diff options
| author | adelon <22380201+adelon@users.noreply.github.com> | 2024-02-10 02:22:14 +0100 |
|---|---|---|
| committer | adelon <22380201+adelon@users.noreply.github.com> | 2024-02-10 02:22:14 +0100 |
| commit | 442d732696ad431b84f6e5c72b6ee785be4fd968 (patch) | |
| tree | b476f395e7e91d67bacb6758bc84914b8711593f /test/golden/inductive/generating tasks.golden | |
Initial commit
Diffstat (limited to 'test/golden/inductive/generating tasks.golden')
| -rw-r--r-- | test/golden/inductive/generating tasks.golden | 8965 |
1 files changed, 8965 insertions, 0 deletions
diff --git a/test/golden/inductive/generating tasks.golden b/test/golden/inductive/generating tasks.golden new file mode 100644 index 0000000..2fb04fe --- /dev/null +++ b/test/golden/inductive/generating tasks.golden @@ -0,0 +1,8965 @@ +[ 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" ) + ] + ] + ) + } +]
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