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 | |
Initial commit
Diffstat (limited to 'test/golden')
126 files changed, 46408 insertions, 0 deletions
diff --git a/test/golden/abbr/encoding tasks.golden b/test/golden/abbr/encoding tasks.golden new file mode 100644 index 0000000..18ba749 --- /dev/null +++ b/test/golden/abbr/encoding tasks.golden @@ -0,0 +1,26 @@ +fof(dummy_abbr_test_adj,conjecture,~?[Xy]:elem(Xy,fx)=>~?[Xy]:elem(Xy,fx)). +------------------ +fof(dummy_abbr_test_noun,conjecture,fx=fx). +fof(dummy_abbr_test_adj,axiom,![Xx]:(~?[Xy]:elem(Xy,Xx)=>~?[Xy]:elem(Xy,Xx))). +------------------ +fof(dummy_abbr_test_verb,conjecture,fx=fy=>fx=fy). +fof(dummy_abbr_test_noun,axiom,![Xx]:Xx=Xx). +fof(dummy_abbr_test_adj,axiom,![Xx]:(~?[Xy]:elem(Xy,Xx)=>~?[Xy]:elem(Xy,Xx))). +------------------ +fof(abbr_test_notin,conjecture,~elem(fx,fy)=>~elem(fx,fy)). +fof(dummy_abbr_test_verb,axiom,![Xx,Xy]:(Xx=Xy=>Xx=Xy)). +fof(dummy_abbr_test_noun,axiom,![Xx]:Xx=Xx). +fof(dummy_abbr_test_adj,axiom,![Xx]:(~?[Xy]:elem(Xy,Xx)=>~?[Xy]:elem(Xy,Xx))). +------------------ +fof(abbr_test_elementof_is_in,conjecture,elem(fx,fy)=>elem(fx,fy)). +fof(abbr_test_notin,axiom,![Xx,Xy]:(~elem(Xx,Xy)=>~elem(Xx,Xy))). +fof(dummy_abbr_test_verb,axiom,![Xx,Xy]:(Xx=Xy=>Xx=Xy)). +fof(dummy_abbr_test_noun,axiom,![Xx]:Xx=Xx). +fof(dummy_abbr_test_adj,axiom,![Xx]:(~?[Xy]:elem(Xy,Xx)=>~?[Xy]:elem(Xy,Xx))). +------------------ +fof(abbr_test_equals_is_eq,conjecture,fx=fy=>fx=fy). +fof(abbr_test_elementof_is_in,axiom,![Xx,Xy]:(elem(Xx,Xy)=>elem(Xx,Xy))). +fof(abbr_test_notin,axiom,![Xx,Xy]:(~elem(Xx,Xy)=>~elem(Xx,Xy))). +fof(dummy_abbr_test_verb,axiom,![Xx,Xy]:(Xx=Xy=>Xx=Xy)). +fof(dummy_abbr_test_noun,axiom,![Xx]:Xx=Xx). +fof(dummy_abbr_test_adj,axiom,![Xx]:(~?[Xy]:elem(Xy,Xx)=>~?[Xy]:elem(Xy,Xx))).
\ No newline at end of file diff --git a/test/golden/abbr/generating tasks.golden b/test/golden/abbr/generating tasks.golden new file mode 100644 index 0000000..397fafe --- /dev/null +++ b/test/golden/abbr/generating tasks.golden @@ -0,0 +1,836 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "dummy_abbr_test_adj" + , taskConjecture = Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "x" ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "x" ) + ) + ) + ] + ) + ) + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "dummy_abbr_test_adj" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "dummy_abbr_test_noun" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "dummy_abbr_test_noun" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "dummy_abbr_test_adj" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "dummy_abbr_test_verb" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "dummy_abbr_test_verb" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "dummy_abbr_test_noun" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "dummy_abbr_test_adj" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "abbr_test_notin" + , taskConjecture = Connected Implication + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "abbr_test_notin" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "dummy_abbr_test_verb" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "dummy_abbr_test_noun" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "dummy_abbr_test_adj" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "abbr_test_elementof_is_in" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "abbr_test_elementof_is_in" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "abbr_test_notin" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "dummy_abbr_test_verb" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "dummy_abbr_test_noun" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "dummy_abbr_test_adj" + , Quantified Universally + ( Scope + ( Connected Implication + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "abbr_test_equals_is_eq" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/abbr/glossing.golden b/test/golden/abbr/glossing.golden new file mode 100644 index 0000000..152fbe1 --- /dev/null +++ b/test/golden/abbr/glossing.golden @@ -0,0 +1,384 @@ +[ BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "empty" ) + ( Abbreviation + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "empty" ) + ] + ) + ) + ( Scope + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( F + ( TermVar + ( B 0 ) + ) + ) + ] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_adj" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "empty" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "empty" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ) + ) +, BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "function" ) + ( Abbreviation + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "function" ) + ] + , pl = + [ Just + ( Word "functions" ) + ] + } + ) + ) + ) + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B 0 ) + , TermVar + ( B 0 ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_noun" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "function" ) + ] + , pl = + [ Just + ( Word "functions" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 21 + , sourceColumn = Pos 1 + } + ) + ( Marker "converges" ) + ( Abbreviation + ( SymbolPredicate + ( PredicateVerb + ( SgPl + { sg = + [ Just + ( Word "converges" ) + , Just + ( Word "to" ) + , Nothing + ] + , pl = + [ Just + ( Word "converge" ) + , Just + ( Word "to" ) + , Nothing + ] + } + ) + ) + ) + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B 0 ) + , TermVar + ( B 1 ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_verb" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateVerb + ( SgPl + { sg = + [ Just + ( Word "converges" ) + , Just + ( Word "to" ) + , Nothing + ] + , pl = + [ Just + ( Word "converge" ) + , Just + ( Word "to" ) + , Nothing + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 31 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_notin" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "notin" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 37 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_elementof_is_in" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "element" ) + , Just + ( Word "of" ) + , Nothing + ] + , pl = + [ Just + ( Word "elements" ) + , Just + ( Word "of" ) + , Nothing + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 43 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_equals_is_eq" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateVerb + ( SgPl + { sg = + [ Just + ( Word "equals" ) + , Nothing + ] + , pl = + [ Just + ( Word "equal" ) + , Nothing + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/abbr/parsing.golden b/test/golden/abbr/parsing.golden new file mode 100644 index 0000000..bad58c3 --- /dev/null +++ b/test/golden/abbr/parsing.golden @@ -0,0 +1,408 @@ +[ BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "empty" ) + ( AbbreviationAdj + ( NamedVar "x" ) + ( Adj + [ Just + ( Word "empty" ) + ] [] + ) + ( StmtNeg + ( SymbolicQuantified Existentially + ( NamedVar "y" :| [] ) Unbounded Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_adj" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "empty" ) + ] [] :| [] + ) + ) + ) + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "empty" ) + ] [] :| [] + ) + ) + ) + ) + ) +, BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "function" ) + ( AbbreviationNoun + ( NamedVar "x" ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "function" ) + ] + , pl = + [ Just + ( Word "functions" ) + ] + } + ) [] + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_noun" ) + ( Lemma [] + ( StmtNoun + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "function" ) + ] + , pl = + [ Just + ( Word "functions" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) + ) +, BlockAbbr + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 21 + , sourceColumn = Pos 1 + } + ) + ( Marker "converges" ) + ( AbbreviationVerb + ( NamedVar "x" ) + ( Verb + ( SgPl + { sg = + [ Just + ( Word "converges" ) + , Just + ( Word "to" ) + , Nothing + ] + , pl = + [ Just + ( Word "converge" ) + , Just + ( Word "to" ) + , Nothing + ] + } + ) + [ NamedVar "y" ] + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Marker "dummy_abbr_test_verb" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPVerb + ( Verb + ( SgPl + { sg = + [ Just + ( Word "converges" ) + , Just + ( Word "to" ) + , Nothing + ] + , pl = + [ Just + ( Word "converge" ) + , Just + ( Word "to" ) + , Nothing + ] + } + ) + [ TermExpr + ( ExprVar + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 31 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_notin" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "notin" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Negative + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 37 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_elementof_is_in" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtNoun + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "element" ) + , Just + ( Word "of" ) + , Nothing + ] + , pl = + [ Just + ( Word "elements" ) + , Just + ( Word "of" ) + , Nothing + ] + } + ) + [ TermExpr + ( ExprVar + ( NamedVar "y" ) + ) + ] + ) ( Nothing ) ( [] ) ( Nothing ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/abbr.tex" + , sourceLine = Pos 43 + , sourceColumn = Pos 1 + } + ) + ( Marker "abbr_test_equals_is_eq" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPVerb + ( Verb + ( SgPl + { sg = + [ Just + ( Word "equals" ) + , Nothing + ] + , pl = + [ Just + ( Word "equal" ) + , Nothing + ] + } + ) + [ TermExpr + ( ExprVar + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/abbr/scanning.golden b/test/golden/abbr/scanning.golden new file mode 100644 index 0000000..397e257 --- /dev/null +++ b/test/golden/abbr/scanning.golden @@ -0,0 +1,19 @@ +[ ScanAdj + [ Just + ( Word "empty" ) + ] + ( Marker "empty" ) +, ScanNoun + [ Just + ( Word "function" ) + ] + ( Marker "function" ) +, ScanVerb + [ Just + ( Word "converges" ) + , Just + ( Word "to" ) + , Nothing + ] + ( Marker "converges" ) +]
\ No newline at end of file diff --git a/test/golden/abbr/tokenizing.golden b/test/golden/abbr/tokenizing.golden new file mode 100644 index 0000000..8da4b07 --- /dev/null +++ b/test/golden/abbr/tokenizing.golden @@ -0,0 +1,164 @@ +[ BeginEnv "abbreviation" +, Label "empty" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "empty" +, Word "iff" +, Word "there" +, Word "exists" +, Word "no" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Word "such" +, Word "that" +, BeginEnv "math" +, Variable "y" +, Command "in" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "abbreviation" +, BeginEnv "proposition" +, Label "dummy_abbr_test_adj" +, Word "if" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "empty" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "empty" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "abbreviation" +, Label "function" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "a" +, Word "function" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "abbreviation" +, BeginEnv "proposition" +, Label "dummy_abbr_test_noun" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "a" +, Word "function" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "abbreviation" +, Label "converges" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "converges" +, Word "to" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "abbreviation" +, BeginEnv "proposition" +, Label "dummy_abbr_test_verb" +, Word "if" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "converges" +, Word "to" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "abbr_test_notin" +, Word "if" +, BeginEnv "math" +, Variable "x" +, Command "notin" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "not" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "abbr_test_elementof_is_in" +, Word "if" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "an" +, Word "element" +, Word "of" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "abbr_test_equals_is_eq" +, Word "if" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "equals" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/abbr/verification.golden b/test/golden/abbr/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/abbr/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/byRef/encoding tasks.golden b/test/golden/byRef/encoding tasks.golden new file mode 100644 index 0000000..75c9e78 --- /dev/null +++ b/test/golden/byRef/encoding tasks.golden @@ -0,0 +1,22 @@ +fof(first_proposition,conjecture,fa=fa). +------------------ +fof(second_proposition,conjecture,fb=fb). +fof(first_proposition,axiom,![Xa]:Xa=Xa). +------------------ +fof(third_proposition,conjecture,fc=fc). +fof(first_proposition,axiom,![Xa]:Xa=Xa). +------------------ +fof(fourth_proposition,conjecture,![Xd]:Xd=Xd). +fof(first_proposition,axiom,![Xa]:Xa=Xa). +------------------ +fof(fourth_proposition,conjecture,fe=fe). +fof(third_proposition,axiom,![Xc]:Xc=Xc). +fof(second_proposition,axiom,![Xb]:Xb=Xb). +fof(first_proposition,axiom,![Xa]:Xa=Xa). +fof(fourth_proposition1,axiom,![Xd]:Xd=Xd). +------------------ +fof(fifth_proposition,conjecture,ff=ff). +fof(fourth_proposition,axiom,![Xe]:Xe=Xe). +fof(third_proposition,axiom,![Xc]:Xc=Xc). +fof(second_proposition,axiom,![Xb]:Xb=Xb). +fof(first_proposition,axiom,![Xa]:Xa=Xa).
\ No newline at end of file diff --git a/test/golden/byRef/generating tasks.golden b/test/golden/byRef/generating tasks.golden new file mode 100644 index 0000000..3187198 --- /dev/null +++ b/test/golden/byRef/generating tasks.golden @@ -0,0 +1,352 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "first_proposition" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "a" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "first_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "second_proposition" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "b" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "first_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "third_proposition" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "c" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "first_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "fourth_proposition" + , taskConjecture = Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "third_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ) + , + ( Marker "second_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + , + ( Marker "first_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + , + ( Marker "fourth_proposition1" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "fourth_proposition" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "e" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "fourth_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + ] + ) + ) + ) + , + ( Marker "third_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ) + , + ( Marker "second_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + , + ( Marker "first_proposition" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "fifth_proposition" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "f" ) + , TermVar + ( NamedVar "f" ) + ] + } +]
\ No newline at end of file diff --git a/test/golden/byRef/glossing.golden b/test/golden/byRef/glossing.golden new file mode 100644 index 0000000..e213bc9 --- /dev/null +++ b/test/golden/byRef/glossing.golden @@ -0,0 +1,155 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "first_proposition" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "a" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "second_proposition" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "third_proposition" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "c" ) + ] + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Qed + ( JustificationRef + ( Marker "first_proposition" :| [] ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 16 + , sourceColumn = Pos 1 + } + ) + ( Marker "fourth_proposition" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "e" ) + ] + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Have + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ) + ( JustificationRef + ( Marker "first_proposition" :| [] ) + ) ( Qed JustificationEmpty ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 23 + , sourceColumn = Pos 1 + } + ) + ( Marker "fifth_proposition" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "f" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) +]
\ No newline at end of file diff --git a/test/golden/byRef/parsing.golden b/test/golden/byRef/parsing.golden new file mode 100644 index 0000000..2cf91b6 --- /dev/null +++ b/test/golden/byRef/parsing.golden @@ -0,0 +1,168 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "first_proposition" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "a" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "second_proposition" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "b" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "third_proposition" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "c" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "c" ) :| [] + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Qed + ( JustificationRef + ( Marker "first_proposition" :| [] ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 16 + , sourceColumn = Pos 1 + } + ) + ( Marker "fourth_proposition" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "e" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "e" ) :| [] + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Have Nothing + ( SymbolicQuantified Universally + ( NamedVar "d" :| [] ) Unbounded Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "d" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "d" ) :| [] + ) + ) + ) + ) + ) + ( JustificationRef + ( Marker "first_proposition" :| [] ) + ) ( Qed JustificationEmpty ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/byRef.tex" + , sourceLine = Pos 23 + , sourceColumn = Pos 1 + } + ) + ( Marker "fifth_proposition" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "f" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "f" ) :| [] + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/byRef/scanning.golden b/test/golden/byRef/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/byRef/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/byRef/tokenizing.golden b/test/golden/byRef/tokenizing.golden new file mode 100644 index 0000000..2ae8ea6 --- /dev/null +++ b/test/golden/byRef/tokenizing.golden @@ -0,0 +1,71 @@ +[ BeginEnv "proposition" +, Label "first_proposition" +, BeginEnv "math" +, Variable "a" +, Symbol "=" +, Variable "a" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "second_proposition" +, BeginEnv "math" +, Variable "b" +, Symbol "=" +, Variable "b" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "third_proposition" +, BeginEnv "math" +, Variable "c" +, Symbol "=" +, Variable "c" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "follows" +, Word "by" +, Ref + ( "first_proposition" :| [] ) +, Symbol "." +, EndEnv "proof" +, BeginEnv "proposition" +, Label "fourth_proposition" +, BeginEnv "math" +, Variable "e" +, Symbol "=" +, Variable "e" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "for" +, Word "all" +, BeginEnv "math" +, Variable "d" +, EndEnv "math" +, Word "we" +, Word "have" +, BeginEnv "math" +, Variable "d" +, Symbol "=" +, Variable "d" +, EndEnv "math" +, Word "by" +, Ref + ( "first_proposition" :| [] ) +, Symbol "." +, EndEnv "proof" +, BeginEnv "proposition" +, Label "fifth_proposition" +, BeginEnv "math" +, Variable "f" +, Symbol "=" +, Variable "f" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/byRef/verification.golden b/test/golden/byRef/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/byRef/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/calc/encoding tasks.golden b/test/golden/calc/encoding tasks.golden new file mode 100644 index 0000000..d4104e6 --- /dev/null +++ b/test/golden/calc/encoding tasks.golden @@ -0,0 +1,30 @@ +fof(trivial,conjecture,fx=fx). +------------------ +fof(irrelevant,conjecture,fz=fz). +fof(trivial,axiom,![Xx]:Xx=Xx). +------------------ +fof(alsotrivial,conjecture,fy=fy). +fof(irrelevant,axiom,![Xz]:Xz=Xz). +fof(trivial,axiom,![Xx]:Xx=Xx). +------------------ +fof(alsotrivial,conjecture,fy=fy). +fof(trivial,axiom,![Xx]:Xx=Xx). +------------------ +fof(alsotrivial,conjecture,fy=fy). +fof(irrelevant,axiom,![Xz]:Xz=Xz). +fof(trivial,axiom,![Xx]:Xx=Xx). +fof(alsotrivial1,axiom,fy=fy). +------------------ +fof(trivial_biconditionals,conjecture,fy=fy). +fof(alsotrivial,axiom,![Xy]:Xy=Xy). +fof(irrelevant,axiom,![Xz]:Xz=Xz). +fof(trivial,axiom,![Xx]:Xx=Xx). +------------------ +fof(trivial_biconditionals,conjecture,fy=fy). +fof(trivial,axiom,![Xx]:Xx=Xx). +------------------ +fof(trivial_biconditionals,conjecture,fy=fy). +fof(alsotrivial,axiom,![Xy]:Xy=Xy). +fof(irrelevant,axiom,![Xz]:Xz=Xz). +fof(trivial,axiom,![Xx]:Xx=Xx). +fof(trivial_biconditionals1,axiom,fy=fy<=>fy=fy).
\ No newline at end of file diff --git a/test/golden/calc/generating tasks.golden b/test/golden/calc/generating tasks.golden new file mode 100644 index 0000000..6bd518c --- /dev/null +++ b/test/golden/calc/generating tasks.golden @@ -0,0 +1,464 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "trivial" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "irrelevant" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "z" ) + , TermVar + ( NamedVar "z" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "irrelevant" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + , + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "alsotrivial" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "alsotrivial" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "irrelevant" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + , + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "alsotrivial1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ] + , taskConjectureLabel = Marker "alsotrivial" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "alsotrivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + , + ( Marker "irrelevant" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + , + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "trivial_biconditionals" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ] + , taskConjectureLabel = Marker "trivial_biconditionals" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "alsotrivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + , + ( Marker "irrelevant" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + , + ( Marker "trivial" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "trivial_biconditionals1" + , Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ] + , taskConjectureLabel = Marker "trivial_biconditionals" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + } +]
\ No newline at end of file diff --git a/test/golden/calc/glossing.golden b/test/golden/calc/glossing.golden new file mode 100644 index 0000000..96366d4 --- /dev/null +++ b/test/golden/calc/glossing.golden @@ -0,0 +1,160 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "trivial" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "irrelevant" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "z" ) + , TermVar + ( NamedVar "z" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "alsotrivial" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Calc + ( Equation + ( TermVar + ( NamedVar "y" ) + ) + ( + ( TermVar + ( NamedVar "y" ) + , JustificationEmpty + ) :| + [ + ( TermVar + ( NamedVar "y" ) + , JustificationRef + ( Marker "trivial" :| [] ) + ) + ] + ) + ) ( Qed JustificationEmpty ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 22 + , sourceColumn = Pos 1 + } + ) + ( Marker "trivial_biconditionals" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Calc + ( Biconditionals + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( + ( PropositionalConstant IsTop + , JustificationEmpty + ) :| + [ + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "y" ) + ] + , JustificationRef + ( Marker "trivial" :| [] ) + ) + ] + ) + ) ( Qed JustificationEmpty ) + ) +]
\ No newline at end of file diff --git a/test/golden/calc/parsing.golden b/test/golden/calc/parsing.golden new file mode 100644 index 0000000..3d86683 --- /dev/null +++ b/test/golden/calc/parsing.golden @@ -0,0 +1,174 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "trivial" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "irrelevant" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "z" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "z" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "alsotrivial" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Calc + ( Equation + ( ExprVar + ( NamedVar "y" ) + ) + ( + ( ExprVar + ( NamedVar "y" ) + , JustificationEmpty + ) :| + [ + ( ExprVar + ( NamedVar "y" ) + , JustificationRef + ( Marker "trivial" :| [] ) + ) + ] + ) + ) ( Qed JustificationEmpty ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 22 + , sourceColumn = Pos 1 + } + ) + ( Marker "trivial_biconditionals" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/calc.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Calc + ( Biconditionals + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ( + ( PropositionalConstant IsTop + , JustificationEmpty + ) :| + [ + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + , JustificationRef + ( Marker "trivial" :| [] ) + ) + ] + ) + ) ( Qed JustificationEmpty ) + ) +]
\ No newline at end of file diff --git a/test/golden/calc/scanning.golden b/test/golden/calc/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/calc/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/calc/tokenizing.golden b/test/golden/calc/tokenizing.golden new file mode 100644 index 0000000..a99980c --- /dev/null +++ b/test/golden/calc/tokenizing.golden @@ -0,0 +1,71 @@ +[ BeginEnv "proposition" +, Label "trivial" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "irrelevant" +, BeginEnv "math" +, Variable "z" +, Symbol "=" +, Variable "z" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "alsotrivial" +, BeginEnv "math" +, Variable "y" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, BeginEnv "align*" +, Variable "y" +, Symbol "&=" +, Variable "y" +, Symbol "&=" +, Variable "y" +, BeginEnv "text" +, Word "by" +, Ref + ( "trivial" :| [] ) +, EndEnv "text" +, EndEnv "align*" +, EndEnv "proof" +, BeginEnv "proposition" +, Label "trivial_biconditionals" +, BeginEnv "math" +, Variable "y" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, BeginEnv "align*" +, Variable "y" +, Symbol "=" +, Variable "y" +, Symbol "&" +, Command "iff" +, Command "top" +, Symbol "&" +, Command "iff" +, Variable "y" +, Symbol "=" +, Variable "y" +, BeginEnv "text" +, Word "by" +, Ref + ( "trivial" :| [] ) +, EndEnv "text" +, EndEnv "align*" +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/calc/verification.golden b/test/golden/calc/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/calc/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/coord/encoding tasks.golden b/test/golden/coord/encoding tasks.golden new file mode 100644 index 0000000..3776aed --- /dev/null +++ b/test/golden/coord/encoding tasks.golden @@ -0,0 +1,41 @@ +fof(nouns,conjecture,fx=fx). +fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)). +fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)). +fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)). +fof(nouns1,axiom,bar(fy)). +fof(nouns2,axiom,bar(fx)). +------------------ +fof(adj_nouns,conjecture,fx=fx). +fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)). +fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)). +fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)). +fof(adj_nouns1,axiom,bar(fy)&foo(fy)). +fof(adj_nouns2,axiom,bar(fx)&foo(fx)). +------------------ +fof(nouns_suchthat,conjecture,fx=fx). +fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)). +fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)). +fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)). +fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)). +fof(nouns_suchthat1,axiom,bar(fy)). +fof(nouns_suchthat2,axiom,bar(fx)). +fof(nouns_suchthat3,axiom,foo(fx)&baz(fy)). +------------------ +fof(noun_verb,conjecture,fx=fy<=>(bar(fx)&fx=fy)). +fof(nouns_suchthat,axiom,![Xx,Xy]:((foo(Xx)&baz(Xy)&bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)). +fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)). +fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)). +fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)). +------------------ +fof(adjs,conjecture,foo(fx)&baz(fx)). +fof(noun_verb,axiom,![Xx,Xy]:(Xx=Xy<=>(bar(Xx)&Xx=Xy))). +fof(nouns_suchthat,axiom,![Xx,Xy]:((foo(Xx)&baz(Xy)&bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(adj_nouns,axiom,![Xx,Xy]:((bar(Xx)&foo(Xx)&bar(Xy)&foo(Xy))=>Xx=Xx)). +fof(nouns,axiom,![Xx,Xy]:((bar(Xx)&bar(Xy))=>Xx=Xx)). +fof(baz,axiom,![Xx]:(baz(Xx)<=>Xx=Xx)). +fof(foo,axiom,![Xx]:(foo(Xx)<=>Xx=Xx)). +fof(bar,axiom,![Xx]:(bar(Xx)<=>Xx=Xx)).
\ No newline at end of file diff --git a/test/golden/coord/generating tasks.golden b/test/golden/coord/generating tasks.golden new file mode 100644 index 0000000..0e43d0e --- /dev/null +++ b/test/golden/coord/generating tasks.golden @@ -0,0 +1,1968 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "baz" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "foo" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "bar" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "nouns1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "nouns2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ] + , taskConjectureLabel = Marker "nouns" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "baz" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "foo" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "bar" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "adj_nouns1" + , Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ) + , + ( Marker "adj_nouns2" + , Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ) + ] + , taskConjectureLabel = Marker "adj_nouns" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "adj_nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "baz" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "foo" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "bar" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "nouns_suchthat1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "nouns_suchthat2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , + ( Marker "nouns_suchthat3" + , Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ) + ] + , taskConjectureLabel = Marker "nouns_suchthat" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "nouns_suchthat" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "adj_nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "baz" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "foo" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "bar" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "noun_verb" + , taskConjecture = Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "noun_verb" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "nouns_suchthat" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "adj_nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "nouns" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "baz" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "foo" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "bar" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "adjs" + , taskConjecture = Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/coord/glossing.golden b/test/golden/coord/glossing.golden new file mode 100644 index 0000000..c051fe9 --- /dev/null +++ b/test/golden/coord/glossing.golden @@ -0,0 +1,437 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "bar" ) + ( DefnPredicate [] + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ( NamedVar "x" :| [] ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "foo" ) + ( DefnPredicate [] + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ( NamedVar "x" :| [] ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "baz" ) + ( DefnPredicate [] + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ( NamedVar "x" :| [] ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "nouns" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Marker "adj_nouns" ) + ( Lemma + [ Asm + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ) + , Asm + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 24 + , sourceColumn = Pos 1 + } + ) + ( Marker "nouns_suchthat" ) + ( Lemma + [ Asm + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 30 + , sourceColumn = Pos 1 + } + ) + ( Marker "noun_verb" ) + ( Lemma [] + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 35 + , sourceColumn = Pos 1 + } + ) + ( Marker "adjs" ) + ( Lemma [] + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "foo" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "baz" ) + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/coord/parsing.golden b/test/golden/coord/parsing.golden new file mode 100644 index 0000000..555b86b --- /dev/null +++ b/test/golden/coord/parsing.golden @@ -0,0 +1,367 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "bar" ) + ( Defn [] + ( DefnNoun + ( NamedVar "x" ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) [] + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "foo" ) + ( Defn [] + ( DefnAdj Nothing + ( NamedVar "x" ) + ( Adj + [ Just + ( Word "foo" ) + ] [] + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "baz" ) + ( Defn [] + ( DefnAdj Nothing + ( NamedVar "x" ) + ( Adj + [ Just + ( Word "baz" ) + ] [] + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "nouns" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Marker "adj_nouns" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" ] + ) NounPhrase + ( + [ AdjL + [ Just + ( Word "foo" ) + ] [] + ] + ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 24 + , sourceColumn = Pos 1 + } + ) + ( Marker "nouns_suchthat" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) + ( Just + ( StmtConnected Conjunction + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "foo" ) + ] [] :| [] + ) + ) + ) + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "y" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "baz" ) + ] [] :| [] + ) + ) + ) + ) + ) + ] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 30 + , sourceColumn = Pos 1 + } + ) + ( Marker "noun_verb" ) + ( Lemma [] + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtNoun + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "bar" ) + ] + , pl = + [ Just + ( Word "bars" ) + ] + } + ) [] + ) ( Nothing ) + ( + [ AdjR + [ Just + ( Word "equal" ) + , Just + ( Word "to" ) + , Nothing + ] + [ TermExpr + ( ExprVar + ( NamedVar "y" ) + ) + ] + ] + ) ( Nothing ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/coord.tex" + , sourceLine = Pos 35 + , sourceColumn = Pos 1 + } + ) + ( Marker "adjs" ) + ( Lemma [] + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "foo" ) + ] [] :| + [ Adj + [ Just + ( Word "baz" ) + ] [] + ] + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/coord/scanning.golden b/test/golden/coord/scanning.golden new file mode 100644 index 0000000..f405a1f --- /dev/null +++ b/test/golden/coord/scanning.golden @@ -0,0 +1,16 @@ +[ ScanNoun + [ Just + ( Word "bar" ) + ] + ( Marker "bar" ) +, ScanAdj + [ Just + ( Word "foo" ) + ] + ( Marker "foo" ) +, ScanAdj + [ Just + ( Word "baz" ) + ] + ( Marker "baz" ) +]
\ No newline at end of file diff --git a/test/golden/coord/tokenizing.golden b/test/golden/coord/tokenizing.golden new file mode 100644 index 0000000..0516d7a --- /dev/null +++ b/test/golden/coord/tokenizing.golden @@ -0,0 +1,150 @@ +[ BeginEnv "definition" +, Label "bar" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "a" +, Word "bar" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "foo" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "foo" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "baz" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "baz" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "proposition" +, Label "nouns" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, EndEnv "math" +, Word "be" +, Word "bars" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "adj_nouns" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, EndEnv "math" +, Word "be" +, Word "foo" +, Word "bars" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "nouns_suchthat" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, EndEnv "math" +, Word "be" +, Word "bars" +, Word "such" +, Word "that" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "foo" +, Word "and" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Word "is" +, Word "baz" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "noun_verb" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "a" +, Word "bar" +, Word "equal" +, Word "to" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "adjs" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "foo" +, Word "and" +, Word "baz" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/coord/verification.golden b/test/golden/coord/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/coord/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/finite-set-terms/encoding tasks.golden b/test/golden/finite-set-terms/encoding tasks.golden new file mode 100644 index 0000000..381bdf0 --- /dev/null +++ b/test/golden/finite-set-terms/encoding tasks.golden @@ -0,0 +1,3 @@ +fof(emptyset_in_unit,conjecture,elem(emptyset,unit)). +fof(unit,axiom,![Xany]:(elem(Xany,unit)<=>(elem(Xany,emptyset)|Xany=emptyset))). +fof(cons,axiom,![Xx,Xy,XX]:(elem(Xx,cons(Xy,XX))<=>(Xx=Xy|elem(Xx,XX)))).
\ No newline at end of file diff --git a/test/golden/finite-set-terms/generating tasks.golden b/test/golden/finite-set-terms/generating tasks.golden new file mode 100644 index 0000000..84df2ba --- /dev/null +++ b/test/golden/finite-set-terms/generating tasks.golden @@ -0,0 +1,165 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "unit" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) + ) + ) + ) + , + ( Marker "cons" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "emptyset_in_unit" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + } +]
\ No newline at end of file diff --git a/test/golden/finite-set-terms/glossing.golden b/test/golden/finite-set-terms/glossing.golden new file mode 100644 index 0000000..7bafb15 --- /dev/null +++ b/test/golden/finite-set-terms/glossing.golden @@ -0,0 +1,135 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( Axiom [] + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "X" ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "X" ) + ] + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "unit" ) + ( DefnOp + [ Just + ( Command "unit" ) + ] [] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "emptyset_in_unit" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ) + ) +]
\ No newline at end of file diff --git a/test/golden/finite-set-terms/parsing.golden b/test/golden/finite-set-terms/parsing.golden new file mode 100644 index 0000000..c30f70b --- /dev/null +++ b/test/golden/finite-set-terms/parsing.golden @@ -0,0 +1,124 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( Axiom [] + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "y" ) + , ExprVar + ( NamedVar "X" ) + ] :| [] + ) + ) + ) + ) + ( StmtConnected Disjunction + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "X" ) :| [] + ) + ) + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "unit" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "unit" ) + ] [] + ) + ( ExprFiniteSet + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] :| [] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/finite-set-terms.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "emptyset_in_unit" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "unit" ) + ] [] :| [] + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/finite-set-terms/scanning.golden b/test/golden/finite-set-terms/scanning.golden new file mode 100644 index 0000000..1a9f920 --- /dev/null +++ b/test/golden/finite-set-terms/scanning.golden @@ -0,0 +1,6 @@ +[ ScanFunctionSymbol + [ Just + ( Command "unit" ) + ] + ( Marker "unit" ) +]
\ No newline at end of file diff --git a/test/golden/finite-set-terms/tokenizing.golden b/test/golden/finite-set-terms/tokenizing.golden new file mode 100644 index 0000000..761cbde --- /dev/null +++ b/test/golden/finite-set-terms/tokenizing.golden @@ -0,0 +1,48 @@ +[ BeginEnv "axiom" +, Label "cons" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Command "cons" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "X" +, InvisibleBraceR +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Word "or" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "X" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "definition" +, Label "unit" +, BeginEnv "math" +, Command "unit" +, Symbol "=" +, VisibleBraceL +, Command "emptyset" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "proposition" +, Label "emptyset_in_unit" +, BeginEnv "math" +, Command "emptyset" +, Command "in" +, Command "unit" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/finite-set-terms/verification.golden b/test/golden/finite-set-terms/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/finite-set-terms/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/formula/encoding tasks.golden b/test/golden/formula/encoding tasks.golden new file mode 100644 index 0000000..ab149dd --- /dev/null +++ b/test/golden/formula/encoding tasks.golden @@ -0,0 +1,4 @@ +fof(formula_test_forall,conjecture,![Xx,Xy]:(Xx=Xx&Xy=Xy)). +------------------ +fof(formula_test_exists,conjecture,?[Xx,Xy]:Xx=Xy). +fof(formula_test_forall,axiom,![Xx,Xy]:(Xx=Xx&Xy=Xy)).
\ No newline at end of file diff --git a/test/golden/formula/generating tasks.golden b/test/golden/formula/generating tasks.golden new file mode 100644 index 0000000..db5d39e --- /dev/null +++ b/test/golden/formula/generating tasks.golden @@ -0,0 +1,108 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "formula_test_forall" + , taskConjecture = Quantified Universally + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "formula_test_forall" + , Quantified Universally + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "formula_test_exists" + , taskConjecture = Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + } +]
\ No newline at end of file diff --git a/test/golden/formula/glossing.golden b/test/golden/formula/glossing.golden new file mode 100644 index 0000000..bb72370 --- /dev/null +++ b/test/golden/formula/glossing.golden @@ -0,0 +1,79 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/formula.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "formula_test_forall" ) + ( Lemma [] + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/formula.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "formula_test_exists" ) + ( Lemma [] + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/formula/parsing.golden b/test/golden/formula/parsing.golden new file mode 100644 index 0000000..4c6321d --- /dev/null +++ b/test/golden/formula/parsing.golden @@ -0,0 +1,76 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/formula.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "formula_test_forall" ) + ( Lemma [] + ( StmtFormula + ( FormulaQuantified Universally + ( NamedVar "x" :| + [ NamedVar "y" ] + ) Unbounded + ( Connected Conjunction + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/formula.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "formula_test_exists" ) + ( Lemma [] + ( StmtFormula + ( FormulaQuantified Existentially + ( NamedVar "x" :| + [ NamedVar "y" ] + ) Unbounded + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/formula/scanning.golden b/test/golden/formula/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/formula/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/formula/tokenizing.golden b/test/golden/formula/tokenizing.golden new file mode 100644 index 0000000..3cb9b0e --- /dev/null +++ b/test/golden/formula/tokenizing.golden @@ -0,0 +1,33 @@ +[ BeginEnv "proposition" +, Label "formula_test_forall" +, BeginEnv "math" +, Command "forall" +, Variable "x" +, Symbol "," +, Variable "y" +, Symbol "." +, Variable "x" +, Symbol "=" +, Variable "x" +, Command "land" +, Variable "y" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "formula_test_exists" +, BeginEnv "math" +, Command "exists" +, Variable "x" +, Symbol "," +, Variable "y" +, Symbol "." +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/formula/verification.golden b/test/golden/formula/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/formula/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/geometry/encoding tasks.golden b/test/golden/geometry/encoding tasks.golden new file mode 100644 index 0000000..f4bbc14 --- /dev/null +++ b/test/golden/geometry/encoding tasks.golden @@ -0,0 +1,109 @@ +fof(cong_refl,conjecture,'Cong'(fa,fb,fa,fb)). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_refl1,axiom,point(fb)). +fof(cong_refl2,axiom,point(fa)). +------------------ +fof(cong_sym,conjecture,'Cong'(fc,fd,fa,fb)). +fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_sym1,axiom,'Cong'(fa,fb,fc,fd)). +fof(cong_sym2,axiom,point(fd)). +fof(cong_sym3,axiom,point(fc)). +fof(cong_sym4,axiom,point(fb)). +fof(cong_sym5,axiom,point(fa)). +------------------ +fof(cong_transitive,conjecture,('Cong'(fa,fb,fc,fd)&'Cong'(fc,fd,fe,ff))=>'Cong'(fa,fb,fe,ff)). +fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))). +fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_transitive1,axiom,point(ff)). +fof(cong_transitive2,axiom,point(fe)). +fof(cong_transitive3,axiom,point(fd)). +fof(cong_transitive4,axiom,point(fc)). +fof(cong_transitive5,axiom,point(fb)). +fof(cong_transitive6,axiom,point(fa)). +------------------ +fof(cong_shuffle_left,conjecture,'Cong'(fa,fb,fc,fd)=>'Cong'(fb,fa,fc,fd)). +fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))). +fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_shuffle_left1,axiom,point(fd)). +fof(cong_shuffle_left2,axiom,point(fc)). +fof(cong_shuffle_left3,axiom,point(fb)). +fof(cong_shuffle_left4,axiom,point(fa)). +------------------ +fof(cong_shuffle_right,conjecture,'Cong'(fa,fb,fc,fd)=>'Cong'(fb,fa,fd,fc)). +fof(cong_shuffle_left,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xc,Xd)))). +fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))). +fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_shuffle_right1,axiom,point(fd)). +fof(cong_shuffle_right2,axiom,point(fc)). +fof(cong_shuffle_right3,axiom,point(fb)). +fof(cong_shuffle_right4,axiom,point(fa)). +------------------ +fof(cong_zero,conjecture,'Cong'(fa,fa,fb,fb)). +fof(cong_shuffle_right,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xd,Xc)))). +fof(cong_shuffle_left,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>('Cong'(Xa,Xb,Xc,Xd)=>'Cong'(Xb,Xa,Xc,Xd)))). +fof(cong_transitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xe)&point(Xf))=>(('Cong'(Xa,Xb,Xc,Xd)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_sym,axiom,![Xa,Xb,Xc,Xd]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&'Cong'(Xa,Xb,Xc,Xd))=>'Cong'(Xc,Xd,Xa,Xb))). +fof(cong_refl,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xa,Xb))). +fof(upperdim,axiom,![Xx,Xy,Xz,Xu,Xv]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv))=>(('Cong'(Xx,Xu,Xx,Xv)&'Cong'(Xy,Xu,Xy,Xv)&'Cong'(Xz,Xu,Xz,Xv)&Xu!=Xv)=>collinear(Xx,Xy,Xz)))). +fof(innerpasch,axiom,![Xx,Xy,Xz,Xu,Xv,Xw]:((point(Xx)&point(Xy)&point(Xz)&point(Xu)&point(Xv)&point(Xw))=>(('Betw'(Xx,Xu,Xz)&'Betw'(Xy,Xv,Xz))=>?[Xw]:(point(Xw)&'Betw'(Xu,Xw,Xy)&'Betw'(Xv,Xw,Xx))))). +fof(betw_id,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>('Betw'(Xa,Xb,Xa)=>Xa=Xb))). +fof(five_segment,axiom,![Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime]:((point(Xa)&point(Xb)&point(Xc)&point(Xd)&point(Xaprime)&point(Xbprime)&point(Xcprime)&point(Xdprime))=>(('OFS'(Xa,Xb,Xc,Xd,Xaprime,Xbprime,Xcprime,Xdprime)&Xa!=Xb)=>'Cong'(Xc,Xd,Xcprime,Xdprime)))). +fof(ofs,axiom,![Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp]:((point(Xx)&point(Xy)&point(Xz)&point(Xr)&point(Xu)&point(Xv)&point(Xw)&point(Xp))=>('OFS'(Xx,Xy,Xz,Xr,Xu,Xv,Xw,Xp)<=>('Betw'(Xx,Xy,Xz)&'Betw'(Xu,Xv,Xw)&'Cong'(Xx,Xy,Xu,Xv)&'Cong'(Xy,Xz,Xv,Xw)&'Cong'(Xx,Xr,Xu,Xp)&'Cong'(Xy,Xr,Xv,Xp))))). +fof(segment_construction,axiom,![Xa,Xb,Xd,Xe]:?[Xc]:(point(Xc)&'Betw'(Xa,Xb,Xc)&'Cong'(Xb,Xc,Xd,Xe))). +fof(cong_id,axiom,![Xa,Xb,Xc]:((point(Xa)&point(Xb)&point(Xc))=>('Cong'(Xa,Xb,Xc,Xc)=>Xa=Xb))). +fof(cong_pseudotransitive,axiom,![Xa,Xb,Xc,Xd,Xe,Xf]:((point(Xa)&point(Xb)&point(Xc)&point(Xd))=>(('Cong'(Xc,Xd,Xa,Xb)&'Cong'(Xc,Xd,Xe,Xf))=>'Cong'(Xa,Xb,Xe,Xf)))). +fof(cong_refl_swap,axiom,![Xa,Xb]:((point(Xa)&point(Xb))=>'Cong'(Xa,Xb,Xb,Xa))). +fof(collinear,axiom,![Xa,Xb,Xc]:(collinear(Xa,Xb,Xc)<=>('Betw'(Xa,Xb,Xc)|'Betw'(Xb,Xc,Xa)|'Betw'(Xc,Xa,Xb)))). +fof(cong_zero1,axiom,point(fb)). +fof(cong_zero2,axiom,point(fa)).
\ No newline at end of file diff --git a/test/golden/geometry/generating tasks.golden b/test/golden/geometry/generating tasks.golden new file mode 100644 index 0000000..a2869ea --- /dev/null +++ b/test/golden/geometry/generating tasks.golden @@ -0,0 +1,14419 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_refl1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_refl2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_refl" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "cong_refl" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_sym1" + , TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + , + ( Marker "cong_sym2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , + ( Marker "cong_sym3" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , + ( Marker "cong_sym4" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_sym5" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_sym" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "cong_sym" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "cong_refl" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_transitive1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "f" ) + ] + ) + , + ( Marker "cong_transitive2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "e" ) + ] + ) + , + ( Marker "cong_transitive3" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , + ( Marker "cong_transitive4" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , + ( Marker "cong_transitive5" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_transitive6" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_transitive" + , taskConjecture = Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "cong_transitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "e" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_sym" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "cong_refl" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_shuffle_left1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , + ( Marker "cong_shuffle_left2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , + ( Marker "cong_shuffle_left3" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_shuffle_left4" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_shuffle_left" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "cong_shuffle_left" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_transitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "e" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_sym" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "cong_refl" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_shuffle_right1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , + ( Marker "cong_shuffle_right2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , + ( Marker "cong_shuffle_right3" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_shuffle_right4" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_shuffle_right" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "c" ) + ] + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "cong_shuffle_right" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_shuffle_left" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_transitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "e" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_sym" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "cong_refl" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "upperdim" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "innerpasch" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "betw_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "five_segment" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "aprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "bprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "cprime" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "aprime" ) + ) + , TermVar + ( B + ( NamedVar "bprime" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "cprime" ) + ) + , TermVar + ( B + ( NamedVar "dprime" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "ofs" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "r" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "u" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "v" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ) + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( B + ( NamedVar "r" ) + ) + , TermVar + ( B + ( NamedVar "u" ) + ) + , TermVar + ( B + ( NamedVar "v" ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( B + ( NamedVar "p" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "z" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "w" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "x" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "u" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "y" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "r" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "v" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "p" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "segment_construction" + , Quantified Universally + ( Scope + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "d" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "e" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_id" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_pseudotransitive" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "d" ) + ) + ] + ) + ) + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( B + ( NamedVar "d" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "e" ) + ) + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + ) + ) + , + ( Marker "cong_refl_swap" + , Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "a" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "collinear" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "c" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "b" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cong_zero1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , + ( Marker "cong_zero2" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + ] + , taskConjectureLabel = Marker "cong_zero" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "b" ) + ] + } +]
\ No newline at end of file diff --git a/test/golden/geometry/glossing.golden b/test/golden/geometry/glossing.golden new file mode 100644 index 0000000..f1e1bd2 --- /dev/null +++ b/test/golden/geometry/glossing.golden @@ -0,0 +1,2187 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "collinear" ) + ( DefnPredicate [] + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "a" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_refl_swap" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + ] + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 10 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_pseudotransitive" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + ] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_id" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + ] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "c" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 21 + , sourceColumn = Pos 1 + } + ) + ( Marker "segment_construction" ) + ( Axiom [] + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "a" ) + ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "b" ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "b" ) + ) + ) + , TermVar + ( B + ( NamedVar "c" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "d" ) + ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "e" ) + ) + ) + ] + ) + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 26 + , sourceColumn = Pos 1 + } + ) + ( Marker "ofs" ) + ( DefnPredicate + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "z" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "r" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "u" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "v" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "w" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "p" ) + ] + ) + ] + ( PredicateSymbol "OFS" ) + ( NamedVar "x" :| + [ NamedVar "y" + , NamedVar "z" + , NamedVar "r" + , NamedVar "u" + , NamedVar "v" + , NamedVar "w" + , NamedVar "p" + ] + ) + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "z" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "v" ) + , TermVar + ( NamedVar "w" ) + ] + ) + ) + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "v" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "z" ) + , TermVar + ( NamedVar "v" ) + , TermVar + ( NamedVar "w" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "r" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "p" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "r" ) + , TermVar + ( NamedVar "v" ) + , TermVar + ( NamedVar "p" ) + ] + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 39 + , sourceColumn = Pos 1 + } + ) + ( Marker "five_segment" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "aprime" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "bprime" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "cprime" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "dprime" ) + ] + ) + ] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "OFS" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "aprime" ) + , TermVar + ( NamedVar "bprime" ) + , TermVar + ( NamedVar "cprime" ) + , TermVar + ( NamedVar "dprime" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "cprime" ) + , TermVar + ( NamedVar "dprime" ) + ] + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 46 + , sourceColumn = Pos 1 + } + ) + ( Marker "betw_id" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + ] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 52 + , sourceColumn = Pos 1 + } + ) + ( Marker "innerpasch" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "z" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "u" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "v" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "w" ) + ] + ) + ] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "z" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "v" ) + , TermVar + ( NamedVar "z" ) + ] + ) + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "w" ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "u" ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "y" ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Betw" ) + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "v" ) + ) + ) + , TermVar + ( B + ( NamedVar "w" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "x" ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 66 + , sourceColumn = Pos 1 + } + ) + ( Marker "upperdim" ) + ( Axiom + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "x" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "y" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "z" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "u" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "v" ) + ] + ) + ] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "v" ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "v" ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "z" ) + , TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "z" ) + , TermVar + ( NamedVar "v" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "neq" ) + ) + ) + [ TermVar + ( NamedVar "u" ) + , TermVar + ( NamedVar "v" ) + ] + ) + ) + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "z" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 82 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_refl" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 88 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_sym" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 95 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_transitive" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "e" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "f" ) + ] + ) + ] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "e" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 102 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_shuffle_left" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + ] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 109 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_shuffle_right" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "c" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "d" ) + ] + ) + ] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "c" ) + , TermVar + ( NamedVar "d" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "d" ) + , TermVar + ( NamedVar "c" ) + ] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 116 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_zero" ) + ( Lemma + [ Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "a" ) + ] + ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "b" ) + ] + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateSymbol "Cong" ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) +]
\ No newline at end of file diff --git a/test/golden/geometry/parsing.golden b/test/golden/geometry/parsing.golden new file mode 100644 index 0000000..b57f76c --- /dev/null +++ b/test/golden/geometry/parsing.golden @@ -0,0 +1,1198 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "collinear" ) + ( Defn [] + ( DefnAdj Nothing + ( NamedVar "a" ) + ( Adj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + [ NamedVar "b" + , NamedVar "c" + ] + ) + ) + ( StmtConnected Disjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + ] + ) + ) + ) + ( StmtConnected Disjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "b" ) :| + [ ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "a" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_refl_swap" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "a" ) + ] + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 10 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_pseudotransitive" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "e" ) + , ExprVar + ( NamedVar "f" ) + ] + ) + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "e" ) + , ExprVar + ( NamedVar "f" ) + ] + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_id" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "c" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 21 + , sourceColumn = Pos 1 + } + ) + ( Marker "segment_construction" ) + ( Axiom [] + ( StmtExists NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) + ( + [ NamedVar "c" ] + ) ( [] ) + ( Just + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "b" ) :| + [ ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "e" ) + ] + ) + ) + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 26 + , sourceColumn = Pos 1 + } + ) + ( Marker "ofs" ) + ( Defn + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" + , NamedVar "z" + , NamedVar "r" + , NamedVar "u" + , NamedVar "v" + , NamedVar "w" + , NamedVar "p" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( DefnSymbolicPredicate + ( PrefixPredicate "OFS" 8 ) + ( NamedVar "x" :| + [ NamedVar "y" + , NamedVar "z" + , NamedVar "r" + , NamedVar "u" + , NamedVar "v" + , NamedVar "w" + , NamedVar "p" + ] + ) + ) + ( StmtConnected Conjunction + ( StmtFormula + ( Connected Conjunction + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "x" ) :| + [ ExprVar + ( NamedVar "y" ) + , ExprVar + ( NamedVar "z" ) + ] + ) + ) + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "u" ) :| + [ ExprVar + ( NamedVar "v" ) + , ExprVar + ( NamedVar "w" ) + ] + ) + ) + ) + ) + ( StmtFormula + ( Connected Conjunction + ( Connected Conjunction + ( Connected Conjunction + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "x" ) :| + [ ExprVar + ( NamedVar "y" ) + , ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "v" ) + ] + ) + ) + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "y" ) :| + [ ExprVar + ( NamedVar "z" ) + , ExprVar + ( NamedVar "v" ) + , ExprVar + ( NamedVar "w" ) + ] + ) + ) + ) + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "x" ) :| + [ ExprVar + ( NamedVar "r" ) + , ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "p" ) + ] + ) + ) + ) + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "y" ) :| + [ ExprVar + ( NamedVar "r" ) + , ExprVar + ( NamedVar "v" ) + , ExprVar + ( NamedVar "p" ) + ] + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 39 + , sourceColumn = Pos 1 + } + ) + ( Marker "five_segment" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + , NamedVar "aprime" + , NamedVar "bprime" + , NamedVar "cprime" + , NamedVar "dprime" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "OFS" 8 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "aprime" ) + , ExprVar + ( NamedVar "bprime" ) + , ExprVar + ( NamedVar "cprime" ) + , ExprVar + ( NamedVar "dprime" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "neq" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "cprime" ) + , ExprVar + ( NamedVar "dprime" ) + ] + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 46 + , sourceColumn = Pos 1 + } + ) + ( Marker "betw_id" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "a" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 52 + , sourceColumn = Pos 1 + } + ) + ( Marker "innerpasch" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" + , NamedVar "z" + , NamedVar "u" + , NamedVar "v" + , NamedVar "w" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "x" ) :| + [ ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "z" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "y" ) :| + [ ExprVar + ( NamedVar "v" ) + , ExprVar + ( NamedVar "z" ) + ] + ) + ) + ) + ) + ( StmtExists NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) + ( + [ NamedVar "w" ] + ) ( [] ) + ( Just + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "u" ) :| + [ ExprVar + ( NamedVar "w" ) + , ExprVar + ( NamedVar "y" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Betw" 3 ) + ( ExprVar + ( NamedVar "v" ) :| + [ ExprVar + ( NamedVar "w" ) + , ExprVar + ( NamedVar "x" ) + ] + ) + ) + ) + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 66 + , sourceColumn = Pos 1 + } + ) + ( Marker "upperdim" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "x" :| + [ NamedVar "y" + , NamedVar "z" + , NamedVar "u" + , NamedVar "v" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "x" ) :| + [ ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "x" ) + , ExprVar + ( NamedVar "v" ) + ] + ) + ) + ) + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "y" ) :| + [ ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "y" ) + , ExprVar + ( NamedVar "v" ) + ] + ) + ) + ) + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "z" ) :| + [ ExprVar + ( NamedVar "u" ) + , ExprVar + ( NamedVar "z" ) + , ExprVar + ( NamedVar "v" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "u" ) :| [] + ) Positive + ( RelationSymbol + ( Command "neq" ) + ) + ( ExprVar + ( NamedVar "v" ) :| [] + ) + ) + ) + ) + ) + ) + ) + ( StmtVerbPhrase + ( TermExpr + ( ExprVar + ( NamedVar "x" ) + ) :| [] + ) + ( VPAdj + ( Adj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + [ TermExpr + ( ExprVar + ( NamedVar "y" ) + ) + , TermExpr + ( ExprVar + ( NamedVar "z" ) + ) + ] :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 82 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_refl" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 88 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_sym" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + , AsmSuppose + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + ] + ) + ) + ) + ] + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 95 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_transitive" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + , NamedVar "e" + , NamedVar "f" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "c" ) :| + [ ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "e" ) + , ExprVar + ( NamedVar "f" ) + ] + ) + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "e" ) + , ExprVar + ( NamedVar "f" ) + ] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 102 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_shuffle_left" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "b" ) :| + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + ] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 109 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_shuffle_right" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" + , NamedVar "c" + , NamedVar "d" + ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Implication + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + , ExprVar + ( NamedVar "d" ) + ] + ) + ) + ) + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "b" ) :| + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "d" ) + , ExprVar + ( NamedVar "c" ) + ] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/geometry.tex" + , sourceLine = Pos 116 + , sourceColumn = Pos 1 + } + ) + ( Marker "cong_zero" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "a" :| + [ NamedVar "b" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "point" ) + ] + , pl = + [ Just + ( Word "points" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtFormula + ( FormulaPredicate + ( PrefixPredicate "Cong" 4 ) + ( ExprVar + ( NamedVar "a" ) :| + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/geometry/scanning.golden b/test/golden/geometry/scanning.golden new file mode 100644 index 0000000..c041c1a --- /dev/null +++ b/test/golden/geometry/scanning.golden @@ -0,0 +1,15 @@ +[ ScanAdj + [ Just + ( Word "collinear" ) + , Just + ( Word "with" ) + , Nothing + , Just + ( Word "and" ) + , Nothing + ] + ( Marker "collinear" ) +, ScanPrefixPredicate + ( PrefixPredicate "OFS" 8 ) + ( Marker "ofs" ) +]
\ No newline at end of file diff --git a/test/golden/geometry/tokenizing.golden b/test/golden/geometry/tokenizing.golden new file mode 100644 index 0000000..ab899fe --- /dev/null +++ b/test/golden/geometry/tokenizing.golden @@ -0,0 +1,975 @@ +[ BeginEnv "definition" +, Label "collinear" +, BeginEnv "math" +, Variable "a" +, EndEnv "math" +, Word "is" +, Word "collinear" +, Word "with" +, BeginEnv "math" +, Variable "b" +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "c" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, EndEnv "math" +, Word "or" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, EndEnv "math" +, Word "or" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "axiom" +, BracketL +, Word "reflexivity" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_refl_swap" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "pseudotransitivity" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_pseudotransitive" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "e" +, InvisibleBraceR +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "e" +, InvisibleBraceR +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "identity" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_id" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Variable "a" +, Symbol "=" +, Variable "b" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "segment" +, Word "construction" +, BracketR +, Label "segment_construction" +, Word "there" +, Word "exists" +, Word "a" +, Word "point" +, BeginEnv "math" +, Variable "c" +, EndEnv "math" +, Word "such" +, Word "that" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "e" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "definition" +, Label "ofs" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, Symbol "," +, Variable "z" +, Symbol "," +, Variable "r" +, Symbol "," +, Variable "u" +, Symbol "," +, Variable "v" +, Symbol "," +, Variable "w" +, Symbol "," +, Variable "p" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, BeginEnv "math" +, Command "OFS" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, InvisibleBraceL +, Variable "r" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "w" +, InvisibleBraceR +, InvisibleBraceL +, Variable "p" +, InvisibleBraceR +, EndEnv "math" +, Word "if" +, Word "and" +, Word "only" +, Word "if" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, Command "land" +, Command "Betw" +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "w" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, Command "land" +, Command "Cong" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "w" +, InvisibleBraceR +, Command "land" +, Command "Cong" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "r" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "p" +, InvisibleBraceR +, Command "land" +, Command "Cong" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "r" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "p" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "axiom" +, BracketL +, Word "five" +, Word "segment" +, Word "axiom" +, BracketR +, Label "five_segment" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, Symbol "," +, Variable "aprime" +, Symbol "," +, Variable "bprime" +, Symbol "," +, Variable "cprime" +, Symbol "," +, Variable "dprime" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "OFS" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "aprime" +, InvisibleBraceR +, InvisibleBraceL +, Variable "bprime" +, InvisibleBraceR +, InvisibleBraceL +, Variable "cprime" +, InvisibleBraceR +, InvisibleBraceL +, Variable "dprime" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "a" +, Command "neq" +, Variable "b" +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "cprime" +, InvisibleBraceR +, InvisibleBraceL +, Variable "dprime" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "identity" +, Word "of" +, Word "betweenness" +, BracketR +, Label "betw_id" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Variable "a" +, Symbol "=" +, Variable "b" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "inner" +, Word "pasch" +, BracketR +, Label "innerpasch" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, Symbol "," +, Variable "z" +, Symbol "," +, Variable "u" +, Symbol "," +, Variable "v" +, Symbol "," +, Variable "w" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, Word "there" +, Word "exists" +, Word "a" +, Word "point" +, BeginEnv "math" +, Variable "w" +, EndEnv "math" +, Word "such" +, Word "that" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "w" +, InvisibleBraceR +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Betw" +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, InvisibleBraceL +, Variable "w" +, InvisibleBraceR +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, BracketL +, Word "upper" +, Word "dimension" +, BracketR +, Label "upperdim" +, Word "let" +, BeginEnv "math" +, Variable "x" +, Symbol "," +, Variable "y" +, Symbol "," +, Variable "z" +, Symbol "," +, Variable "u" +, Symbol "," +, Variable "v" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, InvisibleBraceL +, Variable "u" +, InvisibleBraceR +, InvisibleBraceL +, Variable "z" +, InvisibleBraceR +, InvisibleBraceL +, Variable "v" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "u" +, Command "neq" +, Variable "v" +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "is" +, Word "collinear" +, Word "with" +, BeginEnv "math" +, Variable "y" +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "z" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "lemma" +, BracketL +, Word "reflexivity" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_refl" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "lemma" +, BracketL +, Word "symmetry" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_sym" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "suppose" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "lemma" +, BracketL +, Word "transitivity" +, Word "of" +, Word "congruence" +, BracketR +, Label "cong_transitive" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, Symbol "," +, Variable "e" +, Symbol "," +, Variable "f" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "e" +, InvisibleBraceR +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "e" +, InvisibleBraceR +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "lemma" +, Label "cong_shuffle_left" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "lemma" +, Label "cong_shuffle_right" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, Symbol "," +, Variable "c" +, Symbol "," +, Variable "d" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "if" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, EndEnv "math" +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "d" +, InvisibleBraceR +, InvisibleBraceL +, Variable "c" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "lemma" +, BracketL +, Word "zero" +, Word "segments" +, Word "are" +, Word "congruent" +, BracketR +, Label "cong_zero" +, Word "let" +, BeginEnv "math" +, Variable "a" +, Symbol "," +, Variable "b" +, EndEnv "math" +, Word "be" +, Word "points" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Command "Cong" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, InvisibleBraceL +, Variable "b" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +]
\ No newline at end of file diff --git a/test/golden/geometry/verification.golden b/test/golden/geometry/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/geometry/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/indefinite-terms/encoding tasks.golden b/test/golden/indefinite-terms/encoding tasks.golden new file mode 100644 index 0000000..54d9e2a --- /dev/null +++ b/test/golden/indefinite-terms/encoding tasks.golden @@ -0,0 +1,3 @@ +fof(indefinite_test_forall,conjecture,$true). +------------------ +fof(indefinite_test_exists,conjecture,$true).
\ No newline at end of file diff --git a/test/golden/indefinite-terms/generating tasks.golden b/test/golden/indefinite-terms/generating tasks.golden new file mode 100644 index 0000000..1f573ac --- /dev/null +++ b/test/golden/indefinite-terms/generating tasks.golden @@ -0,0 +1,13 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "indefinite_test_forall" + , taskConjecture = PropositionalConstant IsTop + } +, Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "indefinite_test_exists" + , taskConjecture = PropositionalConstant IsTop + } +]
\ No newline at end of file diff --git a/test/golden/indefinite-terms/glossing.golden b/test/golden/indefinite-terms/glossing.golden new file mode 100644 index 0000000..b7d3d2a --- /dev/null +++ b/test/golden/indefinite-terms/glossing.golden @@ -0,0 +1,31 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/indefinite-terms.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "indefinite_test_forall" ) + ( Lemma [] + ( Quantified Universally + ( Scope + ( Connected Implication ( PropositionalConstant IsTop ) ( PropositionalConstant IsTop ) ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/indefinite-terms.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "indefinite_test_exists" ) + ( Lemma [] + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) ( PropositionalConstant IsTop ) ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/indefinite-terms/parsing.golden b/test/golden/indefinite-terms/parsing.golden new file mode 100644 index 0000000..8c468ab --- /dev/null +++ b/test/golden/indefinite-terms/parsing.golden @@ -0,0 +1,81 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/indefinite-terms.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "indefinite_test_forall" ) + ( Lemma [] + ( StmtNoun + ( TermQuantified Universally NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/indefinite-terms.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "indefinite_test_exists" ) + ( Lemma [] + ( StmtNoun + ( TermQuantified Existentially NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/indefinite-terms/scanning.golden b/test/golden/indefinite-terms/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/indefinite-terms/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/indefinite-terms/tokenizing.golden b/test/golden/indefinite-terms/tokenizing.golden new file mode 100644 index 0000000..39b9bcf --- /dev/null +++ b/test/golden/indefinite-terms/tokenizing.golden @@ -0,0 +1,19 @@ +[ BeginEnv "theorem" +, Label "indefinite_test_forall" +, Word "every" +, Word "set" +, Word "is" +, Word "a" +, Word "set" +, Symbol "." +, EndEnv "theorem" +, BeginEnv "theorem" +, Label "indefinite_test_exists" +, Word "some" +, Word "set" +, Word "is" +, Word "a" +, Word "set" +, Symbol "." +, EndEnv "theorem" +]
\ No newline at end of file diff --git a/test/golden/indefinite-terms/verification.golden b/test/golden/indefinite-terms/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/indefinite-terms/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/inductive/encoding tasks.golden b/test/golden/inductive/encoding tasks.golden new file mode 100644 index 0000000..2e9a2d5 --- /dev/null +++ b/test/golden/inductive/encoding tasks.golden @@ -0,0 +1,170 @@ +fof(fin,conjecture,elem(emptyset,pow(fA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(fin,conjecture,(elem(fa,fA)&elem(fB,pow(fA)))=>elem(cons(fa,fB),pow(fA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(fin_mono,conjecture,subseteq(fin(fA),fin(fB))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +fof(fin_mono1,axiom,subseteq(fA,fB)). +------------------ +fof(tracl,conjecture,elem(fw,fR)=>elem(fw,times(fld(fR),fld(fR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(tracl,conjecture,(elem(pair(fa,fb),times(fld(fR),fld(fR)))&elem(pair(fb,fc),fR))=>elem(pair(fa,fc),times(fld(fR),fld(fR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(quasirefltracl,conjecture,elem(fa,fld(fR))=>elem(pair(fa,fa),times(fld(fR),fld(fR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(quasirefltracl,conjecture,(elem(pair(fa,fb),times(fld(fR),fld(fR)))&elem(pair(fb,fc),fR))=>elem(pair(fa,fc),times(fld(fR),fld(fR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(refltracl,conjecture,elem(fa,fA)=>elem(pair(fa,fa),times(fA,fA))). +fof(quasirefltracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),quasirefltracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![Xa,XR]:(elem(Xa,fld(XR))=>elem(pair(Xa,Xa),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![XR]:subseteq(quasirefltracl(XR),times(fld(XR),fld(XR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(refltracl,conjecture,(elem(pair(fa,fb),times(fA,fA))&elem(pair(fb,fc),fR))=>elem(pair(fa,fc),times(fA,fA))). +fof(quasirefltracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),quasirefltracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![Xa,XR]:(elem(Xa,fld(XR))=>elem(pair(Xa,Xa),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![XR]:subseteq(quasirefltracl(XR),times(fld(XR),fld(XR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(acc,conjecture,![Xxa,Xxb]:(subseteq(Xxa,Xxb)=>subseteq(pow(Xxa),pow(Xxb)))). +fof(refltracl,axiom,![Xa,Xb,XA,XR,Xc]:((elem(pair(Xa,Xb),refltracl(XA,XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),refltracl(XA,XR)))). +fof(refltracl,axiom,![Xa,XA,XR]:(elem(Xa,XA)=>elem(pair(Xa,Xa),refltracl(XA,XR)))). +fof(refltracl,axiom,![XA,XR]:subseteq(refltracl(XA,XR),times(XA,XA))). +fof(quasirefltracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),quasirefltracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![Xa,XR]:(elem(Xa,fld(XR))=>elem(pair(Xa,Xa),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![XR]:subseteq(quasirefltracl(XR),times(fld(XR),fld(XR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)). +------------------ +fof(acc,conjecture,(elem(fa,fld(fR))&elem(preimg(fR,cons(fa,emptyset)),pow(fld(fR))))=>elem(fa,fld(fR))). +fof(refltracl,axiom,![Xa,Xb,XA,XR,Xc]:((elem(pair(Xa,Xb),refltracl(XA,XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),refltracl(XA,XR)))). +fof(refltracl,axiom,![Xa,XA,XR]:(elem(Xa,XA)=>elem(pair(Xa,Xa),refltracl(XA,XR)))). +fof(refltracl,axiom,![XA,XR]:subseteq(refltracl(XA,XR),times(XA,XA))). +fof(quasirefltracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),quasirefltracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![Xa,XR]:(elem(Xa,fld(XR))=>elem(pair(Xa,Xa),quasirefltracl(XR)))). +fof(quasirefltracl,axiom,![XR]:subseteq(quasirefltracl(XR),times(fld(XR),fld(XR)))). +fof(tracl,axiom,![Xa,Xb,XR,Xc]:((elem(pair(Xa,Xb),tracl(XR))&elem(pair(Xb,Xc),XR))=>elem(pair(Xa,Xc),tracl(XR)))). +fof(tracl,axiom,![Xw,XR]:(elem(Xw,XR)=>elem(Xw,tracl(XR)))). +fof(tracl,axiom,![XR]:subseteq(tracl(XR),times(fld(XR),fld(XR)))). +fof(fin_mono,axiom,![XA,XB]:(subseteq(XA,XB)=>subseteq(fin(XA),fin(XB)))). +fof(fin,axiom,![Xa,XA,XB]:((elem(Xa,XA)&elem(XB,fin(XA)))=>elem(cons(Xa,XB),fin(XA)))). +fof(fin,axiom,![XA]:elem(emptyset,fin(XA))). +fof(fin,axiom,![XA]:subseteq(fin(XA),pow(XA))). +fof(lmao,axiom,![Xx]:elem(Xx,emptyset)). +fof(preimg,axiom,![XR,XA]:preimg(XR,XA)=emptyset). +fof(fld,axiom,![XR]:fld(XR)=emptyset). +fof(times,axiom,![XA,XB]:times(XA,XB)=emptyset). +fof(cons,axiom,![Xa,XB]:cons(Xa,XB)=emptyset). +fof(pow,axiom,![XA]:pow(XA)=emptyset). +fof(subseteq,axiom,![XA,XB]:(subseteq(XA,XB)<=>XA=XB)).
\ No newline at end of file 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" ) + ] + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/inductive/glossing.golden b/test/golden/inductive/glossing.golden new file mode 100644 index 0000000..e76a88f --- /dev/null +++ b/test/golden/inductive/glossing.golden @@ -0,0 +1,1136 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 3 + , sourceColumn = Pos 1 + } + ) + ( Marker "subseteq" ) + ( DefnPredicate [] + ( PredicateRelation + ( Command "subseteq" ) + ) + ( NamedVar "A" :| + [ NamedVar "B" ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "B" ) + ] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 7 + , sourceColumn = Pos 1 + } + ) + ( Marker "pow" ) + ( DefnOp + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "A" ] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( DefnOp + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "a" + , NamedVar "B" + ] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "times" ) + ( DefnOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ NamedVar "A" + , NamedVar "B" + ] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Marker "fld" ) + ( DefnOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" ] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 23 + , sourceColumn = Pos 1 + } + ) + ( Marker "preimg" ) + ( DefnOp + [ Just + ( Command "preimg" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" + , NamedVar "A" + ] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 27 + , sourceColumn = Pos 1 + } + ) + ( Marker "lmao" ) + ( Axiom [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 31 + , sourceColumn = Pos 1 + } + ) + ( Marker "fin" ) + ( Inductive + { inductiveSymbol = + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + , inductiveParams = + [ NamedVar "A" ] + , inductiveDomain = TermSymbol + ( SymbolMixfix + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + ] + , inductiveIntros = IntroRule + { introConditions = [] + , introResult = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + ] + ] + } :| + [ IntroRule + { introConditions = + [ TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "A" ) + ] + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "B" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + ] + ] + ] + , introResult = 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 "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + ] + ] + } + ] + } + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 39 + , sourceColumn = Pos 1 + } + ) + ( Marker "fin_mono" ) + ( Lemma + [ Asm ( PropositionalConstant IsTop ) + , Asm ( PropositionalConstant IsTop ) + , Asm + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "subseteq" ) + ) + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "B" ) + ] + ) + ] + ( 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" ) + ] + ] + ) + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 45 + , sourceColumn = Pos 1 + } + ) + ( Marker "tracl" ) + ( Inductive + { inductiveSymbol = + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + , inductiveParams = + [ NamedVar "R" ] + , inductiveDomain = 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" ) + ] + ] + , inductiveIntros = IntroRule + { introConditions = + [ TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "w" ) + , TermVar + ( NamedVar "R" ) + ] + ] + , introResult = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "w" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + } :| + [ IntroRule + { introConditions = + [ 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 + [ Just + ( Command "tracl" ) + , 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" ) + ] + ] + , introResult = 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 + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 53 + , sourceColumn = Pos 1 + } + ) + ( Marker "quasirefltracl" ) + ( Inductive + { inductiveSymbol = + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + , inductiveParams = + [ NamedVar "R" ] + , inductiveDomain = 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" ) + ] + ] + , inductiveIntros = IntroRule + { introConditions = + [ TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + ] + , introResult = 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 + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + } :| + [ IntroRule + { introConditions = + [ 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 + [ Just + ( Command "qrefltracl" ) + , 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" ) + ] + ] + , introResult = 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 + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 61 + , sourceColumn = Pos 1 + } + ) + ( Marker "refltracl" ) + ( Inductive + { inductiveSymbol = + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + , inductiveParams = + [ NamedVar "A" + , NamedVar "R" + ] + , inductiveDomain = TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "A" ) + ] + , inductiveIntros = IntroRule + { introConditions = + [ TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "A" ) + ] + ] + , introResult = 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 + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "R" ) + ] + ] + } :| + [ IntroRule + { introConditions = + [ 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 + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + , 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" ) + ] + ] + , introResult = 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 + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "R" ) + ] + ] + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 69 + , sourceColumn = Pos 1 + } + ) + ( Marker "acc" ) + ( Inductive + { inductiveSymbol = + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + , inductiveParams = + [ NamedVar "R" ] + , inductiveDomain = TermSymbol + ( SymbolMixfix + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + , inductiveIntros = IntroRule + { introConditions = + [ 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 "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + ] + ] + , introResult = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "R" ) + ] + ] + } :| [] + } + ) +]
\ No newline at end of file diff --git a/test/golden/inductive/parsing.golden b/test/golden/inductive/parsing.golden new file mode 100644 index 0000000..7438daa --- /dev/null +++ b/test/golden/inductive/parsing.golden @@ -0,0 +1,1076 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 3 + , sourceColumn = Pos 1 + } + ) + ( Marker "subseteq" ) + ( Defn [] + ( DefnRel + ( NamedVar "A" ) + ( Command "subseteq" ) + ( NamedVar "B" ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "A" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "B" ) :| [] + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 7 + , sourceColumn = Pos 1 + } + ) + ( Marker "pow" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "A" ] + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "a" + , NamedVar "B" + ] + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "times" ) + ( DefnOp + ( SymbolPattern + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ NamedVar "A" + , NamedVar "B" + ] + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Marker "fld" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" ] + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 23 + , sourceColumn = Pos 1 + } + ) + ( Marker "preimg" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "preimg" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" + , NamedVar "A" + ] + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 27 + , sourceColumn = Pos 1 + } + ) + ( Marker "lmao" ) + ( Axiom [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] :| [] + ) + ) + ) + ) + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 31 + , sourceColumn = Pos 1 + } + ) + ( Marker "fin" ) + ( Inductive + { inductiveSymbolPattern = SymbolPattern + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "A" ] + , inductiveDomain = ExprOp + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + ] + , inductiveIntros = IntroRule + { introConditions = [] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + ] :| [] + ) + ) + } :| + [ IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "A" ) :| [] + ) + ) + , FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "B" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + ] :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "B" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + ] :| [] + ) + ) + } + ] + } + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 39 + , sourceColumn = Pos 1 + } + ) + ( Marker "fin_mono" ) + ( Lemma + [ AsmLetNoun + ( NamedVar "A" :| + [ NamedVar "B" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + , AsmSuppose + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "A" ) :| [] + ) Positive + ( RelationSymbol + ( Command "subseteq" ) + ) + ( ExprVar + ( NamedVar "B" ) :| [] + ) + ) + ) + ) + ] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "subseteq" ) + ) + ( ExprOp + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "B" ) + ] :| [] + ) + ) + ) + ) + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 45 + , sourceColumn = Pos 1 + } + ) + ( Marker "tracl" ) + ( Inductive + { inductiveSymbolPattern = SymbolPattern + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" ] + , inductiveDomain = ExprOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + , ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + ] + , inductiveIntros = IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "w" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "w" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } :| + [ IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + , FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 53 + , sourceColumn = Pos 1 + } + ) + ( Marker "quasirefltracl" ) + ( Inductive + { inductiveSymbolPattern = SymbolPattern + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" ] + , inductiveDomain = ExprOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + , ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + ] + , inductiveIntros = IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "a" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } :| + [ IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + , FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 61 + , sourceColumn = Pos 1 + } + ) + ( Marker "refltracl" ) + ( Inductive + { inductiveSymbolPattern = SymbolPattern + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "A" + , NamedVar "R" + ] + , inductiveDomain = ExprOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "A" ) + ] + , inductiveIntros = IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "A" ) :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "a" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } :| + [ IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + , FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "b" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "c" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } + ] + } + ) +, BlockInductive + ( SourcePos + { sourceName = "test/examples/inductive.tex" + , sourceLine = Pos 69 + , sourceColumn = Pos 1 + } + ) + ( Marker "acc" ) + ( Inductive + { inductiveSymbolPattern = SymbolPattern + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "R" ] + , inductiveDomain = ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + , inductiveIntros = IntroRule + { introConditions = + [ FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + , FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "preimg" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + , ExprFiniteSet + ( ExprVar + ( NamedVar "a" ) :| [] + ) + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprOp + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] + ] :| [] + ) + ) + ] + , introResult = FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "R" ) + ] :| [] + ) + ) + } :| [] + } + ) +]
\ No newline at end of file diff --git a/test/golden/inductive/scanning.golden b/test/golden/inductive/scanning.golden new file mode 100644 index 0000000..c3ad452 --- /dev/null +++ b/test/golden/inductive/scanning.golden @@ -0,0 +1,92 @@ +[ ScanRelationSymbol + ( Command "subseteq" ) + ( Marker "subseteq" ) +, ScanFunctionSymbol + [ Just + ( Command "pow" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "pow" ) +, ScanFunctionSymbol + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "cons" ) +, ScanFunctionSymbol + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ( Marker "times" ) +, ScanFunctionSymbol + [ Just + ( Command "fld" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "fld" ) +, ScanFunctionSymbol + [ Just + ( Command "preimg" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "preimg" ) +, ScanFunctionSymbol + [ Just + ( Command "fin" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "fin" ) +, ScanFunctionSymbol + [ Just + ( Command "tracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "tracl" ) +, ScanFunctionSymbol + [ Just + ( Command "qrefltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "quasirefltracl" ) +, ScanFunctionSymbol + [ Just + ( Command "refltracl" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "refltracl" ) +, ScanFunctionSymbol + [ Just + ( Command "acc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "acc" ) +]
\ No newline at end of file diff --git a/test/golden/inductive/tokenizing.golden b/test/golden/inductive/tokenizing.golden new file mode 100644 index 0000000..b43d176 --- /dev/null +++ b/test/golden/inductive/tokenizing.golden @@ -0,0 +1,514 @@ +[ BeginEnv "definition" +, Label "subseteq" +, BeginEnv "math" +, Variable "A" +, Command "subseteq" +, Variable "B" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "A" +, Symbol "=" +, Variable "B" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "pow" +, BeginEnv "math" +, Command "pow" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, Symbol "=" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "cons" +, BeginEnv "math" +, Command "cons" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "B" +, InvisibleBraceR +, Symbol "=" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "times" +, BeginEnv "math" +, Variable "A" +, Command "times" +, Variable "B" +, Symbol "=" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "fld" +, BeginEnv "math" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Symbol "=" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "preimg" +, BeginEnv "math" +, Command "preimg" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, Symbol "=" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "axiom" +, Label "lmao" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Command "emptyset" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "inductive" +, Label "fin" +, Word "define" +, BeginEnv "math" +, Command "fin" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, Command "subseteq" +, Command "pow" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, EndEnv "math" +, Word "inductively" +, Word "as" +, Word "follows" +, Symbol "." +, BeginEnv "enumerate" +, Command "item" +, BeginEnv "math" +, Command "emptyset" +, Command "in" +, Command "fin" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, Command "item" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "B" +, Command "in" +, Command "fin" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Command "cons" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, InvisibleBraceL +, Variable "B" +, InvisibleBraceR +, Command "in" +, Command "fin" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "enumerate" +, EndEnv "inductive" +, BeginEnv "lemma" +, Label "fin_mono" +, Word "let" +, BeginEnv "math" +, Variable "A" +, Symbol "," +, Variable "B" +, EndEnv "math" +, Word "be" +, Word "sets" +, Symbol "." +, Word "suppose" +, BeginEnv "math" +, Variable "A" +, Command "subseteq" +, Variable "B" +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Command "fin" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, Command "subseteq" +, Command "fin" +, InvisibleBraceL +, Variable "B" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "lemma" +, BeginEnv "inductive" +, Label "tracl" +, Word "define" +, BeginEnv "math" +, Command "tracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "subseteq" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "times" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "inductively" +, Word "as" +, Word "follows" +, Symbol "." +, BeginEnv "enumerate" +, Command "item" +, Word "if" +, BeginEnv "math" +, Variable "w" +, Command "in" +, Variable "R" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "w" +, Command "in" +, Command "tracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, Command "item" +, Word "if" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "b" +, ParenR +, Command "in" +, Command "tracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, ParenL +, Variable "b" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Variable "R" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Command "tracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "enumerate" +, EndEnv "inductive" +, BeginEnv "inductive" +, Label "quasirefltracl" +, Word "define" +, BeginEnv "math" +, Command "qrefltracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "subseteq" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "times" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "inductively" +, Word "as" +, Word "follows" +, Symbol "." +, BeginEnv "enumerate" +, Command "item" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "a" +, ParenR +, Command "in" +, Command "qrefltracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, Command "item" +, Word "if" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "b" +, ParenR +, Command "in" +, Command "qrefltracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, ParenL +, Variable "b" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Variable "R" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Command "qrefltracl" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "enumerate" +, EndEnv "inductive" +, BeginEnv "inductive" +, Label "refltracl" +, Word "define" +, BeginEnv "math" +, Command "refltracl" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "subseteq" +, Variable "A" +, Command "times" +, Variable "A" +, EndEnv "math" +, Word "inductively" +, Word "as" +, Word "follows" +, Symbol "." +, BeginEnv "enumerate" +, Command "item" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "a" +, ParenR +, Command "in" +, Command "refltracl" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, Command "item" +, Word "if" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "b" +, ParenR +, Command "in" +, Command "refltracl" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, ParenL +, Variable "b" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Variable "R" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, ParenL +, Variable "a" +, Symbol "," +, Variable "c" +, ParenR +, Command "in" +, Command "refltracl" +, InvisibleBraceL +, Variable "A" +, InvisibleBraceR +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "enumerate" +, EndEnv "inductive" +, BeginEnv "inductive" +, Label "acc" +, Word "define" +, BeginEnv "math" +, Command "acc" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Command "subseteq" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "inductively" +, Word "as" +, Word "follows" +, Symbol "." +, BeginEnv "enumerate" +, Command "item" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Command "fld" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Command "preimg" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, InvisibleBraceL +, VisibleBraceL +, Variable "a" +, VisibleBraceR +, InvisibleBraceR +, Command "in" +, Command "pow" +, InvisibleBraceL +, Command "acc" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, InvisibleBraceR +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Command "acc" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "enumerate" +, EndEnv "inductive" +]
\ No newline at end of file diff --git a/test/golden/inductive/verification.golden b/test/golden/inductive/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/inductive/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/encoding tasks.golden b/test/golden/no-reflexive-set/encoding tasks.golden new file mode 100644 index 0000000..dc79b95 --- /dev/null +++ b/test/golden/no-reflexive-set/encoding tasks.golden @@ -0,0 +1,2 @@ +fof(in_irrefl,conjecture,~elem(fA,fA)). +fof(in_irrefl1,axiom,![XIndAntecedent]:(elem(XIndAntecedent,fA)=>~elem(XIndAntecedent,XIndAntecedent))).
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/generating tasks.golden b/test/golden/no-reflexive-set/generating tasks.golden new file mode 100644 index 0000000..3ed340b --- /dev/null +++ b/test/golden/no-reflexive-set/generating tasks.golden @@ -0,0 +1,64 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "in_irrefl1" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "IndAntecedent" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "A" ) + ) + ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "IndAntecedent" ) + ) + , TermVar + ( B + ( NamedVar "IndAntecedent" ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "in_irrefl" + , taskConjecture = Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "A" ) + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/glossing.golden b/test/golden/no-reflexive-set/glossing.golden new file mode 100644 index 0000000..a58b5b7 --- /dev/null +++ b/test/golden/no-reflexive-set/glossing.golden @@ -0,0 +1,43 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/no-reflexive-set.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "in_irrefl" ) + ( Lemma [] + ( Quantified Universally + ( Scope + ( Connected Implication ( PropositionalConstant IsTop ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "A" ) + ) + , TermVar + ( B + ( NamedVar "A" ) + ) + ] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/no-reflexive-set.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( BySetInduction Nothing ( Qed JustificationEmpty ) ) +]
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/parsing.golden b/test/golden/no-reflexive-set/parsing.golden new file mode 100644 index 0000000..3de5dcc --- /dev/null +++ b/test/golden/no-reflexive-set/parsing.golden @@ -0,0 +1,54 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/no-reflexive-set.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "in_irrefl" ) + ( Lemma [] + ( StmtQuantPhrase + ( QuantPhrase Universally NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) + ( + [ NamedVar "A" ] + ) ( [] ) ( Nothing ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "A" ) :| [] + ) Negative + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "A" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/no-reflexive-set.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( BySetInduction Nothing ( Qed JustificationEmpty ) ) +]
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/scanning.golden b/test/golden/no-reflexive-set/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/no-reflexive-set/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/tokenizing.golden b/test/golden/no-reflexive-set/tokenizing.golden new file mode 100644 index 0000000..16835be --- /dev/null +++ b/test/golden/no-reflexive-set/tokenizing.golden @@ -0,0 +1,29 @@ +[ BeginEnv "proposition" +, Label "in_irrefl" +, Word "for" +, Word "all" +, Word "sets" +, BeginEnv "math" +, Variable "A" +, EndEnv "math" +, Word "we" +, Word "have" +, BeginEnv "math" +, Variable "A" +, Command "not" +, Command "in" +, Variable "A" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, BracketL +, Word "proof" +, Word "by" +, Command "in" +, Word "-induction" +, BracketR +, Word "straightforward" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/no-reflexive-set/verification.golden b/test/golden/no-reflexive-set/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/no-reflexive-set/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/proofassume/encoding tasks.golden b/test/golden/proofassume/encoding tasks.golden new file mode 100644 index 0000000..43cc166 --- /dev/null +++ b/test/golden/proofassume/encoding tasks.golden @@ -0,0 +1,17 @@ +fof(assumetest,conjecture,elem(fx,fy)). +fof(assumetest1,axiom,elem(fx,fy)). +------------------ +fof(assumetest,conjecture,elem(fx,fy)). +fof(assumetest1,axiom,elem(fx,fy)). +fof(assumetest2,axiom,elem(fx,fy)). +------------------ +fof(assumetesttwo,conjecture,elem(fx,fy)). +fof(assumetest,axiom,![Xx,Xy]:(elem(Xx,Xy)=>elem(Xx,Xy))). +fof(assumetesttwo1,axiom,elem(fx,fy)). +fof(assumetesttwo2,axiom,elem(fa,fb)). +------------------ +fof(assumetesttwo,conjecture,elem(fx,fy)). +fof(assumetest,axiom,![Xx,Xy]:(elem(Xx,Xy)=>elem(Xx,Xy))). +fof(assumetesttwo1,axiom,elem(fx,fy)). +fof(assumetesttwo2,axiom,elem(fx,fy)). +fof(assumetesttwo3,axiom,elem(fa,fb)).
\ No newline at end of file diff --git a/test/golden/proofassume/generating tasks.golden b/test/golden/proofassume/generating tasks.golden new file mode 100644 index 0000000..e66cf4a --- /dev/null +++ b/test/golden/proofassume/generating tasks.golden @@ -0,0 +1,261 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "assumetest1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ] + , taskConjectureLabel = Marker "assumetest" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "assumetest1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "assumetest2" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ] + , taskConjectureLabel = Marker "assumetest" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "assumetest" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "assumetesttwo1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "assumetesttwo2" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ] + , taskConjectureLabel = Marker "assumetesttwo" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "assumetest" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "assumetesttwo1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "assumetesttwo2" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + , + ( Marker "assumetesttwo3" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ] + , taskConjectureLabel = Marker "assumetesttwo" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + } +]
\ No newline at end of file diff --git a/test/golden/proofassume/glossing.golden b/test/golden/proofassume/glossing.golden new file mode 100644 index 0000000..28b0e79 --- /dev/null +++ b/test/golden/proofassume/glossing.golden @@ -0,0 +1,171 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetest" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( Assume + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( Have + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetesttwo" ) + ( Lemma [] + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Assume + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "b" ) + ] + ) + ( Assume + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( Have + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/proofassume/parsing.golden b/test/golden/proofassume/parsing.golden new file mode 100644 index 0000000..57e542c --- /dev/null +++ b/test/golden/proofassume/parsing.golden @@ -0,0 +1,201 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetest" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( Assume + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( Have Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetesttwo" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtConnected Conjunction + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofassume.tex" + , sourceLine = Pos 12 + , sourceColumn = Pos 1 + } + ) + ( Assume + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "b" ) :| [] + ) + ) + ) + ) + ( Assume + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( Have Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/proofassume/scanning.golden b/test/golden/proofassume/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/proofassume/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/proofassume/tokenizing.golden b/test/golden/proofassume/tokenizing.golden new file mode 100644 index 0000000..cc97454 --- /dev/null +++ b/test/golden/proofassume/tokenizing.golden @@ -0,0 +1,80 @@ +[ BeginEnv "proposition" +, Label "assumetest" +, Word "if" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "assume" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proof" +, BeginEnv "proposition" +, Label "assumetesttwo" +, Word "if" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Word "and" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "b" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "assume" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "b" +, EndEnv "math" +, Symbol "." +, Word "assume" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/proofassume/verification.golden b/test/golden/proofassume/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/proofassume/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/encoding tasks.golden b/test/golden/proofdefinefunction/encoding tasks.golden new file mode 100644 index 0000000..36c916f --- /dev/null +++ b/test/golden/proofdefinefunction/encoding tasks.golden @@ -0,0 +1,9 @@ +fof(definefunctiontest,conjecture,elem(fx,fy)=>elem(fx,fy)). +fof(relation,axiom,![Xf]:(relation(Xf)<=>Xf=Xf)). +fof(rightunique,axiom,![Xf]:(rightunique(Xf)<=>Xf=Xf)). +fof(dom,axiom,![Xf]:dom(Xf)=Xf). +fof(apply,axiom,![Xf,Xx]:apply(Xf,Xx)=Xx). +fof(definefunctiontest1,axiom,relation(ff)). +fof(definefunctiontest2,axiom,rightunique(ff)). +fof(definefunctiontest3,axiom,![Xz]:(elem(Xz,fx)=>apply(ff,Xz)=Xz)). +fof(definefunctiontest4,axiom,dom(ff)=fx).
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/generating tasks.golden b/test/golden/proofdefinefunction/generating tasks.golden new file mode 100644 index 0000000..3ab9857 --- /dev/null +++ b/test/golden/proofdefinefunction/generating tasks.golden @@ -0,0 +1,332 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "relation" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "relation" ) + ] + , pl = + [ Just + ( Word "relations" ) + ] + } + ) + ) + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "f" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "f" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "rightunique" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "right-unique" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "f" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "f" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "dom" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "dom" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + ] + , TermVar + ( B + ( NamedVar "f" ) + ) + ] + ) + ) + ) + , + ( Marker "apply" + , Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "apply" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "f" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + , + ( Marker "definefunctiontest1" + , TermSymbol + ( SymbolPredicate + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "relation" ) + ] + , pl = + [ Just + ( Word "relations" ) + ] + } + ) + ) + ) + [ TermVar + ( NamedVar "f" ) + ] + ) + , + ( Marker "definefunctiontest2" + , TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "right-unique" ) + ] + ) + ) + [ TermVar + ( NamedVar "f" ) + ] + ) + , + ( Marker "definefunctiontest3" + , Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "z" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "x" ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "apply" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "f" ) + ) + ) + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + , TermVar + ( B + ( NamedVar "z" ) + ) + ] + ) + ) + ) + ) + , + ( Marker "definefunctiontest4" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "dom" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "f" ) + ] + , TermVar + ( NamedVar "x" ) + ] + ) + ] + , taskConjectureLabel = Marker "definefunctiontest" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/glossing.golden b/test/golden/proofdefinefunction/glossing.golden new file mode 100644 index 0000000..931e5da --- /dev/null +++ b/test/golden/proofdefinefunction/glossing.golden @@ -0,0 +1,163 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 3 + , sourceColumn = Pos 1 + } + ) + ( Marker "apply" ) + ( DefnOp + [ Just + ( Command "apply" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "f" + , NamedVar "x" + ] + ( TermVar + ( NamedVar "x" ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 8 + , sourceColumn = Pos 1 + } + ) + ( Marker "dom" ) + ( DefnOp + [ Just + ( Command "dom" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "f" ] + ( TermVar + ( NamedVar "f" ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "rightunique" ) + ( DefnPredicate [] + ( PredicateAdj + [ Just + ( Word "right-unique" ) + ] + ) + ( NamedVar "f" :| [] ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "f" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Marker "relation" ) + ( DefnPredicate [] + ( PredicateNoun + ( SgPl + { sg = + [ Just + ( Word "relation" ) + ] + , pl = + [ Just + ( Word "relations" ) + ] + } + ) + ) + ( NamedVar "f" :| [] ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "f" ) + , TermVar + ( NamedVar "f" ) + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 22 + , sourceColumn = Pos 1 + } + ) + ( Marker "definefunctiontest" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( DefineFunction + ( NamedVar "f" ) + ( NamedVar "z" ) + ( TermVar + ( NamedVar "z" ) + ) + ( TermVar + ( NamedVar "x" ) + ) ( Qed JustificationEmpty ) + ) +]
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/parsing.golden b/test/golden/proofdefinefunction/parsing.golden new file mode 100644 index 0000000..eba14ec --- /dev/null +++ b/test/golden/proofdefinefunction/parsing.golden @@ -0,0 +1,184 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 3 + , sourceColumn = Pos 1 + } + ) + ( Marker "apply" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "apply" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "f" + , NamedVar "x" + ] + ) + ( ExprVar + ( NamedVar "x" ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 8 + , sourceColumn = Pos 1 + } + ) + ( Marker "dom" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "dom" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "f" ] + ) + ( ExprVar + ( NamedVar "f" ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "rightunique" ) + ( Defn [] + ( DefnAdj Nothing + ( NamedVar "f" ) + ( Adj + [ Just + ( Word "right-unique" ) + ] [] + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "f" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "f" ) :| [] + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Marker "relation" ) + ( Defn [] + ( DefnNoun + ( NamedVar "f" ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "relation" ) + ] + , pl = + [ Just + ( Word "relations" ) + ] + } + ) [] + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "f" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "f" ) :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 22 + , sourceColumn = Pos 1 + } + ) + ( Marker "definefunctiontest" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/proofdefinefunction.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( DefineFunction + ( NamedVar "f" ) + ( NamedVar "z" ) + ( ExprVar + ( NamedVar "z" ) + ) + ( NamedVar "z" ) + ( ExprVar + ( NamedVar "x" ) + ) ( Qed JustificationEmpty ) + ) +]
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/scanning.golden b/test/golden/proofdefinefunction/scanning.golden new file mode 100644 index 0000000..e5d7748 --- /dev/null +++ b/test/golden/proofdefinefunction/scanning.golden @@ -0,0 +1,30 @@ +[ ScanFunctionSymbol + [ Just + ( Command "apply" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "apply" ) +, ScanFunctionSymbol + [ Just + ( Command "dom" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "dom" ) +, ScanAdj + [ Just + ( Word "right-unique" ) + ] + ( Marker "rightunique" ) +, ScanNoun + [ Just + ( Word "relation" ) + ] + ( Marker "relation" ) +]
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/tokenizing.golden b/test/golden/proofdefinefunction/tokenizing.golden new file mode 100644 index 0000000..542a89c --- /dev/null +++ b/test/golden/proofdefinefunction/tokenizing.golden @@ -0,0 +1,94 @@ +[ BeginEnv "definition" +, Label "apply" +, BeginEnv "math" +, Command "apply" +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, InvisibleBraceL +, Variable "x" +, InvisibleBraceR +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "dom" +, BeginEnv "math" +, Command "dom" +, InvisibleBraceL +, Variable "f" +, InvisibleBraceR +, Symbol "=" +, Variable "f" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "rightunique" +, BeginEnv "math" +, Variable "f" +, EndEnv "math" +, Word "is" +, Word "right-unique" +, Word "iff" +, BeginEnv "math" +, Variable "f" +, Symbol "=" +, Variable "f" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "relation" +, BeginEnv "math" +, Variable "f" +, EndEnv "math" +, Word "is" +, Word "a" +, Word "relation" +, Word "iff" +, BeginEnv "math" +, Variable "f" +, Symbol "=" +, Variable "f" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "proposition" +, Label "definefunctiontest" +, Word "if" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "let" +, BeginEnv "math" +, Variable "f" +, ParenL +, Variable "z" +, ParenR +, Symbol "=" +, Variable "z" +, EndEnv "math" +, Word "for" +, BeginEnv "math" +, Variable "z" +, Command "in" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/proofdefinefunction/verification.golden b/test/golden/proofdefinefunction/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/proofdefinefunction/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/prooffix/encoding tasks.golden b/test/golden/prooffix/encoding tasks.golden new file mode 100644 index 0000000..b92e552 --- /dev/null +++ b/test/golden/prooffix/encoding tasks.golden @@ -0,0 +1,4 @@ +fof(assumetest,conjecture,fx=fx). +------------------ +fof(assumetest,conjecture,fx=fx). +fof(assumetest1,axiom,fx=fx).
\ No newline at end of file diff --git a/test/golden/prooffix/generating tasks.golden b/test/golden/prooffix/generating tasks.golden new file mode 100644 index 0000000..7bba761 --- /dev/null +++ b/test/golden/prooffix/generating tasks.golden @@ -0,0 +1,48 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "assumetest" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "assumetest1" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) + ] + , taskConjectureLabel = Marker "assumetest" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + } +]
\ No newline at end of file diff --git a/test/golden/prooffix/glossing.golden b/test/golden/prooffix/glossing.golden new file mode 100644 index 0000000..1b84ecc --- /dev/null +++ b/test/golden/prooffix/glossing.golden @@ -0,0 +1,55 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/prooffix.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetest" ) + ( Lemma [] + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/prooffix.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( Fix + ( NamedVar "x" :| [] ) ( PropositionalConstant IsTop ) + ( Have + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "x" ) + ] + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/prooffix/parsing.golden b/test/golden/prooffix/parsing.golden new file mode 100644 index 0000000..26b2b35 --- /dev/null +++ b/test/golden/prooffix/parsing.golden @@ -0,0 +1,56 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/prooffix.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "assumetest" ) + ( Lemma [] + ( SymbolicQuantified Universally + ( NamedVar "x" :| [] ) Unbounded Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/prooffix.tex" + , sourceLine = Pos 4 + , sourceColumn = Pos 1 + } + ) + ( FixSymbolic + ( NamedVar "x" :| [] ) Unbounded + ( Have Nothing + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/prooffix/scanning.golden b/test/golden/prooffix/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/prooffix/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/prooffix/tokenizing.golden b/test/golden/prooffix/tokenizing.golden new file mode 100644 index 0000000..55064a0 --- /dev/null +++ b/test/golden/prooffix/tokenizing.golden @@ -0,0 +1,31 @@ +[ BeginEnv "proposition" +, Label "assumetest" +, Word "for" +, Word "all" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "we" +, Word "have" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "fix" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "x" +, EndEnv "math" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/prooffix/verification.golden b/test/golden/prooffix/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/prooffix/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/relation-notation/encoding tasks.golden b/test/golden/relation-notation/encoding tasks.golden new file mode 100644 index 0000000..0b26422 --- /dev/null +++ b/test/golden/relation-notation/encoding tasks.golden @@ -0,0 +1 @@ +fof(mathrel_notation_test,conjecture,elem(pair(fx,fy),fR)=>elem(pair(fx,fy),fR)).
\ No newline at end of file diff --git a/test/golden/relation-notation/generating tasks.golden b/test/golden/relation-notation/generating tasks.golden new file mode 100644 index 0000000..401b93f --- /dev/null +++ b/test/golden/relation-notation/generating tasks.golden @@ -0,0 +1,61 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "mathrel_notation_test" + , taskConjecture = Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + , 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 "x" ) + , TermVar + ( NamedVar "y" ) + ] + , TermVar + ( NamedVar "R" ) + ] + ) + } +]
\ No newline at end of file diff --git a/test/golden/relation-notation/glossing.golden b/test/golden/relation-notation/glossing.golden new file mode 100644 index 0000000..4e4aa89 --- /dev/null +++ b/test/golden/relation-notation/glossing.golden @@ -0,0 +1,67 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/relation-notation.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "mathrel_notation_test" ) + ( Lemma [] + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + , 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 "x" ) + , TermVar + ( NamedVar "y" ) + ] + , TermVar + ( NamedVar "R" ) + ] + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/relation-notation/parsing.golden b/test/golden/relation-notation/parsing.golden new file mode 100644 index 0000000..33f2808 --- /dev/null +++ b/test/golden/relation-notation/parsing.golden @@ -0,0 +1,47 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/relation-notation.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "mathrel_notation_test" ) + ( Lemma [] + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationExpr + ( ExprVar + ( NamedVar "R" ) + ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationExpr + ( ExprVar + ( NamedVar "R" ) + ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/relation-notation/scanning.golden b/test/golden/relation-notation/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/relation-notation/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/relation-notation/tokenizing.golden b/test/golden/relation-notation/tokenizing.golden new file mode 100644 index 0000000..6799562 --- /dev/null +++ b/test/golden/relation-notation/tokenizing.golden @@ -0,0 +1,24 @@ +[ BeginEnv "proposition" +, Label "mathrel_notation_test" +, Word "if" +, BeginEnv "math" +, Variable "x" +, Command "mathrel" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Variable "y" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "x" +, Command "mathrel" +, InvisibleBraceL +, Variable "R" +, InvisibleBraceR +, Variable "y" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/relation-notation/verification.golden b/test/golden/relation-notation/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/relation-notation/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/replace/encoding tasks.golden b/test/golden/replace/encoding tasks.golden new file mode 100644 index 0000000..a939ff9 --- /dev/null +++ b/test/golden/replace/encoding tasks.golden @@ -0,0 +1,17 @@ +fof(pair_emptyset_in_times_unit,conjecture,elem(pair(emptyset,emptyset),times(unit,unit))). +fof(unit,axiom,![Xany]:(elem(Xany,unit)<=>(elem(Xany,emptyset)|Xany=emptyset))). +fof(times,axiom,![XA,XB]:![Xfrv]:(elem(Xfrv,times(XA,XB))<=>?[Xa,Xb]:(elem(Xa,XA)&elem(Xb,XB)&pair(Xa,Xb)=Xfrv))). +fof(cons,axiom,![Xx,Xy,XX]:(elem(Xx,cons(Xy,XX))<=>(Xx=Xy|elem(Xx,XX)))). +------------------ +fof(suc,conjecture,![X0]:(elem(X0,fa)=>![X1,X2]:((X1=cons(X0,emptyset)&X2=cons(X0,emptyset))=>X1=X2))). +fof(pair_emptyset_in_times_unit,axiom,elem(pair(emptyset,emptyset),times(unit,unit))). +fof(unit,axiom,![Xany]:(elem(Xany,unit)<=>(elem(Xany,emptyset)|Xany=emptyset))). +fof(times,axiom,![XA,XB]:![Xfrv]:(elem(Xfrv,times(XA,XB))<=>?[Xa,Xb]:(elem(Xa,XA)&elem(Xb,XB)&pair(Xa,Xb)=Xfrv))). +fof(cons,axiom,![Xx,Xy,XX]:(elem(Xx,cons(Xy,XX))<=>(Xx=Xy|elem(Xx,XX)))). +------------------ +fof(times_replacement_test,conjecture,![Xfrv]:(elem(Xfrv,times(fA,fB))<=>?[Xa,Xb]:(elem(Xa,fA)&elem(Xb,fB)&pair(Xa,Xb)=Xfrv))). +fof(suc,axiom,![X1,Xa]:(elem(X1,suc(Xa))<=>?[X0]:(elem(X0,Xa)&X1=cons(X0,emptyset)))). +fof(pair_emptyset_in_times_unit,axiom,elem(pair(emptyset,emptyset),times(unit,unit))). +fof(unit,axiom,![Xany]:(elem(Xany,unit)<=>(elem(Xany,emptyset)|Xany=emptyset))). +fof(times,axiom,![XA,XB]:![Xfrv]:(elem(Xfrv,times(XA,XB))<=>?[Xa,Xb]:(elem(Xa,XA)&elem(Xb,XB)&pair(Xa,Xb)=Xfrv))). +fof(cons,axiom,![Xx,Xy,XX]:(elem(Xx,cons(Xy,XX))<=>(Xx=Xy|elem(Xx,XX)))).
\ No newline at end of file diff --git a/test/golden/replace/generating tasks.golden b/test/golden/replace/generating tasks.golden new file mode 100644 index 0000000..2d8fc5d --- /dev/null +++ b/test/golden/replace/generating tasks.golden @@ -0,0 +1,1378 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "unit" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) + ) + ) + ) + , + ( Marker "times" + , Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "frv" ) + ) + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ] + ] + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "frv" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cons" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "pair_emptyset_in_times_unit" + , taskConjecture = TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ] + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "pair_emptyset_in_times_unit" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ] + ) + , + ( Marker "unit" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) + ) + ) + ) + , + ( Marker "times" + , Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "frv" ) + ) + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ] + ] + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "frv" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cons" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "suc" + , taskConjecture = Quantified Universally + ( Scope + ( Connected Implication + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "a" ) + ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Connected Implication + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( FreshVar 1 ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( F + ( TermVar + ( B + ( FreshVar 0 ) + ) + ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( FreshVar 2 ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( F + ( TermVar + ( B + ( FreshVar 0 ) + ) + ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( FreshVar 1 ) + ) + , TermVar + ( B + ( FreshVar 2 ) + ) + ] + ) + ) + ) + ) + ) + ) + } +, Task + { taskDirectness = Direct + , taskHypotheses = + [ + ( Marker "suc" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( FreshVar 1 ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "suc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + ] + ] + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "a" ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( F + ( TermVar + ( B + ( FreshVar 1 ) + ) + ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ] + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "pair_emptyset_in_times_unit" + , TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ] + ) + , + ( Marker "unit" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "any" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) + ) + ) + ) + , + ( Marker "times" + , Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "frv" ) + ) + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ] + ] + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "A" ) + ) + ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "B" ) + ) + ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "frv" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "cons" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "y" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "y" ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "X" ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "times_replacement_test" + , taskConjecture = Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "frv" ) + ) + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( F + ( TermVar + ( NamedVar "A" ) + ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "B" ) + ) + ) + ] + ] + ) + ( Quantified Existentially + ( Scope + ( Connected Conjunction + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( NamedVar "A" ) + ) + ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "b" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( NamedVar "B" ) + ) + ) + ) + ) + ] + ) + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + , TermVar + ( F + ( TermVar + ( B + ( NamedVar "frv" ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + } +]
\ No newline at end of file diff --git a/test/golden/replace/glossing.golden b/test/golden/replace/glossing.golden new file mode 100644 index 0000000..d6219fe --- /dev/null +++ b/test/golden/replace/glossing.golden @@ -0,0 +1,350 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( Axiom [] + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( NamedVar "y" ) + , TermVar + ( NamedVar "X" ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "y" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "x" ) + , TermVar + ( NamedVar "X" ) + ] + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "times" ) + ( DefnOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ NamedVar "A" + , NamedVar "B" + ] + ( ReplaceFun + ( + ( NamedVar "a" + , TermVar + ( NamedVar "A" ) + ) :| + [ + ( NamedVar "b" + , TermVar + ( NamedVar "B" ) + ) + ] + ) + ( Scope + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Scope ( PropositionalConstant IsTop ) ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "unit" ) + ( DefnOp + [ Just + ( Command "unit" ) + ] [] + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "pair_emptyset_in_times_unit" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "unit" ) + ] + ) [] + ] + ] + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Marker "suc" ) + ( DefnOp + [ Just + ( Command "suc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "a" ] + ( ReplacePred + ( NamedVar "y" ) + ( NamedVar "x" ) + ( TermVar + ( NamedVar "a" ) + ) + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar ( B ReplacementRangeVar ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar ( B ReplacementDomVar ) + , TermSymbol + ( SymbolMixfix + [ Just + ( Command "emptyset" ) + ] + ) [] + ] + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Marker "times_replacement_test" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "B" ) + ] + , ReplaceFun + ( + ( NamedVar "a" + , TermVar + ( NamedVar "A" ) + ) :| + [ + ( NamedVar "b" + , TermVar + ( NamedVar "B" ) + ) + ] + ) + ( Scope + ( TermSymbol + ( SymbolMixfix + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( B + ( NamedVar "b" ) + ) + ] + ) + ) + ( Scope ( PropositionalConstant IsTop ) ) + ] + ) + ) +]
\ No newline at end of file diff --git a/test/golden/replace/parsing.golden b/test/golden/replace/parsing.golden new file mode 100644 index 0000000..c2cd815 --- /dev/null +++ b/test/golden/replace/parsing.golden @@ -0,0 +1,304 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "cons" ) + ( Axiom [] + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Just + ( Command "cons" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "y" ) + , ExprVar + ( NamedVar "X" ) + ] :| [] + ) + ) + ) + ) + ( StmtConnected Disjunction + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "y" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "X" ) :| [] + ) + ) + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 5 + , sourceColumn = Pos 1 + } + ) + ( Marker "times" ) + ( DefnOp + ( SymbolPattern + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ NamedVar "A" + , NamedVar "B" + ] + ) + ( ExprReplace + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ( + ( NamedVar "a" + , ExprVar + ( NamedVar "A" ) + ) :| + [ + ( NamedVar "b" + , ExprVar + ( NamedVar "B" ) + ) + ] + ) Nothing + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 9 + , sourceColumn = Pos 1 + } + ) + ( Marker "unit" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "unit" ) + ] [] + ) + ( ExprFiniteSet + ( ExprOp + [ Just + ( Command "emptyset" ) + ] [] :| [] + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 13 + , sourceColumn = Pos 1 + } + ) + ( Marker "pair_emptyset_in_times_unit" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprOp + [ Just + ( Command "emptyset" ) + ] [] + , ExprOp + [ Just + ( Command "emptyset" ) + ] [] + ] :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ ExprOp + [ Just + ( Command "unit" ) + ] [] + , ExprOp + [ Just + ( Command "unit" ) + ] [] + ] :| [] + ) + ) + ) + ) + ) +, BlockDefn + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 19 + , sourceColumn = Pos 1 + } + ) + ( Marker "suc" ) + ( DefnOp + ( SymbolPattern + [ Just + ( Command "suc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ NamedVar "a" ] + ) + ( ExprReplacePred + ( NamedVar "y" ) + ( NamedVar "x" ) + ( ExprVar + ( NamedVar "a" ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "y" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprFiniteSet + ( ExprVar + ( NamedVar "x" ) :| [] + ) :| [] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/replace.tex" + , sourceLine = Pos 25 + , sourceColumn = Pos 1 + } + ) + ( Marker "times_replacement_test" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprReplace + ( ExprOp + [ Just + ( Command "pair" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + [ ExprVar + ( NamedVar "a" ) + , ExprVar + ( NamedVar "b" ) + ] + ) + ( + ( NamedVar "a" + , ExprVar + ( NamedVar "A" ) + ) :| + [ + ( NamedVar "b" + , ExprVar + ( NamedVar "B" ) + ) + ] + ) Nothing :| [] + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/replace/scanning.golden b/test/golden/replace/scanning.golden new file mode 100644 index 0000000..050e544 --- /dev/null +++ b/test/golden/replace/scanning.golden @@ -0,0 +1,21 @@ +[ ScanFunctionSymbol + [ Nothing + , Just + ( Command "times" ) + , Nothing + ] + ( Marker "times" ) +, ScanFunctionSymbol + [ Just + ( Command "unit" ) + ] + ( Marker "unit" ) +, ScanFunctionSymbol + [ Just + ( Command "suc" ) + , Just InvisibleBraceL + , Nothing + , Just InvisibleBraceR + ] + ( Marker "suc" ) +]
\ No newline at end of file diff --git a/test/golden/replace/tokenizing.golden b/test/golden/replace/tokenizing.golden new file mode 100644 index 0000000..3b9f65c --- /dev/null +++ b/test/golden/replace/tokenizing.golden @@ -0,0 +1,129 @@ +[ BeginEnv "axiom" +, Label "cons" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Command "cons" +, InvisibleBraceL +, Variable "y" +, InvisibleBraceR +, InvisibleBraceL +, Variable "X" +, InvisibleBraceR +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "x" +, Symbol "=" +, Variable "y" +, EndEnv "math" +, Word "or" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "X" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "definition" +, Label "times" +, BeginEnv "math" +, Variable "A" +, Command "times" +, Variable "B" +, Symbol "=" +, VisibleBraceL +, ParenL +, Variable "a" +, Symbol "," +, Variable "b" +, ParenR +, Command "mid" +, Variable "a" +, Command "in" +, Variable "A" +, Symbol "," +, Variable "b" +, Command "in" +, Variable "B" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "definition" +, Label "unit" +, BeginEnv "math" +, Command "unit" +, Symbol "=" +, VisibleBraceL +, Command "emptyset" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "proposition" +, Label "pair_emptyset_in_times_unit" +, BeginEnv "math" +, ParenL +, Command "emptyset" +, Symbol "," +, Command "emptyset" +, ParenR +, Command "in" +, Command "unit" +, Command "times" +, Command "unit" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "definition" +, Label "suc" +, BeginEnv "math" +, Command "suc" +, InvisibleBraceL +, Variable "a" +, InvisibleBraceR +, Symbol "=" +, VisibleBraceL +, Variable "y" +, Command "mid" +, Command "exists" +, Variable "x" +, Command "in" +, Variable "a" +, Symbol "." +, Variable "y" +, Symbol "=" +, VisibleBraceL +, Variable "x" +, VisibleBraceR +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "proposition" +, Label "times_replacement_test" +, BeginEnv "math" +, Variable "A" +, Command "times" +, Variable "B" +, Symbol "=" +, VisibleBraceL +, ParenL +, Variable "a" +, Symbol "," +, Variable "b" +, ParenR +, Command "mid" +, Variable "a" +, Command "in" +, Variable "A" +, Symbol "," +, Variable "b" +, Command "in" +, Variable "B" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/replace/verification.golden b/test/golden/replace/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/replace/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/russell/encoding tasks.golden b/test/golden/russell/encoding tasks.golden new file mode 100644 index 0000000..c8fa769 --- /dev/null +++ b/test/golden/russell/encoding tasks.golden @@ -0,0 +1,24 @@ +fof(no_universal_set,conjecture,?[XV]:universal_set(XV)). +fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))). +fof(no_universal_set1,axiom,~~?[X0]:universal_set(X0)). +------------------ +fof(no_universal_set,conjecture,elem(fR,fR)<=>~elem(fR,fR)). +fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))). +fof(no_universal_set1,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))). +fof(no_universal_set2,axiom,universal_set(fV)). +fof(no_universal_set3,axiom,~~?[X0]:universal_set(X0)). +------------------ +fof(no_universal_set,conjecture,$false). +fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))). +fof(no_universal_set1,axiom,elem(fR,fR)<=>~elem(fR,fR)). +fof(no_universal_set2,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))). +fof(no_universal_set3,axiom,universal_set(fV)). +fof(no_universal_set4,axiom,~~?[X0]:universal_set(X0)). +------------------ +fof(no_universal_set,conjecture,$false). +fof(universal_set,axiom,![XV]:(universal_set(XV)<=>![Xx]:elem(Xx,XV))). +fof(no_universal_set1,axiom,$false). +fof(no_universal_set2,axiom,elem(fR,fR)<=>~elem(fR,fR)). +fof(no_universal_set3,axiom,![Xx]:(elem(Xx,fR)<=>(elem(Xx,fV)&~elem(Xx,Xx)))). +fof(no_universal_set4,axiom,universal_set(fV)). +fof(no_universal_set5,axiom,~~?[X0]:universal_set(X0)).
\ No newline at end of file diff --git a/test/golden/russell/generating tasks.golden b/test/golden/russell/generating tasks.golden new file mode 100644 index 0000000..a509323 --- /dev/null +++ b/test/golden/russell/generating tasks.golden @@ -0,0 +1,769 @@ +[ Task + { taskDirectness = Indirect + ( Not + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + , taskHypotheses = + [ + ( Marker "universal_set" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "V" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "V" ) + ) + ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set1" + , Not + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "no_universal_set" + , taskConjecture = Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "V" ) + ) + ] + ) + ) + } +, Task + { taskDirectness = Indirect + ( Not + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + , taskHypotheses = + [ + ( Marker "universal_set" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "V" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "V" ) + ) + ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set1" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "R" ) + ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "V" ) + ) + ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set2" + , TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( NamedVar "V" ) + ] + ) + , + ( Marker "no_universal_set3" + , Not + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "no_universal_set" + , taskConjecture = Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ) + } +, Task + { taskDirectness = Indirect + ( Not + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + , taskHypotheses = + [ + ( Marker "universal_set" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "V" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "V" ) + ) + ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set1" + , Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ) + ) + , + ( Marker "no_universal_set2" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "R" ) + ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "V" ) + ) + ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set3" + , TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( NamedVar "V" ) + ] + ) + , + ( Marker "no_universal_set4" + , Not + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "no_universal_set" + , taskConjecture = PropositionalConstant IsBottom + } +, Task + { taskDirectness = Indirect + ( Not + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + , taskHypotheses = + [ + ( Marker "universal_set" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( NamedVar "V" ) + ) + ] + ) + ( Quantified Universally + ( Scope + ( Quantified Universally + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( F + ( TermVar + ( B + ( NamedVar "V" ) + ) + ) + ) + ) + ) + ] + ) + ) + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set1" + , PropositionalConstant IsBottom + ) + , + ( Marker "no_universal_set2" + , Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ) + ) + , + ( Marker "no_universal_set3" + , Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "R" ) + ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "V" ) + ) + ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + ) + ) + , + ( Marker "no_universal_set4" + , TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( NamedVar "V" ) + ] + ) + , + ( Marker "no_universal_set5" + , Not + ( Not + ( Quantified Existentially + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + ] + , taskConjectureLabel = Marker "no_universal_set" + , taskConjecture = PropositionalConstant IsBottom + } +]
\ No newline at end of file diff --git a/test/golden/russell/glossing.golden b/test/golden/russell/glossing.golden new file mode 100644 index 0000000..e8ef25d --- /dev/null +++ b/test/golden/russell/glossing.golden @@ -0,0 +1,155 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "universal_set" ) + ( DefnPredicate [] + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ( NamedVar "V" :| [] ) + ( Quantified Universally + ( Scope + ( Connected Implication ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "V" ) + ) + ) + ] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 7 + , sourceColumn = Pos 1 + } + ) + ( Marker "no_universal_set" ) + ( Lemma [] + ( Not + ( Quantified Existentially + ( Scope + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( B + ( FreshVar 0 ) + ) + ] + ) + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 10 + , sourceColumn = Pos 1 + } + ) + ( ByContradiction + ( Take + ( NamedVar "V" :| [] ) + ( Connected Conjunction ( PropositionalConstant IsTop ) + ( TermSymbol + ( SymbolPredicate + ( PredicateAdj + [ Just + ( Word "universal" ) + ] + ) + ) + [ TermVar + ( NamedVar "V" ) + ] + ) + ) JustificationEmpty + ( Define + ( NamedVar "R" ) + ( TermSep + ( NamedVar "x" ) + ( TermVar + ( NamedVar "V" ) + ) + ( Scope + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B () ) + , TermVar + ( B () ) + ] + ) + ) + ) + ) + ( Have + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ( Not + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "R" ) + , TermVar + ( NamedVar "R" ) + ] + ) + ) + ) JustificationEmpty + ( Have ( PropositionalConstant IsBottom ) JustificationEmpty ( Qed JustificationEmpty ) ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/russell/parsing.golden b/test/golden/russell/parsing.golden new file mode 100644 index 0000000..f924229 --- /dev/null +++ b/test/golden/russell/parsing.golden @@ -0,0 +1,198 @@ +[ BlockDefn + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "universal_set" ) + ( Defn [] + ( DefnAdj + ( Just NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ) + ( NamedVar "V" ) + ( Adj + [ Just + ( Word "universal" ) + ] [] + ) + ) + ( StmtQuantPhrase + ( QuantPhrase Universally NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) + ( + [ NamedVar "x" ] + ) ( [] ) ( Nothing ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "V" ) :| [] + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 7 + , sourceColumn = Pos 1 + } + ) + ( Marker "no_universal_set" ) + ( Lemma [] + ( StmtNeg + ( StmtExists NounPhrase + ( + [ AdjL + [ Just + ( Word "universal" ) + ] [] + ] + ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( [] ) ( [] ) ( Nothing ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/russell.tex" + , sourceLine = Pos 10 + , sourceColumn = Pos 1 + } + ) + ( ByContradiction + ( TakeNoun NounPhrase + ( + [ AdjL + [ Just + ( Word "universal" ) + ] [] + ] + ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) + ( + [ NamedVar "V" ] + ) ( [] ) ( Nothing ) JustificationEmpty + ( Define + ( NamedVar "R" ) + ( ExprSep + ( NamedVar "x" ) + ( ExprVar + ( NamedVar "V" ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Negative + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) + ) + ( Have Nothing + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "R" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "R" ) :| [] + ) Negative + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "R" ) :| [] + ) + ) + ) + ) + ) JustificationEmpty + ( Have Nothing + ( StmtFormula ( PropositionalConstant IsBottom ) ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/russell/scanning.golden b/test/golden/russell/scanning.golden new file mode 100644 index 0000000..c0111b2 --- /dev/null +++ b/test/golden/russell/scanning.golden @@ -0,0 +1,6 @@ +[ ScanAdj + [ Just + ( Word "universal" ) + ] + ( Marker "universal_set" ) +]
\ No newline at end of file diff --git a/test/golden/russell/tokenizing.golden b/test/golden/russell/tokenizing.golden new file mode 100644 index 0000000..c2de55f --- /dev/null +++ b/test/golden/russell/tokenizing.golden @@ -0,0 +1,80 @@ +[ BeginEnv "definition" +, Label "universal_set" +, Word "a" +, Word "set" +, BeginEnv "math" +, Variable "V" +, EndEnv "math" +, Word "is" +, Word "universal" +, Word "iff" +, Word "for" +, Word "all" +, Word "sets" +, BeginEnv "math" +, Variable "x" +, EndEnv "math" +, Word "we" +, Word "have" +, BeginEnv "math" +, Variable "x" +, Command "in" +, Variable "V" +, EndEnv "math" +, Symbol "." +, EndEnv "definition" +, BeginEnv "theorem" +, Label "no_universal_set" +, Word "there" +, Word "exists" +, Word "no" +, Word "universal" +, Word "set" +, Symbol "." +, EndEnv "theorem" +, BeginEnv "proof" +, Word "suppose" +, Word "not" +, Symbol "." +, Word "take" +, Word "a" +, Word "universal" +, Word "set" +, BeginEnv "math" +, Variable "V" +, EndEnv "math" +, Symbol "." +, Word "let" +, BeginEnv "math" +, Variable "R" +, Symbol "=" +, VisibleBraceL +, Variable "x" +, Command "in" +, Variable "V" +, Command "mid" +, Variable "x" +, Command "not" +, Command "in" +, Variable "x" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "R" +, Command "in" +, Variable "R" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "R" +, Command "not" +, Command "in" +, Variable "R" +, EndEnv "math" +, Symbol "." +, Word "contradiction" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/russell/verification.golden b/test/golden/russell/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/russell/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/separation/encoding tasks.golden b/test/golden/separation/encoding tasks.golden new file mode 100644 index 0000000..5d0994b --- /dev/null +++ b/test/golden/separation/encoding tasks.golden @@ -0,0 +1 @@ +fof(sep_test,conjecture,![Xx]:(elem(Xx,fX)<=>(elem(Xx,fX)&Xx=Xx))).
\ No newline at end of file diff --git a/test/golden/separation/generating tasks.golden b/test/golden/separation/generating tasks.golden new file mode 100644 index 0000000..889906b --- /dev/null +++ b/test/golden/separation/generating tasks.golden @@ -0,0 +1,65 @@ +[ Task + { taskDirectness = Direct + , taskHypotheses = [] + , taskConjectureLabel = Marker "sep_test" + , taskConjecture = Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "X" ) + ) + ) + ] + ) + ( Connected Conjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "X" ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B + ( NamedVar "x" ) + ) + , TermVar + ( B + ( NamedVar "x" ) + ) + ] + ) + ) + ) + ) + } +]
\ No newline at end of file diff --git a/test/golden/separation/glossing.golden b/test/golden/separation/glossing.golden new file mode 100644 index 0000000..47d574b --- /dev/null +++ b/test/golden/separation/glossing.golden @@ -0,0 +1,40 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/separation.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "sep_test" ) + ( Lemma [] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "X" ) + , TermSep + ( NamedVar "x" ) + ( TermVar + ( NamedVar "X" ) + ) + ( Scope + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( B () ) + , TermVar + ( B () ) + ] + ) + ) + ] + ) + ) +]
\ No newline at end of file diff --git a/test/golden/separation/parsing.golden b/test/golden/separation/parsing.golden new file mode 100644 index 0000000..2a2110f --- /dev/null +++ b/test/golden/separation/parsing.golden @@ -0,0 +1,44 @@ +[ BlockLemma + ( SourcePos + { sourceName = "test/examples/separation.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "sep_test" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "X" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprSep + ( NamedVar "x" ) + ( ExprVar + ( NamedVar "X" ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "x" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "x" ) :| [] + ) + ) + ) + ) :| [] + ) + ) + ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/separation/scanning.golden b/test/golden/separation/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/separation/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/separation/tokenizing.golden b/test/golden/separation/tokenizing.golden new file mode 100644 index 0000000..40b30d8 --- /dev/null +++ b/test/golden/separation/tokenizing.golden @@ -0,0 +1,18 @@ +[ BeginEnv "proposition" +, Label "sep_test" +, BeginEnv "math" +, Variable "X" +, Symbol "=" +, VisibleBraceL +, Variable "x" +, Command "in" +, Variable "X" +, Command "mid" +, Variable "x" +, Symbol "=" +, Variable "x" +, VisibleBraceR +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +]
\ No newline at end of file diff --git a/test/golden/separation/verification.golden b/test/golden/separation/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/separation/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file diff --git a/test/golden/union/encoding tasks.golden b/test/golden/union/encoding tasks.golden new file mode 100644 index 0000000..34d92fd --- /dev/null +++ b/test/golden/union/encoding tasks.golden @@ -0,0 +1,21 @@ +fof(union_comm,conjecture,union(fA,fB)=union(fB,fA)). +fof(union_defn,axiom,![Xa,XA,XB]:(elem(Xa,union(XA,XB))<=>(elem(Xa,XA)|elem(Xa,XB)))). +fof(ext,axiom,![XA,XB]:(![Xa]:(elem(Xa,XA)<=>elem(Xa,XB))=>XA=XB)). +------------------ +fof(union_assoc,conjecture,![Xa]:(elem(Xa,union(union(fA,fB),fC))=>elem(Xa,union(fA,union(fB,fC))))). +fof(union_comm,axiom,![XA,XB]:union(XA,XB)=union(XB,XA)). +fof(union_defn,axiom,![Xa,XA,XB]:(elem(Xa,union(XA,XB))<=>(elem(Xa,XA)|elem(Xa,XB)))). +fof(ext,axiom,![XA,XB]:(![Xa]:(elem(Xa,XA)<=>elem(Xa,XB))=>XA=XB)). +------------------ +fof(union_assoc,conjecture,![Xa]:(elem(Xa,union(fA,union(fB,fC)))=>elem(Xa,union(union(fA,fB),fC)))). +fof(union_comm,axiom,![XA,XB]:union(XA,XB)=union(XB,XA)). +fof(union_defn,axiom,![Xa,XA,XB]:(elem(Xa,union(XA,XB))<=>(elem(Xa,XA)|elem(Xa,XB)))). +fof(ext,axiom,![XA,XB]:(![Xa]:(elem(Xa,XA)<=>elem(Xa,XB))=>XA=XB)). +fof(union_assoc1,axiom,![Xa]:(elem(Xa,union(union(fA,fB),fC))=>elem(Xa,union(fA,union(fB,fC))))). +------------------ +fof(union_assoc,conjecture,union(union(fA,fB),fC)=union(fA,union(fB,fC))). +fof(union_comm,axiom,![XA,XB]:union(XA,XB)=union(XB,XA)). +fof(union_defn,axiom,![Xa,XA,XB]:(elem(Xa,union(XA,XB))<=>(elem(Xa,XA)|elem(Xa,XB)))). +fof(ext,axiom,![XA,XB]:(![Xa]:(elem(Xa,XA)<=>elem(Xa,XB))=>XA=XB)). +fof(union_assoc1,axiom,![Xa]:(elem(Xa,union(fA,union(fB,fC)))=>elem(Xa,union(union(fA,fB),fC)))). +fof(union_assoc2,axiom,![Xa]:(elem(Xa,union(union(fA,fB),fC))=>elem(Xa,union(fA,union(fB,fC))))).
\ No newline at end of file diff --git a/test/golden/union/generating tasks.golden b/test/golden/union/generating tasks.golden new file mode 100644 index 0000000..f7f72bb --- /dev/null +++ b/test/golden/union/generating tasks.golden @@ -0,0 +1,1335 @@ +[ 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" ) + ] + ] + ] + } +]
\ No newline at end of file diff --git a/test/golden/union/glossing.golden b/test/golden/union/glossing.golden new file mode 100644 index 0000000..1925c15 --- /dev/null +++ b/test/golden/union/glossing.golden @@ -0,0 +1,456 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "ext" ) + ( Axiom + [ Asm + ( Quantified Universally + ( Scope + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "A" ) + ) + ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( B + ( NamedVar "a" ) + ) + , TermVar + ( F + ( TermVar + ( NamedVar "B" ) + ) + ) + ] + ) + ) + ) + ) + ] + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Symbol "=" ) + ) + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "B" ) + ] + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 6 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_defn" ) + ( Axiom + [ Asm ( PropositionalConstant IsTop ) + , Asm ( PropositionalConstant IsTop ) + ] + ( Connected Equivalence + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermSymbol + ( SymbolMixfix + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + ) + [ TermVar + ( NamedVar "A" ) + , TermVar + ( NamedVar "B" ) + ] + ] + ) + ( Connected Disjunction + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "A" ) + ] + ) + ( TermSymbol + ( SymbolPredicate + ( PredicateRelation + ( Command "in" ) + ) + ) + [ TermVar + ( NamedVar "a" ) + , TermVar + ( NamedVar "B" ) + ] + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_comm" ) + ( Lemma [] + ( 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" ) + ] + ] + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_assoc" ) + ( Lemma [] + ( 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" ) + ] + ] + ] + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Have + ( 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" ) + ) + ) + ] + ] + ] + ) + ) + ) + ) JustificationEmpty + ( Have + ( 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" ) + ) + ) + ] + ] + ) + ) + ) + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/union/parsing.golden b/test/golden/union/parsing.golden new file mode 100644 index 0000000..391f039 --- /dev/null +++ b/test/golden/union/parsing.golden @@ -0,0 +1,406 @@ +[ BlockAxiom + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 1 + , sourceColumn = Pos 1 + } + ) + ( Marker "ext" ) + ( Axiom + [ AsmSuppose + ( SymbolicQuantified Universally + ( NamedVar "a" :| [] ) Unbounded Nothing + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "A" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "B" ) :| [] + ) + ) + ) + ) + ) + ) + ] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "A" ) :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprVar + ( NamedVar "B" ) :| [] + ) + ) + ) + ) + ) +, BlockAxiom + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 6 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_defn" ) + ( Axiom + [ AsmLetNoun + ( NamedVar "A" :| + [ NamedVar "B" ] + ) NounPhrase ( [] ) + ( Noun + ( SgPl + { sg = + [ Just + ( Word "set" ) + ] + , pl = + [ Just + ( Word "sets" ) + ] + } + ) [] + ) ( Nothing ) ( [] ) ( Nothing ) + ] + ( StmtConnected Equivalence + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] :| [] + ) + ) + ) + ) + ( StmtConnected Disjunction + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "A" ) :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprVar + ( NamedVar "B" ) :| [] + ) + ) + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 11 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_comm" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "B" ) + , ExprVar + ( NamedVar "A" ) + ] :| [] + ) + ) + ) + ) + ) +, BlockLemma + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 15 + , sourceColumn = Pos 1 + } + ) + ( Marker "union_assoc" ) + ( Lemma [] + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] + , ExprVar + ( NamedVar "C" ) + ] :| [] + ) Positive + ( RelationSymbol + ( Symbol "=" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "B" ) + , ExprVar + ( NamedVar "C" ) + ] + ] :| [] + ) + ) + ) + ) + ) +, BlockProof + ( SourcePos + { sourceName = "test/examples/union.tex" + , sourceLine = Pos 18 + , sourceColumn = Pos 1 + } + ) + ( Have Nothing + ( SymbolicQuantified Universally + ( NamedVar "a" :| [] ) Unbounded Nothing + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] + , ExprVar + ( NamedVar "C" ) + ] :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "B" ) + , ExprVar + ( NamedVar "C" ) + ] + ] :| [] + ) + ) + ) + ) + ) + ) JustificationEmpty + ( Have Nothing + ( SymbolicQuantified Universally + ( NamedVar "a" :| [] ) Unbounded Nothing + ( StmtConnected Implication + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "B" ) + , ExprVar + ( NamedVar "C" ) + ] + ] :| [] + ) + ) + ) + ) + ( StmtFormula + ( FormulaChain + ( ChainBase + ( ExprVar + ( NamedVar "a" ) :| [] + ) Positive + ( RelationSymbol + ( Command "in" ) + ) + ( ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprOp + [ Nothing + , Just + ( Command "union" ) + , Nothing + ] + [ ExprVar + ( NamedVar "A" ) + , ExprVar + ( NamedVar "B" ) + ] + , ExprVar + ( NamedVar "C" ) + ] :| [] + ) + ) + ) + ) + ) + ) JustificationEmpty ( Qed JustificationEmpty ) + ) + ) +]
\ No newline at end of file diff --git a/test/golden/union/scanning.golden b/test/golden/union/scanning.golden new file mode 100644 index 0000000..0637a08 --- /dev/null +++ b/test/golden/union/scanning.golden @@ -0,0 +1 @@ +[]
\ No newline at end of file diff --git a/test/golden/union/tokenizing.golden b/test/golden/union/tokenizing.golden new file mode 100644 index 0000000..e336098 --- /dev/null +++ b/test/golden/union/tokenizing.golden @@ -0,0 +1,168 @@ +[ BeginEnv "axiom" +, BracketL +, Word "extensionality" +, BracketR +, Label "ext" +, Word "suppose" +, Word "for" +, Word "all" +, BeginEnv "math" +, Variable "a" +, EndEnv "math" +, Word "we" +, Word "have" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "B" +, EndEnv "math" +, Symbol "." +, Word "then" +, BeginEnv "math" +, Variable "A" +, Symbol "=" +, Variable "B" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "axiom" +, Label "union_defn" +, Word "let" +, BeginEnv "math" +, Variable "A" +, Symbol "," +, Variable "B" +, EndEnv "math" +, Word "be" +, Word "sets" +, Symbol "." +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, Command "union" +, Variable "B" +, EndEnv "math" +, Word "iff" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, EndEnv "math" +, Word "or" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "B" +, EndEnv "math" +, Symbol "." +, EndEnv "axiom" +, BeginEnv "proposition" +, Label "union_comm" +, BeginEnv "math" +, Variable "A" +, Command "union" +, Variable "B" +, Symbol "=" +, Variable "B" +, Command "union" +, Variable "A" +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proposition" +, Label "union_assoc" +, BeginEnv "math" +, ParenL +, Variable "A" +, Command "union" +, Variable "B" +, ParenR +, Command "union" +, Variable "C" +, Symbol "=" +, Variable "A" +, Command "union" +, ParenL +, Variable "B" +, Command "union" +, Variable "C" +, ParenR +, EndEnv "math" +, Symbol "." +, EndEnv "proposition" +, BeginEnv "proof" +, Word "for" +, Word "all" +, BeginEnv "math" +, Variable "a" +, EndEnv "math" +, Word "we" +, Word "have" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, ParenL +, Variable "A" +, Command "union" +, Variable "B" +, ParenR +, Command "union" +, Variable "C" +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, Command "union" +, ParenL +, Variable "B" +, Command "union" +, Variable "C" +, ParenR +, EndEnv "math" +, Symbol "." +, Word "for" +, Word "all" +, BeginEnv "math" +, Variable "a" +, EndEnv "math" +, Word "we" +, Word "have" +, Word "if" +, BeginEnv "math" +, Variable "a" +, Command "in" +, Variable "A" +, Command "union" +, ParenL +, Variable "B" +, Command "union" +, Variable "C" +, ParenR +, EndEnv "math" +, Symbol "," +, Word "then" +, BeginEnv "math" +, Variable "a" +, Command "in" +, ParenL +, Variable "A" +, Command "union" +, Variable "B" +, ParenR +, Command "union" +, Variable "C" +, EndEnv "math" +, Symbol "." +, EndEnv "proof" +]
\ No newline at end of file diff --git a/test/golden/union/verification.golden b/test/golden/union/verification.golden new file mode 100644 index 0000000..69b9873 --- /dev/null +++ b/test/golden/union/verification.golden @@ -0,0 +1 @@ +VerificationSuccess
\ No newline at end of file |