%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV166^5 : 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 08:55:33 AM UTC 2026 % Result : Theorem 0.47s 0.68s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV166^5 : 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 % 0.16/0.33 % Computer : n003.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:17:14 EDT 2026 % 0.16/0.34 % CPUTime : % 0.19/0.48 %----Proving TH0 % 0.47/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.47/0.68 % SZS status Theorem % 0.47/0.68 % SZS output start Proof % 0.47/0.68 ( % 0.47/0.68 (declare-sort tptp.a 0) % 0.47/0.68 (define @t1 () (@var "Xv" tptp.a)) % 0.47/0.68 (define @t2 () (@var "Xy" tptp.a)) % 0.47/0.68 (define @t3 () (@var "Xu" tptp.a)) % 0.47/0.68 (define @t4 () (@var "Xx" tptp.a)) % 0.47/0.68 (define @t5 () (and (= @t4 @t3) (= @t2 @t1))) % 0.47/0.68 (define @t6 () (@var "Xg" (-> tptp.a tptp.a tptp.a))) % 0.47/0.68 (define @t7 () (_ (_ @t6 @t3) @t1)) % 0.47/0.68 (define @t8 () (@list @t6)) % 0.47/0.68 (define @t9 () (lambda @t8 @t7)) % 0.47/0.68 (define @t10 () (_ (_ @t6 @t4) @t2)) % 0.47/0.68 (define @t11 () (lambda @t8 @t10)) % 0.47/0.68 (define @t12 () (= @t11 @t9)) % 0.47/0.68 (define @t13 () (= @t12 @t5)) % 0.47/0.68 (define @t14 () (@list @t4 @t2 @t3 @t1)) % 0.47/0.68 (define @t15 () (forall @t14 @t13)) % 0.47/0.68 (define @t16 () (not @t15)) % 0.47/0.68 (define @t17 () (_ @t6 @t3 @t1)) % 0.47/0.68 (define @t18 () (_ @t6 @t4 @t2)) % 0.47/0.68 (define @t19 () (= (lambda @t8 @t18) (lambda @t8 @t17))) % 0.47/0.68 (define @t20 () (forall @t14 (= @t5 @t19))) % 0.47/0.68 (define @t21 () (@quantifiers_skolemize @t20 3)) % 0.47/0.68 (define @t22 () (@quantifiers_skolemize @t20 1)) % 0.47/0.68 (define @t23 () (= @t22 @t21)) % 0.47/0.68 (define @t24 () (@quantifiers_skolemize @t20 2)) % 0.47/0.68 (define @t25 () (@quantifiers_skolemize @t20 0)) % 0.47/0.68 (define @t26 () (= @t25 @t24)) % 0.47/0.68 (define @t27 () (and @t26 @t23)) % 0.47/0.68 (define @t28 () (not @t27)) % 0.47/0.68 (define @t29 () (_ @t6 @t25 @t22)) % 0.47/0.68 (define @t30 () (lambda @t8 @t29)) % 0.47/0.68 (define @t31 () (@purify @t30)) % 0.47/0.68 (define @t32 () (_ @t6 @t24 @t21)) % 0.47/0.68 (define @t33 () (lambda @t8 @t32)) % 0.47/0.68 (define @t34 () (@purify @t33)) % 0.47/0.68 (define @t35 () (= @t34 @t31)) % 0.47/0.68 (define @t36 () (= @t27 @t35)) % 0.47/0.68 (define @t37 () (not @t36)) % 0.47/0.68 (define @t38 () (not @t20)) % 0.47/0.68 (define @t39 () (= @t30 @t33)) % 0.47/0.68 (define @t40 () (= @t27 @t39)) % 0.47/0.68 (define @t41 () (not @t40)) % 0.47/0.68 (define @t42 () (@list true)) % 0.47/0.68 (define @t43 () (forall @t8 (= @t32 @t29))) % 0.47/0.68 (define @t44 () (=> @t35 @t43)) % 0.47/0.68 (define @t45 () (@var "BOUND_VARIABLE_14857" tptp.a)) % 0.47/0.68 (define @t46 () (@var "BOUND_VARIABLE_14856" tptp.a)) % 0.47/0.68 (define @t47 () (@list @t46 @t45)) % 0.47/0.68 (define @t48 () (lambda @t47 @t45)) % 0.47/0.68 (define @t49 () (_ @t48 @t24 @t21)) % 0.47/0.68 (define @t50 () (_ @t48 @t25 @t22)) % 0.47/0.68 (define @t51 () (= @t50 @t49)) % 0.47/0.68 (define @t52 () (forall @t8 (= @t29 @t32))) % 0.47/0.68 (define @t53 () (not @t52)) % 0.47/0.68 (define @t54 () (@const 0 (-> tptp.a tptp.a tptp.a))) % 0.47/0.68 (define @t55 () (_ @t54 @t25 @t22)) % 0.47/0.68 (define @t56 () (_ @t54 @t24 @t21)) % 0.47/0.68 (define @t57 () (= @t55 @t56)) % 0.47/0.68 (define @t58 () (= (_ @t30 @t54) @t55)) % 0.47/0.68 (define @t59 () (_ @t31 @t54)) % 0.47/0.68 (define @t60 () (= (_ @t33 @t54) @t56)) % 0.47/0.68 (define @t61 () (_ @t34 @t54)) % 0.47/0.68 (define @t62 () (= @t61 @t59)) % 0.47/0.68 (define @t63 () (not @t62)) % 0.47/0.68 (define @t64 () (or @t35 @t63)) % 0.47/0.68 (define @t65 () (not @t26)) % 0.47/0.68 (define @t66 () (@list false)) % 0.47/0.68 (define @t67 () (lambda @t47 @t46)) % 0.47/0.68 (define @t68 () (_ @t67 @t24 @t21)) % 0.47/0.68 (define @t69 () (_ @t67 @t25 @t22)) % 0.47/0.68 (define @t70 () (= @t69 @t68)) % 0.47/0.68 (assume @p1 @t16) % 0.47/0.68 (assume @p2 true) % 0.47/0.68 (step @p3 :rule cnf_and_pos :args (@t27 1)) % 0.47/0.68 (step @p4 :rule reordering :premises (@p3) :args ((or @t23 @t28))) % 0.47/0.68 (step @p5 :rule eq-symm :args (@t19 @t5)) % 0.47/0.68 (step @p6 :rule cong :premises (@p5) :args ((forall @t14 (= @t19 @t5)))) % 0.47/0.68 (step @p7 :rule refl :args (@t5)) % 0.47/0.68 (step @p8 :rule refl :args (@t17)) % 0.47/0.68 (step @p9 :rule refl :args (@t7)) % 0.47/0.68 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t7 @t17))) % 0.47/0.68 (step @p11 :rule symm :premises (@p10)) % 0.47/0.68 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.47/0.68 (step @p13 :rule cong :premises (@p12) :args (@t9)) % 0.47/0.68 (step @p14 :rule refl :args (@t18)) % 0.47/0.68 (step @p15 :rule refl :args (@t10)) % 0.47/0.68 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t10 @t18))) % 0.47/0.68 (step @p17 :rule symm :premises (@p16)) % 0.47/0.68 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 0.47/0.68 (step @p19 :rule cong :premises (@p18) :args (@t11)) % 0.47/0.68 (step @p20 :rule cong :premises (@p19 @p13) :args (@t12)) % 0.47/0.68 (step @p21 :rule cong :premises (@p20 @p7) :args (@t13)) % 0.47/0.68 (step @p22 :rule cong :premises (@p21) :args (@t15)) % 0.47/0.68 (step @p23 :rule trans :premises (@p22 @p6)) % 0.47/0.68 (step @p24 :rule cong :premises (@p23) :args (@t16)) % 0.47/0.68 (step @p25 :rule eq_resolve :premises (@p1 @p24)) % 0.47/0.68 (step @p26 :rule refl :args (@t37)) % 0.47/0.68 (step @p27 :rule bool-double-not-elim :args (@t20)) % 0.47/0.68 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or (not @t38) @t37))) % 0.47/0.68 (step @p29 :rule eq-symm :args (@t31 @t34)) % 0.47/0.68 (step @p30 :rule eq-refl :args (@t33)) % 0.47/0.68 (step @p31 :rule skolem_intro :args (@t34)) % 0.47/0.68 (step @p32 :rule refl :args (@t33)) % 0.47/0.68 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t33 @t34))) % 0.47/0.68 (step @p34 :rule trans :premises (@p33 @p30)) % 0.47/0.68 (step @p35 :rule true_elim :premises (@p34)) % 0.47/0.68 (step @p36 :rule eq-refl :args (@t30)) % 0.47/0.68 (step @p37 :rule skolem_intro :args (@t31)) % 0.47/0.68 (step @p38 :rule refl :args (@t30)) % 0.47/0.68 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t30 @t31))) % 0.47/0.68 (step @p40 :rule trans :premises (@p39 @p36)) % 0.47/0.68 (step @p41 :rule true_elim :premises (@p40)) % 0.47/0.68 (step @p42 :rule cong :premises (@p41 @p35) :args (@t39)) % 0.47/0.68 (step @p43 :rule trans :premises (@p42 @p29)) % 0.47/0.68 (step @p44 :rule refl :args (@t27)) % 0.47/0.68 (step @p45 :rule cong :premises (@p44 @p43) :args (@t40)) % 0.47/0.68 (step @p46 :rule cong :premises (@p45) :args (@t41)) % 0.47/0.68 (step @p47 :rule refl :args (@t38)) % 0.47/0.68 (step @p48 :rule cong :premises (@p47 @p46) :args ((=> @t38 @t41))) % 0.47/0.68 (assume-push @p141 @t38) % 0.47/0.68 (step @p50 :rule skolemize :premises (@p25)) % 0.47/0.68 (step-pop @p142 :rule scope :premises (@p50)) % 0.47/0.68 (step @p51 :rule process_scope :premises (@p142) :args (@t41)) % 0.47/0.68 (step @p53 :rule eq_resolve :premises (@p51 @p48)) % 0.47/0.68 (step @p54 :rule implies_elim :premises (@p53)) % 0.47/0.68 (step @p55 :rule eq_resolve :premises (@p54 @p28)) % 0.47/0.68 (step @p56 :rule chain_m_resolution :premises (@p55 @p25) :args (@t37 @t42 (@list @t20))) % 0.47/0.68 (step @p57 :rule cnf_equiv_neg1 :args (@t36)) % 0.47/0.68 (step @p58 :rule reordering :premises (@p57) :args ((or @t27 @t35 @t36))) % 0.47/0.68 (step @p59 :rule eq-symm :args (@t32 @t29)) % 0.47/0.68 (step @p60 :rule cong :premises (@p59) :args (@t43)) % 0.47/0.68 (step @p61 :rule refl :args (@t35)) % 0.47/0.68 (step @p62 :rule cong :premises (@p61 @p60) :args (@t44)) % 0.47/0.68 ; WARNING: add trust step for TRUST % 0.47/0.68 ; trust TRUST THEORY_LEMMA % 0.47/0.68 (step @p63 :rule trust :premises () :args (@t44)) % 0.47/0.68 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.47/0.68 (step @p65 :rule implies_elim :premises (@p64)) % 0.47/0.68 (step @p66 :rule beta-reduce :args ((= @t49 @t21))) % 0.47/0.68 (step @p67 :rule beta-reduce :args ((= @t50 @t22))) % 0.47/0.68 (step @p68 :rule cong :premises (@p67 @p66) :args (@t51)) % 0.47/0.68 (step @p69 :rule refl :args (@t52)) % 0.47/0.68 (step @p70 :rule cong :premises (@p69 @p68) :args ((=> @t52 @t51))) % 0.47/0.68 (assume-push @p143 @t52) % 0.47/0.68 (step @p72 :rule instantiate :premises (@p143) :args ((@list @t48))) % 0.47/0.68 (step-pop @p144 :rule scope :premises (@p72)) % 0.47/0.68 (step @p73 :rule process_scope :premises (@p144) :args (@t51)) % 0.47/0.68 (step @p75 :rule eq_resolve :premises (@p73 @p70)) % 0.47/0.68 (step @p76 :rule implies_elim :premises (@p75)) % 0.47/0.68 (step @p77 :rule reordering :premises (@p76) :args ((or @t23 @t53))) % 0.47/0.68 (step @p78 :rule chain_m_resolution :premises (@p77 @p65 @p58 @p56 @p4) :args (@t23 (@list false false true true) (@list @t52 @t35 @t36 @t27))) % 0.47/0.68 (step @p79 :rule cnf_and_neg :args (@t27)) % 0.47/0.68 (step @p80 :rule cnf_equiv_neg2 :args (@t36)) % 0.47/0.68 (assume-push @p145 @t26) % 0.47/0.68 (assume-push @p146 @t23) % 0.47/0.68 (assume-push @p147 @t26) % 0.47/0.68 (assume-push @p148 @t23) % 0.47/0.68 (step @p85 :rule cong :premises (@p145 @p146) :args (@t55)) % 0.47/0.68 (step-pop @p149 :rule scope :premises (@p85)) % 0.47/0.68 (step-pop @p150 :rule scope :premises (@p149)) % 0.47/0.68 (step @p86 :rule process_scope :premises (@p150) :args (@t57)) % 0.47/0.68 (step @p89 :rule and_intro :premises (@p145 @p146)) % 0.47/0.68 (step @p90 :rule modus_ponens :premises (@p89 @p86)) % 0.47/0.68 (step-pop @p151 :rule scope :premises (@p90)) % 0.47/0.68 (step-pop @p152 :rule scope :premises (@p151)) % 0.47/0.68 (step @p91 :rule process_scope :premises (@p152) :args (@t57)) % 0.47/0.68 (step @p94 :rule implies_elim :premises (@p91)) % 0.47/0.68 (step @p95 :rule resolution :premises (@p79 @p94) :args (true @t27)) % 0.47/0.68 (step @p96 :rule eq-symm :args (@t56 @t55)) % 0.47/0.68 (step @p97 :rule eq-refl :args (@t55)) % 0.47/0.68 (step @p98 :rule refl :args (@t55)) % 0.47/0.68 (step @p99 :rule beta-reduce :args (@t58)) % 0.47/0.68 (step @p100 :rule cong :premises (@p99 @p98) :args (@t58)) % 0.47/0.68 (step @p101 :rule trans :premises (@p100 @p97)) % 0.47/0.68 (step @p102 :rule refl :args (@t54)) % 0.47/0.68 (step @p103 :rule ho_cong :premises (@p37 @p102)) % 0.47/0.68 (step @p104 :rule cong :premises (@p103 @p98) :args ((= @t59 @t55))) % 0.47/0.68 (step @p105 :rule trans :premises (@p104 @p101)) % 0.47/0.68 (step @p106 :rule true_elim :premises (@p105)) % 0.47/0.68 (step @p107 :rule eq-refl :args (@t56)) % 0.47/0.68 (step @p108 :rule refl :args (@t56)) % 0.47/0.68 (step @p109 :rule beta-reduce :args (@t60)) % 0.47/0.68 (step @p110 :rule cong :premises (@p109 @p108) :args (@t60)) % 0.47/0.68 (step @p111 :rule trans :premises (@p110 @p107)) % 0.47/0.68 (step @p112 :rule ho_cong :premises (@p31 @p102)) % 0.47/0.68 (step @p113 :rule cong :premises (@p112 @p108) :args ((= @t61 @t56))) % 0.47/0.68 (step @p114 :rule trans :premises (@p113 @p111)) % 0.47/0.68 (step @p115 :rule true_elim :premises (@p114)) % 0.47/0.68 (step @p116 :rule cong :premises (@p115 @p106) :args (@t62)) % 0.47/0.68 (step @p117 :rule trans :premises (@p116 @p96)) % 0.47/0.68 (step @p118 :rule cong :premises (@p117) :args (@t63)) % 0.47/0.68 (step @p119 :rule nary_cong :premises (@p61 @p118) :args (@t64)) % 0.47/0.68 ; trust TRUST THEORY_LEMMA % 0.47/0.68 (step @p120 :rule trust :premises () :args (@t64)) % 0.47/0.68 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.47/0.68 (step @p122 :rule chain_m_resolution :premises (@p121 @p95 @p80 @p56 @p79) :args ((or @t65 (not @t23)) (@list false true true false) (@list @t57 @t35 @t36 @t27))) % 0.47/0.68 (step @p123 :rule chain_m_resolution :premises (@p122 @p78) :args (@t65 @t66 (@list @t23))) % 0.47/0.68 (step @p124 :rule cnf_and_pos :args (@t27 0)) % 0.47/0.68 (step @p125 :rule reordering :premises (@p124) :args ((or @t26 @t28))) % 0.47/0.68 (step @p126 :rule chain_m_resolution :premises (@p125 @p123) :args (@t28 @t42 (@list @t26))) % 0.47/0.68 (step @p127 :rule chain_m_resolution :premises (@p58 @p126 @p56) :args (@t35 (@list true true) (@list @t27 @t36))) % 0.47/0.68 (step @p128 :rule chain_m_resolution :premises (@p65 @p127) :args (@t52 @t66 (@list @t35))) % 0.47/0.68 (step @p129 :rule beta-reduce :args ((= @t68 @t24))) % 0.47/0.68 (step @p130 :rule beta-reduce :args ((= @t69 @t25))) % 0.47/0.68 (step @p131 :rule cong :premises (@p130 @p129) :args (@t70)) % 0.47/0.68 (step @p132 :rule cong :premises (@p69 @p131) :args ((=> @t52 @t70))) % 0.47/0.68 (assume-push @p153 @t52) % 0.47/0.68 (step @p134 :rule instantiate :premises (@p153) :args ((@list @t67))) % 0.47/0.68 (step-pop @p154 :rule scope :premises (@p134)) % 0.47/0.68 (step @p135 :rule process_scope :premises (@p154) :args (@t70)) % 0.47/0.68 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 0.47/0.68 (step @p138 :rule implies_elim :premises (@p137)) % 0.47/0.68 (step @p139 :rule reordering :premises (@p138) :args ((or @t26 @t53))) % 0.47/0.68 (step @p140 false :rule chain_m_resolution :premises (@p139 @p128 @p123) :args (false (@list false true) (@list @t52 @t26))) % 0.47/0.68 ) % 0.47/0.68 % SZS output end Proof % 0.47/0.68 % cvc5 exiting %------------------------------------------------------------------------------