%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET010^5 : 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 : n028.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 08:46:54 AM UTC 2026 % Result : Theorem 0.31s 0.55s % Output : Proof 0.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET010^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n028.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:40:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.31/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.55 % SZS status Theorem % 0.31/0.55 % SZS output start Proof % 0.31/0.55 ( % 0.31/0.55 (declare-sort tptp.a 0) % 0.31/0.55 (define @t1 () (@var "Xz" tptp.a)) % 0.31/0.55 (define @t2 () (@var "Z" (-> tptp.a Bool))) % 0.31/0.55 (define @t3 () (_ @t2 @t1)) % 0.31/0.55 (define @t4 () (not @t3)) % 0.31/0.55 (define @t5 () (@var "X" (-> tptp.a Bool))) % 0.31/0.55 (define @t6 () (_ @t5 @t1)) % 0.31/0.55 (define @t7 () (and @t6 @t4)) % 0.31/0.55 (define @t8 () (@var "Y" (-> tptp.a Bool))) % 0.31/0.55 (define @t9 () (_ @t8 @t1)) % 0.31/0.55 (define @t10 () (not @t9)) % 0.31/0.55 (define @t11 () (and @t6 @t10)) % 0.31/0.55 (define @t12 () (or @t11 @t7)) % 0.31/0.55 (define @t13 () (@list @t1)) % 0.31/0.55 (define @t14 () (lambda @t13 @t12)) % 0.31/0.55 (define @t15 () (@var "Xx" tptp.a)) % 0.31/0.55 (define @t16 () (_ @t2 @t15)) % 0.31/0.55 (define @t17 () (_ @t8 @t15)) % 0.31/0.55 (define @t18 () (and @t17 @t16)) % 0.31/0.55 (define @t19 () (not @t18)) % 0.31/0.55 (define @t20 () (_ @t5 @t15)) % 0.31/0.55 (define @t21 () (and @t20 @t19)) % 0.31/0.55 (define @t22 () (@list @t15)) % 0.31/0.55 (define @t23 () (lambda @t22 @t21)) % 0.31/0.55 (define @t24 () (= @t23 @t14)) % 0.31/0.55 (define @t25 () (@list @t5 @t8 @t2)) % 0.31/0.55 (define @t26 () (forall @t25 @t24)) % 0.31/0.55 (define @t27 () (not @t26)) % 0.31/0.55 (define @t28 () (@const 0 tptp.a)) % 0.31/0.55 (define @t29 () (_ @t2 @t1)) % 0.31/0.55 (define @t30 () (_ @t5 @t1)) % 0.31/0.55 (define @t31 () (_ @t8 @t1)) % 0.31/0.55 (define @t32 () (_ @t2 @t15)) % 0.31/0.55 (define @t33 () (_ @t8 @t15)) % 0.31/0.55 (define @t34 () (_ @t5 @t15)) % 0.31/0.55 (define @t35 () (forall @t25 (= (lambda @t22 (and @t34 (not (and @t33 @t32)))) (lambda @t13 (or (and @t30 (not @t31)) (and @t30 (not @t29))))))) % 0.31/0.55 (define @t36 () (@quantifiers_skolemize @t35 2)) % 0.31/0.55 (define @t37 () (_ @t36 @t28)) % 0.31/0.55 (define @t38 () (@quantifiers_skolemize @t35 1)) % 0.31/0.55 (define @t39 () (_ @t38 @t28)) % 0.31/0.55 (define @t40 () (and @t39 @t37)) % 0.31/0.55 (define @t41 () (not @t40)) % 0.31/0.55 (define @t42 () (@quantifiers_skolemize @t35 0)) % 0.31/0.55 (define @t43 () (_ @t42 @t28)) % 0.31/0.55 (define @t44 () (not @t43)) % 0.31/0.55 (define @t45 () (not @t39)) % 0.31/0.55 (define @t46 () (and @t43 @t45)) % 0.31/0.55 (define @t47 () (and @t43 @t41)) % 0.31/0.55 (define @t48 () (not @t37)) % 0.31/0.55 (define @t49 () (and @t43 @t48)) % 0.31/0.55 (define @t50 () (or @t46 @t49)) % 0.31/0.55 (define @t51 () (lambda @t22 (and (_ @t42 @t15) (not (and (_ @t38 @t15) (_ @t36 @t15)))))) % 0.31/0.55 (define @t52 () (@purify @t51)) % 0.31/0.55 (define @t53 () (_ @t42 @t1)) % 0.31/0.55 (define @t54 () (lambda @t13 (or (and @t53 (not (_ @t38 @t1))) (and @t53 (not (_ @t36 @t1)))))) % 0.31/0.55 (define @t55 () (@purify @t54)) % 0.31/0.55 (define @t56 () (= @t55 @t52)) % 0.31/0.55 (define @t57 () (not @t56)) % 0.31/0.55 (define @t58 () (not @t35)) % 0.31/0.55 (define @t59 () (= @t51 @t54)) % 0.31/0.55 (define @t60 () (not @t59)) % 0.31/0.55 (define @t61 () (@list true)) % 0.31/0.55 (define @t62 () (= (_ @t51 @t28) @t47)) % 0.31/0.55 (define @t63 () (_ @t52 @t28)) % 0.31/0.55 (define @t64 () (= (_ @t54 @t28) @t50)) % 0.31/0.55 (define @t65 () (_ @t55 @t28)) % 0.31/0.55 (define @t66 () (= @t65 @t63)) % 0.31/0.55 (define @t67 () (not @t66)) % 0.31/0.55 (define @t68 () (or @t56 @t67)) % 0.31/0.55 (define @t69 () (= @t47 @t50)) % 0.31/0.55 (define @t70 () (@list true false false false true)) % 0.31/0.55 (define @t71 () (not @t46)) % 0.31/0.55 (define @t72 () (not @t49)) % 0.31/0.55 (define @t73 () (not @t47)) % 0.31/0.55 (define @t74 () (@list @t43)) % 0.31/0.55 (assume @p1 @t27) % 0.31/0.55 (assume @p2 true) % 0.31/0.55 (step @p3 :rule cnf_and_pos :args (@t40 0)) % 0.31/0.55 (step @p4 :rule reordering :premises (@p3) :args ((or @t39 @t41))) % 0.31/0.55 (step @p5 :rule bool-double-not-elim :args (@t39)) % 0.31/0.55 (step @p6 :rule refl :args (@t44)) % 0.31/0.55 (step @p7 :rule refl :args (@t46)) % 0.31/0.55 (step @p8 :rule nary_cong :premises (@p7 @p6 @p5) :args ((or @t46 @t44 (not @t45)))) % 0.31/0.55 (step @p9 :rule cnf_and_neg :args (@t46)) % 0.31/0.55 (step @p10 :rule eq_resolve :premises (@p9 @p8)) % 0.31/0.55 (step @p11 :rule reordering :premises (@p10) :args ((or @t39 @t46 @t44))) % 0.31/0.55 (step @p12 :rule bool-double-not-elim :args (@t40)) % 0.31/0.55 (step @p13 :rule refl :args (@t47)) % 0.31/0.55 (step @p14 :rule nary_cong :premises (@p13 @p6 @p12) :args ((or @t47 @t44 (not @t41)))) % 0.31/0.55 (step @p15 :rule cnf_and_neg :args (@t47)) % 0.31/0.55 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.31/0.55 (step @p17 :rule reordering :premises (@p16) :args ((or @t40 @t47 @t44))) % 0.31/0.55 (step @p18 :rule cnf_or_neg :args (@t50 0)) % 0.31/0.55 (step @p19 :rule refl :args (@t29)) % 0.31/0.55 (step @p20 :rule refl :args (@t3)) % 0.31/0.55 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t3 @t29))) % 0.31/0.55 (step @p22 :rule symm :premises (@p21)) % 0.31/0.55 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.31/0.55 (step @p24 :rule cong :premises (@p23) :args (@t4)) % 0.31/0.55 (step @p25 :rule refl :args (@t30)) % 0.31/0.55 (step @p26 :rule refl :args (@t6)) % 0.31/0.55 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t6 @t30))) % 0.31/0.55 (step @p28 :rule symm :premises (@p27)) % 0.31/0.55 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.31/0.55 (step @p30 :rule nary_cong :premises (@p29 @p24) :args (@t7)) % 0.31/0.55 (step @p31 :rule refl :args (@t31)) % 0.31/0.55 (step @p32 :rule refl :args (@t9)) % 0.31/0.55 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t9 @t31))) % 0.31/0.55 (step @p34 :rule symm :premises (@p33)) % 0.31/0.55 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.31/0.55 (step @p36 :rule cong :premises (@p35) :args (@t10)) % 0.31/0.55 (step @p37 :rule nary_cong :premises (@p29 @p36) :args (@t11)) % 0.31/0.55 (step @p38 :rule nary_cong :premises (@p37 @p30) :args (@t12)) % 0.31/0.55 (step @p39 :rule cong :premises (@p38) :args (@t14)) % 0.31/0.55 (step @p40 :rule refl :args (@t32)) % 0.31/0.55 (step @p41 :rule refl :args (@t16)) % 0.31/0.55 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t16 @t32))) % 0.31/0.55 (step @p43 :rule symm :premises (@p42)) % 0.31/0.55 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.31/0.55 (step @p45 :rule refl :args (@t33)) % 0.31/0.55 (step @p46 :rule refl :args (@t17)) % 0.31/0.55 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t17 @t33))) % 0.31/0.55 (step @p48 :rule symm :premises (@p47)) % 0.31/0.55 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.31/0.55 (step @p50 :rule nary_cong :premises (@p49 @p44) :args (@t18)) % 0.31/0.55 (step @p51 :rule cong :premises (@p50) :args (@t19)) % 0.31/0.55 (step @p52 :rule refl :args (@t34)) % 0.31/0.55 (step @p53 :rule refl :args (@t20)) % 0.31/0.55 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t20 @t34))) % 0.31/0.55 (step @p55 :rule symm :premises (@p54)) % 0.31/0.55 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.31/0.55 (step @p57 :rule nary_cong :premises (@p56 @p51) :args (@t21)) % 0.31/0.55 (step @p58 :rule cong :premises (@p57) :args (@t23)) % 0.31/0.55 (step @p59 :rule cong :premises (@p58 @p39) :args (@t24)) % 0.31/0.55 (step @p60 :rule cong :premises (@p59) :args (@t26)) % 0.31/0.55 (step @p61 :rule cong :premises (@p60) :args (@t27)) % 0.31/0.55 (step @p62 :rule eq_resolve :premises (@p1 @p61)) % 0.31/0.55 (step @p63 :rule refl :args (@t57)) % 0.31/0.55 (step @p64 :rule bool-double-not-elim :args (@t35)) % 0.31/0.55 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or (not @t58) @t57))) % 0.31/0.55 (step @p66 :rule eq-symm :args (@t52 @t55)) % 0.31/0.55 (step @p67 :rule eq-refl :args (@t54)) % 0.31/0.55 (step @p68 :rule skolem_intro :args (@t55)) % 0.31/0.55 (step @p69 :rule refl :args (@t54)) % 0.31/0.55 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t54 @t55))) % 0.31/0.55 (step @p71 :rule trans :premises (@p70 @p67)) % 0.31/0.55 (step @p72 :rule true_elim :premises (@p71)) % 0.31/0.55 (step @p73 :rule eq-refl :args (@t51)) % 0.31/0.55 (step @p74 :rule skolem_intro :args (@t52)) % 0.31/0.55 (step @p75 :rule refl :args (@t51)) % 0.31/0.55 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t51 @t52))) % 0.31/0.55 (step @p77 :rule trans :premises (@p76 @p73)) % 0.31/0.55 (step @p78 :rule true_elim :premises (@p77)) % 0.31/0.55 (step @p79 :rule cong :premises (@p78 @p72) :args (@t59)) % 0.31/0.55 (step @p80 :rule trans :premises (@p79 @p66)) % 0.31/0.55 (step @p81 :rule cong :premises (@p80) :args (@t60)) % 0.31/0.55 (step @p82 :rule refl :args (@t58)) % 0.31/0.55 (step @p83 :rule cong :premises (@p82 @p81) :args ((=> @t58 @t60))) % 0.31/0.55 (assume-push @p154 @t58) % 0.31/0.55 (step @p85 :rule skolemize :premises (@p62)) % 0.31/0.55 (step-pop @p155 :rule scope :premises (@p85)) % 0.31/0.55 (step @p86 :rule process_scope :premises (@p155) :args (@t60)) % 0.31/0.55 (step @p88 :rule eq_resolve :premises (@p86 @p83)) % 0.31/0.55 (step @p89 :rule implies_elim :premises (@p88)) % 0.31/0.55 (step @p90 :rule eq_resolve :premises (@p89 @p65)) % 0.31/0.55 (step @p91 :rule chain_m_resolution :premises (@p90 @p62) :args (@t57 @t61 (@list @t35))) % 0.31/0.55 (step @p92 :rule eq-symm :args (@t50 @t47)) % 0.31/0.55 (step @p93 :rule eq-refl :args (@t47)) % 0.31/0.55 (step @p94 :rule beta-reduce :args (@t62)) % 0.31/0.55 (step @p95 :rule cong :premises (@p94 @p13) :args (@t62)) % 0.31/0.55 (step @p96 :rule trans :premises (@p95 @p93)) % 0.31/0.55 (step @p97 :rule refl :args (@t28)) % 0.31/0.55 (step @p98 :rule ho_cong :premises (@p74 @p97)) % 0.31/0.55 (step @p99 :rule cong :premises (@p98 @p13) :args ((= @t63 @t47))) % 0.31/0.55 (step @p100 :rule trans :premises (@p99 @p96)) % 0.31/0.55 (step @p101 :rule true_elim :premises (@p100)) % 0.31/0.55 (step @p102 :rule eq-refl :args (@t50)) % 0.31/0.55 (step @p103 :rule refl :args (@t50)) % 0.31/0.55 (step @p104 :rule beta-reduce :args (@t64)) % 0.31/0.55 (step @p105 :rule cong :premises (@p104 @p103) :args (@t64)) % 0.31/0.55 (step @p106 :rule trans :premises (@p105 @p102)) % 0.31/0.55 (step @p107 :rule ho_cong :premises (@p68 @p97)) % 0.31/0.55 (step @p108 :rule cong :premises (@p107 @p103) :args ((= @t65 @t50))) % 0.31/0.55 (step @p109 :rule trans :premises (@p108 @p106)) % 0.31/0.55 (step @p110 :rule true_elim :premises (@p109)) % 0.31/0.55 (step @p111 :rule cong :premises (@p110 @p101) :args (@t66)) % 0.31/0.55 (step @p112 :rule trans :premises (@p111 @p92)) % 0.31/0.55 (step @p113 :rule cong :premises (@p112) :args (@t67)) % 0.31/0.55 (step @p114 :rule refl :args (@t56)) % 0.31/0.55 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t68)) % 0.31/0.55 ; WARNING: add trust step for TRUST % 0.31/0.55 ; trust TRUST THEORY_LEMMA % 0.31/0.55 (step @p116 :rule trust :premises () :args (@t68)) % 0.31/0.55 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.31/0.55 (step @p118 :rule chain_m_resolution :premises (@p117 @p91) :args ((not @t69) @t61 (@list @t56))) % 0.31/0.55 (step @p119 :rule cnf_equiv_neg2 :args (@t69)) % 0.31/0.55 (step @p120 :rule chain_m_resolution :premises (@p119 @p118 @p18 @p17 @p11 @p4) :args ((or @t39 @t44) @t70 (@list @t69 @t50 @t47 @t46 @t40))) % 0.31/0.55 (step @p121 :rule cnf_and_pos :args (@t46 1)) % 0.31/0.55 (step @p122 :rule reordering :premises (@p121) :args ((or @t45 @t71))) % 0.31/0.55 (step @p123 :rule cnf_and_pos :args (@t40 1)) % 0.31/0.55 (step @p124 :rule reordering :premises (@p123) :args ((or @t37 @t41))) % 0.31/0.55 (step @p125 :rule bool-double-not-elim :args (@t37)) % 0.31/0.55 (step @p126 :rule refl :args (@t49)) % 0.31/0.55 (step @p127 :rule nary_cong :premises (@p126 @p6 @p125) :args ((or @t49 @t44 (not @t48)))) % 0.31/0.55 (step @p128 :rule cnf_and_neg :args (@t49)) % 0.31/0.55 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.31/0.55 (step @p130 :rule reordering :premises (@p129) :args ((or @t37 @t49 @t44))) % 0.31/0.55 (step @p131 :rule cnf_or_neg :args (@t50 1)) % 0.31/0.55 (step @p132 :rule chain_m_resolution :premises (@p119 @p118 @p131 @p17 @p130 @p124) :args ((or @t37 @t44) @t70 (@list @t69 @t50 @t47 @t49 @t40))) % 0.31/0.55 (step @p133 :rule cnf_and_neg :args (@t40)) % 0.31/0.55 (step @p134 :rule cnf_and_pos :args (@t49 1)) % 0.31/0.55 (step @p135 :rule reordering :premises (@p134) :args ((or @t48 @t72))) % 0.31/0.55 (step @p136 :rule cnf_and_pos :args (@t47 1)) % 0.31/0.55 (step @p137 :rule reordering :premises (@p136) :args ((or @t41 @t73))) % 0.31/0.55 (step @p138 :rule cnf_or_pos :args (@t50)) % 0.31/0.55 (step @p139 :rule reordering :premises (@p138) :args ((or @t46 @t49 (not @t50)))) % 0.31/0.55 (step @p140 :rule cnf_equiv_neg1 :args (@t69)) % 0.31/0.55 (step @p141 :rule reordering :premises (@p140) :args ((or @t47 @t50 @t69))) % 0.31/0.55 (step @p142 :rule chain_m_resolution :premises (@p141 @p118 @p139 @p137 @p135 @p133 @p132 @p122 @p120) :args (@t44 (@list true true true true false false true false) (@list @t69 @t50 @t47 @t49 @t40 @t37 @t46 @t39))) % 0.31/0.55 (step @p143 :rule cnf_and_pos :args (@t46 0)) % 0.31/0.55 (step @p144 :rule reordering :premises (@p143) :args ((or @t43 @t71))) % 0.31/0.55 (step @p145 :rule chain_m_resolution :premises (@p144 @p142) :args (@t71 @t61 @t74)) % 0.31/0.55 (step @p146 :rule cnf_and_pos :args (@t49 0)) % 0.31/0.55 (step @p147 :rule reordering :premises (@p146) :args ((or @t43 @t72))) % 0.31/0.55 (step @p148 :rule chain_m_resolution :premises (@p147 @p142) :args (@t72 @t61 @t74)) % 0.31/0.55 (step @p149 :rule cnf_and_pos :args (@t47 0)) % 0.31/0.55 (step @p150 :rule reordering :premises (@p149) :args ((or @t43 @t73))) % 0.31/0.55 (step @p151 :rule chain_m_resolution :premises (@p150 @p142) :args (@t73 @t61 @t74)) % 0.31/0.55 (step @p152 :rule chain_m_resolution :premises (@p141 @p151 @p118) :args (@t50 (@list true true) (@list @t47 @t69))) % 0.31/0.55 (step @p153 false :rule chain_m_resolution :premises (@p139 @p152 @p148 @p145) :args (false (@list false true true) (@list @t50 @t49 @t46))) % 0.31/0.55 ) % 0.31/0.55 % SZS output end Proof % 0.31/0.55 % cvc5 exiting %------------------------------------------------------------------------------