%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:22:55 AM UTC 2026 % Result : Theorem 27.14s 27.79s % Output : Proof 27.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n006.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 12:39:16 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.44 %----Proving TF0_NAR, FOF, or CNF % 27.14/27.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 27.14/27.79 --- Run --no-e-matching --full-saturate-quant at 6... % 27.14/27.79 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.14/27.79 % SZS status Theorem % 27.14/27.79 % SZS output start Proof % 27.14/27.79 ( % 27.14/27.79 (declare-sort $$unsorted 0) % 27.14/27.79 (declare-const tptp.op_equiv Bool) % 27.14/27.79 (declare-const tptp.op_implies_or Bool) % 27.14/27.79 (declare-const tptp.op_and Bool) % 27.14/27.79 (declare-const tptp.r4 Bool) % 27.14/27.79 (declare-const tptp.r3 Bool) % 27.14/27.79 (declare-const tptp.implies_2 Bool) % 27.14/27.79 (declare-const tptp.and_2 Bool) % 27.14/27.79 (declare-const tptp.modus_tollens Bool) % 27.14/27.79 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 27.14/27.79 (declare-const tptp.op_or Bool) % 27.14/27.79 (declare-const tptp.or_1 Bool) % 27.14/27.79 (declare-const tptp.equivalence_3 Bool) % 27.14/27.79 (declare-const tptp.and_1 Bool) % 27.14/27.79 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 27.14/27.79 (declare-const tptp.implies_3 Bool) % 27.14/27.79 (declare-const tptp.substitution_of_equivalents Bool) % 27.14/27.79 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 27.14/27.79 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 27.14/27.79 (declare-const tptp.op_implies_and Bool) % 27.14/27.79 (declare-const tptp.or_3 Bool) % 27.14/27.79 (declare-const tptp.equivalence_2 Bool) % 27.14/27.79 (declare-const tptp.modus_ponens Bool) % 27.14/27.79 (declare-const tptp.implies_1 Bool) % 27.14/27.79 (declare-const tptp.equivalence_1 Bool) % 27.14/27.79 (declare-const tptp.op_implies Bool) % 27.14/27.79 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 27.14/27.79 (declare-const tptp.r5 Bool) % 27.14/27.79 (declare-const tptp.and_3 Bool) % 27.14/27.79 (declare-const tptp.cn3 Bool) % 27.14/27.79 (declare-const tptp.or_2 Bool) % 27.14/27.79 (declare-const tptp.kn1 Bool) % 27.14/27.79 (declare-const tptp.cn1 Bool) % 27.14/27.79 (declare-const tptp.kn2 Bool) % 27.14/27.79 (declare-const tptp.cn2 Bool) % 27.14/27.79 (declare-const tptp.kn3 Bool) % 27.14/27.79 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 27.14/27.79 (declare-const tptp.r1 Bool) % 27.14/27.79 (declare-const tptp.r2 Bool) % 27.14/27.79 (define @t1 () (@var "Y" $$unsorted)) % 27.14/27.79 (define @t2 () (tptp.is_a_theorem @t1)) % 27.14/27.79 (define @t3 () (@var "X" $$unsorted)) % 27.14/27.79 (define @t4 () (tptp.implies @t3 @t1)) % 27.14/27.79 (define @t5 () (tptp.is_a_theorem @t4)) % 27.14/27.79 (define @t6 () (tptp.is_a_theorem @t3)) % 27.14/27.79 (define @t7 () (and @t6 @t5)) % 27.14/27.79 (define @t8 () (@list @t3 @t1)) % 27.14/27.79 (define @t9 () (forall @t8 (=> @t7 @t2))) % 27.14/27.79 (define @t10 () (= tptp.modus_ponens @t9)) % 27.14/27.79 (define @t11 () (tptp.equiv @t3 @t1)) % 27.14/27.79 (define @t12 () (tptp.not @t3)) % 27.14/27.79 (define @t13 () (tptp.not @t1)) % 27.14/27.79 (define @t14 () (tptp.implies @t1 @t3)) % 27.14/27.79 (define @t15 () (@var "Z" $$unsorted)) % 27.14/27.79 (define @t16 () (tptp.implies @t3 @t15)) % 27.14/27.79 (define @t17 () (tptp.implies @t1 @t15)) % 27.14/27.79 (define @t18 () (@list @t3 @t1 @t15)) % 27.14/27.79 (define @t19 () (tptp.and @t3 @t1)) % 27.14/27.79 (define @t20 () (tptp.or @t3 @t1)) % 27.14/27.79 (define @t21 () (@var "P" $$unsorted)) % 27.14/27.79 (define @t22 () (@list @t21)) % 27.14/27.79 (define @t23 () (@var "Q" $$unsorted)) % 27.14/27.79 (define @t24 () (@list @t21 @t23)) % 27.14/27.79 (define @t25 () (@var "R" $$unsorted)) % 27.14/27.79 (define @t26 () (tptp.implies @t21 @t23)) % 27.14/27.79 (define @t27 () (@list @t21 @t23 @t25)) % 27.14/27.79 (define @t28 () (tptp.implies @t23 @t25)) % 27.14/27.79 (define @t29 () (tptp.not @t21)) % 27.14/27.79 (define @t30 () (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.implies @t29 @t21) @t21)))) % 27.14/27.79 (define @t31 () (tptp.or @t21 @t23)) % 27.14/27.79 (define @t32 () (tptp.or @t21 @t25)) % 27.14/27.79 (define @t33 () (forall @t8 (= @t20 (tptp.not (tptp.and @t12 @t13))))) % 27.14/27.79 (define @t34 () (=> tptp.op_or @t33)) % 27.14/27.79 (define @t35 () (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13))))) % 27.14/27.79 (define @t36 () (=> tptp.op_implies_and @t35)) % 27.14/27.79 (define @t37 () (not tptp.cn3)) % 27.14/27.79 (define @t38 () (not @t5)) % 27.14/27.79 (define @t39 () (not @t6)) % 27.14/27.79 (define @t40 () (or @t39 @t38 @t2)) % 27.14/27.79 (define @t41 () (@quantifiers_skolemize @t30 0)) % 27.14/27.79 (define @t42 () (tptp.implies (tptp.or @t41 @t41) @t41)) % 27.14/27.79 (define @t43 () (tptp.implies @t41 @t41)) % 27.14/27.79 (define @t44 () (@list @t41 @t41)) % 27.14/27.79 (define @t45 () (tptp.is_a_theorem @t42)) % 27.14/27.79 (define @t46 () (tptp.implies @t41 @t43)) % 27.14/27.79 (define @t47 () (tptp.is_a_theorem @t43)) % 27.14/27.79 (define @t48 () (tptp.is_a_theorem (tptp.implies @t46 @t43))) % 27.14/27.79 (define @t49 () (not @t48)) % 27.14/27.79 (define @t50 () (tptp.is_a_theorem @t46)) % 27.14/27.79 (define @t51 () (not @t50)) % 27.14/27.79 (define @t52 () (or @t51 @t49 @t47)) % 27.14/27.79 (define @t53 () (tptp.implies @t43 @t42)) % 27.14/27.79 (define @t54 () (tptp.is_a_theorem @t53)) % 27.14/27.79 (define @t55 () (not @t54)) % 27.14/27.79 (define @t56 () (not @t47)) % 27.14/27.79 (define @t57 () (or @t56 @t55 @t45)) % 27.14/27.79 (define @t58 () (tptp.is_a_theorem (tptp.implies @t43 @t53))) % 27.14/27.79 (define @t59 () (not @t58)) % 27.14/27.79 (define @t60 () (or @t56 @t59 @t54)) % 27.14/27.79 (define @t61 () (not @t60)) % 27.14/27.79 (define @t62 () (forall @t8 @t40)) % 27.14/27.79 (assume @p1 @t10) % 27.14/27.79 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 27.14/27.79 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 27.14/27.79 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 27.14/27.79 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 27.14/27.79 (assume @p6 (= tptp.implies_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16)))))) % 27.14/27.79 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t3))))) % 27.14/27.79 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t1))))) % 27.14/27.79 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t19)))))) % 27.14/27.79 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t20))))) % 27.14/27.79 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t20))))) % 27.14/27.79 (assume @p12 (= tptp.or_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t20 @t15))))))) % 27.14/27.79 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 27.14/27.79 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 27.14/27.79 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 27.14/27.79 (assume @p16 (= tptp.kn1 (forall @t22 (tptp.is_a_theorem (tptp.implies @t21 (tptp.and @t21 @t21)))))) % 27.14/27.79 (assume @p17 (= tptp.kn2 (forall @t24 (tptp.is_a_theorem (tptp.implies (tptp.and @t21 @t23) @t21))))) % 27.14/27.79 (assume @p18 (= tptp.kn3 (forall @t27 (tptp.is_a_theorem (tptp.implies @t26 (tptp.implies (tptp.not (tptp.and @t23 @t25)) (tptp.not (tptp.and @t25 @t21)))))))) % 27.14/27.79 (assume @p19 (= tptp.cn1 (forall @t27 (tptp.is_a_theorem (tptp.implies @t26 (tptp.implies @t28 (tptp.implies @t21 @t25))))))) % 27.14/27.79 (assume @p20 (= tptp.cn2 (forall @t24 (tptp.is_a_theorem (tptp.implies @t21 (tptp.implies @t29 @t23)))))) % 27.14/27.79 (assume @p21 (= tptp.cn3 @t30)) % 27.14/27.79 (assume @p22 (= tptp.r1 (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 @t21) @t21))))) % 27.14/27.79 (assume @p23 (= tptp.r2 (forall @t24 (tptp.is_a_theorem (tptp.implies @t23 @t31))))) % 27.14/27.79 (assume @p24 (= tptp.r3 (forall @t24 (tptp.is_a_theorem (tptp.implies @t31 (tptp.or @t23 @t21)))))) % 27.14/27.79 (assume @p25 (= tptp.r4 (forall @t27 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 (tptp.or @t23 @t25)) (tptp.or @t23 @t32)))))) % 27.14/27.79 (assume @p26 (= tptp.r5 (forall @t27 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t31 @t32)))))) % 27.14/27.79 (assume @p27 @t34) % 27.14/27.79 (assume @p28 (=> tptp.op_and (forall @t8 (= @t19 (tptp.not (tptp.or @t12 @t13)))))) % 27.14/27.79 (assume @p29 @t36) % 27.14/27.79 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t12 @t1))))) % 27.14/27.79 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 27.14/27.79 (assume @p32 tptp.op_or) % 27.14/27.79 (assume @p33 tptp.op_implies_and) % 27.14/27.79 (assume @p34 tptp.op_equiv) % 27.14/27.79 (assume @p35 tptp.modus_ponens) % 27.14/27.79 (assume @p36 tptp.modus_tollens) % 27.14/27.79 (assume @p37 tptp.implies_1) % 27.14/27.79 (assume @p38 tptp.implies_2) % 27.14/27.79 (assume @p39 tptp.implies_3) % 27.14/27.79 (assume @p40 tptp.and_1) % 27.14/27.79 (assume @p41 tptp.and_2) % 27.14/27.79 (assume @p42 tptp.and_3) % 27.14/27.79 (assume @p43 tptp.or_1) % 27.14/27.79 (assume @p44 tptp.or_2) % 27.14/27.79 (assume @p45 tptp.or_3) % 27.14/27.79 (assume @p46 tptp.equivalence_1) % 27.14/27.79 (assume @p47 tptp.equivalence_2) % 27.14/27.79 (assume @p48 tptp.equivalence_3) % 27.14/27.79 (assume @p49 tptp.substitution_of_equivalents) % 27.14/27.79 (assume @p50 tptp.op_implies) % 27.14/27.79 (assume @p51 @t37) % 27.14/27.79 (assume @p52 true) % 27.14/27.79 (step @p53 :rule aci_norm :args ((= (or (or @t39 @t38) @t2) @t40))) % 27.14/27.79 (step @p54 :rule refl :args (@t2)) % 27.14/27.79 (step @p55 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 27.14/27.79 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or (not @t7) @t2))) % 27.14/27.79 (step @p57 :rule trans :premises (@p56 @p53)) % 27.14/27.79 (step @p58 :rule bool-impl-elim :args (@t7 @t2)) % 27.14/27.79 (step @p59 :rule trans :premises (@p58 @p57)) % 27.14/27.79 (step @p60 :rule cong :premises (@p59) :args (@t9)) % 27.14/27.79 (step @p61 :rule refl :args (tptp.modus_ponens)) % 27.14/27.79 (step @p62 :rule cong :premises (@p61 @p60) :args (@t10)) % 27.14/27.79 (step @p63 :rule eq_resolve :premises (@p1 @p62)) % 27.14/27.79 (step @p64 :rule eq_resolve :premises (@p35 @p63)) % 27.14/27.79 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t43 @t42))) % 27.14/27.79 (step @p66 :rule cong :premises (@p21) :args (@t37)) % 27.14/27.79 (step @p67 :rule eq_resolve :premises (@p51 @p66)) % 27.14/27.79 (step @p68 :rule skolemize :premises (@p67)) % 27.14/27.79 (step @p69 :rule false_intro :premises (@p68)) % 27.14/27.79 (step @p70 :rule refl :args (@t41)) % 27.14/27.79 (step @p71 :rule bool-impl-true2 :args (@t35)) % 27.14/27.79 (step @p72 :rule refl :args (@t35)) % 27.14/27.79 (step @p73 :rule bool-eq-true :args (tptp.op_implies_and)) % 27.14/27.79 (step @p74 :rule symm :premises (@p73)) % 27.14/27.79 (step @p75 :rule eq_resolve :premises (@p33 @p74)) % 27.14/27.79 (step @p76 :rule cong :premises (@p75 @p72) :args (@t36)) % 27.14/27.79 (step @p77 :rule trans :premises (@p76 @p71)) % 27.14/27.79 (step @p78 :rule eq_resolve :premises (@p29 @p77)) % 27.14/27.79 (step @p79 :rule instantiate :premises (@p78) :args ((@list (tptp.not @t41) @t41))) % 27.14/27.79 (step @p80 :rule symm :premises (@p79)) % 27.14/27.79 (step @p81 :rule bool-impl-true2 :args (@t33)) % 27.14/27.79 (step @p82 :rule refl :args (@t33)) % 27.14/27.79 (step @p83 :rule bool-eq-true :args (tptp.op_or)) % 27.14/27.79 (step @p84 :rule symm :premises (@p83)) % 27.14/27.79 (step @p85 :rule eq_resolve :premises (@p32 @p84)) % 27.14/27.79 (step @p86 :rule cong :premises (@p85 @p82) :args (@t34)) % 27.14/27.79 (step @p87 :rule trans :premises (@p86 @p81)) % 27.14/27.79 (step @p88 :rule eq_resolve :premises (@p27 @p87)) % 27.14/27.79 (step @p89 :rule instantiate :premises (@p88) :args (@t44)) % 27.14/27.79 (step @p90 :rule trans :premises (@p89 @p80)) % 27.14/27.79 (step @p91 :rule cong :premises (@p90 @p70) :args (@t42)) % 27.14/27.79 (step @p92 :rule cong :premises (@p91) :args (@t45)) % 27.14/27.79 (step @p93 :rule trans :premises (@p92 @p69)) % 27.14/27.79 (step @p94 :rule false_elim :premises (@p93)) % 27.14/27.79 (step @p95 :rule instantiate :premises (@p64) :args ((@list @t46 @t43))) % 27.14/27.79 (step @p96 :rule eq_resolve :premises (@p38 @p5)) % 27.14/27.79 (step @p97 :rule instantiate :premises (@p96) :args (@t44)) % 27.14/27.79 (step @p98 :rule eq_resolve :premises (@p37 @p4)) % 27.14/27.79 (step @p99 :rule instantiate :premises (@p98) :args (@t44)) % 27.14/27.79 (step @p100 :rule cnf_or_pos :args (@t52)) % 27.14/27.79 (step @p101 :rule reordering :premises (@p100) :args ((or @t47 @t51 @t49 (not @t52)))) % 27.14/27.79 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p97 @p95) :args (@t47 (@list false false false) (@list @t50 @t48 @t52))) % 27.14/27.79 (step @p103 :rule cnf_or_pos :args (@t57)) % 27.14/27.79 (step @p104 :rule reordering :premises (@p103) :args ((or @t56 @t45 @t55 (not @t57)))) % 27.14/27.79 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p94 @p65) :args (@t55 (@list false true false) (@list @t47 @t45 @t57))) % 27.14/27.79 (step @p106 :rule eq_resolve :premises (@p45 @p12)) % 27.14/27.79 (step @p107 :rule instantiate :premises (@p106) :args ((@list @t41 @t41 @t41))) % 27.14/27.79 (step @p108 :rule cnf_or_pos :args (@t60)) % 27.14/27.79 (step @p109 :rule reordering :premises (@p108) :args ((or @t56 @t59 @t54 @t61))) % 27.14/27.79 (step @p110 :rule chain_m_resolution :premises (@p109 @p102 @p107 @p105) :args (@t61 (@list false false true) (@list @t47 @t58 @t54))) % 27.14/27.79 (assume-push @p117 @t62) % 27.14/27.79 (step @p112 :rule instantiate :premises (@p64) :args ((@list @t43 @t53))) % 27.14/27.79 (step-pop @p118 :rule scope :premises (@p112)) % 27.14/27.79 (step @p113 :rule process_scope :premises (@p118) :args (@t60)) % 27.14/27.79 (step @p115 :rule implies_elim :premises (@p113)) % 27.14/27.79 (step @p116 false :rule chain_m_resolution :premises (@p115 @p110 @p64) :args (false (@list true false) (@list @t60 @t62))) % 27.14/27.79 ) % 27.14/27.79 % SZS output end Proof % 27.14/27.79 % cvc5 exiting %------------------------------------------------------------------------------