%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO290^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 09:12:22 AM UTC 2026 % Result : Theorem 0.17s 0.36s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO290^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 19:02:30 EDT 2026 % 0.07/0.25 % CPUTime : % 0.17/0.33 %----Proving TH0 % 0.17/0.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.17/0.36 % SZS status Theorem % 0.17/0.36 % SZS output start Proof % 0.17/0.36 ( % 0.17/0.36 (declare-sort tptp.a 0) % 0.17/0.36 (declare-const tptp.p (-> (-> tptp.a tptp.a) Bool)) % 0.17/0.36 (declare-const tptp.g1 (-> tptp.a tptp.a)) % 0.17/0.36 (declare-const tptp.g2 (-> tptp.a tptp.a)) % 0.17/0.36 (define @t1 () (@var "Xx" tptp.a)) % 0.17/0.36 (define @t2 () (_ tptp.g2 @t1)) % 0.17/0.36 (define @t3 () (_ tptp.g1 @t2)) % 0.17/0.36 (define @t4 () (@list @t1)) % 0.17/0.36 (define @t5 () (lambda @t4 @t3)) % 0.17/0.36 (define @t6 () (@var "Xw" tptp.a)) % 0.17/0.36 (define @t7 () (_ tptp.g2 @t6)) % 0.17/0.36 (define @t8 () (_ tptp.g1 @t7)) % 0.17/0.36 (define @t9 () (@list @t6)) % 0.17/0.36 (define @t10 () (lambda @t9 @t8)) % 0.17/0.36 (define @t11 () (not (_ tptp.p @t10))) % 0.17/0.36 (define @t12 () (or @t11 (_ tptp.p @t5))) % 0.17/0.36 (define @t13 () (not @t12)) % 0.17/0.36 (define @t14 () (@purify @t5)) % 0.17/0.36 (define @t15 () (tptp.p @t14)) % 0.17/0.36 (define @t16 () (_ tptp.p @t14)) % 0.17/0.36 (define @t17 () (@purify @t10)) % 0.17/0.36 (define @t18 () (tptp.p @t17)) % 0.17/0.36 (define @t19 () (_ tptp.p @t17)) % 0.17/0.36 (define @t20 () (= @t14 @t17)) % 0.17/0.36 (define @t21 () (not @t20)) % 0.17/0.36 (define @t22 () (not @t18)) % 0.17/0.36 (define @t23 () (not @t15)) % 0.17/0.36 (define @t24 () (and @t23 @t20 @t18)) % 0.17/0.36 (define @t25 () (@const 0 tptp.a)) % 0.17/0.36 (define @t26 () (_ @t17 @t25)) % 0.17/0.36 (define @t27 () (_ @t14 @t25)) % 0.17/0.36 (define @t28 () (= @t27 @t26)) % 0.17/0.36 (define @t29 () (not @t28)) % 0.17/0.36 (define @t30 () (tptp.g2 @t1)) % 0.17/0.36 (define @t31 () (tptp.g1 @t30)) % 0.17/0.36 (define @t32 () (_ @t14 @t1)) % 0.17/0.36 (define @t33 () (= @t3 @t32)) % 0.17/0.36 (define @t34 () (_ @t5 @t1)) % 0.17/0.36 (define @t35 () (= @t32 @t34)) % 0.17/0.36 (define @t36 () (forall @t4 @t35)) % 0.17/0.36 (define @t37 () (@list @t25)) % 0.17/0.36 (define @t38 () (tptp.g2 @t6)) % 0.17/0.36 (define @t39 () (tptp.g1 @t38)) % 0.17/0.36 (define @t40 () (_ @t17 @t6)) % 0.17/0.36 (define @t41 () (= @t8 @t40)) % 0.17/0.36 (define @t42 () (_ @t10 @t6)) % 0.17/0.36 (define @t43 () (= @t40 @t42)) % 0.17/0.36 (define @t44 () (forall @t9 @t43)) % 0.17/0.36 (define @t45 () (tptp.g1 (tptp.g2 @t25))) % 0.17/0.36 (define @t46 () (= @t26 @t45)) % 0.17/0.36 (define @t47 () (not @t46)) % 0.17/0.36 (define @t48 () (= @t27 @t45)) % 0.17/0.36 (define @t49 () (not @t48)) % 0.17/0.36 (define @t50 () (and @t48 @t46 @t29)) % 0.17/0.36 (assume @p1 @t13) % 0.17/0.36 (assume @p2 true) % 0.17/0.36 (step @p3 :rule refl :args (@t15)) % 0.17/0.36 (step @p4 :rule refl :args (@t16)) % 0.17/0.36 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t16 @t15))) % 0.17/0.36 (step @p6 :rule symm :premises (@p5)) % 0.17/0.36 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.17/0.36 (step @p8 :rule eq-refl :args (@t5)) % 0.17/0.36 (step @p9 :rule skolem_intro :args (@t14)) % 0.17/0.36 (step @p10 :rule refl :args (@t5)) % 0.17/0.36 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t5 @t14))) % 0.17/0.36 (step @p12 :rule trans :premises (@p11 @p8)) % 0.17/0.36 (step @p13 :rule true_elim :premises (@p12)) % 0.17/0.36 (step @p14 :rule refl :args (tptp.p)) % 0.17/0.36 (step @p15 :rule ho_cong :premises (@p14 @p13)) % 0.17/0.36 (step @p16 :rule trans :premises (@p15 @p7)) % 0.17/0.36 (step @p17 :rule refl :args (@t18)) % 0.17/0.36 (step @p18 :rule refl :args (@t19)) % 0.17/0.36 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t19 @t18))) % 0.17/0.36 (step @p20 :rule symm :premises (@p19)) % 0.17/0.36 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.17/0.36 (step @p22 :rule eq-refl :args (@t10)) % 0.17/0.36 (step @p23 :rule skolem_intro :args (@t17)) % 0.17/0.36 (step @p24 :rule refl :args (@t10)) % 0.17/0.36 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t10 @t17))) % 0.17/0.36 (step @p26 :rule trans :premises (@p25 @p22)) % 0.17/0.36 (step @p27 :rule true_elim :premises (@p26)) % 0.17/0.36 (step @p28 :rule ho_cong :premises (@p14 @p27)) % 0.17/0.36 (step @p29 :rule trans :premises (@p28 @p21)) % 0.17/0.36 (step @p30 :rule cong :premises (@p29) :args (@t11)) % 0.17/0.36 (step @p31 :rule nary_cong :premises (@p30 @p16) :args (@t12)) % 0.17/0.36 (step @p32 :rule cong :premises (@p31) :args (@t13)) % 0.17/0.36 (step @p33 :rule eq_resolve :premises (@p1 @p32)) % 0.17/0.36 (step @p34 :rule not_or_elim :premises (@p33) :args (0)) % 0.17/0.36 (step @p35 :rule not_not_elim :premises (@p34)) % 0.17/0.36 (step @p36 :rule not_or_elim :premises (@p33) :args (1)) % 0.17/0.36 (step @p37 :rule refl :args (@t21)) % 0.17/0.36 (step @p38 :rule bool-double-not-elim :args (@t15)) % 0.17/0.36 (step @p39 :rule refl :args (@t22)) % 0.17/0.36 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37) :args ((or @t22 (not @t23) @t21))) % 0.17/0.36 (assume-push @p187 @t23) % 0.17/0.36 (assume-push @p188 @t20) % 0.17/0.36 (assume-push @p189 @t18) % 0.17/0.36 (step @p44 :rule evaluate :args ((= true false))) % 0.17/0.36 (step @p45 :rule false_intro :premises (@p36)) % 0.17/0.36 (step @p46 :rule symm :premises (@p188)) % 0.17/0.36 (step @p47 :rule cong :premises (@p46) :args (@t18)) % 0.17/0.36 (step @p48 :rule true_intro :premises (@p35)) % 0.17/0.36 (step @p49 :rule symm :premises (@p48)) % 0.17/0.36 (step @p50 :rule trans :premises (@p49 @p47 @p45)) % 0.17/0.36 (step @p51 false :rule eq_resolve :premises (@p50 @p44)) % 0.17/0.36 (step-pop @p190 :rule scope :premises (@p51)) % 0.17/0.36 (step-pop @p191 :rule scope :premises (@p190)) % 0.17/0.36 (step-pop @p192 :rule scope :premises (@p191)) % 0.17/0.36 (step @p52 :rule process_scope :premises (@p192) :args (false)) % 0.17/0.36 (assume-push @p193 @t18) % 0.17/0.36 (assume-push @p194 @t23) % 0.17/0.36 (assume-push @p195 @t20) % 0.17/0.36 (step @p59 :rule and_intro :premises (@p36 @p195 @p35)) % 0.17/0.36 (step-pop @p196 :rule scope :premises (@p59)) % 0.17/0.36 (step-pop @p197 :rule scope :premises (@p196)) % 0.17/0.36 (step-pop @p198 :rule scope :premises (@p197)) % 0.17/0.36 (step @p60 :rule process_scope :premises (@p198) :args (@t24)) % 0.17/0.36 (step @p64 :rule implies_elim :premises (@p60)) % 0.17/0.36 (step @p65 :rule resolution :premises (@p64 @p52) :args (true @t24)) % 0.17/0.36 (step @p66 :rule not_and :premises (@p65)) % 0.17/0.36 (step @p67 :rule eq_resolve :premises (@p66 @p40)) % 0.17/0.36 (step @p68 :rule reordering :premises (@p67) :args ((or @t15 @t22 @t21))) % 0.17/0.36 (step @p69 :rule chain_m_resolution :premises (@p68 @p36 @p35) :args (@t21 (@list true false) (@list @t15 @t18))) % 0.17/0.36 ; WARNING: add trust step for TRUST % 0.17/0.36 ; trust TRUST THEORY_LEMMA % 0.17/0.36 (step @p70 :rule trust :premises () :args ((or @t20 @t29))) % 0.17/0.36 (step @p71 :rule chain_m_resolution :premises (@p70 @p69) :args (@t29 (@list true) (@list @t20))) % 0.17/0.36 (step @p72 :rule eq-symm :args (@t31 @t32)) % 0.17/0.36 (step @p73 :rule cong :premises (@p72) :args ((forall @t4 (= @t31 @t32)))) % 0.17/0.36 (step @p74 :rule refl :args (@t32)) % 0.17/0.36 (step @p75 :rule refl :args ((tptp.g1 @t2))) % 0.17/0.36 (step @p76 :rule refl :args (@t30)) % 0.17/0.36 (step @p77 :rule cong :premises (@p76) :args (@t31)) % 0.17/0.36 (step @p78 :rule trans :premises (@p77 @p75)) % 0.17/0.36 (step @p79 :rule refl :args (tptp.g1)) % 0.17/0.36 (step @p80 :rule ho_cong :premises (@p79 @p76)) % 0.17/0.36 (step @p81 :rule cong :premises (@p80 @p78) :args ((= (_ tptp.g1 @t30) @t31))) % 0.17/0.36 (step @p82 :rule symm :premises (@p81)) % 0.17/0.36 (step @p83 :rule refl :args (@t3)) % 0.17/0.36 (step @p84 :rule eq_resolve :premises (@p83 @p82)) % 0.17/0.36 (step @p85 :rule refl :args (@t2)) % 0.17/0.36 (step @p86 :rule cong :premises (@p85 @p76) :args ((= @t2 @t30))) % 0.17/0.36 (step @p87 :rule symm :premises (@p86)) % 0.17/0.36 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.17/0.36 (step @p89 :rule ho_cong :premises (@p79 @p88)) % 0.17/0.36 (step @p90 :rule trans :premises (@p89 @p84)) % 0.17/0.36 (step @p91 :rule cong :premises (@p90 @p74) :args (@t33)) % 0.17/0.36 (step @p92 :rule cong :premises (@p91) :args ((forall @t4 @t33))) % 0.17/0.36 (step @p93 :rule trans :premises (@p92 @p73)) % 0.17/0.36 (step @p94 :rule eq-symm :args (@t32 @t3)) % 0.17/0.36 (step @p95 :rule beta-reduce :args ((= @t34 @t3))) % 0.17/0.36 (step @p96 :rule refl :args (@t32)) % 0.17/0.36 (step @p97 :rule cong :premises (@p96 @p95) :args (@t35)) % 0.17/0.36 (step @p98 :rule trans :premises (@p97 @p94)) % 0.17/0.36 (step @p99 :rule cong :premises (@p98) :args (@t36)) % 0.17/0.36 (step @p100 :rule trans :premises (@p99 @p93)) % 0.17/0.36 (step @p101 :rule quant-unused-vars :args ((= (forall @t4 true) true))) % 0.17/0.36 (step @p102 :rule eq-refl :args (@t34)) % 0.17/0.36 (step @p103 :rule cong :premises (@p102) :args ((forall @t4 (= @t34 @t34)))) % 0.17/0.36 (step @p104 :rule trans :premises (@p103 @p101)) % 0.17/0.36 (step @p105 :rule refl :args (@t34)) % 0.17/0.36 (step @p106 :rule refl :args (@t1)) % 0.17/0.36 (step @p107 :rule ho_cong :premises (@p9 @p106)) % 0.17/0.36 (step @p108 :rule cong :premises (@p107 @p105) :args (@t35)) % 0.17/0.36 (step @p109 :rule cong :premises (@p108) :args (@t36)) % 0.17/0.36 (step @p110 :rule trans :premises (@p109 @p104)) % 0.17/0.36 (step @p111 :rule true_elim :premises (@p110)) % 0.17/0.36 (step @p112 :rule eq_resolve :premises (@p111 @p100)) % 0.17/0.36 (step @p113 :rule instantiate :premises (@p112) :args (@t37)) % 0.17/0.36 (step @p114 :rule eq-symm :args (@t39 @t40)) % 0.17/0.36 (step @p115 :rule cong :premises (@p114) :args ((forall @t9 (= @t39 @t40)))) % 0.17/0.36 (step @p116 :rule refl :args (@t40)) % 0.17/0.36 (step @p117 :rule refl :args ((tptp.g1 @t7))) % 0.17/0.36 (step @p118 :rule refl :args (@t38)) % 0.17/0.36 (step @p119 :rule cong :premises (@p118) :args (@t39)) % 0.17/0.36 (step @p120 :rule trans :premises (@p119 @p117)) % 0.17/0.36 (step @p121 :rule ho_cong :premises (@p79 @p118)) % 0.17/0.36 (step @p122 :rule cong :premises (@p121 @p120) :args ((= (_ tptp.g1 @t38) @t39))) % 0.17/0.36 (step @p123 :rule symm :premises (@p122)) % 0.17/0.36 (step @p124 :rule refl :args (@t8)) % 0.17/0.36 (step @p125 :rule eq_resolve :premises (@p124 @p123)) % 0.17/0.36 (step @p126 :rule refl :args (@t7)) % 0.17/0.36 (step @p127 :rule cong :premises (@p126 @p118) :args ((= @t7 @t38))) % 0.17/0.36 (step @p128 :rule symm :premises (@p127)) % 0.17/0.36 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.17/0.36 (step @p130 :rule ho_cong :premises (@p79 @p129)) % 0.17/0.36 (step @p131 :rule trans :premises (@p130 @p125)) % 0.17/0.36 (step @p132 :rule cong :premises (@p131 @p116) :args (@t41)) % 0.17/0.36 (step @p133 :rule cong :premises (@p132) :args ((forall @t9 @t41))) % 0.17/0.36 (step @p134 :rule trans :premises (@p133 @p115)) % 0.17/0.36 (step @p135 :rule eq-symm :args (@t40 @t8)) % 0.17/0.36 (step @p136 :rule beta-reduce :args ((= @t42 @t8))) % 0.17/0.36 (step @p137 :rule refl :args (@t40)) % 0.17/0.36 (step @p138 :rule cong :premises (@p137 @p136) :args (@t43)) % 0.17/0.36 (step @p139 :rule trans :premises (@p138 @p135)) % 0.17/0.36 (step @p140 :rule cong :premises (@p139) :args (@t44)) % 0.17/0.36 (step @p141 :rule trans :premises (@p140 @p134)) % 0.17/0.36 (step @p142 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 0.17/0.36 (step @p143 :rule eq-refl :args (@t42)) % 0.17/0.36 (step @p144 :rule cong :premises (@p143) :args ((forall @t9 (= @t42 @t42)))) % 0.17/0.36 (step @p145 :rule trans :premises (@p144 @p142)) % 0.17/0.36 (step @p146 :rule refl :args (@t42)) % 0.17/0.36 (step @p147 :rule refl :args (@t6)) % 0.17/0.36 (step @p148 :rule ho_cong :premises (@p23 @p147)) % 0.17/0.36 (step @p149 :rule cong :premises (@p148 @p146) :args (@t43)) % 0.17/0.36 (step @p150 :rule cong :premises (@p149) :args (@t44)) % 0.17/0.36 (step @p151 :rule trans :premises (@p150 @p145)) % 0.17/0.36 (step @p152 :rule true_elim :premises (@p151)) % 0.17/0.36 (step @p153 :rule eq_resolve :premises (@p152 @p141)) % 0.17/0.36 (step @p154 :rule instantiate :premises (@p153) :args (@t37)) % 0.17/0.36 (step @p155 :rule refl :args (@t47)) % 0.17/0.36 (step @p156 :rule refl :args (@t49)) % 0.17/0.36 (step @p157 :rule bool-double-not-elim :args (@t28)) % 0.17/0.36 (step @p158 :rule nary_cong :premises (@p157 @p156 @p155) :args ((or (not @t29) @t49 @t47))) % 0.17/0.36 (assume-push @p199 @t48) % 0.17/0.36 (assume-push @p200 @t46) % 0.17/0.36 (assume-push @p201 @t29) % 0.17/0.36 (step @p162 :rule evaluate :args ((= false true))) % 0.17/0.36 (step @p163 :rule symm :premises (@p154)) % 0.17/0.36 (step @p164 :rule trans :premises (@p113 @p163)) % 0.17/0.36 (step @p165 :rule true_intro :premises (@p164)) % 0.17/0.36 (step @p166 :rule false_intro :premises (@p201)) % 0.17/0.36 (step @p167 :rule symm :premises (@p166)) % 0.17/0.36 (step @p168 :rule trans :premises (@p167 @p165)) % 0.17/0.36 (step @p169 false :rule eq_resolve :premises (@p168 @p162)) % 0.17/0.36 (step-pop @p202 :rule scope :premises (@p169)) % 0.17/0.36 (step-pop @p203 :rule scope :premises (@p202)) % 0.17/0.36 (step-pop @p204 :rule scope :premises (@p203)) % 0.17/0.36 (step @p170 :rule process_scope :premises (@p204) :args (false)) % 0.17/0.36 (assume-push @p205 @t29) % 0.17/0.36 (assume-push @p206 @t48) % 0.17/0.36 (assume-push @p207 @t46) % 0.17/0.36 (step @p177 :rule and_intro :premises (@p113 @p154 @p205)) % 0.17/0.36 (step-pop @p208 :rule scope :premises (@p177)) % 0.17/0.36 (step-pop @p209 :rule scope :premises (@p208)) % 0.17/0.36 (step-pop @p210 :rule scope :premises (@p209)) % 0.17/0.36 (step @p178 :rule process_scope :premises (@p210) :args (@t50)) % 0.17/0.36 (step @p182 :rule implies_elim :premises (@p178)) % 0.17/0.36 (step @p183 :rule resolution :premises (@p182 @p170) :args (true @t50)) % 0.17/0.36 (step @p184 :rule not_and :premises (@p183)) % 0.17/0.36 (step @p185 :rule eq_resolve :premises (@p184 @p158)) % 0.17/0.36 (step @p186 false :rule chain_m_resolution :premises (@p185 @p154 @p113 @p71) :args (false (@list false false true) (@list @t46 @t48 @t28))) % 0.17/0.36 ) % 0.17/0.36 % SZS output end Proof % 0.17/0.36 % cvc5 exiting %------------------------------------------------------------------------------