%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO351^5 : 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 : n024.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 09:12:28 AM UTC 2026 % Result : Theorem 0.14s 0.36s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO351^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n024.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Tue Jun 2 19:05:15 EDT 2026 % 0.06/0.25 % CPUTime : % 0.06/0.32 %----Proving TH0 % 0.14/0.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.14/0.36 % SZS status Theorem % 0.14/0.36 % SZS output start Proof % 0.14/0.36 ( % 0.14/0.36 (declare-sort tptp.a 0) % 0.14/0.36 (define @t1 () (@var "Xy" (-> tptp.a Bool))) % 0.14/0.36 (define @t2 () (@var "Xx" tptp.a)) % 0.14/0.36 (define @t3 () (@list @t2)) % 0.14/0.36 (define @t4 () (lambda @t3 false)) % 0.14/0.36 (define @t5 () (= @t4 @t1)) % 0.14/0.36 (define @t6 () (@list @t1)) % 0.14/0.36 (define @t7 () (lambda @t6 @t5)) % 0.14/0.36 (define @t8 () (@var "R" (-> tptp.a Bool))) % 0.14/0.36 (define @t9 () (_ @t8 @t2)) % 0.14/0.36 (define @t10 () (forall @t3 (=> @t9 false))) % 0.14/0.36 (define @t11 () (@list @t8)) % 0.14/0.36 (define @t12 () (lambda @t11 @t10)) % 0.14/0.36 (define @t13 () (= @t12 @t7)) % 0.14/0.36 (define @t14 () (not @t13)) % 0.14/0.36 (define @t15 () (_ @t8 @t2)) % 0.14/0.36 (define @t16 () (lambda @t11 (forall @t3 (not @t15)))) % 0.14/0.36 (define @t17 () (@purify @t16)) % 0.14/0.36 (define @t18 () (@var "BOUND_VARIABLE_7485" tptp.a)) % 0.14/0.36 (define @t19 () (lambda (@list @t18) false)) % 0.14/0.36 (define @t20 () (@var "BOUND_VARIABLE_7443" (-> tptp.a Bool))) % 0.14/0.36 (define @t21 () (= @t20 @t19)) % 0.14/0.36 (define @t22 () (@list @t20)) % 0.14/0.36 (define @t23 () (lambda @t22 (ite @t21 true false))) % 0.14/0.36 (define @t24 () (@purify @t23)) % 0.14/0.36 (define @t25 () (= @t16 @t23)) % 0.14/0.36 (define @t26 () (not @t9)) % 0.14/0.36 (define @t27 () (@purify @t19)) % 0.14/0.36 (define @t28 () (@const 0 (-> tptp.a Bool))) % 0.14/0.36 (define @t29 () (= @t28 @t27)) % 0.14/0.36 (define @t30 () (forall @t3 (not (_ @t28 @t2)))) % 0.14/0.36 (define @t31 () (= (_ @t16 @t28) @t30)) % 0.14/0.36 (define @t32 () (_ @t17 @t28)) % 0.14/0.36 (define @t33 () (= @t19 @t28)) % 0.14/0.36 (define @t34 () (= @t28 @t19)) % 0.14/0.36 (define @t35 () (_ @t23 @t28)) % 0.14/0.36 (define @t36 () (_ @t24 @t28)) % 0.14/0.36 (define @t37 () (= @t36 @t32)) % 0.14/0.36 (define @t38 () (not @t37)) % 0.14/0.36 (define @t39 () (= @t24 @t17)) % 0.14/0.36 (define @t40 () (or @t39 @t38)) % 0.14/0.36 (define @t41 () (= @t30 @t29)) % 0.14/0.36 (define @t42 () (@list true)) % 0.14/0.36 (define @t43 () (@const 1 tptp.a)) % 0.14/0.36 (define @t44 () (_ @t28 @t43)) % 0.14/0.36 (define @t45 () (_ @t19 @t43)) % 0.14/0.36 (define @t46 () (_ @t27 @t43)) % 0.14/0.36 (define @t47 () (= @t44 @t46)) % 0.14/0.36 (define @t48 () (not @t47)) % 0.14/0.36 (define @t49 () (or @t29 @t48)) % 0.14/0.36 (define @t50 () (not @t30)) % 0.14/0.36 (define @t51 () (_ @t28 (@quantifiers_skolemize @t30 0))) % 0.14/0.36 (define @t52 () (not (not @t51))) % 0.14/0.36 (define @t53 () (=> @t29 (= @t51 false))) % 0.14/0.36 (assume @p1 @t14) % 0.14/0.36 (assume @p2 true) % 0.14/0.36 (step @p3 :rule eq-symm :args (@t17 @t24)) % 0.14/0.36 (step @p4 :rule eq-refl :args (@t23)) % 0.14/0.36 (step @p5 :rule refl :args (@t23)) % 0.14/0.36 (step @p6 :rule symm :premises (@p5)) % 0.14/0.36 (step @p7 :rule aci_norm :args ((= (or @t21 false) @t21))) % 0.14/0.36 (step @p8 :rule ite-then-true :args (@t21 false)) % 0.14/0.36 (step @p9 :rule trans :premises (@p8 @p7)) % 0.14/0.36 (step @p10 :rule symm :premises (@p9)) % 0.14/0.36 (step @p11 :rule eq-symm :args (@t19 @t20)) % 0.14/0.36 (step @p12 :rule trans :premises (@p11 @p10)) % 0.14/0.36 (step @p13 :rule cong :premises (@p12) :args ((lambda @t22 (= @t19 @t20)))) % 0.14/0.36 (step @p14 :rule trans :premises (@p13 @p6)) % 0.14/0.36 (step @p15 :rule eq-symm :args (@t20 @t19)) % 0.14/0.36 (step @p16 :rule trans :premises (@p8 @p7)) % 0.14/0.36 (step @p17 :rule trans :premises (@p16 @p15)) % 0.14/0.36 (step @p18 :rule cong :premises (@p17) :args (@t23)) % 0.14/0.36 (step @p19 :rule trans :premises (@p18 @p14)) % 0.14/0.36 (step @p20 :rule refl :args (@t23)) % 0.14/0.36 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t23 @t23))) % 0.14/0.36 (step @p22 :rule trans :premises (@p21 @p4)) % 0.14/0.36 (step @p23 :rule skolem_intro :args (@t24)) % 0.14/0.36 (step @p24 :rule cong :premises (@p20 @p23) :args ((= @t23 @t24))) % 0.14/0.36 (step @p25 :rule trans :premises (@p24 @p22)) % 0.14/0.36 (step @p26 :rule true_elim :premises (@p25)) % 0.14/0.36 (step @p27 :rule eq-refl :args (@t16)) % 0.14/0.36 (step @p28 :rule skolem_intro :args (@t17)) % 0.14/0.36 (step @p29 :rule refl :args (@t16)) % 0.14/0.36 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t16 @t17))) % 0.14/0.36 (step @p31 :rule trans :premises (@p30 @p27)) % 0.14/0.36 (step @p32 :rule true_elim :premises (@p31)) % 0.14/0.36 (step @p33 :rule cong :premises (@p32 @p26) :args (@t25)) % 0.14/0.36 (step @p34 :rule trans :premises (@p33 @p3)) % 0.14/0.36 (step @p35 :rule cong :premises (@p34) :args ((not @t25))) % 0.14/0.36 (step @p36 :rule cong :premises (@p10) :args ((lambda @t22 @t21))) % 0.14/0.36 (step @p37 :rule alpha_equiv :args ((lambda @t6 (= @t1 @t19)) (@list @t1) (@list @t20))) % 0.14/0.36 (step @p38 :rule trans :premises (@p37 @p36)) % 0.14/0.36 (step @p39 :rule trans :premises (@p38 @p6)) % 0.14/0.36 (step @p40 :rule eq-symm :args (@t19 @t1)) % 0.14/0.36 (step @p41 :rule refl :args (@t1)) % 0.14/0.36 (step @p42 :rule refl :args (@t19)) % 0.14/0.36 (step @p43 :rule symm :premises (@p42)) % 0.14/0.36 (step @p44 :rule alpha_equiv :args (@t4 (@list @t2) (@list @t18))) % 0.14/0.36 (step @p45 :rule trans :premises (@p44 @p43)) % 0.14/0.36 (step @p46 :rule cong :premises (@p45 @p41) :args (@t5)) % 0.14/0.36 (step @p47 :rule trans :premises (@p46 @p40)) % 0.14/0.36 (step @p48 :rule cong :premises (@p47) :args (@t7)) % 0.14/0.36 (step @p49 :rule trans :premises (@p48 @p39)) % 0.14/0.36 (step @p50 :rule refl :args (@t15)) % 0.14/0.36 (step @p51 :rule refl :args (@t9)) % 0.14/0.36 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t9 @t15))) % 0.14/0.36 (step @p53 :rule symm :premises (@p52)) % 0.14/0.36 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.14/0.36 (step @p55 :rule cong :premises (@p54) :args (@t26)) % 0.14/0.36 (step @p56 :rule cong :premises (@p55) :args ((forall @t3 @t26))) % 0.14/0.36 (step @p57 :rule bool-impl-false1 :args (@t9)) % 0.14/0.36 (step @p58 :rule cong :premises (@p57) :args (@t10)) % 0.14/0.36 (step @p59 :rule trans :premises (@p58 @p56)) % 0.14/0.36 (step @p60 :rule cong :premises (@p59) :args (@t12)) % 0.14/0.36 (step @p61 :rule cong :premises (@p60 @p49) :args (@t13)) % 0.14/0.36 (step @p62 :rule cong :premises (@p61) :args (@t14)) % 0.14/0.36 (step @p63 :rule trans :premises (@p62 @p35)) % 0.14/0.36 (step @p64 :rule eq_resolve :premises (@p1 @p63)) % 0.14/0.36 (step @p65 :rule eq-symm :args (@t29 @t30)) % 0.14/0.36 (step @p66 :rule eq-refl :args (@t30)) % 0.14/0.36 (step @p67 :rule refl :args (@t30)) % 0.14/0.36 (step @p68 :rule beta-reduce :args (@t31)) % 0.14/0.36 (step @p69 :rule cong :premises (@p68 @p67) :args (@t31)) % 0.14/0.36 (step @p70 :rule trans :premises (@p69 @p66)) % 0.14/0.36 (step @p71 :rule refl :args (@t28)) % 0.14/0.36 (step @p72 :rule ho_cong :premises (@p28 @p71)) % 0.14/0.36 (step @p73 :rule cong :premises (@p72 @p67) :args ((= @t32 @t30))) % 0.14/0.36 (step @p74 :rule trans :premises (@p73 @p70)) % 0.14/0.36 (step @p75 :rule true_elim :premises (@p74)) % 0.14/0.36 (step @p76 :rule eq-symm :args (@t27 @t28)) % 0.14/0.36 (step @p77 :rule eq-refl :args (@t19)) % 0.14/0.36 (step @p78 :rule refl :args (@t19)) % 0.14/0.36 (step @p79 :rule cong :premises (@p78 @p43) :args ((= @t19 @t19))) % 0.14/0.36 (step @p80 :rule trans :premises (@p79 @p77)) % 0.14/0.36 (step @p81 :rule skolem_intro :args (@t27)) % 0.14/0.36 (step @p82 :rule cong :premises (@p78 @p81) :args ((= @t19 @t27))) % 0.14/0.36 (step @p83 :rule trans :premises (@p82 @p80)) % 0.14/0.36 (step @p84 :rule true_elim :premises (@p83)) % 0.14/0.36 (step @p85 :rule cong :premises (@p84 @p71) :args (@t33)) % 0.14/0.36 (step @p86 :rule trans :premises (@p85 @p76)) % 0.14/0.36 (step @p87 :rule eq-refl :args (@t33)) % 0.14/0.36 (step @p88 :rule refl :args (@t33)) % 0.14/0.36 (step @p89 :rule eq-symm :args (@t28 @t19)) % 0.14/0.36 (step @p90 :rule aci_norm :args ((= (or @t34 false) @t34))) % 0.14/0.36 (step @p91 :rule ite-then-true :args (@t34 false)) % 0.14/0.36 (step @p92 :rule trans :premises (@p91 @p90)) % 0.14/0.36 (step @p93 :rule trans :premises (@p92 @p89)) % 0.14/0.36 (step @p94 :rule beta-reduce :args ((= @t35 (ite @t34 true false)))) % 0.14/0.36 (step @p95 :rule trans :premises (@p94 @p93)) % 0.14/0.36 (step @p96 :rule cong :premises (@p95 @p88) :args ((= @t35 @t33))) % 0.14/0.36 (step @p97 :rule trans :premises (@p96 @p87)) % 0.14/0.36 (step @p98 :rule ho_cong :premises (@p23 @p71)) % 0.14/0.36 (step @p99 :rule cong :premises (@p98 @p88) :args ((= @t36 @t33))) % 0.14/0.36 (step @p100 :rule trans :premises (@p99 @p97)) % 0.14/0.36 (step @p101 :rule true_elim :premises (@p100)) % 0.14/0.36 (step @p102 :rule trans :premises (@p101 @p86)) % 0.14/0.36 (step @p103 :rule cong :premises (@p102 @p75) :args (@t37)) % 0.14/0.36 (step @p104 :rule trans :premises (@p103 @p65)) % 0.14/0.36 (step @p105 :rule cong :premises (@p104) :args (@t38)) % 0.14/0.36 (step @p106 :rule refl :args (@t39)) % 0.14/0.36 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t40)) % 0.14/0.36 ; WARNING: add trust step for TRUST % 0.14/0.36 ; trust TRUST THEORY_LEMMA % 0.14/0.36 (step @p108 :rule trust :premises () :args (@t40)) % 0.14/0.36 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.14/0.36 (step @p110 :rule chain_m_resolution :premises (@p109 @p64) :args ((not @t41) @t42 (@list @t39))) % 0.14/0.36 (step @p111 :rule cnf_equiv_neg2 :args (@t41)) % 0.14/0.36 (step @p112 :rule bool-double-not-elim :args (@t44)) % 0.14/0.36 (step @p113 :rule bool-eq-false :args (@t44)) % 0.14/0.36 (step @p114 :rule evaluate :args ((not false))) % 0.14/0.36 (step @p115 :rule beta-reduce :args ((= @t45 false))) % 0.14/0.36 (step @p116 :rule cong :premises (@p115) :args ((not @t45))) % 0.14/0.36 (step @p117 :rule trans :premises (@p116 @p114)) % 0.14/0.36 (step @p118 :rule refl :args (@t43)) % 0.14/0.36 (step @p119 :rule ho_cong :premises (@p81 @p118)) % 0.14/0.36 (step @p120 :rule cong :premises (@p119) :args ((not @t46))) % 0.14/0.36 (step @p121 :rule bool-eq-false :args (@t46)) % 0.14/0.36 (step @p122 :rule trans :premises (@p121 @p120 @p117)) % 0.14/0.36 (step @p123 :rule true_elim :premises (@p122)) % 0.14/0.36 (step @p124 :rule refl :args (@t44)) % 0.14/0.36 (step @p125 :rule cong :premises (@p124 @p123) :args (@t47)) % 0.14/0.36 (step @p126 :rule trans :premises (@p125 @p113)) % 0.14/0.36 (step @p127 :rule cong :premises (@p126) :args (@t48)) % 0.14/0.36 (step @p128 :rule trans :premises (@p127 @p112)) % 0.14/0.36 (step @p129 :rule refl :args (@t29)) % 0.14/0.36 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t49)) % 0.14/0.36 ; trust TRUST THEORY_LEMMA % 0.14/0.36 (step @p131 :rule trust :premises () :args (@t49)) % 0.14/0.36 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.14/0.36 (assume-push @p162 @t30) % 0.14/0.36 (step @p134 :rule instantiate :premises (@p162) :args ((@list @t43))) % 0.14/0.36 (step-pop @p163 :rule scope :premises (@p134)) % 0.14/0.36 (step @p135 :rule process_scope :premises (@p163) :args ((not @t44))) % 0.14/0.36 (step @p137 :rule implies_elim :premises (@p135)) % 0.14/0.36 (step @p138 :rule chain_m_resolution :premises (@p137 @p132 @p111 @p110) :args (@t50 (@list false true true) (@list @t44 @t29 @t41))) % 0.14/0.36 (step @p139 :rule cnf_equiv_neg1 :args (@t41)) % 0.14/0.36 (step @p140 :rule reordering :premises (@p139) :args ((or @t30 @t29 @t41))) % 0.14/0.36 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p110) :args (@t29 (@list true true) (@list @t30 @t41))) % 0.14/0.36 (step @p142 :rule refl :args (@t51)) % 0.14/0.36 (step @p143 :rule bool-double-not-elim :args (@t30)) % 0.14/0.36 (step @p144 :rule nary_cong :premises (@p143 @p142) :args ((or (not @t50) @t51))) % 0.14/0.36 (step @p145 :rule bool-double-not-elim :args (@t51)) % 0.14/0.36 (step @p146 :rule refl :args (@t50)) % 0.14/0.36 (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t50 @t52))) % 0.14/0.36 (assume-push @p164 @t50) % 0.14/0.36 (step @p149 :rule skolemize :premises (@p164)) % 0.14/0.36 (step-pop @p165 :rule scope :premises (@p149)) % 0.14/0.36 (step @p150 :rule process_scope :premises (@p165) :args (@t52)) % 0.14/0.36 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 0.14/0.36 (step @p153 :rule implies_elim :premises (@p152)) % 0.14/0.36 (step @p154 :rule eq_resolve :premises (@p153 @p144)) % 0.14/0.36 (step @p155 :rule chain_m_resolution :premises (@p154 @p138) :args (@t51 @t42 (@list @t30))) % 0.14/0.36 (step @p156 :rule bool-eq-false :args (@t51)) % 0.14/0.36 (step @p157 :rule cong :premises (@p129 @p156) :args (@t53)) % 0.14/0.36 ; trust TRUST THEORY_LEMMA % 0.14/0.36 (step @p158 :rule trust :premises () :args (@t53)) % 0.14/0.36 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.14/0.36 (step @p160 :rule implies_elim :premises (@p159)) % 0.14/0.36 (step @p161 false :rule chain_m_resolution :premises (@p160 @p155 @p141) :args (false (@list false false) (@list @t51 @t29))) % 0.14/0.36 ) % 0.14/0.36 % SZS output end Proof % 0.14/0.36 % cvc5 exiting %------------------------------------------------------------------------------