%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET613^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:48:14 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 : SET613^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % 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 16:04:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.50 %----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 "Xz" tptp.a)) % 0.30/0.56 (define @t2 () (@var "X" (-> tptp.a Bool))) % 0.30/0.56 (define @t3 () (_ @t2 @t1)) % 0.30/0.56 (define @t4 () (not @t3)) % 0.30/0.56 (define @t5 () (@var "Y" (-> tptp.a Bool))) % 0.30/0.56 (define @t6 () (_ @t5 @t1)) % 0.30/0.56 (define @t7 () (and @t6 @t4)) % 0.30/0.56 (define @t8 () (not @t6)) % 0.30/0.56 (define @t9 () (and @t3 @t8)) % 0.30/0.56 (define @t10 () (or @t9 @t7)) % 0.30/0.56 (define @t11 () (@list @t1)) % 0.30/0.56 (define @t12 () (lambda @t11 @t10)) % 0.30/0.56 (define @t13 () (@var "Xx" tptp.a)) % 0.30/0.56 (define @t14 () (_ @t5 @t13)) % 0.30/0.56 (define @t15 () (_ @t2 @t13)) % 0.30/0.56 (define @t16 () (and @t15 @t14)) % 0.30/0.56 (define @t17 () (not @t16)) % 0.30/0.56 (define @t18 () (or @t15 @t14)) % 0.30/0.56 (define @t19 () (and @t18 @t17)) % 0.30/0.56 (define @t20 () (@list @t13)) % 0.30/0.56 (define @t21 () (lambda @t20 @t19)) % 0.30/0.56 (define @t22 () (= @t21 @t12)) % 0.30/0.56 (define @t23 () (@list @t2 @t5)) % 0.30/0.56 (define @t24 () (forall @t23 @t22)) % 0.30/0.56 (define @t25 () (not @t24)) % 0.30/0.56 (define @t26 () (_ @t2 @t1)) % 0.30/0.56 (define @t27 () (_ @t5 @t1)) % 0.30/0.56 (define @t28 () (_ @t5 @t13)) % 0.30/0.56 (define @t29 () (_ @t2 @t13)) % 0.30/0.56 (define @t30 () (forall @t23 (= (lambda @t20 (and (or @t29 @t28) (not (and @t29 @t28)))) (lambda @t11 (or (and @t26 (not @t27)) (and @t27 (not @t26))))))) % 0.30/0.56 (define @t31 () (@quantifiers_skolemize @t30 1)) % 0.30/0.56 (define @t32 () (_ @t31 @t13)) % 0.30/0.56 (define @t33 () (@quantifiers_skolemize @t30 0)) % 0.30/0.56 (define @t34 () (_ @t33 @t13)) % 0.30/0.56 (define @t35 () (lambda @t20 (and (or @t34 @t32) (not (and @t34 @t32))))) % 0.30/0.56 (define @t36 () (@purify @t35)) % 0.30/0.56 (define @t37 () (_ @t33 @t1)) % 0.30/0.56 (define @t38 () (_ @t31 @t1)) % 0.30/0.56 (define @t39 () (lambda @t11 (or (and @t37 (not @t38)) (and @t38 (not @t37))))) % 0.30/0.56 (define @t40 () (@purify @t39)) % 0.30/0.56 (define @t41 () (= @t40 @t36)) % 0.30/0.56 (define @t42 () (not @t41)) % 0.30/0.56 (define @t43 () (not @t30)) % 0.30/0.56 (define @t44 () (= @t35 @t39)) % 0.30/0.56 (define @t45 () (not @t44)) % 0.30/0.56 (define @t46 () (@list true)) % 0.30/0.56 (define @t47 () (@const 0 tptp.a)) % 0.30/0.56 (define @t48 () (_ @t33 @t47)) % 0.30/0.56 (define @t49 () (not @t48)) % 0.30/0.56 (define @t50 () (_ @t31 @t47)) % 0.30/0.56 (define @t51 () (and @t50 @t49)) % 0.30/0.56 (define @t52 () (not @t50)) % 0.30/0.56 (define @t53 () (and @t48 @t52)) % 0.30/0.56 (define @t54 () (or @t53 @t51)) % 0.30/0.56 (define @t55 () (and @t48 @t50)) % 0.30/0.56 (define @t56 () (not @t55)) % 0.30/0.56 (define @t57 () (or @t48 @t50)) % 0.30/0.56 (define @t58 () (and @t57 @t56)) % 0.30/0.56 (define @t59 () (= (_ @t35 @t47) @t58)) % 0.30/0.56 (define @t60 () (_ @t36 @t47)) % 0.30/0.56 (define @t61 () (= (_ @t39 @t47) @t54)) % 0.30/0.56 (define @t62 () (_ @t40 @t47)) % 0.30/0.56 (define @t63 () (= @t62 @t60)) % 0.30/0.56 (define @t64 () (not @t63)) % 0.30/0.56 (define @t65 () (or @t41 @t64)) % 0.30/0.56 (define @t66 () (= @t58 @t54)) % 0.30/0.56 (define @t67 () (not @t51)) % 0.30/0.56 (define @t68 () (not @t57)) % 0.30/0.56 (define @t69 () (not @t53)) % 0.30/0.56 (define @t70 () (not @t58)) % 0.30/0.56 (define @t71 () (not @t54)) % 0.30/0.56 (define @t72 () (@list @t48)) % 0.30/0.56 (define @t73 () (@list true true)) % 0.30/0.56 (assume @p1 @t25) % 0.30/0.56 (assume @p2 true) % 0.30/0.56 (step @p3 :rule refl :args (@t26)) % 0.30/0.56 (step @p4 :rule refl :args (@t3)) % 0.30/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t3 @t26))) % 0.30/0.56 (step @p6 :rule symm :premises (@p5)) % 0.30/0.56 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.30/0.56 (step @p8 :rule cong :premises (@p7) :args (@t4)) % 0.30/0.56 (step @p9 :rule refl :args (@t27)) % 0.30/0.57 (step @p10 :rule refl :args (@t6)) % 0.30/0.57 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t6 @t27))) % 0.30/0.57 (step @p12 :rule symm :premises (@p11)) % 0.30/0.57 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 0.30/0.57 (step @p14 :rule nary_cong :premises (@p13 @p8) :args (@t7)) % 0.30/0.57 (step @p15 :rule cong :premises (@p13) :args (@t8)) % 0.30/0.57 (step @p16 :rule nary_cong :premises (@p7 @p15) :args (@t9)) % 0.30/0.57 (step @p17 :rule nary_cong :premises (@p16 @p14) :args (@t10)) % 0.30/0.57 (step @p18 :rule cong :premises (@p17) :args (@t12)) % 0.30/0.57 (step @p19 :rule refl :args (@t28)) % 0.30/0.57 (step @p20 :rule refl :args (@t14)) % 0.30/0.57 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t14 @t28))) % 0.30/0.57 (step @p22 :rule symm :premises (@p21)) % 0.30/0.57 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.30/0.57 (step @p24 :rule refl :args (@t29)) % 0.30/0.57 (step @p25 :rule refl :args (@t15)) % 0.30/0.57 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t15 @t29))) % 0.30/0.57 (step @p27 :rule symm :premises (@p26)) % 0.30/0.57 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.30/0.57 (step @p29 :rule nary_cong :premises (@p28 @p23) :args (@t16)) % 0.30/0.57 (step @p30 :rule cong :premises (@p29) :args (@t17)) % 0.30/0.57 (step @p31 :rule nary_cong :premises (@p28 @p23) :args (@t18)) % 0.30/0.57 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t19)) % 0.30/0.57 (step @p33 :rule cong :premises (@p32) :args (@t21)) % 0.30/0.57 (step @p34 :rule cong :premises (@p33 @p18) :args (@t22)) % 0.30/0.57 (step @p35 :rule cong :premises (@p34) :args (@t24)) % 0.30/0.57 (step @p36 :rule cong :premises (@p35) :args (@t25)) % 0.30/0.57 (step @p37 :rule eq_resolve :premises (@p1 @p36)) % 0.30/0.57 (step @p38 :rule refl :args (@t42)) % 0.30/0.57 (step @p39 :rule bool-double-not-elim :args (@t30)) % 0.30/0.57 (step @p40 :rule nary_cong :premises (@p39 @p38) :args ((or (not @t43) @t42))) % 0.30/0.57 (step @p41 :rule eq-symm :args (@t36 @t40)) % 0.30/0.57 (step @p42 :rule eq-refl :args (@t39)) % 0.30/0.57 (step @p43 :rule skolem_intro :args (@t40)) % 0.30/0.57 (step @p44 :rule refl :args (@t39)) % 0.30/0.57 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t39 @t40))) % 0.30/0.57 (step @p46 :rule trans :premises (@p45 @p42)) % 0.30/0.57 (step @p47 :rule true_elim :premises (@p46)) % 0.30/0.57 (step @p48 :rule eq-refl :args (@t35)) % 0.30/0.57 (step @p49 :rule skolem_intro :args (@t36)) % 0.30/0.57 (step @p50 :rule refl :args (@t35)) % 0.30/0.57 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t35 @t36))) % 0.30/0.57 (step @p52 :rule trans :premises (@p51 @p48)) % 0.30/0.57 (step @p53 :rule true_elim :premises (@p52)) % 0.30/0.57 (step @p54 :rule cong :premises (@p53 @p47) :args (@t44)) % 0.30/0.57 (step @p55 :rule trans :premises (@p54 @p41)) % 0.30/0.57 (step @p56 :rule cong :premises (@p55) :args (@t45)) % 0.30/0.57 (step @p57 :rule refl :args (@t43)) % 0.30/0.57 (step @p58 :rule cong :premises (@p57 @p56) :args ((=> @t43 @t45))) % 0.30/0.57 (assume-push @p154 @t43) % 0.30/0.57 (step @p60 :rule skolemize :premises (@p37)) % 0.30/0.57 (step-pop @p155 :rule scope :premises (@p60)) % 0.30/0.57 (step @p61 :rule process_scope :premises (@p155) :args (@t45)) % 0.30/0.57 (step @p63 :rule eq_resolve :premises (@p61 @p58)) % 0.30/0.57 (step @p64 :rule implies_elim :premises (@p63)) % 0.30/0.57 (step @p65 :rule eq_resolve :premises (@p64 @p40)) % 0.30/0.57 (step @p66 :rule chain_m_resolution :premises (@p65 @p37) :args (@t42 @t46 (@list @t30))) % 0.30/0.57 (step @p67 :rule eq-symm :args (@t54 @t58)) % 0.30/0.57 (step @p68 :rule eq-refl :args (@t58)) % 0.30/0.57 (step @p69 :rule refl :args (@t58)) % 0.30/0.57 (step @p70 :rule beta-reduce :args (@t59)) % 0.30/0.57 (step @p71 :rule cong :premises (@p70 @p69) :args (@t59)) % 0.30/0.57 (step @p72 :rule trans :premises (@p71 @p68)) % 0.30/0.57 (step @p73 :rule refl :args (@t47)) % 0.30/0.57 (step @p74 :rule ho_cong :premises (@p49 @p73)) % 0.30/0.57 (step @p75 :rule cong :premises (@p74 @p69) :args ((= @t60 @t58))) % 0.30/0.57 (step @p76 :rule trans :premises (@p75 @p72)) % 0.30/0.57 (step @p77 :rule true_elim :premises (@p76)) % 0.30/0.57 (step @p78 :rule eq-refl :args (@t54)) % 0.30/0.57 (step @p79 :rule refl :args (@t54)) % 0.30/0.57 (step @p80 :rule beta-reduce :args (@t61)) % 0.30/0.57 (step @p81 :rule cong :premises (@p80 @p79) :args (@t61)) % 0.30/0.57 (step @p82 :rule trans :premises (@p81 @p78)) % 0.30/0.57 (step @p83 :rule ho_cong :premises (@p43 @p73)) % 0.30/0.57 (step @p84 :rule cong :premises (@p83 @p79) :args ((= @t62 @t54))) % 0.30/0.57 (step @p85 :rule trans :premises (@p84 @p82)) % 0.30/0.57 (step @p86 :rule true_elim :premises (@p85)) % 0.30/0.57 (step @p87 :rule cong :premises (@p86 @p77) :args (@t63)) % 0.30/0.57 (step @p88 :rule trans :premises (@p87 @p67)) % 0.30/0.57 (step @p89 :rule cong :premises (@p88) :args (@t64)) % 0.30/0.57 (step @p90 :rule refl :args (@t41)) % 0.30/0.57 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t65)) % 0.30/0.57 ; WARNING: add trust step for TRUST % 0.30/0.57 ; trust TRUST THEORY_LEMMA % 0.30/0.57 (step @p92 :rule trust :premises () :args (@t65)) % 0.30/0.57 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.30/0.57 (step @p94 :rule chain_m_resolution :premises (@p93 @p66) :args ((not @t66) @t46 (@list @t41))) % 0.30/0.57 (step @p95 :rule cnf_or_neg :args (@t57 1)) % 0.30/0.57 (step @p96 :rule cnf_and_pos :args (@t51 1)) % 0.30/0.57 (step @p97 :rule reordering :premises (@p96) :args ((or @t49 @t67))) % 0.30/0.57 (step @p98 :rule cnf_or_neg :args (@t57 0)) % 0.30/0.57 (step @p99 :rule cnf_and_pos :args (@t55 1)) % 0.30/0.57 (step @p100 :rule reordering :premises (@p99) :args ((or @t50 @t56))) % 0.30/0.57 (step @p101 :rule bool-double-not-elim :args (@t50)) % 0.30/0.57 (step @p102 :rule refl :args (@t49)) % 0.30/0.57 (step @p103 :rule refl :args (@t53)) % 0.30/0.57 (step @p104 :rule nary_cong :premises (@p103 @p102 @p101) :args ((or @t53 @t49 (not @t52)))) % 0.30/0.57 (step @p105 :rule cnf_and_neg :args (@t53)) % 0.30/0.57 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 0.30/0.57 (step @p107 :rule reordering :premises (@p106) :args ((or @t50 @t53 @t49))) % 0.30/0.57 (step @p108 :rule bool-double-not-elim :args (@t55)) % 0.30/0.57 (step @p109 :rule refl :args (@t68)) % 0.30/0.57 (step @p110 :rule nary_cong :premises (@p69 @p109 @p108) :args ((or @t58 @t68 (not @t56)))) % 0.30/0.57 (step @p111 :rule cnf_and_neg :args (@t58)) % 0.30/0.57 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.30/0.57 (step @p113 :rule reordering :premises (@p112) :args ((or @t55 @t58 @t68))) % 0.30/0.57 (step @p114 :rule cnf_or_neg :args (@t54 0)) % 0.30/0.57 (step @p115 :rule cnf_equiv_neg2 :args (@t66)) % 0.30/0.57 (step @p116 :rule chain_m_resolution :premises (@p115 @p94 @p114 @p113 @p107 @p100 @p98) :args ((or @t50 @t49) (@list true false false false true false) (@list @t66 @t54 @t58 @t53 @t55 @t57))) % 0.30/0.57 (step @p117 :rule cnf_and_neg :args (@t55)) % 0.30/0.57 (step @p118 :rule reordering :premises (@p117) :args ((or @t55 @t52 @t49))) % 0.30/0.57 (step @p119 :rule cnf_and_pos :args (@t53 1)) % 0.30/0.57 (step @p120 :rule reordering :premises (@p119) :args ((or @t52 @t69))) % 0.30/0.57 (step @p121 :rule cnf_and_pos :args (@t58 1)) % 0.30/0.57 (step @p122 :rule reordering :premises (@p121) :args ((or @t56 @t70))) % 0.30/0.57 (step @p123 :rule cnf_or_pos :args (@t54)) % 0.30/0.57 (step @p124 :rule reordering :premises (@p123) :args ((or @t53 @t51 @t71))) % 0.30/0.57 (step @p125 :rule cnf_equiv_neg1 :args (@t66)) % 0.30/0.57 (step @p126 :rule reordering :premises (@p125) :args ((or @t58 @t54 @t66))) % 0.30/0.57 (step @p127 :rule chain_m_resolution :premises (@p126 @p94 @p124 @p122 @p120 @p118 @p116 @p97) :args (@t49 (@list true true true true false false true) (@list @t66 @t54 @t58 @t53 @t55 @t50 @t51))) % 0.30/0.57 (step @p128 :rule bool-double-not-elim :args (@t48)) % 0.30/0.57 (step @p129 :rule refl :args (@t52)) % 0.30/0.57 (step @p130 :rule refl :args (@t51)) % 0.30/0.57 (step @p131 :rule nary_cong :premises (@p130 @p129 @p128) :args ((or @t51 @t52 (not @t49)))) % 0.30/0.57 (step @p132 :rule cnf_and_neg :args (@t51)) % 0.30/0.57 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.30/0.57 (step @p134 :rule reordering :premises (@p133) :args ((or @t48 @t52 @t51))) % 0.30/0.57 (step @p135 :rule cnf_and_pos :args (@t55 0)) % 0.30/0.57 (step @p136 :rule reordering :premises (@p135) :args ((or @t48 @t56))) % 0.30/0.57 (step @p137 :rule chain_m_resolution :premises (@p136 @p127) :args (@t56 @t46 @t72)) % 0.30/0.57 (step @p138 :rule cnf_or_neg :args (@t54 1)) % 0.30/0.57 (step @p139 :rule chain_m_resolution :premises (@p115 @p94 @p138 @p113 @p137 @p134 @p127 @p95) :args (@t52 (@list true false false true false true false) (@list @t66 @t54 @t58 @t55 @t51 @t48 @t57))) % 0.30/0.57 (step @p140 :rule cnf_or_pos :args (@t57)) % 0.30/0.57 (step @p141 :rule reordering :premises (@p140) :args ((or @t48 @t50 @t68))) % 0.30/0.57 (step @p142 :rule chain_m_resolution :premises (@p141 @p127 @p139) :args (@t68 @t73 (@list @t48 @t50))) % 0.30/0.57 (step @p143 :rule cnf_and_pos :args (@t58 0)) % 0.30/0.57 (step @p144 :rule reordering :premises (@p143) :args ((or @t57 @t70))) % 0.30/0.57 (step @p145 :rule chain_m_resolution :premises (@p144 @p142) :args (@t70 @t46 (@list @t57))) % 0.30/0.57 (step @p146 :rule cnf_and_pos :args (@t51 0)) % 0.30/0.57 (step @p147 :rule reordering :premises (@p146) :args ((or @t50 @t67))) % 0.30/0.57 (step @p148 :rule chain_m_resolution :premises (@p147 @p139) :args (@t67 @t46 (@list @t50))) % 0.30/0.57 (step @p149 :rule cnf_and_pos :args (@t53 0)) % 0.30/0.57 (step @p150 :rule reordering :premises (@p149) :args ((or @t48 @t69))) % 0.30/0.57 (step @p151 :rule chain_m_resolution :premises (@p150 @p127) :args (@t69 @t46 @t72)) % 0.30/0.57 (step @p152 :rule chain_m_resolution :premises (@p124 @p151 @p148) :args (@t71 @t73 (@list @t53 @t51))) % 0.30/0.57 (step @p153 false :rule chain_m_resolution :premises (@p126 @p152 @p145 @p94) :args (false (@list true true true) (@list @t54 @t58 @t66))) % 0.30/0.57 ) % 0.30/0.57 % SZS output end Proof % 0.30/0.57 % cvc5 exiting %------------------------------------------------------------------------------