%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET615^5 : 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 : n002.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 0.27s 0.55s % Output : Proof 0.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET615^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.36 % Computer : n002.cluster.edu % 0.18/0.36 % Model : x86_64 x86_64 % 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.36 % Memory : 8042.1875MB % 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.36 % CPULimit : 300 % 0.18/0.36 % WCLimit : 300 % 0.18/0.36 % DateTime : Tue Jun 2 16:05:03 EDT 2026 % 0.19/0.36 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.27/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.27/0.55 % SZS status Theorem % 0.27/0.55 % SZS output start Proof % 0.27/0.55 ( % 0.27/0.55 (declare-sort tptp.a 0) % 0.27/0.55 (define @t1 () (@var "Xz" tptp.a)) % 0.27/0.55 (define @t2 () (@var "Z" (-> tptp.a Bool))) % 0.27/0.55 (define @t3 () (_ @t2 @t1)) % 0.27/0.55 (define @t4 () (not @t3)) % 0.27/0.55 (define @t5 () (@var "Y" (-> tptp.a Bool))) % 0.27/0.55 (define @t6 () (_ @t5 @t1)) % 0.27/0.55 (define @t7 () (and @t6 @t4)) % 0.27/0.55 (define @t8 () (@var "X" (-> tptp.a Bool))) % 0.27/0.55 (define @t9 () (_ @t8 @t1)) % 0.27/0.55 (define @t10 () (and @t9 @t4)) % 0.27/0.55 (define @t11 () (or @t10 @t7)) % 0.27/0.55 (define @t12 () (@list @t1)) % 0.27/0.55 (define @t13 () (lambda @t12 @t11)) % 0.27/0.55 (define @t14 () (@var "Xx" tptp.a)) % 0.27/0.55 (define @t15 () (_ @t2 @t14)) % 0.27/0.55 (define @t16 () (not @t15)) % 0.27/0.55 (define @t17 () (_ @t5 @t14)) % 0.27/0.55 (define @t18 () (_ @t8 @t14)) % 0.27/0.55 (define @t19 () (or @t18 @t17)) % 0.27/0.55 (define @t20 () (and @t19 @t16)) % 0.27/0.55 (define @t21 () (@list @t14)) % 0.27/0.55 (define @t22 () (lambda @t21 @t20)) % 0.27/0.55 (define @t23 () (= @t22 @t13)) % 0.27/0.55 (define @t24 () (@list @t8 @t5 @t2)) % 0.27/0.55 (define @t25 () (forall @t24 @t23)) % 0.27/0.55 (define @t26 () (not @t25)) % 0.27/0.55 (define @t27 () (_ @t2 @t1)) % 0.27/0.55 (define @t28 () (_ @t5 @t1)) % 0.27/0.55 (define @t29 () (_ @t8 @t1)) % 0.27/0.55 (define @t30 () (_ @t2 @t14)) % 0.27/0.55 (define @t31 () (_ @t5 @t14)) % 0.27/0.55 (define @t32 () (_ @t8 @t14)) % 0.27/0.55 (define @t33 () (not @t27)) % 0.27/0.55 (define @t34 () (forall @t24 (= (lambda @t21 (and (or @t32 @t31) (not @t30))) (lambda @t12 (or (and @t29 @t33) (and @t28 @t33)))))) % 0.27/0.55 (define @t35 () (@quantifiers_skolemize @t34 2)) % 0.27/0.55 (define @t36 () (@quantifiers_skolemize @t34 1)) % 0.27/0.55 (define @t37 () (@quantifiers_skolemize @t34 0)) % 0.27/0.55 (define @t38 () (lambda @t21 (and (or (_ @t37 @t14) (_ @t36 @t14)) (not (_ @t35 @t14))))) % 0.27/0.55 (define @t39 () (@purify @t38)) % 0.27/0.55 (define @t40 () (not (_ @t35 @t1))) % 0.27/0.55 (define @t41 () (lambda @t12 (or (and (_ @t37 @t1) @t40) (and (_ @t36 @t1) @t40)))) % 0.27/0.55 (define @t42 () (@purify @t41)) % 0.27/0.55 (define @t43 () (= @t42 @t39)) % 0.27/0.55 (define @t44 () (not @t43)) % 0.27/0.55 (define @t45 () (not @t34)) % 0.27/0.55 (define @t46 () (= @t38 @t41)) % 0.27/0.55 (define @t47 () (not @t46)) % 0.27/0.55 (define @t48 () (@list true)) % 0.27/0.55 (define @t49 () (@const 0 tptp.a)) % 0.27/0.55 (define @t50 () (_ @t35 @t49)) % 0.27/0.55 (define @t51 () (not @t50)) % 0.27/0.55 (define @t52 () (_ @t36 @t49)) % 0.27/0.55 (define @t53 () (and @t52 @t51)) % 0.27/0.55 (define @t54 () (_ @t37 @t49)) % 0.27/0.55 (define @t55 () (and @t54 @t51)) % 0.27/0.55 (define @t56 () (or @t55 @t53)) % 0.27/0.55 (define @t57 () (or @t54 @t52)) % 0.27/0.55 (define @t58 () (and @t57 @t51)) % 0.27/0.55 (define @t59 () (= (_ @t38 @t49) @t58)) % 0.27/0.55 (define @t60 () (_ @t39 @t49)) % 0.27/0.55 (define @t61 () (= (_ @t41 @t49) @t56)) % 0.27/0.55 (define @t62 () (_ @t42 @t49)) % 0.27/0.55 (define @t63 () (= @t62 @t60)) % 0.27/0.55 (define @t64 () (not @t63)) % 0.27/0.55 (define @t65 () (or @t43 @t64)) % 0.27/0.55 (define @t66 () (= @t58 @t56)) % 0.27/0.55 (define @t67 () (not @t58)) % 0.27/0.55 (define @t68 () (not @t55)) % 0.27/0.55 (define @t69 () (not @t53)) % 0.27/0.55 (define @t70 () (not @t56)) % 0.27/0.55 (define @t71 () (not @t52)) % 0.27/0.55 (define @t72 () (not @t51)) % 0.27/0.55 (define @t73 () (not @t57)) % 0.27/0.55 (define @t74 () (not @t54)) % 0.27/0.55 (define @t75 () (@list true true)) % 0.27/0.55 (assume @p1 @t26) % 0.27/0.55 (assume @p2 true) % 0.27/0.55 (step @p3 :rule refl :args (@t27)) % 0.27/0.55 (step @p4 :rule refl :args (@t3)) % 0.27/0.55 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t3 @t27))) % 0.27/0.55 (step @p6 :rule symm :premises (@p5)) % 0.27/0.55 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.27/0.55 (step @p8 :rule cong :premises (@p7) :args (@t4)) % 0.27/0.55 (step @p9 :rule refl :args (@t28)) % 0.27/0.55 (step @p10 :rule refl :args (@t6)) % 0.27/0.55 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t6 @t28))) % 0.27/0.55 (step @p12 :rule symm :premises (@p11)) % 0.27/0.55 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 0.27/0.55 (step @p14 :rule nary_cong :premises (@p13 @p8) :args (@t7)) % 0.27/0.55 (step @p15 :rule refl :args (@t29)) % 0.27/0.55 (step @p16 :rule refl :args (@t9)) % 0.27/0.55 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t9 @t29))) % 0.27/0.55 (step @p18 :rule symm :premises (@p17)) % 0.27/0.55 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.27/0.55 (step @p20 :rule nary_cong :premises (@p19 @p8) :args (@t10)) % 0.27/0.55 (step @p21 :rule nary_cong :premises (@p20 @p14) :args (@t11)) % 0.27/0.55 (step @p22 :rule cong :premises (@p21) :args (@t13)) % 0.27/0.55 (step @p23 :rule refl :args (@t30)) % 0.27/0.55 (step @p24 :rule refl :args (@t15)) % 0.27/0.55 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t15 @t30))) % 0.27/0.55 (step @p26 :rule symm :premises (@p25)) % 0.27/0.55 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.27/0.55 (step @p28 :rule cong :premises (@p27) :args (@t16)) % 0.27/0.55 (step @p29 :rule refl :args (@t31)) % 0.27/0.55 (step @p30 :rule refl :args (@t17)) % 0.27/0.55 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t17 @t31))) % 0.27/0.55 (step @p32 :rule symm :premises (@p31)) % 0.27/0.55 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.27/0.55 (step @p34 :rule refl :args (@t32)) % 0.27/0.55 (step @p35 :rule refl :args (@t18)) % 0.27/0.55 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t18 @t32))) % 0.27/0.55 (step @p37 :rule symm :premises (@p36)) % 0.27/0.55 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.27/0.55 (step @p39 :rule nary_cong :premises (@p38 @p33) :args (@t19)) % 0.27/0.55 (step @p40 :rule nary_cong :premises (@p39 @p28) :args (@t20)) % 0.27/0.55 (step @p41 :rule cong :premises (@p40) :args (@t22)) % 0.27/0.55 (step @p42 :rule cong :premises (@p41 @p22) :args (@t23)) % 0.27/0.55 (step @p43 :rule cong :premises (@p42) :args (@t25)) % 0.27/0.55 (step @p44 :rule cong :premises (@p43) :args (@t26)) % 0.27/0.55 (step @p45 :rule eq_resolve :premises (@p1 @p44)) % 0.27/0.55 (step @p46 :rule refl :args (@t44)) % 0.27/0.55 (step @p47 :rule bool-double-not-elim :args (@t34)) % 0.27/0.55 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or (not @t45) @t44))) % 0.27/0.55 (step @p49 :rule eq-symm :args (@t39 @t42)) % 0.27/0.55 (step @p50 :rule eq-refl :args (@t41)) % 0.27/0.55 (step @p51 :rule skolem_intro :args (@t42)) % 0.27/0.55 (step @p52 :rule refl :args (@t41)) % 0.27/0.55 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t41 @t42))) % 0.27/0.55 (step @p54 :rule trans :premises (@p53 @p50)) % 0.27/0.55 (step @p55 :rule true_elim :premises (@p54)) % 0.27/0.55 (step @p56 :rule eq-refl :args (@t38)) % 0.27/0.55 (step @p57 :rule skolem_intro :args (@t39)) % 0.27/0.55 (step @p58 :rule refl :args (@t38)) % 0.27/0.55 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t38 @t39))) % 0.27/0.55 (step @p60 :rule trans :premises (@p59 @p56)) % 0.27/0.55 (step @p61 :rule true_elim :premises (@p60)) % 0.27/0.55 (step @p62 :rule cong :premises (@p61 @p55) :args (@t46)) % 0.27/0.55 (step @p63 :rule trans :premises (@p62 @p49)) % 0.27/0.55 (step @p64 :rule cong :premises (@p63) :args (@t47)) % 0.27/0.55 (step @p65 :rule refl :args (@t45)) % 0.27/0.55 (step @p66 :rule cong :premises (@p65 @p64) :args ((=> @t45 @t47))) % 0.27/0.55 (assume-push @p154 @t45) % 0.27/0.55 (step @p68 :rule skolemize :premises (@p45)) % 0.27/0.55 (step-pop @p155 :rule scope :premises (@p68)) % 0.27/0.55 (step @p69 :rule process_scope :premises (@p155) :args (@t47)) % 0.27/0.55 (step @p71 :rule eq_resolve :premises (@p69 @p66)) % 0.27/0.55 (step @p72 :rule implies_elim :premises (@p71)) % 0.27/0.55 (step @p73 :rule eq_resolve :premises (@p72 @p48)) % 0.27/0.55 (step @p74 :rule chain_m_resolution :premises (@p73 @p45) :args (@t44 @t48 (@list @t34))) % 0.27/0.55 (step @p75 :rule eq-symm :args (@t56 @t58)) % 0.27/0.55 (step @p76 :rule eq-refl :args (@t58)) % 0.27/0.55 (step @p77 :rule refl :args (@t58)) % 0.27/0.55 (step @p78 :rule beta-reduce :args (@t59)) % 0.27/0.55 (step @p79 :rule cong :premises (@p78 @p77) :args (@t59)) % 0.27/0.55 (step @p80 :rule trans :premises (@p79 @p76)) % 0.27/0.55 (step @p81 :rule refl :args (@t49)) % 0.27/0.55 (step @p82 :rule ho_cong :premises (@p57 @p81)) % 0.27/0.55 (step @p83 :rule cong :premises (@p82 @p77) :args ((= @t60 @t58))) % 0.27/0.55 (step @p84 :rule trans :premises (@p83 @p80)) % 0.27/0.55 (step @p85 :rule true_elim :premises (@p84)) % 0.27/0.55 (step @p86 :rule eq-refl :args (@t56)) % 0.27/0.55 (step @p87 :rule refl :args (@t56)) % 0.27/0.55 (step @p88 :rule beta-reduce :args (@t61)) % 0.27/0.55 (step @p89 :rule cong :premises (@p88 @p87) :args (@t61)) % 0.27/0.55 (step @p90 :rule trans :premises (@p89 @p86)) % 0.27/0.55 (step @p91 :rule ho_cong :premises (@p51 @p81)) % 0.27/0.55 (step @p92 :rule cong :premises (@p91 @p87) :args ((= @t62 @t56))) % 0.27/0.55 (step @p93 :rule trans :premises (@p92 @p90)) % 0.27/0.55 (step @p94 :rule true_elim :premises (@p93)) % 0.27/0.55 (step @p95 :rule cong :premises (@p94 @p85) :args (@t63)) % 0.27/0.55 (step @p96 :rule trans :premises (@p95 @p75)) % 0.27/0.55 (step @p97 :rule cong :premises (@p96) :args (@t64)) % 0.27/0.55 (step @p98 :rule refl :args (@t43)) % 0.27/0.55 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t65)) % 0.27/0.55 ; WARNING: add trust step for TRUST % 0.27/0.55 ; trust TRUST THEORY_LEMMA % 0.27/0.55 (step @p100 :rule trust :premises () :args (@t65)) % 0.27/0.55 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.27/0.55 (step @p102 :rule chain_m_resolution :premises (@p101 @p74) :args ((not @t66) @t48 (@list @t43))) % 0.27/0.55 (step @p103 :rule cnf_or_neg :args (@t57 1)) % 0.27/0.55 (step @p104 :rule cnf_and_pos :args (@t58 1)) % 0.27/0.55 (step @p105 :rule reordering :premises (@p104) :args ((or @t51 @t67))) % 0.27/0.55 (step @p106 :rule cnf_and_pos :args (@t55 1)) % 0.27/0.55 (step @p107 :rule reordering :premises (@p106) :args ((or @t51 @t68))) % 0.27/0.55 (step @p108 :rule cnf_and_pos :args (@t53 1)) % 0.27/0.55 (step @p109 :rule reordering :premises (@p108) :args ((or @t51 @t69))) % 0.27/0.55 (step @p110 :rule cnf_equiv_neg1 :args (@t66)) % 0.27/0.55 (step @p111 :rule reordering :premises (@p110) :args ((or @t58 @t56 @t66))) % 0.27/0.55 (step @p112 :rule cnf_or_pos :args (@t56)) % 0.27/0.55 (step @p113 :rule reordering :premises (@p112) :args ((or @t55 @t53 @t70))) % 0.27/0.55 (step @p114 :rule chain_m_resolution :premises (@p113 @p111 @p102 @p109 @p107 @p105) :args (@t51 (@list false true true true true) (@list @t56 @t66 @t53 @t55 @t58))) % 0.27/0.55 (step @p115 :rule bool-double-not-elim :args (@t50)) % 0.27/0.55 (step @p116 :rule refl :args (@t71)) % 0.27/0.55 (step @p117 :rule refl :args (@t53)) % 0.27/0.55 (step @p118 :rule nary_cong :premises (@p117 @p116 @p115) :args ((or @t53 @t71 @t72))) % 0.27/0.55 (step @p119 :rule cnf_and_neg :args (@t53)) % 0.27/0.55 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.27/0.55 (step @p121 :rule reordering :premises (@p120) :args ((or @t50 @t53 @t71))) % 0.27/0.55 (step @p122 :rule refl :args (@t73)) % 0.27/0.55 (step @p123 :rule nary_cong :premises (@p77 @p122 @p115) :args ((or @t58 @t73 @t72))) % 0.27/0.55 (step @p124 :rule cnf_and_neg :args (@t58)) % 0.27/0.55 (step @p125 :rule eq_resolve :premises (@p124 @p123)) % 0.27/0.55 (step @p126 :rule reordering :premises (@p125) :args ((or @t50 @t58 @t73))) % 0.27/0.55 (step @p127 :rule cnf_or_neg :args (@t56 1)) % 0.27/0.55 (step @p128 :rule cnf_equiv_neg2 :args (@t66)) % 0.27/0.55 (step @p129 :rule chain_m_resolution :premises (@p128 @p102 @p127 @p126 @p114 @p121 @p114 @p103) :args (@t71 (@list true false false true false true false) (@list @t66 @t56 @t58 @t50 @t53 @t50 @t57))) % 0.27/0.55 (step @p130 :rule cnf_or_neg :args (@t57 0)) % 0.27/0.55 (step @p131 :rule refl :args (@t74)) % 0.27/0.55 (step @p132 :rule refl :args (@t55)) % 0.27/0.55 (step @p133 :rule nary_cong :premises (@p132 @p131 @p115) :args ((or @t55 @t74 @t72))) % 0.27/0.55 (step @p134 :rule cnf_and_neg :args (@t55)) % 0.27/0.55 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.27/0.55 (step @p136 :rule reordering :premises (@p135) :args ((or @t50 @t55 @t74))) % 0.27/0.55 (step @p137 :rule cnf_or_neg :args (@t56 0)) % 0.27/0.55 (step @p138 :rule chain_m_resolution :premises (@p137 @p128 @p102 @p136 @p126 @p130) :args ((or @t50 @t74) (@list true true false false false) (@list @t56 @t66 @t55 @t58 @t57))) % 0.27/0.55 (step @p139 :rule chain_m_resolution :premises (@p138 @p114) :args (@t74 @t48 (@list @t50))) % 0.27/0.55 (step @p140 :rule cnf_or_pos :args (@t57)) % 0.27/0.55 (step @p141 :rule reordering :premises (@p140) :args ((or @t54 @t52 @t73))) % 0.27/0.55 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p129) :args (@t73 @t75 (@list @t54 @t52))) % 0.27/0.55 (step @p143 :rule cnf_and_pos :args (@t58 0)) % 0.27/0.55 (step @p144 :rule reordering :premises (@p143) :args ((or @t57 @t67))) % 0.27/0.55 (step @p145 :rule chain_m_resolution :premises (@p144 @p142) :args (@t67 @t48 (@list @t57))) % 0.27/0.55 (step @p146 :rule cnf_and_pos :args (@t53 0)) % 0.27/0.55 (step @p147 :rule reordering :premises (@p146) :args ((or @t52 @t69))) % 0.27/0.55 (step @p148 :rule chain_m_resolution :premises (@p147 @p129) :args (@t69 @t48 (@list @t52))) % 0.27/0.55 (step @p149 :rule cnf_and_pos :args (@t55 0)) % 0.27/0.55 (step @p150 :rule reordering :premises (@p149) :args ((or @t54 @t68))) % 0.27/0.55 (step @p151 :rule chain_m_resolution :premises (@p150 @p139) :args (@t68 @t48 (@list @t54))) % 0.27/0.55 (step @p152 :rule chain_m_resolution :premises (@p113 @p151 @p148) :args (@t70 @t75 (@list @t55 @t53))) % 0.27/0.55 (step @p153 false :rule chain_m_resolution :premises (@p111 @p152 @p145 @p102) :args (false (@list true true true) (@list @t56 @t58 @t66))) % 0.27/0.55 ) % 0.27/0.55 % SZS output end Proof % 0.27/0.55 % cvc5 exiting %------------------------------------------------------------------------------