvisibleBraceL
                                    , Nothing
                                    , Just InvisibleBraceR
                                    ]
                                )
                                [ TermVar
                                    ( B
                                        ( NamedVar "A" )
                                    )
                                ]
                            ]
                        )
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "fin"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "subseteq" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fin" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        ]
                    )
                )
            )
        ,
            ( Marker "lmao"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "x" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "preimg"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "preimg" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "fld"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "fld" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "R" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "times"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "times" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "cons"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "cons" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "pow"
            , Quantified Universally
                ( Scope
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Symbol "=" )
                            )
                        )
                        [ TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "pow" )
                                , Just InvisibleBraceL
                                , Nothing
                                , Just InvisibleBraceR
                                ]
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            ]
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    )
                )
            )
        ,
            ( Marker "subseteq"
            , Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "subseteq" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "A" )
                                )
                            , TermVar
                                ( B
                                    ( NamedVar "B" )
                                )
                            ]
                        )
                        ( Quantified Universally
                            ( Scope
                                ( TermSymbol
                                    ( SymbolPredicate
                                        ( PredicateRelation
                                            ( Symbol "=" )
                                        )
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "A" )
                                                )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( B
                                                    ( NamedVar "B" )
                                                )
                                            )
                                        )
                                    ]
                                )
                            )
                        )
                    )
                )
            )
        ]
    , taskConjectureLabel = Marker "acc"
    , taskConjecture = Connected Implication
        ( Connected Conjunction
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "fld" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    ]
                ]
            )
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "preimg" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermVar
                        ( NamedVar "R" )
                    , TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "cons" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "a" )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Just
                                    ( Command "emptyset" )
                                ]
                            ) []
                        ]
                    ]
                , TermSymbol
                    ( SymbolMixfix
                        [ Just
                            ( Command "pow" )
                        , Just InvisibleBraceL
                        , Nothing
                        , Just InvisibleBraceR
                        ]
                    )
                    [ TermSymbol
                        ( SymbolMixfix
                            [ Just
                                ( Command "fld" )
                            , Just InvisibleBraceL
                            , Nothing
                            , Just InvisibleBraceR
                            ]
                        )
                        [ TermVar
                            ( NamedVar "R" )
                        ]
                    ]
                ]
            )
        )
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Command "in" )
                )
            )
            [ TermVar
                ( NamedVar "a" )
            , TermSymbol
                ( SymbolMixfix
                    [ Just
                        ( Command "fld" )
                    , Just InvisibleBraceL
                    , Nothing
                    , Just InvisibleBraceR
                    ]
                )
                [ TermVar
                    ( NamedVar "R" )
                ]
            ]
        )
    }
]