%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO549^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n001.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 09:13:06 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO549^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n001.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 00:21:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.26/0.50 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-const tptp.p (-> (-> Bool Bool) (-> Bool Bool) Bool)) % 0.38/0.58 (declare-const tptp.f (-> Bool Bool)) % 0.38/0.58 (declare-const tptp.g (-> Bool Bool)) % 0.38/0.58 (define @t1 () (@var "X" Bool)) % 0.38/0.58 (define @t2 () (not (not @t1))) % 0.38/0.58 (define @t3 () (@list @t1)) % 0.38/0.58 (define @t4 () (lambda @t3 (_ tptp.f @t2))) % 0.38/0.58 (define @t5 () (lambda @t3 (_ tptp.g @t2))) % 0.38/0.58 (define @t6 () (_ tptp.p tptp.f)) % 0.38/0.58 (define @t7 () (not (_ @t6 @t5))) % 0.38/0.58 (define @t8 () (tptp.f @t1)) % 0.38/0.58 (define @t9 () (_ tptp.f @t1)) % 0.38/0.58 (define @t10 () (lambda @t3 @t9)) % 0.38/0.58 (define @t11 () (@purify @t10)) % 0.38/0.58 (define @t12 () (_ @t11 @t1)) % 0.38/0.58 (define @t13 () (= @t9 @t12)) % 0.38/0.58 (define @t14 () (_ @t10 @t1)) % 0.38/0.58 (define @t15 () (= @t12 @t14)) % 0.38/0.58 (define @t16 () (forall @t3 @t15)) % 0.38/0.58 (define @t17 () (tptp.g @t1)) % 0.38/0.58 (define @t18 () (_ tptp.g @t1)) % 0.38/0.58 (define @t19 () (lambda @t3 @t18)) % 0.38/0.58 (define @t20 () (@purify @t19)) % 0.38/0.58 (define @t21 () (_ @t20 @t1)) % 0.38/0.58 (define @t22 () (= @t18 @t21)) % 0.38/0.58 (define @t23 () (_ @t19 @t1)) % 0.38/0.58 (define @t24 () (= @t21 @t23)) % 0.38/0.58 (define @t25 () (forall @t3 @t24)) % 0.38/0.58 (define @t26 () (@const 0 Bool)) % 0.38/0.58 (define @t27 () (@purify @t26)) % 0.38/0.58 (define @t28 () (tptp.g @t27)) % 0.38/0.58 (define @t29 () (_ @t20 @t27)) % 0.38/0.58 (define @t30 () (_ @t20 @t26)) % 0.38/0.58 (define @t31 () (tptp.g @t26)) % 0.38/0.58 (define @t32 () (= @t31 @t30)) % 0.38/0.58 (define @t33 () (not @t32)) % 0.38/0.58 (define @t34 () (= tptp.g @t20)) % 0.38/0.58 (define @t35 () (or @t34 @t33)) % 0.38/0.58 (define @t36 () (tptp.p @t11 tptp.g)) % 0.38/0.58 (define @t37 () (_ (_ tptp.p @t11) tptp.g)) % 0.38/0.58 (define @t38 () (tptp.p tptp.f @t20)) % 0.38/0.58 (define @t39 () (_ @t6 @t20)) % 0.38/0.58 (define @t40 () (= tptp.f @t11)) % 0.38/0.58 (define @t41 () (not @t40)) % 0.38/0.58 (define @t42 () (not @t34)) % 0.38/0.58 (define @t43 () (not @t36)) % 0.38/0.58 (define @t44 () (not @t38)) % 0.38/0.58 (define @t45 () (and @t36 @t40 @t34 @t44)) % 0.38/0.58 (define @t46 () (@const 1 Bool)) % 0.38/0.58 (define @t47 () (@purify @t46)) % 0.38/0.58 (define @t48 () (tptp.f @t47)) % 0.38/0.58 (define @t49 () (_ @t11 @t47)) % 0.38/0.58 (define @t50 () (_ @t11 @t46)) % 0.38/0.58 (define @t51 () (tptp.f @t46)) % 0.38/0.58 (define @t52 () (= @t51 @t50)) % 0.38/0.58 (define @t53 () (not @t52)) % 0.38/0.58 (define @t54 () (or @t40 @t53)) % 0.38/0.58 (define @t55 () (= @t49 @t48)) % 0.38/0.58 (define @t56 () (forall @t3 (= @t12 @t8))) % 0.38/0.58 (assume @p1 (_ (_ tptp.p @t4) tptp.g)) % 0.38/0.58 (assume @p2 @t7) % 0.38/0.58 (assume @p3 true) % 0.38/0.58 (step @p4 :rule eq-symm :args (@t8 @t12)) % 0.38/0.58 (step @p5 :rule cong :premises (@p4) :args ((forall @t3 (= @t8 @t12)))) % 0.38/0.58 (step @p6 :rule refl :args (@t12)) % 0.38/0.58 (step @p7 :rule refl :args (@t8)) % 0.38/0.58 (step @p8 :rule refl :args (@t9)) % 0.38/0.58 (step @p9 :rule cong :premises (@p8 @p7) :args ((= @t9 @t8))) % 0.38/0.58 (step @p10 :rule symm :premises (@p9)) % 0.38/0.58 (step @p11 :rule eq_resolve :premises (@p8 @p10)) % 0.38/0.58 (step @p12 :rule cong :premises (@p11 @p6) :args (@t13)) % 0.38/0.58 (step @p13 :rule cong :premises (@p12) :args ((forall @t3 @t13))) % 0.38/0.58 (step @p14 :rule trans :premises (@p13 @p5)) % 0.38/0.58 (step @p15 :rule eq-symm :args (@t12 @t9)) % 0.38/0.58 (step @p16 :rule beta-reduce :args ((= @t14 @t9))) % 0.38/0.58 (step @p17 :rule refl :args (@t12)) % 0.38/0.58 (step @p18 :rule cong :premises (@p17 @p16) :args (@t15)) % 0.38/0.58 (step @p19 :rule trans :premises (@p18 @p15)) % 0.38/0.58 (step @p20 :rule cong :premises (@p19) :args (@t16)) % 0.38/0.58 (step @p21 :rule trans :premises (@p20 @p14)) % 0.38/0.58 (step @p22 :rule quant-unused-vars :args ((= (forall @t3 true) true))) % 0.38/0.58 (step @p23 :rule eq-refl :args (@t14)) % 0.38/0.58 (step @p24 :rule cong :premises (@p23) :args ((forall @t3 (= @t14 @t14)))) % 0.38/0.58 (step @p25 :rule trans :premises (@p24 @p22)) % 0.38/0.58 (step @p26 :rule refl :args (@t14)) % 0.38/0.58 (step @p27 :rule refl :args (@t1)) % 0.38/0.58 (step @p28 :rule skolem_intro :args (@t11)) % 0.38/0.58 (step @p29 :rule ho_cong :premises (@p28 @p27)) % 0.38/0.58 (step @p30 :rule cong :premises (@p29 @p26) :args (@t15)) % 0.38/0.58 (step @p31 :rule cong :premises (@p30) :args (@t16)) % 0.38/0.58 (step @p32 :rule trans :premises (@p31 @p25)) % 0.38/0.58 (step @p33 :rule true_elim :premises (@p32)) % 0.38/0.58 (step @p34 :rule eq_resolve :premises (@p33 @p21)) % 0.38/0.58 (step @p35 :rule eq-symm :args (@t17 @t21)) % 0.38/0.58 (step @p36 :rule cong :premises (@p35) :args ((forall @t3 (= @t17 @t21)))) % 0.38/0.58 (step @p37 :rule refl :args (@t21)) % 0.38/0.58 (step @p38 :rule refl :args (@t17)) % 0.38/0.58 (step @p39 :rule refl :args (@t18)) % 0.38/0.58 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t18 @t17))) % 0.38/0.58 (step @p41 :rule symm :premises (@p40)) % 0.38/0.58 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.38/0.58 (step @p43 :rule cong :premises (@p42 @p37) :args (@t22)) % 0.38/0.58 (step @p44 :rule cong :premises (@p43) :args ((forall @t3 @t22))) % 0.38/0.58 (step @p45 :rule trans :premises (@p44 @p36)) % 0.38/0.58 (step @p46 :rule eq-symm :args (@t21 @t18)) % 0.38/0.58 (step @p47 :rule beta-reduce :args ((= @t23 @t18))) % 0.38/0.58 (step @p48 :rule refl :args (@t21)) % 0.38/0.58 (step @p49 :rule cong :premises (@p48 @p47) :args (@t24)) % 0.38/0.58 (step @p50 :rule trans :premises (@p49 @p46)) % 0.38/0.58 (step @p51 :rule cong :premises (@p50) :args (@t25)) % 0.38/0.58 (step @p52 :rule trans :premises (@p51 @p45)) % 0.38/0.58 (step @p53 :rule eq-refl :args (@t23)) % 0.38/0.58 (step @p54 :rule cong :premises (@p53) :args ((forall @t3 (= @t23 @t23)))) % 0.38/0.58 (step @p55 :rule trans :premises (@p54 @p22)) % 0.38/0.58 (step @p56 :rule refl :args (@t23)) % 0.38/0.58 (step @p57 :rule skolem_intro :args (@t20)) % 0.38/0.58 (step @p58 :rule ho_cong :premises (@p57 @p27)) % 0.38/0.58 (step @p59 :rule cong :premises (@p58 @p56) :args (@t24)) % 0.38/0.58 (step @p60 :rule cong :premises (@p59) :args (@t25)) % 0.38/0.58 (step @p61 :rule trans :premises (@p60 @p55)) % 0.38/0.58 (step @p62 :rule true_elim :premises (@p61)) % 0.38/0.58 (step @p63 :rule eq_resolve :premises (@p62 @p52)) % 0.38/0.58 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t27))) % 0.38/0.58 (step @p65 :rule eq-symm :args (@t28 @t29)) % 0.38/0.58 (step @p66 :rule eq-refl :args (@t26)) % 0.38/0.58 (step @p67 :rule skolem_intro :args (@t27)) % 0.38/0.58 (step @p68 :rule refl :args (@t26)) % 0.38/0.58 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t26 @t27))) % 0.38/0.58 (step @p70 :rule trans :premises (@p69 @p66)) % 0.38/0.58 (step @p71 :rule true_elim :premises (@p70)) % 0.38/0.58 (step @p72 :rule cong :premises (@p71) :args (@t30)) % 0.38/0.58 (step @p73 :rule cong :premises (@p71) :args (@t31)) % 0.38/0.58 (step @p74 :rule cong :premises (@p73 @p72) :args (@t32)) % 0.38/0.58 (step @p75 :rule trans :premises (@p74 @p65)) % 0.38/0.58 (step @p76 :rule cong :premises (@p75) :args (@t33)) % 0.38/0.58 (step @p77 :rule refl :args (@t34)) % 0.38/0.58 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t35)) % 0.38/0.58 ; WARNING: add trust step for TRUST % 0.38/0.58 ; trust TRUST THEORY_LEMMA % 0.38/0.58 (step @p79 :rule trust :premises () :args (@t35)) % 0.38/0.58 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.38/0.58 (step @p81 :rule chain_m_resolution :premises (@p80 @p64) :args (@t34 (@list false) (@list (= @t29 @t28)))) % 0.38/0.58 (step @p82 :rule refl :args (@t36)) % 0.38/0.58 (step @p83 :rule refl :args (@t37)) % 0.38/0.58 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t37 @t36))) % 0.38/0.58 (step @p85 :rule symm :premises (@p84)) % 0.38/0.58 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.38/0.58 (step @p87 :rule refl :args (tptp.g)) % 0.38/0.58 (step @p88 :rule eq-refl :args (@t10)) % 0.38/0.58 (step @p89 :rule refl :args (@t10)) % 0.38/0.58 (step @p90 :rule cong :premises (@p89 @p28) :args ((= @t10 @t11))) % 0.38/0.58 (step @p91 :rule trans :premises (@p90 @p88)) % 0.38/0.58 (step @p92 :rule true_elim :premises (@p91)) % 0.38/0.58 (step @p93 :rule refl :args (tptp.p)) % 0.38/0.58 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.38/0.58 (step @p95 :rule ho_cong :premises (@p94 @p87)) % 0.38/0.58 (step @p96 :rule trans :premises (@p95 @p86)) % 0.38/0.58 (step @p97 :rule bool-double-not-elim :args (@t1)) % 0.38/0.58 (step @p98 :rule refl :args (tptp.f)) % 0.38/0.58 (step @p99 :rule ho_cong :premises (@p98 @p97)) % 0.38/0.58 (step @p100 :rule cong :premises (@p99) :args (@t4)) % 0.38/0.58 (step @p101 :rule ho_cong :premises (@p93 @p100)) % 0.38/0.58 (step @p102 :rule ho_cong :premises (@p101 @p87)) % 0.38/0.58 (step @p103 :rule trans :premises (@p102 @p96)) % 0.38/0.58 (step @p104 :rule eq_resolve :premises (@p1 @p103)) % 0.38/0.58 (step @p105 :rule refl :args (@t38)) % 0.38/0.58 (step @p106 :rule refl :args (@t39)) % 0.38/0.58 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t39 @t38))) % 0.38/0.58 (step @p108 :rule symm :premises (@p107)) % 0.38/0.58 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.38/0.58 (step @p110 :rule eq-refl :args (@t19)) % 0.38/0.58 (step @p111 :rule refl :args (@t19)) % 0.38/0.58 (step @p112 :rule cong :premises (@p111 @p57) :args ((= @t19 @t20))) % 0.38/0.58 (step @p113 :rule trans :premises (@p112 @p110)) % 0.38/0.58 (step @p114 :rule true_elim :premises (@p113)) % 0.38/0.58 (step @p115 :rule refl :args (@t6)) % 0.38/0.58 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.38/0.58 (step @p117 :rule trans :premises (@p116 @p109)) % 0.38/0.58 (step @p118 :rule cong :premises (@p117) :args ((not (_ @t6 @t19)))) % 0.38/0.58 (step @p119 :rule ho_cong :premises (@p87 @p97)) % 0.38/0.58 (step @p120 :rule cong :premises (@p119) :args (@t5)) % 0.38/0.58 (step @p121 :rule ho_cong :premises (@p115 @p120)) % 0.38/0.58 (step @p122 :rule cong :premises (@p121) :args (@t7)) % 0.38/0.58 (step @p123 :rule trans :premises (@p122 @p118)) % 0.38/0.58 (step @p124 :rule eq_resolve :premises (@p2 @p123)) % 0.38/0.58 (step @p125 :rule refl :args (@t41)) % 0.38/0.58 (step @p126 :rule refl :args (@t42)) % 0.38/0.58 (step @p127 :rule bool-double-not-elim :args (@t38)) % 0.38/0.58 (step @p128 :rule refl :args (@t43)) % 0.38/0.58 (step @p129 :rule nary_cong :premises (@p128 @p127 @p126 @p125) :args ((or @t43 (not @t44) @t42 @t41))) % 0.38/0.58 (assume-push @p186 @t36) % 0.38/0.58 (assume-push @p187 @t40) % 0.38/0.58 (assume-push @p188 @t34) % 0.38/0.58 (assume-push @p189 @t44) % 0.38/0.58 (step @p134 :rule evaluate :args ((= false true))) % 0.38/0.58 (step @p135 :rule true_intro :premises (@p104)) % 0.38/0.58 (step @p136 :rule symm :premises (@p81)) % 0.38/0.58 (step @p137 :rule cong :premises (@p187 @p136) :args (@t38)) % 0.38/0.58 (step @p138 :rule false_intro :premises (@p124)) % 0.38/0.58 (step @p139 :rule symm :premises (@p138)) % 0.38/0.58 (step @p140 :rule trans :premises (@p139 @p137 @p135)) % 0.38/0.58 (step @p141 false :rule eq_resolve :premises (@p140 @p134)) % 0.38/0.58 (step-pop @p190 :rule scope :premises (@p141)) % 0.38/0.58 (step-pop @p191 :rule scope :premises (@p190)) % 0.38/0.58 (step-pop @p192 :rule scope :premises (@p191)) % 0.38/0.58 (step-pop @p193 :rule scope :premises (@p192)) % 0.38/0.58 (step @p142 :rule process_scope :premises (@p193) :args (false)) % 0.38/0.58 (assume-push @p194 @t36) % 0.38/0.58 (assume-push @p195 @t44) % 0.38/0.58 (assume-push @p196 @t34) % 0.38/0.58 (assume-push @p197 @t40) % 0.38/0.58 (step @p151 :rule and_intro :premises (@p104 @p197 @p81 @p124)) % 0.38/0.58 (step-pop @p198 :rule scope :premises (@p151)) % 0.38/0.58 (step-pop @p199 :rule scope :premises (@p198)) % 0.38/0.58 (step-pop @p200 :rule scope :premises (@p199)) % 0.38/0.58 (step-pop @p201 :rule scope :premises (@p200)) % 0.38/0.58 (step @p152 :rule process_scope :premises (@p201) :args (@t45)) % 0.38/0.58 (step @p157 :rule implies_elim :premises (@p152)) % 0.38/0.58 (step @p158 :rule resolution :premises (@p157 @p142) :args (true @t45)) % 0.38/0.58 (step @p159 :rule not_and :premises (@p158)) % 0.38/0.58 (step @p160 :rule eq_resolve :premises (@p159 @p129)) % 0.38/0.58 (step @p161 :rule reordering :premises (@p160) :args ((or @t38 @t43 @t42 @t41))) % 0.38/0.58 (step @p162 :rule chain_m_resolution :premises (@p161 @p124 @p104 @p81) :args (@t41 (@list true false false) (@list @t38 @t36 @t34))) % 0.38/0.58 (step @p163 :rule eq-symm :args (@t48 @t49)) % 0.38/0.58 (step @p164 :rule eq-refl :args (@t46)) % 0.38/0.58 (step @p165 :rule skolem_intro :args (@t47)) % 0.38/0.58 (step @p166 :rule refl :args (@t46)) % 0.38/0.58 (step @p167 :rule cong :premises (@p166 @p165) :args ((= @t46 @t47))) % 0.38/0.58 (step @p168 :rule trans :premises (@p167 @p164)) % 0.38/0.58 (step @p169 :rule true_elim :premises (@p168)) % 0.38/0.58 (step @p170 :rule cong :premises (@p169) :args (@t50)) % 0.38/0.58 (step @p171 :rule cong :premises (@p169) :args (@t51)) % 0.38/0.58 (step @p172 :rule cong :premises (@p171 @p170) :args (@t52)) % 0.38/0.58 (step @p173 :rule trans :premises (@p172 @p163)) % 0.38/0.58 (step @p174 :rule cong :premises (@p173) :args (@t53)) % 0.38/0.58 (step @p175 :rule refl :args (@t40)) % 0.38/0.58 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t54)) % 0.38/0.58 ; trust TRUST THEORY_LEMMA % 0.38/0.58 (step @p177 :rule trust :premises () :args (@t54)) % 0.38/0.58 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 0.38/0.58 (step @p179 :rule chain_m_resolution :premises (@p178 @p162) :args ((not @t55) (@list true) (@list @t40))) % 0.38/0.58 (assume-push @p202 @t56) % 0.38/0.58 (step @p181 :rule instantiate :premises (@p34) :args ((@list @t47))) % 0.38/0.58 (step-pop @p203 :rule scope :premises (@p181)) % 0.38/0.58 (step @p182 :rule process_scope :premises (@p203) :args (@t55)) % 0.38/0.58 (step @p184 :rule implies_elim :premises (@p182)) % 0.38/0.58 (step @p185 false :rule chain_m_resolution :premises (@p184 @p179 @p34) :args (false (@list true false) (@list @t55 @t56))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------