%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO237^5 : 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 : n026.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 09:12:17 AM UTC 2026 % Result : Theorem 0.31s 0.56s % Output : Proof 0.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO237^5 : TPTP v9.2.1. Released v4.0.0. % 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n026.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 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:01:40 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.31/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.56 % SZS status Theorem % 0.31/0.56 % SZS output start Proof % 0.31/0.56 ( % 0.31/0.56 (declare-sort $$unsorted 0) % 0.31/0.56 (declare-const tptp.f (-> $$unsorted $$unsorted)) % 0.31/0.56 (declare-const tptp.q (-> $$unsorted Bool)) % 0.31/0.56 (declare-const tptp.x $$unsorted) % 0.31/0.56 (declare-const tptp.p (-> (-> $$unsorted $$unsorted) Bool)) % 0.31/0.56 (declare-const tptp.g (-> $$unsorted $$unsorted)) % 0.31/0.56 (define @t1 () (@var "Xx0" $$unsorted)) % 0.31/0.56 (define @t2 () (_ tptp.g @t1)) % 0.31/0.56 (define @t3 () (@list @t1)) % 0.31/0.56 (define @t4 () (lambda @t3 @t2)) % 0.31/0.56 (define @t5 () (_ tptp.q tptp.x)) % 0.31/0.56 (define @t6 () (=> @t5 (_ tptp.p @t4))) % 0.31/0.56 (define @t7 () (_ tptp.f @t1)) % 0.31/0.56 (define @t8 () (lambda @t3 @t7)) % 0.31/0.56 (define @t9 () (=> (_ tptp.p @t8) @t6)) % 0.31/0.56 (define @t10 () (= @t7 @t2)) % 0.31/0.56 (define @t11 () (forall @t3 @t10)) % 0.31/0.56 (define @t12 () (=> @t11 @t9)) % 0.31/0.56 (define @t13 () (not @t12)) % 0.31/0.56 (define @t14 () (@purify @t4)) % 0.31/0.56 (define @t15 () (tptp.p @t14)) % 0.31/0.56 (define @t16 () (_ tptp.p @t14)) % 0.31/0.56 (define @t17 () (tptp.q tptp.x)) % 0.31/0.56 (define @t18 () (@purify @t8)) % 0.31/0.56 (define @t19 () (tptp.p @t18)) % 0.31/0.56 (define @t20 () (_ tptp.p @t18)) % 0.31/0.56 (define @t21 () (tptp.g @t1)) % 0.31/0.56 (define @t22 () (tptp.f @t1)) % 0.31/0.56 (define @t23 () (forall @t3 (= @t22 @t21))) % 0.31/0.56 (define @t24 () (=> @t23 @t9)) % 0.31/0.56 (define @t25 () (_ @t18 @t1)) % 0.31/0.56 (define @t26 () (= @t7 @t25)) % 0.31/0.56 (define @t27 () (_ @t8 @t1)) % 0.31/0.56 (define @t28 () (= @t25 @t27)) % 0.31/0.56 (define @t29 () (forall @t3 @t28)) % 0.31/0.56 (define @t30 () (@const 0 $$unsorted)) % 0.31/0.56 (define @t31 () (tptp.f @t30)) % 0.31/0.56 (define @t32 () (_ @t18 @t30)) % 0.31/0.56 (define @t33 () (forall @t3 (= @t22 @t25))) % 0.31/0.56 (define @t34 () (= @t31 @t32)) % 0.31/0.56 (define @t35 () (@list @t30)) % 0.31/0.56 (define @t36 () (= @t32 @t31)) % 0.31/0.56 (define @t37 () (@list false)) % 0.31/0.56 (define @t38 () (_ @t14 @t1)) % 0.31/0.56 (define @t39 () (= @t2 @t38)) % 0.31/0.56 (define @t40 () (_ @t4 @t1)) % 0.31/0.56 (define @t41 () (= @t38 @t40)) % 0.31/0.56 (define @t42 () (forall @t3 @t41)) % 0.31/0.56 (define @t43 () (tptp.g @t30)) % 0.31/0.56 (define @t44 () (_ @t14 @t30)) % 0.31/0.56 (define @t45 () (forall @t3 (= @t21 @t38))) % 0.31/0.56 (define @t46 () (= @t43 @t44)) % 0.31/0.56 (define @t47 () (= @t44 @t43)) % 0.31/0.56 (define @t48 () (= @t14 @t18)) % 0.31/0.56 (define @t49 () (not @t48)) % 0.31/0.56 (define @t50 () (not @t19)) % 0.31/0.56 (define @t51 () (not @t15)) % 0.31/0.56 (define @t52 () (and @t51 @t48 @t19)) % 0.31/0.56 (define @t53 () (@list true false)) % 0.31/0.56 (define @t54 () (= @t44 @t32)) % 0.31/0.56 (define @t55 () (not @t54)) % 0.31/0.56 (define @t56 () (= @t43 @t31)) % 0.31/0.56 (define @t57 () (not @t56)) % 0.31/0.56 (define @t58 () (not @t36)) % 0.31/0.56 (define @t59 () (not @t47)) % 0.31/0.56 (define @t60 () (and @t55 @t47 @t36)) % 0.31/0.56 (define @t61 () (= @t31 @t43)) % 0.31/0.56 (assume @p1 @t13) % 0.31/0.56 (assume @p2 true) % 0.31/0.56 (step @p3 :rule refl :args (@t15)) % 0.31/0.56 (step @p4 :rule refl :args (@t16)) % 0.31/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t16 @t15))) % 0.31/0.56 (step @p6 :rule symm :premises (@p5)) % 0.31/0.56 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.31/0.56 (step @p8 :rule eq-refl :args (@t4)) % 0.31/0.56 (step @p9 :rule skolem_intro :args (@t14)) % 0.31/0.56 (step @p10 :rule refl :args (@t4)) % 0.31/0.56 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t4 @t14))) % 0.31/0.56 (step @p12 :rule trans :premises (@p11 @p8)) % 0.31/0.56 (step @p13 :rule true_elim :premises (@p12)) % 0.31/0.56 (step @p14 :rule refl :args (tptp.p)) % 0.31/0.56 (step @p15 :rule ho_cong :premises (@p14 @p13)) % 0.31/0.56 (step @p16 :rule trans :premises (@p15 @p7)) % 0.31/0.56 (step @p17 :rule refl :args (@t17)) % 0.31/0.56 (step @p18 :rule refl :args (@t5)) % 0.31/0.56 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t5 @t17))) % 0.31/0.56 (step @p20 :rule symm :premises (@p19)) % 0.31/0.56 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.31/0.56 (step @p22 :rule cong :premises (@p21 @p16) :args (@t6)) % 0.31/0.56 (step @p23 :rule refl :args (@t19)) % 0.31/0.56 (step @p24 :rule refl :args (@t20)) % 0.31/0.56 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t20 @t19))) % 0.31/0.56 (step @p26 :rule symm :premises (@p25)) % 0.31/0.56 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.31/0.56 (step @p28 :rule eq-refl :args (@t8)) % 0.31/0.56 (step @p29 :rule skolem_intro :args (@t18)) % 0.31/0.56 (step @p30 :rule refl :args (@t8)) % 0.31/0.56 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t8 @t18))) % 0.31/0.56 (step @p32 :rule trans :premises (@p31 @p28)) % 0.31/0.56 (step @p33 :rule true_elim :premises (@p32)) % 0.31/0.56 (step @p34 :rule ho_cong :premises (@p14 @p33)) % 0.31/0.56 (step @p35 :rule trans :premises (@p34 @p27)) % 0.31/0.56 (step @p36 :rule cong :premises (@p35 @p22) :args (@t9)) % 0.31/0.56 (step @p37 :rule refl :args (@t23)) % 0.31/0.56 (step @p38 :rule cong :premises (@p37 @p36) :args (@t24)) % 0.31/0.56 (step @p39 :rule cong :premises (@p38) :args ((not @t24))) % 0.31/0.56 (step @p40 :rule refl :args (@t9)) % 0.31/0.56 (step @p41 :rule refl :args (@t21)) % 0.31/0.56 (step @p42 :rule refl :args (@t2)) % 0.31/0.56 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t2 @t21))) % 0.31/0.56 (step @p44 :rule symm :premises (@p43)) % 0.31/0.56 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.31/0.56 (step @p46 :rule refl :args (@t22)) % 0.31/0.56 (step @p47 :rule refl :args (@t7)) % 0.31/0.56 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t7 @t22))) % 0.31/0.56 (step @p49 :rule symm :premises (@p48)) % 0.31/0.56 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.31/0.56 (step @p51 :rule cong :premises (@p50 @p45) :args (@t10)) % 0.31/0.56 (step @p52 :rule cong :premises (@p51) :args (@t11)) % 0.31/0.56 (step @p53 :rule cong :premises (@p52 @p40) :args (@t12)) % 0.31/0.56 (step @p54 :rule cong :premises (@p53) :args (@t13)) % 0.31/0.56 (step @p55 :rule trans :premises (@p54 @p39)) % 0.31/0.56 (step @p56 :rule eq_resolve :premises (@p1 @p55)) % 0.31/0.56 (step @p57 :rule not_implies_elim1 :premises (@p56)) % 0.31/0.56 (step @p58 :rule refl :args (@t25)) % 0.31/0.56 (step @p59 :rule cong :premises (@p50 @p58) :args (@t26)) % 0.31/0.56 (step @p60 :rule cong :premises (@p59) :args ((forall @t3 @t26))) % 0.31/0.56 (step @p61 :rule eq-symm :args (@t25 @t7)) % 0.31/0.56 (step @p62 :rule beta-reduce :args ((= @t27 @t7))) % 0.31/0.56 (step @p63 :rule refl :args (@t25)) % 0.31/0.56 (step @p64 :rule cong :premises (@p63 @p62) :args (@t28)) % 0.31/0.56 (step @p65 :rule trans :premises (@p64 @p61)) % 0.31/0.56 (step @p66 :rule cong :premises (@p65) :args (@t29)) % 0.31/0.56 (step @p67 :rule trans :premises (@p66 @p60)) % 0.31/0.56 (step @p68 :rule quant-unused-vars :args ((= (forall @t3 true) true))) % 0.31/0.56 (step @p69 :rule eq-refl :args (@t27)) % 0.31/0.56 (step @p70 :rule cong :premises (@p69) :args ((forall @t3 (= @t27 @t27)))) % 0.31/0.56 (step @p71 :rule trans :premises (@p70 @p68)) % 0.31/0.56 (step @p72 :rule refl :args (@t27)) % 0.31/0.56 (step @p73 :rule refl :args (@t1)) % 0.31/0.56 (step @p74 :rule ho_cong :premises (@p29 @p73)) % 0.31/0.56 (step @p75 :rule cong :premises (@p74 @p72) :args (@t28)) % 0.31/0.56 (step @p76 :rule cong :premises (@p75) :args (@t29)) % 0.31/0.56 (step @p77 :rule trans :premises (@p76 @p71)) % 0.31/0.56 (step @p78 :rule true_elim :premises (@p77)) % 0.31/0.56 (step @p79 :rule eq_resolve :premises (@p78 @p67)) % 0.31/0.56 (step @p80 :rule eq-symm :args (@t31 @t32)) % 0.31/0.56 (step @p81 :rule refl :args (@t33)) % 0.31/0.56 (step @p82 :rule cong :premises (@p81 @p80) :args ((=> @t33 @t34))) % 0.31/0.56 (assume-push @p198 @t33) % 0.31/0.56 (step @p84 :rule instantiate :premises (@p79) :args (@t35)) % 0.31/0.56 (step-pop @p199 :rule scope :premises (@p84)) % 0.31/0.56 (step @p85 :rule process_scope :premises (@p199) :args (@t34)) % 0.31/0.56 (step @p87 :rule eq_resolve :premises (@p85 @p82)) % 0.31/0.56 (step @p88 :rule implies_elim :premises (@p87)) % 0.31/0.56 (step @p89 :rule chain_m_resolution :premises (@p88 @p79) :args (@t36 @t37 (@list @t33))) % 0.31/0.56 (step @p90 :rule refl :args (@t38)) % 0.31/0.56 (step @p91 :rule cong :premises (@p45 @p90) :args (@t39)) % 0.31/0.56 (step @p92 :rule cong :premises (@p91) :args ((forall @t3 @t39))) % 0.31/0.56 (step @p93 :rule eq-symm :args (@t38 @t2)) % 0.31/0.56 (step @p94 :rule beta-reduce :args ((= @t40 @t2))) % 0.31/0.56 (step @p95 :rule refl :args (@t38)) % 0.31/0.56 (step @p96 :rule cong :premises (@p95 @p94) :args (@t41)) % 0.31/0.56 (step @p97 :rule trans :premises (@p96 @p93)) % 0.31/0.56 (step @p98 :rule cong :premises (@p97) :args (@t42)) % 0.31/0.56 (step @p99 :rule trans :premises (@p98 @p92)) % 0.31/0.56 (step @p100 :rule eq-refl :args (@t40)) % 0.31/0.56 (step @p101 :rule cong :premises (@p100) :args ((forall @t3 (= @t40 @t40)))) % 0.31/0.56 (step @p102 :rule trans :premises (@p101 @p68)) % 0.31/0.56 (step @p103 :rule refl :args (@t40)) % 0.31/0.56 (step @p104 :rule ho_cong :premises (@p9 @p73)) % 0.31/0.56 (step @p105 :rule cong :premises (@p104 @p103) :args (@t41)) % 0.31/0.56 (step @p106 :rule cong :premises (@p105) :args (@t42)) % 0.31/0.56 (step @p107 :rule trans :premises (@p106 @p102)) % 0.31/0.56 (step @p108 :rule true_elim :premises (@p107)) % 0.31/0.56 (step @p109 :rule eq_resolve :premises (@p108 @p99)) % 0.31/0.56 (step @p110 :rule eq-symm :args (@t43 @t44)) % 0.31/0.56 (step @p111 :rule refl :args (@t45)) % 0.31/0.56 (step @p112 :rule cong :premises (@p111 @p110) :args ((=> @t45 @t46))) % 0.31/0.56 (assume-push @p200 @t45) % 0.31/0.56 (step @p114 :rule instantiate :premises (@p109) :args (@t35)) % 0.31/0.56 (step-pop @p201 :rule scope :premises (@p114)) % 0.31/0.56 (step @p115 :rule process_scope :premises (@p201) :args (@t46)) % 0.31/0.56 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 0.31/0.56 (step @p118 :rule implies_elim :premises (@p117)) % 0.31/0.56 (step @p119 :rule chain_m_resolution :premises (@p118 @p109) :args (@t47 @t37 (@list @t45))) % 0.31/0.56 (step @p120 :rule not_implies_elim2 :premises (@p56)) % 0.31/0.56 (step @p121 :rule not_implies_elim1 :premises (@p120)) % 0.31/0.56 (step @p122 :rule not_implies_elim2 :premises (@p120)) % 0.31/0.56 (step @p123 :rule not_implies_elim2 :premises (@p122)) % 0.31/0.56 (step @p124 :rule refl :args (@t49)) % 0.31/0.56 (step @p125 :rule bool-double-not-elim :args (@t15)) % 0.31/0.56 (step @p126 :rule refl :args (@t50)) % 0.31/0.56 (step @p127 :rule nary_cong :premises (@p126 @p125 @p124) :args ((or @t50 (not @t51) @t49))) % 0.31/0.56 (assume-push @p202 @t51) % 0.31/0.56 (assume-push @p203 @t48) % 0.31/0.56 (assume-push @p204 @t19) % 0.31/0.56 (step @p131 :rule evaluate :args ((= true false))) % 0.31/0.56 (step @p132 :rule false_intro :premises (@p123)) % 0.31/0.56 (step @p133 :rule symm :premises (@p203)) % 0.31/0.56 (step @p134 :rule cong :premises (@p133) :args (@t19)) % 0.31/0.56 (step @p135 :rule true_intro :premises (@p121)) % 0.31/0.56 (step @p136 :rule symm :premises (@p135)) % 0.31/0.56 (step @p137 :rule trans :premises (@p136 @p134 @p132)) % 0.31/0.56 (step @p138 false :rule eq_resolve :premises (@p137 @p131)) % 0.31/0.56 (step-pop @p205 :rule scope :premises (@p138)) % 0.31/0.56 (step-pop @p206 :rule scope :premises (@p205)) % 0.31/0.56 (step-pop @p207 :rule scope :premises (@p206)) % 0.31/0.56 (step @p139 :rule process_scope :premises (@p207) :args (false)) % 0.31/0.56 (assume-push @p208 @t19) % 0.31/0.56 (assume-push @p209 @t51) % 0.31/0.56 (assume-push @p210 @t48) % 0.31/0.56 (step @p146 :rule and_intro :premises (@p123 @p210 @p121)) % 0.31/0.56 (step-pop @p211 :rule scope :premises (@p146)) % 0.31/0.56 (step-pop @p212 :rule scope :premises (@p211)) % 0.31/0.56 (step-pop @p213 :rule scope :premises (@p212)) % 0.31/0.56 (step @p147 :rule process_scope :premises (@p213) :args (@t52)) % 0.31/0.56 (step @p151 :rule implies_elim :premises (@p147)) % 0.31/0.56 (step @p152 :rule resolution :premises (@p151 @p139) :args (true @t52)) % 0.31/0.56 (step @p153 :rule not_and :premises (@p152)) % 0.31/0.56 (step @p154 :rule eq_resolve :premises (@p153 @p127)) % 0.31/0.56 (step @p155 :rule reordering :premises (@p154) :args ((or @t15 @t50 @t49))) % 0.31/0.56 (step @p156 :rule chain_m_resolution :premises (@p155 @p123 @p121) :args (@t49 @t53 (@list @t15 @t19))) % 0.31/0.56 ; WARNING: add trust step for TRUST % 0.31/0.56 ; trust TRUST THEORY_LEMMA % 0.31/0.56 (step @p157 :rule trust :premises () :args ((or @t48 @t55))) % 0.31/0.56 (step @p158 :rule chain_m_resolution :premises (@p157 @p156) :args (@t55 (@list true) (@list @t48))) % 0.31/0.56 (step @p159 :rule refl :args (@t57)) % 0.31/0.56 (step @p160 :rule refl :args (@t58)) % 0.31/0.56 (step @p161 :rule refl :args (@t59)) % 0.31/0.56 (step @p162 :rule bool-double-not-elim :args (@t54)) % 0.31/0.56 (step @p163 :rule nary_cong :premises (@p162 @p161 @p160 @p159) :args ((or (not @t55) @t59 @t58 @t57))) % 0.31/0.56 (assume-push @p214 @t55) % 0.31/0.56 (assume-push @p215 @t47) % 0.31/0.56 (assume-push @p216 @t36) % 0.31/0.56 (assume-push @p217 @t47) % 0.31/0.56 (assume-push @p218 @t55) % 0.31/0.56 (assume-push @p219 @t36) % 0.31/0.56 (step @p170 :rule false_intro :premises (@p214)) % 0.31/0.56 (step @p84 :rule instantiate :premises (@p79) :args (@t35)) % 0.31/0.56 (step @p114 :rule instantiate :premises (@p109) :args (@t35)) % 0.31/0.56 (step @p171 :rule cong :premises (@p114 @p84) :args (@t56)) % 0.31/0.56 (step @p172 :rule trans :premises (@p171 @p170)) % 0.31/0.56 (step @p173 :rule false_elim :premises (@p172)) % 0.31/0.56 (step-pop @p220 :rule scope :premises (@p173)) % 0.31/0.56 (step-pop @p221 :rule scope :premises (@p220)) % 0.31/0.56 (step-pop @p222 :rule scope :premises (@p221)) % 0.31/0.56 (step @p174 :rule process_scope :premises (@p222) :args (@t57)) % 0.31/0.56 (step @p178 :rule and_intro :premises (@p119 @p214 @p89)) % 0.31/0.56 (step @p179 :rule modus_ponens :premises (@p178 @p174)) % 0.31/0.56 (step-pop @p223 :rule scope :premises (@p179)) % 0.31/0.56 (step-pop @p224 :rule scope :premises (@p223)) % 0.31/0.56 (step-pop @p225 :rule scope :premises (@p224)) % 0.31/0.56 (step @p180 :rule process_scope :premises (@p225) :args (@t57)) % 0.31/0.56 (step @p184 :rule implies_elim :premises (@p180)) % 0.31/0.56 (step @p185 :rule cnf_and_neg :args (@t60)) % 0.31/0.56 (step @p186 :rule resolution :premises (@p185 @p184) :args (true @t60)) % 0.31/0.56 (step @p187 :rule eq_resolve :premises (@p186 @p163)) % 0.31/0.56 (step @p188 :rule chain_m_resolution :premises (@p187 @p158 @p119 @p89) :args (@t57 (@list true false false) (@list @t54 @t47 @t36))) % 0.31/0.56 (step @p189 :rule eq-symm :args (@t31 @t43)) % 0.31/0.56 (step @p190 :rule cong :premises (@p37 @p189) :args ((=> @t23 @t61))) % 0.31/0.56 (assume-push @p226 @t23) % 0.31/0.56 (step @p192 :rule instantiate :premises (@p57) :args (@t35)) % 0.31/0.56 (step-pop @p227 :rule scope :premises (@p192)) % 0.31/0.56 (step @p193 :rule process_scope :premises (@p227) :args (@t61)) % 0.31/0.56 (step @p195 :rule eq_resolve :premises (@p193 @p190)) % 0.31/0.56 (step @p196 :rule implies_elim :premises (@p195)) % 0.31/0.56 (step @p197 false :rule chain_m_resolution :premises (@p196 @p188 @p57) :args (false @t53 (@list @t56 @t23))) % 0.31/0.56 ) % 0.31/0.56 % SZS output end Proof % 0.31/0.56 % cvc5 exiting %------------------------------------------------------------------------------