[ 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" ) ] ) ) ) ) ]