%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET638^5 : 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 : n026.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 08:48:20 AM UTC 2026 % Result : Theorem 0.30s 0.56s % Output : Proof 0.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET638^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n026.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:05:55 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.30/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.30/0.56 % SZS status Theorem % 0.30/0.56 % SZS output start Proof % 0.30/0.56 ( % 0.30/0.56 (declare-sort tptp.a 0) % 0.30/0.56 (define @t1 () (@var "Xx" tptp.a)) % 0.30/0.56 (define @t2 () (@var "Y" (-> tptp.a Bool))) % 0.30/0.56 (define @t3 () (_ @t2 @t1)) % 0.30/0.56 (define @t4 () (@var "X" (-> tptp.a Bool))) % 0.30/0.56 (define @t5 () (_ @t4 @t1)) % 0.30/0.56 (define @t6 () (@list @t1)) % 0.30/0.56 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.30/0.56 (define @t8 () (lambda @t6 false)) % 0.30/0.56 (define @t9 () (@var "Z" (-> tptp.a Bool))) % 0.30/0.56 (define @t10 () (_ @t9 @t1)) % 0.30/0.56 (define @t11 () (and @t5 @t10)) % 0.30/0.56 (define @t12 () (lambda @t6 @t11)) % 0.30/0.56 (define @t13 () (= @t12 @t8)) % 0.30/0.56 (define @t14 () (or @t3 @t10)) % 0.30/0.56 (define @t15 () (forall @t6 (=> @t5 @t14))) % 0.30/0.56 (define @t16 () (and @t15 @t13)) % 0.30/0.56 (define @t17 () (=> @t16 @t7)) % 0.30/0.56 (define @t18 () (@list @t4 @t2 @t9)) % 0.30/0.56 (define @t19 () (forall @t18 @t17)) % 0.30/0.56 (define @t20 () (not @t19)) % 0.30/0.56 (define @t21 () (@var "BOUND_VARIABLE_7466" tptp.a)) % 0.30/0.56 (define @t22 () (_ @t2 @t21)) % 0.30/0.56 (define @t23 () (not (_ @t4 @t21))) % 0.30/0.56 (define @t24 () (_ @t9 @t1)) % 0.30/0.56 (define @t25 () (_ @t4 @t1)) % 0.30/0.56 (define @t26 () (lambda @t6 (and @t25 @t24))) % 0.30/0.56 (define @t27 () (@var "BOUND_VARIABLE_7536" tptp.a)) % 0.30/0.56 (define @t28 () (lambda (@list @t27) false)) % 0.30/0.56 (define @t29 () (not (= @t28 @t26))) % 0.30/0.56 (define @t30 () (_ @t2 @t1)) % 0.30/0.56 (define @t31 () (not @t25)) % 0.30/0.56 (define @t32 () (forall @t6 (or @t31 @t30 @t24))) % 0.30/0.56 (define @t33 () (not @t32)) % 0.30/0.56 (define @t34 () (or @t33 @t29 @t23 @t22)) % 0.30/0.56 (define @t35 () (or @t23 @t22)) % 0.30/0.56 (define @t36 () (or @t33 @t29 @t35)) % 0.30/0.56 (define @t37 () (@list @t4 @t2 @t9 @t21)) % 0.30/0.56 (define @t38 () (forall @t37 @t36)) % 0.30/0.56 (define @t39 () (@list @t21)) % 0.30/0.56 (define @t40 () (forall @t39 @t36)) % 0.30/0.56 (define @t41 () (forall @t39 @t35)) % 0.30/0.56 (define @t42 () (@list @t1)) % 0.30/0.56 (define @t43 () (or @t33 @t29 @t41)) % 0.30/0.56 (define @t44 () (forall @t6 (or @t31 @t30))) % 0.30/0.56 (define @t45 () (not (= @t26 @t28))) % 0.30/0.56 (define @t46 () (or @t33 @t45 @t44)) % 0.30/0.56 (define @t47 () (= @t12 @t28)) % 0.30/0.56 (define @t48 () (not @t47)) % 0.30/0.56 (define @t49 () (or @t33 @t48 @t44)) % 0.30/0.56 (define @t50 () (and @t32 @t47)) % 0.30/0.56 (define @t51 () (not @t5)) % 0.30/0.56 (define @t52 () (or @t51 @t3)) % 0.30/0.56 (define @t53 () (or @t51 @t3 @t10)) % 0.30/0.56 (define @t54 () (forall @t37 @t34)) % 0.30/0.56 (define @t55 () (@quantifiers_skolemize @t54 3)) % 0.30/0.56 (define @t56 () (@quantifiers_skolemize @t54 1)) % 0.30/0.56 (define @t57 () (_ @t56 @t55)) % 0.30/0.56 (define @t58 () (@quantifiers_skolemize @t54 0)) % 0.30/0.56 (define @t59 () (_ @t58 @t55)) % 0.30/0.56 (define @t60 () (not @t59)) % 0.30/0.56 (define @t61 () (@purify @t28)) % 0.30/0.56 (define @t62 () (@quantifiers_skolemize @t54 2)) % 0.30/0.56 (define @t63 () (_ @t62 @t1)) % 0.30/0.56 (define @t64 () (_ @t58 @t1)) % 0.30/0.56 (define @t65 () (and @t64 @t63)) % 0.30/0.56 (define @t66 () (lambda @t6 @t65)) % 0.30/0.56 (define @t67 () (@purify @t66)) % 0.30/0.56 (define @t68 () (= @t67 @t61)) % 0.30/0.56 (define @t69 () (not @t68)) % 0.30/0.56 (define @t70 () (not @t64)) % 0.30/0.56 (define @t71 () (forall @t6 (or @t70 (_ @t56 @t1) @t63))) % 0.30/0.56 (define @t72 () (not @t71)) % 0.30/0.56 (define @t73 () (or @t72 @t69 @t60 @t57)) % 0.30/0.56 (define @t74 () (not @t73)) % 0.30/0.56 (define @t75 () (not @t54)) % 0.30/0.56 (define @t76 () (= @t28 @t66)) % 0.30/0.56 (define @t77 () (not @t76)) % 0.30/0.56 (define @t78 () (or @t72 @t77 @t60 @t57)) % 0.30/0.56 (define @t79 () (not @t78)) % 0.30/0.56 (define @t80 () (@list true)) % 0.30/0.56 (define @t81 () (@list @t73)) % 0.30/0.56 (define @t82 () (forall @t6 (= @t65 false))) % 0.30/0.56 (define @t83 () (=> @t68 @t82)) % 0.30/0.56 (define @t84 () (@list @t55)) % 0.30/0.56 (define @t85 () (_ @t62 @t55)) % 0.30/0.56 (define @t86 () (or @t60 @t57 @t85)) % 0.30/0.56 (define @t87 () (not @t85)) % 0.30/0.56 (define @t88 () (or @t60 @t87)) % 0.30/0.56 (assume @p1 @t20) % 0.30/0.56 (assume @p2 true) % 0.30/0.56 (step @p3 :rule aci_norm :args ((= @t36 @t34))) % 0.30/0.56 (step @p4 :rule cong :premises (@p3) :args (@t38)) % 0.30/0.56 (step @p5 :rule quant-merge-prenex :args ((= (forall @t18 @t40) @t38))) % 0.30/0.56 (step @p6 :rule alpha_equiv :args (@t41 (@list @t21) @t42)) % 0.30/0.56 (step @p7 :rule refl :args (@t29)) % 0.30/0.56 (step @p8 :rule refl :args (@t33)) % 0.30/0.56 (step @p9 :rule nary_cong :premises (@p8 @p7 @p6) :args (@t43)) % 0.30/0.56 (step @p10 :rule quant-miniscope-or :args ((= @t40 @t43))) % 0.30/0.56 (step @p11 :rule trans :premises (@p10 @p9)) % 0.30/0.56 (step @p12 :rule symm :premises (@p11)) % 0.30/0.56 (step @p13 :rule cong :premises (@p12) :args ((forall @t18 (or @t33 @t29 @t44)))) % 0.30/0.56 (step @p14 :rule trans :premises (@p13 @p5)) % 0.30/0.56 (step @p15 :rule trans :premises (@p14 @p4)) % 0.30/0.56 (step @p16 :rule refl :args (@t44)) % 0.30/0.56 (step @p17 :rule eq-symm :args (@t26 @t28)) % 0.30/0.56 (step @p18 :rule cong :premises (@p17) :args (@t45)) % 0.30/0.56 (step @p19 :rule refl :args (@t33)) % 0.30/0.56 (step @p20 :rule nary_cong :premises (@p19 @p18 @p16) :args (@t46)) % 0.30/0.56 (step @p21 :rule cong :premises (@p20) :args ((forall @t18 @t46))) % 0.30/0.56 (step @p22 :rule trans :premises (@p21 @p15)) % 0.30/0.56 (step @p23 :rule refl :args (@t44)) % 0.30/0.56 (step @p24 :rule refl :args (@t28)) % 0.30/0.56 (step @p25 :rule refl :args (@t24)) % 0.30/0.56 (step @p26 :rule refl :args (@t10)) % 0.30/0.56 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t10 @t24))) % 0.30/0.56 (step @p28 :rule symm :premises (@p27)) % 0.30/0.56 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.30/0.56 (step @p30 :rule refl :args (@t25)) % 0.30/0.56 (step @p31 :rule refl :args (@t5)) % 0.30/0.56 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t5 @t25))) % 0.30/0.56 (step @p33 :rule symm :premises (@p32)) % 0.30/0.56 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.30/0.56 (step @p35 :rule nary_cong :premises (@p34 @p29) :args (@t11)) % 0.30/0.56 (step @p36 :rule cong :premises (@p35) :args (@t12)) % 0.30/0.56 (step @p37 :rule cong :premises (@p36 @p24) :args (@t47)) % 0.30/0.56 (step @p38 :rule cong :premises (@p37) :args (@t48)) % 0.30/0.56 (step @p39 :rule nary_cong :premises (@p8 @p38 @p23) :args (@t49)) % 0.30/0.56 (step @p40 :rule cong :premises (@p39) :args ((forall @t18 @t49))) % 0.30/0.56 (step @p41 :rule trans :premises (@p40 @p22)) % 0.30/0.56 (step @p42 :rule aci_norm :args ((= (or (or @t33 @t48) @t44) @t49))) % 0.30/0.56 (step @p43 :rule bool-and-de-morgan :args (@t32 @t47 true)) % 0.30/0.56 (step @p44 :rule nary_cong :premises (@p43 @p23) :args ((or (not @t50) @t44))) % 0.30/0.56 (step @p45 :rule trans :premises (@p44 @p42)) % 0.30/0.56 (step @p46 :rule bool-impl-elim :args (@t50 @t44)) % 0.30/0.56 (step @p47 :rule trans :premises (@p46 @p45)) % 0.30/0.56 (step @p48 :rule cong :premises (@p47) :args ((forall @t18 (=> @t50 @t44)))) % 0.30/0.56 (step @p49 :rule trans :premises (@p48 @p41)) % 0.30/0.56 (step @p50 :rule refl :args (@t30)) % 0.30/0.56 (step @p51 :rule refl :args (@t3)) % 0.30/0.56 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t3 @t30))) % 0.30/0.56 (step @p53 :rule symm :premises (@p52)) % 0.30/0.56 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.30/0.56 (step @p55 :rule cong :premises (@p34) :args (@t51)) % 0.30/0.56 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t52)) % 0.30/0.56 (step @p57 :rule cong :premises (@p56) :args ((forall @t6 @t52))) % 0.30/0.56 (step @p58 :rule bool-impl-elim :args (@t5 @t3)) % 0.30/0.56 (step @p59 :rule cong :premises (@p58) :args (@t7)) % 0.30/0.56 (step @p60 :rule trans :premises (@p59 @p57)) % 0.30/0.56 (step @p61 :rule refl :args (@t28)) % 0.30/0.56 (step @p62 :rule symm :premises (@p61)) % 0.30/0.56 (step @p63 :rule alpha_equiv :args (@t8 @t42 (@list @t27))) % 0.30/0.56 (step @p64 :rule trans :premises (@p63 @p62)) % 0.30/0.56 (step @p65 :rule refl :args (@t12)) % 0.30/0.56 (step @p66 :rule cong :premises (@p65 @p64) :args (@t13)) % 0.30/0.56 (step @p67 :rule nary_cong :premises (@p55 @p54 @p29) :args (@t53)) % 0.30/0.56 (step @p68 :rule cong :premises (@p67) :args ((forall @t6 @t53))) % 0.30/0.56 (step @p69 :rule aci_norm :args ((= (or @t51 @t14) @t53))) % 0.30/0.56 (step @p70 :rule bool-impl-elim :args (@t5 @t14)) % 0.30/0.56 (step @p71 :rule trans :premises (@p70 @p69)) % 0.30/0.56 (step @p72 :rule cong :premises (@p71) :args (@t15)) % 0.30/0.56 (step @p73 :rule trans :premises (@p72 @p68)) % 0.30/0.56 (step @p74 :rule nary_cong :premises (@p73 @p66) :args (@t16)) % 0.30/0.56 (step @p75 :rule cong :premises (@p74 @p60) :args (@t17)) % 0.30/0.56 (step @p76 :rule cong :premises (@p75) :args (@t19)) % 0.30/0.56 (step @p77 :rule trans :premises (@p76 @p49)) % 0.30/0.56 (step @p78 :rule cong :premises (@p77) :args (@t20)) % 0.30/0.56 (step @p79 :rule eq_resolve :premises (@p1 @p78)) % 0.30/0.56 (step @p80 :rule refl :args (@t74)) % 0.30/0.56 (step @p81 :rule bool-double-not-elim :args (@t54)) % 0.30/0.56 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or (not @t75) @t74))) % 0.30/0.56 (step @p83 :rule refl :args (@t57)) % 0.30/0.56 (step @p84 :rule refl :args (@t60)) % 0.30/0.56 (step @p85 :rule eq-symm :args (@t61 @t67)) % 0.30/0.56 (step @p86 :rule eq-refl :args (@t66)) % 0.30/0.56 (step @p87 :rule skolem_intro :args (@t67)) % 0.30/0.56 (step @p88 :rule refl :args (@t66)) % 0.30/0.56 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t66 @t67))) % 0.30/0.56 (step @p90 :rule trans :premises (@p89 @p86)) % 0.30/0.56 (step @p91 :rule true_elim :premises (@p90)) % 0.30/0.56 (step @p92 :rule eq-refl :args (@t28)) % 0.30/0.56 (step @p93 :rule refl :args (@t28)) % 0.30/0.56 (step @p94 :rule cong :premises (@p93 @p62) :args ((= @t28 @t28))) % 0.30/0.56 (step @p95 :rule trans :premises (@p94 @p92)) % 0.30/0.56 (step @p96 :rule skolem_intro :args (@t61)) % 0.30/0.56 (step @p97 :rule cong :premises (@p93 @p96) :args ((= @t28 @t61))) % 0.30/0.56 (step @p98 :rule trans :premises (@p97 @p95)) % 0.30/0.56 (step @p99 :rule true_elim :premises (@p98)) % 0.30/0.56 (step @p100 :rule cong :premises (@p99 @p91) :args (@t76)) % 0.30/0.56 (step @p101 :rule trans :premises (@p100 @p85)) % 0.30/0.56 (step @p102 :rule cong :premises (@p101) :args (@t77)) % 0.30/0.56 (step @p103 :rule refl :args (@t72)) % 0.30/0.56 (step @p104 :rule nary_cong :premises (@p103 @p102 @p84 @p83) :args (@t78)) % 0.30/0.56 (step @p105 :rule cong :premises (@p104) :args (@t79)) % 0.30/0.56 (step @p106 :rule refl :args (@t75)) % 0.30/0.56 (step @p107 :rule cong :premises (@p106 @p105) :args ((=> @t75 @t79))) % 0.30/0.56 (assume-push @p156 @t75) % 0.30/0.56 (step @p109 :rule skolemize :premises (@p79)) % 0.30/0.56 (step-pop @p157 :rule scope :premises (@p109)) % 0.30/0.56 (step @p110 :rule process_scope :premises (@p157) :args (@t79)) % 0.30/0.56 (step @p112 :rule eq_resolve :premises (@p110 @p107)) % 0.30/0.56 (step @p113 :rule implies_elim :premises (@p112)) % 0.30/0.56 (step @p114 :rule eq_resolve :premises (@p113 @p82)) % 0.30/0.56 (step @p115 :rule chain_m_resolution :premises (@p114 @p79) :args (@t74 @t80 (@list @t54))) % 0.30/0.56 (step @p116 :rule bool-double-not-elim :args (@t59)) % 0.30/0.56 (step @p117 :rule refl :args (@t73)) % 0.30/0.56 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or @t73 (not @t60)))) % 0.30/0.56 (step @p119 :rule cnf_or_neg :args (@t73 2)) % 0.30/0.56 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.30/0.56 (step @p121 :rule reordering :premises (@p120) :args ((or @t59 @t73))) % 0.30/0.56 (step @p122 :rule chain_m_resolution :premises (@p121 @p115) :args (@t59 @t80 @t81)) % 0.30/0.56 (step @p123 :rule bool-double-not-elim :args (@t68)) % 0.30/0.56 (step @p124 :rule nary_cong :premises (@p117 @p123) :args ((or @t73 (not @t69)))) % 0.30/0.56 (step @p125 :rule cnf_or_neg :args (@t73 1)) % 0.30/0.56 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.30/0.56 (step @p127 :rule reordering :premises (@p126) :args ((or @t68 @t73))) % 0.30/0.56 (step @p128 :rule chain_m_resolution :premises (@p127 @p115) :args (@t68 @t80 @t81)) % 0.30/0.56 (step @p129 :rule bool-and-de-morgan :args (@t64 @t63 true)) % 0.30/0.56 (step @p130 :rule cong :premises (@p129) :args ((forall @t6 (not @t65)))) % 0.30/0.56 (step @p131 :rule bool-eq-false :args (@t65)) % 0.30/0.56 (step @p132 :rule cong :premises (@p131) :args (@t82)) % 0.30/0.56 (step @p133 :rule trans :premises (@p132 @p130)) % 0.30/0.56 (step @p134 :rule refl :args (@t68)) % 0.30/0.56 (step @p135 :rule cong :premises (@p134 @p133) :args (@t83)) % 0.30/0.56 ; WARNING: add trust step for TRUST % 0.30/0.56 ; trust TRUST THEORY_LEMMA % 0.30/0.56 (step @p136 :rule trust :premises () :args (@t83)) % 0.30/0.56 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.30/0.56 (step @p138 :rule implies_elim :premises (@p137)) % 0.30/0.56 (step @p139 :rule chain_m_resolution :premises (@p138 @p128) :args ((forall @t6 (or @t70 (not @t63))) (@list false) (@list @t68))) % 0.30/0.56 (step @p140 :rule instantiate :premises (@p139) :args (@t84)) % 0.30/0.56 (step @p141 :rule bool-double-not-elim :args (@t71)) % 0.30/0.56 (step @p142 :rule nary_cong :premises (@p117 @p141) :args ((or @t73 (not @t72)))) % 0.30/0.56 (step @p143 :rule cnf_or_neg :args (@t73 0)) % 0.30/0.56 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.30/0.56 (step @p145 :rule reordering :premises (@p144) :args ((or @t71 @t73))) % 0.30/0.56 (step @p146 :rule chain_m_resolution :premises (@p145 @p115) :args (@t71 @t80 @t81)) % 0.30/0.56 (step @p147 :rule instantiate :premises (@p146) :args (@t84)) % 0.30/0.56 (step @p148 :rule cnf_or_neg :args (@t73 3)) % 0.30/0.56 (step @p149 :rule chain_m_resolution :premises (@p148 @p115) :args ((not @t57) @t80 @t81)) % 0.30/0.56 (step @p150 :rule cnf_or_pos :args (@t86)) % 0.30/0.56 (step @p151 :rule reordering :premises (@p150) :args ((or @t60 @t57 @t85 (not @t86)))) % 0.30/0.56 (step @p152 :rule chain_m_resolution :premises (@p151 @p122 @p149 @p147) :args (@t85 (@list false true false) (@list @t59 @t57 @t86))) % 0.30/0.56 (step @p153 :rule cnf_or_pos :args (@t88)) % 0.30/0.56 (step @p154 :rule reordering :premises (@p153) :args ((or @t60 @t87 (not @t88)))) % 0.30/0.56 (step @p155 false :rule chain_m_resolution :premises (@p154 @p152 @p140 @p122) :args (false (@list false false false) (@list @t85 @t88 @t59))) % 0.30/0.56 ) % 0.30/0.56 % SZS output end Proof % 0.30/0.57 % cvc5 exiting %------------------------------------------------------------------------------