%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO020^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 09:11:47 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO020^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n011.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 23:51:20 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (define tptp.leibeq () (let ((_let_1 (@var "Y" Bool))) (let ((_let_2 (@var "P" (-> Bool Bool)))) (let ((_let_3 (@var "X" Bool))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ _let_2 _let_3) (_ _let_2 _let_1)))))))) % 0.37/0.57 (define @t1 () (@var "Y" Bool)) % 0.37/0.57 (define @t2 () (@var "X" Bool)) % 0.37/0.57 (define @t3 () (not (or (not @t2) (not @t1)))) % 0.37/0.57 (define @t4 () (and @t2 @t1)) % 0.37/0.57 (define @t5 () (@list @t2 @t1)) % 0.37/0.57 (define @t6 () (forall @t5 (_ (_ tptp.leibeq @t4) @t3))) % 0.37/0.57 (define @t7 () (not @t6)) % 0.37/0.57 (define @t8 () (@var "P" (-> Bool Bool))) % 0.37/0.57 (define @t9 () (_ @t8 @t1)) % 0.37/0.57 (define @t10 () (_ @t8 @t2)) % 0.37/0.57 (define @t11 () (@list @t8)) % 0.37/0.57 (define @t12 () (forall @t11 (=> @t10 @t9))) % 0.37/0.57 (define @t13 () (lambda @t5 @t12)) % 0.37/0.57 (define @t14 () (not (_ @t8 @t4))) % 0.37/0.57 (define @t15 () (or @t14 (_ @t8 @t3))) % 0.37/0.57 (define @t16 () (forall (@list @t2 @t1 @t8) @t15)) % 0.37/0.57 (define @t17 () (forall @t11 @t15)) % 0.37/0.57 (define @t18 () (@var "BOUND_VARIABLE_7453" Bool)) % 0.37/0.57 (define @t19 () (_ @t8 @t18)) % 0.37/0.57 (define @t20 () (lambda (@list @t18) (forall @t11 (or @t14 @t19)))) % 0.37/0.57 (define @t21 () (_ @t8 @t2)) % 0.37/0.57 (define @t22 () (not @t21)) % 0.37/0.57 (define @t23 () (_ @t8 @t1)) % 0.37/0.57 (define @t24 () (lambda @t5 (forall @t11 (or @t22 @t23)))) % 0.37/0.57 (define @t25 () (forall @t5 (_ (_ @t24 @t4) @t3))) % 0.37/0.57 (define @t26 () (not @t10)) % 0.37/0.57 (define @t27 () (or @t26 @t9)) % 0.37/0.57 (define @t28 () (@quantifiers_skolemize @t16 1)) % 0.37/0.57 (define @t29 () (not @t28)) % 0.37/0.57 (define @t30 () (@quantifiers_skolemize @t16 0)) % 0.37/0.57 (define @t31 () (not @t30)) % 0.37/0.57 (define @t32 () (or @t31 @t29)) % 0.37/0.57 (define @t33 () (not @t32)) % 0.37/0.57 (define @t34 () (@purify @t33)) % 0.37/0.57 (define @t35 () (@quantifiers_skolemize @t16 2)) % 0.37/0.57 (define @t36 () (_ @t35 @t34)) % 0.37/0.57 (define @t37 () (and @t30 @t28)) % 0.37/0.57 (define @t38 () (@purify @t37)) % 0.37/0.57 (define @t39 () (_ @t35 @t38)) % 0.37/0.57 (define @t40 () (not @t39)) % 0.37/0.57 (define @t41 () (or @t40 @t36)) % 0.37/0.57 (define @t42 () (not @t41)) % 0.37/0.57 (define @t43 () (not @t16)) % 0.37/0.57 (define @t44 () (_ @t35 @t33)) % 0.37/0.57 (define @t45 () (_ @t35 @t37)) % 0.37/0.58 (define @t46 () (not @t45)) % 0.37/0.58 (define @t47 () (or @t46 @t44)) % 0.37/0.58 (define @t48 () (not @t47)) % 0.37/0.58 (define @t49 () (@list true)) % 0.37/0.58 (define @t50 () (@list @t41)) % 0.37/0.58 (define @t51 () (not @t36)) % 0.37/0.58 (define @t52 () (not @t37)) % 0.37/0.58 (define @t53 () (not @t38)) % 0.37/0.58 (define @t54 () (not @t34)) % 0.37/0.58 (define @t55 () (not @t51)) % 0.37/0.58 (define @t56 () (= true false)) % 0.37/0.58 (define @t57 () (and @t51 @t34 @t38 @t39)) % 0.37/0.58 (define @t58 () (@list @t36 @t39 @t38 @t34 @t37 @t32)) % 0.37/0.58 (define @t59 () (@list false)) % 0.37/0.58 (define @t60 () (and @t51 @t54 @t53 @t39)) % 0.37/0.58 (assume @p1 @t7) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 (= tptp.leibeq @t13) :rule refl :args (@t13)) % 0.37/0.58 (step @p4 :rule quant-merge-prenex :args ((= (forall @t5 @t17) @t16))) % 0.37/0.58 (step @p5 :rule beta-reduce :args ((= (_ @t20 @t3) @t17))) % 0.37/0.58 (step @p6 :rule refl :args (@t3)) % 0.37/0.58 (step @p7 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t18) (forall @t11 (or @t22 @t19))) @t4) @t20))) % 0.37/0.58 (step @p8 :rule refl :args (@t4)) % 0.37/0.58 (step @p9 :rule alpha_equiv :args (@t24 (@list @t1) (@list @t18))) % 0.37/0.58 (step @p10 :rule ho_cong :premises (@p9 @p8)) % 0.37/0.58 (step @p11 :rule trans :premises (@p10 @p7)) % 0.37/0.58 (step @p12 :rule ho_cong :premises (@p11 @p6)) % 0.37/0.58 (step @p13 :rule trans :premises (@p12 @p5)) % 0.37/0.58 (step @p14 :rule cong :premises (@p13) :args (@t25)) % 0.37/0.58 (step @p15 :rule trans :premises (@p14 @p4)) % 0.37/0.58 (step @p16 :rule cong :premises (@p15) :args ((not @t25))) % 0.37/0.58 (step @p17 :rule refl :args (@t4)) % 0.37/0.58 (step @p18 :rule refl :args (@t23)) % 0.37/0.58 (step @p19 :rule refl :args (@t9)) % 0.37/0.58 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t9 @t23))) % 0.37/0.58 (step @p21 :rule symm :premises (@p20)) % 0.37/0.58 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.37/0.58 (step @p23 :rule refl :args (@t21)) % 0.37/0.58 (step @p24 :rule refl :args (@t10)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t10 @t21))) % 0.37/0.58 (step @p26 :rule symm :premises (@p25)) % 0.37/0.58 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.37/0.58 (step @p28 :rule cong :premises (@p27) :args (@t26)) % 0.37/0.58 (step @p29 :rule nary_cong :premises (@p28 @p22) :args (@t27)) % 0.37/0.58 (step @p30 :rule cong :premises (@p29) :args ((forall @t11 @t27))) % 0.37/0.58 (step @p31 :rule bool-impl-elim :args (@t10 @t9)) % 0.37/0.58 (step @p32 :rule cong :premises (@p31) :args (@t12)) % 0.37/0.58 (step @p33 :rule trans :premises (@p32 @p30)) % 0.37/0.58 (step @p34 :rule cong :premises (@p33) :args (@t13)) % 0.37/0.58 (step @p35 :rule trans :premises (@p3 @p34)) % 0.37/0.58 (step @p36 :rule ho_cong :premises (@p35 @p17)) % 0.37/0.58 (step @p37 :rule ho_cong :premises (@p36 @p6)) % 0.37/0.58 (step @p38 :rule cong :premises (@p37) :args (@t6)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38) :args (@t7)) % 0.37/0.58 (step @p40 :rule trans :premises (@p39 @p16)) % 0.37/0.58 (step @p41 :rule eq_resolve :premises (@p1 @p40)) % 0.37/0.58 (step @p42 :rule refl :args (@t42)) % 0.37/0.58 (step @p43 :rule bool-double-not-elim :args (@t16)) % 0.37/0.58 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or (not @t43) @t42))) % 0.37/0.58 (step @p45 :rule eq-refl :args (@t33)) % 0.37/0.58 (step @p46 :rule skolem_intro :args (@t34)) % 0.37/0.58 (step @p47 :rule refl :args (@t33)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t33 @t34))) % 0.37/0.58 (step @p49 :rule trans :premises (@p48 @p45)) % 0.37/0.58 (step @p50 :rule true_elim :premises (@p49)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50) :args (@t44)) % 0.37/0.58 (step @p52 :rule eq-refl :args (@t37)) % 0.37/0.58 (step @p53 :rule skolem_intro :args (@t38)) % 0.37/0.58 (step @p54 :rule refl :args (@t37)) % 0.37/0.58 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t37 @t38))) % 0.37/0.58 (step @p56 :rule trans :premises (@p55 @p52)) % 0.37/0.58 (step @p57 :rule true_elim :premises (@p56)) % 0.37/0.58 (step @p58 :rule cong :premises (@p57) :args (@t45)) % 0.37/0.58 (step @p59 :rule cong :premises (@p58) :args (@t46)) % 0.37/0.58 (step @p60 :rule nary_cong :premises (@p59 @p51) :args (@t47)) % 0.37/0.58 (step @p61 :rule cong :premises (@p60) :args (@t48)) % 0.37/0.58 (step @p62 :rule refl :args (@t43)) % 0.37/0.58 (step @p63 :rule cong :premises (@p62 @p61) :args ((=> @t43 @t48))) % 0.37/0.58 (assume-push @p184 @t43) % 0.37/0.58 (step @p65 :rule skolemize :premises (@p41)) % 0.37/0.58 (step-pop @p185 :rule scope :premises (@p65)) % 0.37/0.58 (step @p66 :rule process_scope :premises (@p185) :args (@t48)) % 0.37/0.58 (step @p68 :rule eq_resolve :premises (@p66 @p63)) % 0.37/0.58 (step @p69 :rule implies_elim :premises (@p68)) % 0.37/0.58 (step @p70 :rule eq_resolve :premises (@p69 @p44)) % 0.37/0.58 (step @p71 :rule chain_m_resolution :premises (@p70 @p41) :args (@t42 @t49 (@list @t16))) % 0.37/0.58 (step @p72 :rule bool-double-not-elim :args (@t39)) % 0.37/0.58 (step @p73 :rule refl :args (@t41)) % 0.37/0.58 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t41 (not @t40)))) % 0.37/0.58 (step @p75 :rule cnf_or_neg :args (@t41 0)) % 0.37/0.58 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.37/0.58 (step @p77 :rule reordering :premises (@p76) :args ((or @t39 @t41))) % 0.37/0.58 (step @p78 :rule chain_m_resolution :premises (@p77 @p71) :args (@t39 @t49 @t50)) % 0.37/0.58 (step @p79 :rule cnf_or_neg :args (@t41 1)) % 0.37/0.58 (step @p80 :rule chain_m_resolution :premises (@p79 @p71) :args (@t51 @t49 @t50)) % 0.37/0.58 (step @p81 :rule cnf_or_pos :args (@t32)) % 0.37/0.58 (step @p82 :rule reordering :premises (@p81) :args ((or @t31 @t29 @t33))) % 0.37/0.58 (step @p83 :rule cnf_and_neg :args (@t37)) % 0.37/0.58 (step @p84 :rule refl :args (@t34)) % 0.37/0.58 (step @p85 :rule bool-double-not-elim :args (@t32)) % 0.37/0.58 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or (not @t33) @t34))) % 0.37/0.58 (step @p87 :rule equiv_elim1 :premises (@p50)) % 0.37/0.58 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.37/0.58 (step @p89 :rule equiv_elim1 :premises (@p57)) % 0.37/0.58 (step @p90 :rule reordering :premises (@p89) :args ((or @t38 @t52))) % 0.37/0.58 (step @p91 :rule bool-double-not-elim :args (@t36)) % 0.37/0.58 (step @p92 :rule refl :args (@t40)) % 0.37/0.58 (step @p93 :rule refl :args (@t53)) % 0.37/0.58 (step @p94 :rule refl :args (@t54)) % 0.37/0.58 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92 @p91) :args ((or @t54 @t53 @t40 @t55))) % 0.37/0.58 (assume-push @p186 @t51) % 0.37/0.58 (assume-push @p187 @t34) % 0.37/0.58 (assume-push @p188 @t38) % 0.37/0.58 (assume-push @p189 @t39) % 0.37/0.58 (step @p100 :rule evaluate :args (@t56)) % 0.37/0.58 (step @p101 :rule false_intro :premises (@p80)) % 0.37/0.58 (step @p102 :rule true_intro :premises (@p187)) % 0.37/0.58 (step @p103 :rule symm :premises (@p102)) % 0.37/0.58 (step @p104 :rule true_intro :premises (@p188)) % 0.37/0.58 (step @p105 :rule trans :premises (@p104 @p103)) % 0.37/0.58 (step @p106 :rule cong :premises (@p105) :args (@t39)) % 0.37/0.58 (step @p107 :rule true_intro :premises (@p78)) % 0.37/0.58 (step @p108 :rule symm :premises (@p107)) % 0.37/0.58 (step @p109 :rule trans :premises (@p108 @p106 @p101)) % 0.37/0.58 (step @p110 false :rule eq_resolve :premises (@p109 @p100)) % 0.37/0.58 (step-pop @p190 :rule scope :premises (@p110)) % 0.37/0.58 (step-pop @p191 :rule scope :premises (@p190)) % 0.37/0.58 (step-pop @p192 :rule scope :premises (@p191)) % 0.37/0.58 (step-pop @p193 :rule scope :premises (@p192)) % 0.37/0.58 (step @p111 :rule process_scope :premises (@p193) :args (false)) % 0.37/0.58 (assume-push @p194 @t34) % 0.37/0.58 (assume-push @p195 @t38) % 0.37/0.58 (assume-push @p196 @t39) % 0.37/0.58 (assume-push @p197 @t51) % 0.37/0.58 (step @p120 :rule and_intro :premises (@p80 @p194 @p195 @p78)) % 0.37/0.58 (step-pop @p198 :rule scope :premises (@p120)) % 0.37/0.58 (step-pop @p199 :rule scope :premises (@p198)) % 0.37/0.58 (step-pop @p200 :rule scope :premises (@p199)) % 0.37/0.58 (step-pop @p201 :rule scope :premises (@p200)) % 0.37/0.58 (step @p121 :rule process_scope :premises (@p201) :args (@t57)) % 0.37/0.58 (step @p126 :rule implies_elim :premises (@p121)) % 0.37/0.58 (step @p127 :rule resolution :premises (@p126 @p111) :args (true @t57)) % 0.37/0.58 (step @p128 :rule not_and :premises (@p127)) % 0.37/0.58 (step @p129 :rule eq_resolve :premises (@p128 @p95)) % 0.37/0.58 (step @p130 :rule reordering :premises (@p129) :args ((or @t36 @t40 @t54 @t53))) % 0.37/0.58 (step @p131 :rule chain_m_resolution :premises (@p130 @p80 @p78 @p90 @p88 @p83 @p82) :args (@t32 (@list true false false false false true) @t58)) % 0.37/0.58 (step @p132 :rule equiv_elim2 :premises (@p50)) % 0.37/0.58 (step @p133 :rule chain_m_resolution :premises (@p132 @p131) :args (@t54 @t59 (@list @t32))) % 0.37/0.58 (step @p134 :rule bool-double-not-elim :args (@t28)) % 0.37/0.58 (step @p135 :rule refl :args (@t32)) % 0.37/0.58 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or @t32 (not @t29)))) % 0.37/0.58 (step @p137 :rule cnf_or_neg :args (@t32 1)) % 0.37/0.58 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.37/0.58 (step @p139 :rule reordering :premises (@p138) :args ((or @t28 @t32))) % 0.37/0.58 (step @p140 :rule cnf_and_pos :args (@t37 1)) % 0.37/0.58 (step @p141 :rule reordering :premises (@p140) :args ((or @t28 @t52))) % 0.37/0.58 (step @p142 :rule equiv_elim2 :premises (@p57)) % 0.37/0.58 (step @p143 :rule bool-double-not-elim :args (@t38)) % 0.37/0.58 (step @p144 :rule bool-double-not-elim :args (@t34)) % 0.37/0.58 (step @p145 :rule nary_cong :premises (@p92 @p91 @p144 @p143) :args ((or @t40 @t55 (not @t54) (not @t53)))) % 0.37/0.58 (assume-push @p202 @t51) % 0.37/0.58 (assume-push @p203 @t54) % 0.37/0.58 (assume-push @p204 @t53) % 0.37/0.58 (assume-push @p205 @t39) % 0.37/0.58 (step @p100 :rule evaluate :args (@t56)) % 0.37/0.58 (step @p101 :rule false_intro :premises (@p80)) % 0.37/0.58 (step @p150 :rule false_intro :premises (@p203)) % 0.37/0.58 (step @p151 :rule symm :premises (@p150)) % 0.37/0.58 (step @p152 :rule false_intro :premises (@p204)) % 0.37/0.58 (step @p153 :rule trans :premises (@p152 @p151)) % 0.37/0.58 (step @p154 :rule cong :premises (@p153) :args (@t39)) % 0.37/0.58 (step @p107 :rule true_intro :premises (@p78)) % 0.37/0.58 (step @p108 :rule symm :premises (@p107)) % 0.37/0.58 (step @p155 :rule trans :premises (@p108 @p154 @p101)) % 0.37/0.58 (step @p156 false :rule eq_resolve :premises (@p155 @p100)) % 0.37/0.58 (step-pop @p206 :rule scope :premises (@p156)) % 0.37/0.58 (step-pop @p207 :rule scope :premises (@p206)) % 0.37/0.58 (step-pop @p208 :rule scope :premises (@p207)) % 0.37/0.58 (step-pop @p209 :rule scope :premises (@p208)) % 0.37/0.58 (step @p157 :rule process_scope :premises (@p209) :args (false)) % 0.37/0.58 (assume-push @p210 @t39) % 0.37/0.58 (assume-push @p211 @t51) % 0.37/0.58 (assume-push @p212 @t54) % 0.37/0.58 (assume-push @p213 @t53) % 0.37/0.58 (step @p166 :rule and_intro :premises (@p80 @p212 @p213 @p78)) % 0.37/0.58 (step-pop @p214 :rule scope :premises (@p166)) % 0.37/0.58 (step-pop @p215 :rule scope :premises (@p214)) % 0.37/0.58 (step-pop @p216 :rule scope :premises (@p215)) % 0.37/0.58 (step-pop @p217 :rule scope :premises (@p216)) % 0.37/0.58 (step @p167 :rule process_scope :premises (@p217) :args (@t60)) % 0.37/0.58 (step @p172 :rule implies_elim :premises (@p167)) % 0.37/0.58 (step @p173 :rule resolution :premises (@p172 @p157) :args (true @t60)) % 0.37/0.58 (step @p174 :rule not_and :premises (@p173)) % 0.37/0.58 (step @p175 :rule eq_resolve :premises (@p174 @p145)) % 0.37/0.58 (step @p176 :rule reordering :premises (@p175) :args ((or @t34 @t36 @t38 @t40))) % 0.37/0.58 (step @p177 :rule chain_m_resolution :premises (@p176 @p80 @p78 @p142 @p132 @p141 @p139) :args (@t28 (@list true false true true true false) @t58)) % 0.37/0.58 (step @p178 :rule chain_m_resolution :premises (@p131 @p177) :args (@t31 @t59 (@list @t28))) % 0.37/0.58 (step @p179 :rule cnf_and_pos :args (@t37 0)) % 0.37/0.58 (step @p180 :rule reordering :premises (@p179) :args ((or @t30 @t52))) % 0.37/0.58 (step @p181 :rule chain_m_resolution :premises (@p180 @p178) :args (@t52 @t49 (@list @t30))) % 0.37/0.58 (step @p182 :rule chain_m_resolution :premises (@p142 @p181) :args (@t53 @t49 (@list @t37))) % 0.37/0.58 (step @p183 false :rule chain_m_resolution :premises (@p176 @p182 @p133 @p80 @p78) :args (false (@list true true true false) (@list @t38 @t34 @t36 @t39))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------