[ Task { taskDirectness = Direct , taskHypotheses = [ ( Marker "union_defn" , Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ) , ( Marker "ext" , Quantified Universally ( Scope ( Connected Implication ( Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "A" ) ) ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "B" ) ) ) ) ] ) ) ) ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ] , taskConjectureLabel = Marker "union_comm" , taskConjecture = TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( NamedVar "A" ) , TermVar ( NamedVar "B" ) ] , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( NamedVar "B" ) , TermVar ( NamedVar "A" ) ] ] } , Task { taskDirectness = Direct , taskHypotheses = [ ( Marker "union_comm" , Quantified Universally ( Scope ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "B" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ] ) ) ) , ( Marker "union_defn" , Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ) , ( Marker "ext" , Quantified Universally ( Scope ( Connected Implication ( Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "A" ) ) ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "B" ) ) ) ) ] ) ) ) ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ] , taskConjectureLabel = Marker "union_assoc" , taskConjecture = Quantified Universally ( Scope ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermVar ( F ( TermVar ( NamedVar "B" ) ) ) ] , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "B" ) ) ) , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ] ) ) ) } , Task { taskDirectness = Direct , taskHypotheses = [ ( Marker "union_comm" , Quantified Universally ( Scope ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "B" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ] ) ) ) , ( Marker "union_defn" , Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ) , ( Marker "ext" , Quantified Universally ( Scope ( Connected Implication ( Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "A" ) ) ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "B" ) ) ) ) ] ) ) ) ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) , ( Marker "union_assoc1" , Quantified Universally ( Scope ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermVar ( F ( TermVar ( NamedVar "B" ) ) ) ] , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "B" ) ) ) , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ] ) ) ) ) ] , taskConjectureLabel = Marker "union_assoc" , taskConjecture = Quantified Universally ( Scope ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "B" ) ) ) , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermVar ( F ( TermVar ( NamedVar "B" ) ) ) ] , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ) ) ) } , Task { taskDirectness = Direct , taskHypotheses = [ ( Marker "union_comm" , Quantified Universally ( Scope ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "B" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ] ) ) ) , ( Marker "union_defn" , Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "A" ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) ) , ( Marker "ext" , Quantified Universally ( Scope ( Connected Implication ( Quantified Universally ( Scope ( Connected Equivalence ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "A" ) ) ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermVar ( F ( TermVar ( B ( NamedVar "B" ) ) ) ) ] ) ) ) ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( B ( NamedVar "A" ) ) , TermVar ( B ( NamedVar "B" ) ) ] ) ) ) ) , ( Marker "union_assoc1" , Quantified Universally ( Scope ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "B" ) ) ) , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermVar ( F ( TermVar ( NamedVar "B" ) ) ) ] , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ) ) ) ) , ( Marker "union_assoc2" , Quantified Universally ( Scope ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermVar ( F ( TermVar ( NamedVar "B" ) ) ) ] , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "in" ) ) ) [ TermVar ( B ( NamedVar "a" ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "A" ) ) ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( F ( TermVar ( NamedVar "B" ) ) ) , TermVar ( F ( TermVar ( NamedVar "C" ) ) ) ] ] ] ) ) ) ) ] , taskConjectureLabel = Marker "union_assoc" , taskConjecture = TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( NamedVar "A" ) , TermVar ( NamedVar "B" ) ] , TermVar ( NamedVar "C" ) ] , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( NamedVar "A" ) , TermSymbol ( SymbolMixfix [ Nothing , Just ( Command "union" ) , Nothing ] ) [ TermVar ( NamedVar "B" ) , TermVar ( NamedVar "C" ) ] ] ] } ]