%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN059^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:07:56 AM UTC 2026 % Result : Theorem 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN059^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n003.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 23:19:29 EDT 2026 % 0.18/0.36 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.40/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.cF (-> $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.cH (-> $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.cG (-> $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.cJ (-> $$unsorted Bool)) % 0.40/0.58 (define @t1 () (@var "Xx" $$unsorted)) % 0.40/0.58 (define @t2 () (_ tptp.cJ @t1)) % 0.40/0.58 (define @t3 () (_ tptp.cG @t1)) % 0.40/0.58 (define @t4 () (@list @t1)) % 0.40/0.58 (define @t5 () (forall @t4 (=> @t3 @t2))) % 0.40/0.58 (define @t6 () (@var "Xy" $$unsorted)) % 0.40/0.58 (define @t7 () (_ tptp.cJ @t6)) % 0.40/0.58 (define @t8 () (_ tptp.cH @t1)) % 0.40/0.58 (define @t9 () (and @t8 @t7)) % 0.40/0.58 (define @t10 () (_ tptp.cG @t6)) % 0.40/0.58 (define @t11 () (_ tptp.cF @t1)) % 0.40/0.58 (define @t12 () (and @t11 @t10)) % 0.40/0.58 (define @t13 () (@list @t1 @t6)) % 0.40/0.58 (define @t14 () (forall @t13 (=> @t12 @t9))) % 0.40/0.58 (define @t15 () (=> @t14 @t5)) % 0.40/0.58 (define @t16 () (forall @t4 (=> @t11 @t8))) % 0.40/0.58 (define @t17 () (and @t16 @t5)) % 0.40/0.58 (define @t18 () (=> @t17 @t14)) % 0.40/0.58 (define @t19 () (and @t18 @t15)) % 0.40/0.58 (define @t20 () (exists @t4 @t3)) % 0.40/0.58 (define @t21 () (exists @t4 @t11)) % 0.40/0.58 (define @t22 () (and @t21 @t20)) % 0.40/0.58 (define @t23 () (=> @t22 @t19)) % 0.40/0.58 (define @t24 () (not @t23)) % 0.40/0.58 (define @t25 () (tptp.cJ @t1)) % 0.40/0.58 (define @t26 () (tptp.cG @t1)) % 0.40/0.58 (define @t27 () (forall @t4 (or (not @t26) @t25))) % 0.40/0.58 (define @t28 () (tptp.cH @t1)) % 0.40/0.58 (define @t29 () (tptp.cF @t1)) % 0.40/0.58 (define @t30 () (not @t29)) % 0.40/0.58 (define @t31 () (forall @t4 (or @t30 @t28))) % 0.40/0.58 (define @t32 () (and @t31 @t27)) % 0.40/0.58 (define @t33 () (not @t32)) % 0.40/0.58 (define @t34 () (tptp.cJ @t6)) % 0.40/0.58 (define @t35 () (tptp.cG @t6)) % 0.40/0.58 (define @t36 () (forall @t13 (or @t30 (not @t35) (and @t28 @t34)))) % 0.40/0.58 (define @t37 () (=> @t32 @t36)) % 0.40/0.58 (define @t38 () (not @t3)) % 0.40/0.58 (define @t39 () (or @t38 @t2)) % 0.40/0.58 (define @t40 () (not @t10)) % 0.40/0.58 (define @t41 () (not @t11)) % 0.40/0.58 (define @t42 () (or @t41 @t40 @t9)) % 0.40/0.58 (define @t43 () (or @t41 @t8)) % 0.40/0.58 (define @t44 () (forall @t4 @t38)) % 0.40/0.58 (define @t45 () (not @t44)) % 0.40/0.58 (define @t46 () (forall @t4 @t41)) % 0.40/0.58 (define @t47 () (not @t46)) % 0.40/0.58 (define @t48 () (=> @t36 @t27)) % 0.40/0.58 (define @t49 () (@quantifiers_skolemize @t27 0)) % 0.40/0.58 (define @t50 () (tptp.cJ @t49)) % 0.40/0.58 (define @t51 () (tptp.cG @t49)) % 0.40/0.58 (define @t52 () (not @t51)) % 0.40/0.58 (define @t53 () (or @t52 @t50)) % 0.40/0.58 (define @t54 () (not @t53)) % 0.40/0.58 (define @t55 () (not @t27)) % 0.40/0.58 (define @t56 () (forall @t4 @t30)) % 0.40/0.58 (define @t57 () (@quantifiers_skolemize @t56 0)) % 0.40/0.58 (define @t58 () (and (tptp.cH @t57) @t50)) % 0.40/0.58 (define @t59 () (tptp.cF @t57)) % 0.40/0.58 (define @t60 () (not @t59)) % 0.40/0.58 (define @t61 () (or @t60 @t52 @t58)) % 0.40/0.58 (define @t62 () (not @t56)) % 0.40/0.58 (define @t63 () (not @t60)) % 0.40/0.58 (define @t64 () (@list true)) % 0.40/0.58 (define @t65 () (@quantifiers_skolemize @t36 1)) % 0.40/0.58 (define @t66 () (tptp.cJ @t65)) % 0.40/0.58 (define @t67 () (@quantifiers_skolemize @t36 0)) % 0.40/0.58 (define @t68 () (tptp.cH @t67)) % 0.40/0.58 (define @t69 () (and @t68 @t66)) % 0.40/0.58 (define @t70 () (tptp.cG @t65)) % 0.40/0.58 (define @t71 () (not @t70)) % 0.40/0.58 (define @t72 () (tptp.cF @t67)) % 0.40/0.58 (define @t73 () (not @t72)) % 0.40/0.58 (define @t74 () (or @t73 @t71 @t69)) % 0.40/0.58 (define @t75 () (not @t74)) % 0.40/0.58 (define @t76 () (not @t36)) % 0.40/0.58 (define @t77 () (or @t73 @t68)) % 0.40/0.58 (define @t78 () (not @t77)) % 0.40/0.58 (define @t79 () (or @t71 @t66)) % 0.40/0.58 (define @t80 () (@list false)) % 0.40/0.58 (define @t81 () (@list @t27)) % 0.40/0.58 (assume @p1 @t24) % 0.40/0.58 (assume @p2 true) % 0.40/0.58 (step @p3 :rule cnf_and_pos :args (@t32 1)) % 0.40/0.58 (step @p4 :rule reordering :premises (@p3) :args ((or @t27 @t33))) % 0.40/0.58 (step @p5 :rule cnf_implies_neg1 :args (@t37)) % 0.40/0.58 (step @p6 :rule reordering :premises (@p5) :args ((or @t32 @t37))) % 0.40/0.58 (step @p7 :rule refl :args (@t25)) % 0.40/0.58 (step @p8 :rule refl :args (@t2)) % 0.40/0.58 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t2 @t25))) % 0.40/0.58 (step @p10 :rule symm :premises (@p9)) % 0.40/0.58 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.40/0.58 (step @p12 :rule refl :args (@t26)) % 0.40/0.58 (step @p13 :rule refl :args (@t3)) % 0.40/0.58 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t3 @t26))) % 0.40/0.58 (step @p15 :rule symm :premises (@p14)) % 0.40/0.58 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.40/0.58 (step @p17 :rule cong :premises (@p16) :args (@t38)) % 0.40/0.58 (step @p18 :rule nary_cong :premises (@p17 @p11) :args (@t39)) % 0.40/0.58 (step @p19 :rule cong :premises (@p18) :args ((forall @t4 @t39))) % 0.40/0.58 (step @p20 :rule bool-impl-elim :args (@t3 @t2)) % 0.40/0.58 (step @p21 :rule cong :premises (@p20) :args (@t5)) % 0.40/0.58 (step @p22 :rule trans :premises (@p21 @p19)) % 0.40/0.58 (step @p23 :rule refl :args (@t34)) % 0.40/0.58 (step @p24 :rule refl :args (@t7)) % 0.40/0.58 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t7 @t34))) % 0.40/0.58 (step @p26 :rule symm :premises (@p25)) % 0.40/0.58 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.40/0.58 (step @p28 :rule refl :args (@t28)) % 0.40/0.58 (step @p29 :rule refl :args (@t8)) % 0.40/0.58 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t8 @t28))) % 0.40/0.58 (step @p31 :rule symm :premises (@p30)) % 0.40/0.58 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 0.40/0.58 (step @p33 :rule nary_cong :premises (@p32 @p27) :args (@t9)) % 0.40/0.58 (step @p34 :rule refl :args (@t35)) % 0.40/0.58 (step @p35 :rule refl :args (@t10)) % 0.40/0.58 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t10 @t35))) % 0.40/0.58 (step @p37 :rule symm :premises (@p36)) % 0.40/0.58 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.40/0.58 (step @p39 :rule cong :premises (@p38) :args (@t40)) % 0.40/0.58 (step @p40 :rule refl :args (@t29)) % 0.40/0.58 (step @p41 :rule refl :args (@t11)) % 0.40/0.58 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t11 @t29))) % 0.40/0.58 (step @p43 :rule symm :premises (@p42)) % 0.40/0.58 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.40/0.58 (step @p45 :rule cong :premises (@p44) :args (@t41)) % 0.40/0.58 (step @p46 :rule nary_cong :premises (@p45 @p39 @p33) :args (@t42)) % 0.40/0.58 (step @p47 :rule cong :premises (@p46) :args ((forall @t13 @t42))) % 0.40/0.58 (step @p48 :rule aci_norm :args ((= (or (or @t41 @t40) @t9) @t42))) % 0.40/0.58 (step @p49 :rule refl :args (@t9)) % 0.40/0.58 (step @p50 :rule bool-and-de-morgan :args (@t11 @t10 true)) % 0.40/0.58 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or (not @t12) @t9))) % 0.40/0.58 (step @p52 :rule trans :premises (@p51 @p48)) % 0.40/0.58 (step @p53 :rule bool-impl-elim :args (@t12 @t9)) % 0.40/0.58 (step @p54 :rule trans :premises (@p53 @p52)) % 0.40/0.58 (step @p55 :rule cong :premises (@p54) :args (@t14)) % 0.40/0.58 (step @p56 :rule trans :premises (@p55 @p47)) % 0.40/0.58 (step @p57 :rule cong :premises (@p56 @p22) :args (@t15)) % 0.40/0.58 (step @p58 :rule nary_cong :premises (@p45 @p32) :args (@t43)) % 0.40/0.58 (step @p59 :rule cong :premises (@p58) :args ((forall @t4 @t43))) % 0.40/0.58 (step @p60 :rule bool-impl-elim :args (@t11 @t8)) % 0.40/0.58 (step @p61 :rule cong :premises (@p60) :args (@t16)) % 0.40/0.58 (step @p62 :rule trans :premises (@p61 @p59)) % 0.40/0.58 (step @p63 :rule nary_cong :premises (@p62 @p22) :args (@t17)) % 0.40/0.58 (step @p64 :rule cong :premises (@p63 @p56) :args (@t18)) % 0.40/0.58 (step @p65 :rule nary_cong :premises (@p64 @p57) :args (@t19)) % 0.40/0.58 (step @p66 :rule cong :premises (@p17) :args (@t44)) % 0.40/0.58 (step @p67 :rule cong :premises (@p66) :args (@t45)) % 0.40/0.58 (step @p68 :rule exists-elim :args ((= @t20 @t45))) % 0.40/0.58 (step @p69 :rule trans :premises (@p68 @p67)) % 0.40/0.58 (step @p70 :rule cong :premises (@p45) :args (@t46)) % 0.40/0.58 (step @p71 :rule cong :premises (@p70) :args (@t47)) % 0.40/0.58 (step @p72 :rule exists-elim :args ((= @t21 @t47))) % 0.40/0.58 (step @p73 :rule trans :premises (@p72 @p71)) % 0.40/0.58 (step @p74 :rule nary_cong :premises (@p73 @p69) :args (@t22)) % 0.40/0.58 (step @p75 :rule cong :premises (@p74 @p65) :args (@t23)) % 0.40/0.58 (step @p76 :rule cong :premises (@p75) :args (@t24)) % 0.40/0.58 (step @p77 :rule eq_resolve :premises (@p1 @p76)) % 0.40/0.58 (step @p78 :rule not_implies_elim2 :premises (@p77)) % 0.40/0.58 (step @p79 :rule not_and :premises (@p78)) % 0.40/0.58 (step @p80 :rule cnf_implies_neg1 :args (@t48)) % 0.40/0.58 (step @p81 :rule reordering :premises (@p80) :args ((or @t36 @t48))) % 0.40/0.58 (step @p82 :rule refl :args (@t54)) % 0.40/0.58 (step @p83 :rule bool-double-not-elim :args (@t27)) % 0.40/0.58 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or (not @t55) @t54))) % 0.40/0.58 (assume-push @p171 @t55) % 0.40/0.58 (step @p86 :rule skolemize :premises (@p171)) % 0.40/0.58 (step-pop @p172 :rule scope :premises (@p86)) % 0.40/0.58 (step @p87 :rule process_scope :premises (@p172) :args (@t54)) % 0.40/0.58 (step @p89 :rule implies_elim :premises (@p87)) % 0.40/0.58 (step @p90 :rule eq_resolve :premises (@p89 @p84)) % 0.40/0.58 (step @p91 :rule bool-double-not-elim :args (@t51)) % 0.40/0.58 (step @p92 :rule refl :args (@t53)) % 0.40/0.58 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t53 (not @t52)))) % 0.40/0.58 (step @p94 :rule cnf_or_neg :args (@t53 0)) % 0.40/0.58 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.40/0.58 (step @p96 :rule reordering :premises (@p95) :args ((or @t51 @t53))) % 0.40/0.58 (step @p97 :rule cnf_or_neg :args (@t53 1)) % 0.40/0.58 (step @p98 :rule cnf_and_pos :args (@t58 1)) % 0.40/0.58 (step @p99 :rule reordering :premises (@p98) :args ((or @t50 (not @t58)))) % 0.40/0.58 (assume-push @p173 @t36) % 0.40/0.58 (step @p101 :rule instantiate :premises (@p173) :args ((@list @t57 @t49))) % 0.40/0.58 (step-pop @p174 :rule scope :premises (@p101)) % 0.40/0.58 (step @p102 :rule process_scope :premises (@p174) :args (@t61)) % 0.40/0.58 (step @p104 :rule implies_elim :premises (@p102)) % 0.40/0.58 (step @p105 :rule not_implies_elim1 :premises (@p77)) % 0.40/0.58 (step @p106 :rule and_elim :premises (@p105) :args (0)) % 0.40/0.58 (step @p107 :rule refl :args (@t59)) % 0.40/0.58 (step @p108 :rule bool-double-not-elim :args (@t56)) % 0.40/0.58 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or (not @t62) @t59))) % 0.40/0.58 (step @p110 :rule bool-double-not-elim :args (@t59)) % 0.40/0.58 (step @p111 :rule refl :args (@t62)) % 0.40/0.58 (step @p112 :rule cong :premises (@p111 @p110) :args ((=> @t62 @t63))) % 0.40/0.58 (assume-push @p175 @t62) % 0.40/0.58 (step @p114 :rule skolemize :premises (@p106)) % 0.40/0.58 (step-pop @p176 :rule scope :premises (@p114)) % 0.40/0.58 (step @p115 :rule process_scope :premises (@p176) :args (@t63)) % 0.40/0.58 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 0.40/0.58 (step @p118 :rule implies_elim :premises (@p117)) % 0.40/0.58 (step @p119 :rule eq_resolve :premises (@p118 @p109)) % 0.40/0.58 (step @p120 :rule chain_m_resolution :premises (@p119 @p106) :args (@t59 @t64 (@list @t56))) % 0.40/0.58 (step @p121 :rule cnf_or_pos :args (@t61)) % 0.40/0.58 (step @p122 :rule reordering :premises (@p121) :args ((or @t60 @t52 @t58 (not @t61)))) % 0.40/0.58 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p104 @p99 @p97 @p96 @p90 @p81 @p79 @p6 @p4) :args (@t27 (@list false false true true false true false true false true) (@list @t59 @t61 @t58 @t50 @t51 @t53 @t36 @t48 @t37 @t32))) % 0.40/0.58 (step @p124 :rule cnf_implies_neg2 :args (@t48)) % 0.40/0.58 (step @p125 :rule cnf_implies_neg2 :args (@t37)) % 0.40/0.58 (step @p126 :rule refl :args (@t75)) % 0.40/0.58 (step @p127 :rule bool-double-not-elim :args (@t36)) % 0.40/0.58 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or (not @t76) @t75))) % 0.40/0.58 (assume-push @p177 @t76) % 0.40/0.58 (step @p130 :rule skolemize :premises (@p177)) % 0.40/0.58 (step-pop @p178 :rule scope :premises (@p130)) % 0.40/0.58 (step @p131 :rule process_scope :premises (@p178) :args (@t75)) % 0.40/0.58 (step @p133 :rule implies_elim :premises (@p131)) % 0.40/0.58 (step @p134 :rule eq_resolve :premises (@p133 @p128)) % 0.40/0.58 (step @p135 :rule bool-double-not-elim :args (@t72)) % 0.40/0.58 (step @p136 :rule refl :args (@t74)) % 0.40/0.58 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or @t74 (not @t73)))) % 0.40/0.58 (step @p138 :rule cnf_or_neg :args (@t74 0)) % 0.40/0.58 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.40/0.58 (step @p140 :rule reordering :premises (@p139) :args ((or @t72 @t74))) % 0.40/0.58 (step @p141 :rule bool-double-not-elim :args (@t70)) % 0.40/0.58 (step @p142 :rule nary_cong :premises (@p136 @p141) :args ((or @t74 (not @t71)))) % 0.40/0.58 (step @p143 :rule cnf_or_neg :args (@t74 1)) % 0.40/0.58 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.40/0.58 (step @p145 :rule reordering :premises (@p144) :args ((or @t70 @t74))) % 0.40/0.58 (step @p146 :rule cnf_or_neg :args (@t74 2)) % 0.40/0.58 (step @p147 :rule cnf_or_pos :args (@t77)) % 0.40/0.58 (step @p148 :rule reordering :premises (@p147) :args ((or @t73 @t68 @t78))) % 0.40/0.58 (step @p149 :rule cnf_and_neg :args (@t69)) % 0.40/0.58 (step @p150 :rule cnf_or_pos :args (@t79)) % 0.40/0.58 (step @p151 :rule reordering :premises (@p150) :args ((or @t71 @t66 (not @t79)))) % 0.40/0.58 (assume-push @p179 @t27) % 0.40/0.58 (step @p153 :rule instantiate :premises (@p179) :args ((@list @t65))) % 0.40/0.58 (step-pop @p180 :rule scope :premises (@p153)) % 0.40/0.58 (step @p154 :rule process_scope :premises (@p180) :args (@t79)) % 0.40/0.58 (step @p156 :rule implies_elim :premises (@p154)) % 0.40/0.58 (step @p157 :rule chain_m_resolution :premises (@p156 @p151 @p149 @p148 @p146 @p145 @p140 @p134 @p125 @p79 @p124) :args ((or @t55 @t78) (@list true true false true false false true true true false) (@list @t79 @t66 @t68 @t69 @t70 @t72 @t74 @t36 @t37 @t48))) % 0.40/0.58 (step @p158 :rule chain_m_resolution :premises (@p157 @p123) :args (@t78 @t80 @t81)) % 0.40/0.58 (assume-push @p181 @t31) % 0.40/0.58 (step @p160 :rule instantiate :premises (@p181) :args ((@list @t67))) % 0.40/0.58 (step-pop @p182 :rule scope :premises (@p160)) % 0.40/0.58 (step @p161 :rule process_scope :premises (@p182) :args (@t77)) % 0.40/0.58 (step @p163 :rule implies_elim :premises (@p161)) % 0.40/0.58 (step @p164 :rule chain_m_resolution :premises (@p163 @p158) :args ((not @t31) @t64 (@list @t77))) % 0.40/0.58 (step @p165 :rule chain_m_resolution :premises (@p124 @p123) :args (@t48 @t80 @t81)) % 0.40/0.58 (step @p166 :rule chain_m_resolution :premises (@p79 @p165) :args ((not @t37) @t80 (@list @t48))) % 0.40/0.58 (step @p167 :rule chain_m_resolution :premises (@p6 @p166) :args (@t32 @t64 (@list @t37))) % 0.40/0.58 (step @p168 :rule cnf_and_pos :args (@t32 0)) % 0.40/0.58 (step @p169 :rule reordering :premises (@p168) :args ((or @t31 @t33))) % 0.40/0.58 (step @p170 false :rule chain_m_resolution :premises (@p169 @p167 @p164) :args (false (@list false true) (@list @t32 @t31))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------