%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL454+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 : n019.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 15.31s 15.96s % Output : Proof 15.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL454+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 % 0.10/0.37 % Computer : n019.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 21:41:08 UTC 2026 % 0.10/0.38 % CPUTime : % 0.10/0.45 %----Proving TF0_NAR, FOF, or CNF % 15.31/15.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.31/15.96 --- Run --no-e-matching --full-saturate-quant at 6... % 15.31/15.96 % SZS status Theorem % 15.31/15.96 % SZS output start Proof % 15.31/15.96 ( % 15.31/15.96 (declare-sort $$unsorted 0) % 15.31/15.96 (declare-const tptp.op_equiv Bool) % 15.31/15.96 (declare-const tptp.op_implies_or Bool) % 15.31/15.96 (declare-const tptp.op_and Bool) % 15.31/15.96 (declare-const tptp.r4 Bool) % 15.31/15.96 (declare-const tptp.r3 Bool) % 15.31/15.96 (declare-const tptp.implies_2 Bool) % 15.31/15.96 (declare-const tptp.and_2 Bool) % 15.31/15.96 (declare-const tptp.modus_tollens Bool) % 15.31/15.96 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 15.31/15.96 (declare-const tptp.op_or Bool) % 15.31/15.96 (declare-const tptp.or_1 Bool) % 15.31/15.96 (declare-const tptp.equivalence_3 Bool) % 15.31/15.96 (declare-const tptp.and_1 Bool) % 15.31/15.96 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 15.31/15.96 (declare-const tptp.implies_3 Bool) % 15.31/15.96 (declare-const tptp.substitution_of_equivalents Bool) % 15.31/15.96 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 15.31/15.96 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 15.31/15.96 (declare-const tptp.op_implies_and Bool) % 15.31/15.96 (declare-const tptp.or_3 Bool) % 15.31/15.96 (declare-const tptp.equivalence_2 Bool) % 15.31/15.96 (declare-const tptp.modus_ponens Bool) % 15.31/15.96 (declare-const tptp.implies_1 Bool) % 15.31/15.96 (declare-const tptp.equivalence_1 Bool) % 15.31/15.96 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 15.31/15.96 (declare-const tptp.r5 Bool) % 15.31/15.96 (declare-const tptp.and_3 Bool) % 15.31/15.96 (declare-const tptp.cn3 Bool) % 15.31/15.96 (declare-const tptp.or_2 Bool) % 15.31/15.96 (declare-const tptp.kn1 Bool) % 15.31/15.96 (declare-const tptp.cn1 Bool) % 15.31/15.96 (declare-const tptp.kn2 Bool) % 15.31/15.96 (declare-const tptp.cn2 Bool) % 15.31/15.96 (declare-const tptp.kn3 Bool) % 15.31/15.96 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 15.31/15.96 (declare-const tptp.r1 Bool) % 15.31/15.96 (declare-const tptp.r2 Bool) % 15.31/15.96 (define @t1 () (@var "Y" $$unsorted)) % 15.31/15.96 (define @t2 () (tptp.is_a_theorem @t1)) % 15.31/15.96 (define @t3 () (@var "X" $$unsorted)) % 15.31/15.96 (define @t4 () (tptp.implies @t3 @t1)) % 15.31/15.96 (define @t5 () (tptp.is_a_theorem @t4)) % 15.31/15.96 (define @t6 () (tptp.is_a_theorem @t3)) % 15.31/15.96 (define @t7 () (and @t6 @t5)) % 15.31/15.96 (define @t8 () (@list @t3 @t1)) % 15.31/15.96 (define @t9 () (forall @t8 (=> @t7 @t2))) % 15.31/15.96 (define @t10 () (= tptp.modus_ponens @t9)) % 15.31/15.96 (define @t11 () (tptp.equiv @t3 @t1)) % 15.31/15.96 (define @t12 () (tptp.not @t3)) % 15.31/15.96 (define @t13 () (tptp.not @t1)) % 15.31/15.96 (define @t14 () (tptp.implies @t1 @t3)) % 15.31/15.96 (define @t15 () (@var "Z" $$unsorted)) % 15.31/15.96 (define @t16 () (tptp.implies @t3 @t15)) % 15.31/15.96 (define @t17 () (tptp.implies @t1 @t15)) % 15.31/15.96 (define @t18 () (@list @t3 @t1 @t15)) % 15.31/15.96 (define @t19 () (tptp.and @t3 @t1)) % 15.31/15.96 (define @t20 () (tptp.or @t3 @t1)) % 15.31/15.96 (define @t21 () (@var "P" $$unsorted)) % 15.31/15.96 (define @t22 () (@list @t21)) % 15.31/15.96 (define @t23 () (@var "Q" $$unsorted)) % 15.31/15.96 (define @t24 () (@list @t21 @t23)) % 15.31/15.96 (define @t25 () (@var "R" $$unsorted)) % 15.31/15.96 (define @t26 () (tptp.implies @t21 @t23)) % 15.31/15.96 (define @t27 () (@list @t21 @t23 @t25)) % 15.31/15.96 (define @t28 () (tptp.implies @t23 @t25)) % 15.31/15.96 (define @t29 () (tptp.not @t21)) % 15.31/15.96 (define @t30 () (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 @t21) @t21)))) % 15.31/15.96 (define @t31 () (tptp.or @t21 @t23)) % 15.31/15.96 (define @t32 () (tptp.or @t21 @t25)) % 15.31/15.96 (define @t33 () (not tptp.r1)) % 15.31/15.96 (define @t34 () (not @t5)) % 15.31/15.96 (define @t35 () (not @t6)) % 15.31/15.96 (define @t36 () (or @t35 @t34 @t2)) % 15.31/15.96 (define @t37 () (@quantifiers_skolemize @t30 0)) % 15.31/15.96 (define @t38 () (tptp.implies (tptp.or @t37 @t37) @t37)) % 15.31/15.96 (define @t39 () (tptp.implies @t37 @t37)) % 15.31/15.96 (define @t40 () (tptp.implies @t37 @t39)) % 15.31/15.96 (define @t41 () (@list @t37 @t37)) % 15.31/15.96 (define @t42 () (tptp.is_a_theorem @t39)) % 15.31/15.96 (define @t43 () (tptp.is_a_theorem (tptp.implies @t40 @t39))) % 15.31/15.96 (define @t44 () (not @t43)) % 15.31/15.96 (define @t45 () (tptp.is_a_theorem @t40)) % 15.31/15.96 (define @t46 () (not @t45)) % 15.31/15.96 (define @t47 () (or @t46 @t44 @t42)) % 15.31/15.96 (define @t48 () (tptp.is_a_theorem @t38)) % 15.31/15.96 (define @t49 () (tptp.implies @t39 @t38)) % 15.31/15.96 (define @t50 () (tptp.is_a_theorem @t49)) % 15.31/15.96 (define @t51 () (not @t50)) % 15.31/15.96 (define @t52 () (not @t42)) % 15.31/15.96 (define @t53 () (or @t52 @t51 @t48)) % 15.31/15.96 (define @t54 () (tptp.is_a_theorem (tptp.implies @t39 @t49))) % 15.31/15.96 (define @t55 () (not @t54)) % 15.31/15.96 (define @t56 () (or @t52 @t55 @t50)) % 15.31/15.96 (define @t57 () (not @t56)) % 15.31/15.96 (define @t58 () (forall @t8 @t36)) % 15.31/15.96 (assume @p1 @t10) % 15.31/15.96 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 15.31/15.96 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 15.31/15.96 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 15.31/15.96 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 15.31/15.96 (assume @p6 (= tptp.implies_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16)))))) % 15.31/15.96 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t3))))) % 15.31/15.96 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t1))))) % 15.31/15.96 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t19)))))) % 15.31/15.96 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t20))))) % 15.31/15.96 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t20))))) % 15.31/15.96 (assume @p12 (= tptp.or_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t20 @t15))))))) % 15.31/15.96 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 15.31/15.96 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 15.31/15.96 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 15.31/15.96 (assume @p16 (= tptp.kn1 (forall @t22 (tptp.is_a_theorem (tptp.implies @t21 (tptp.and @t21 @t21)))))) % 15.31/15.96 (assume @p17 (= tptp.kn2 (forall @t24 (tptp.is_a_theorem (tptp.implies (tptp.and @t21 @t23) @t21))))) % 15.31/15.96 (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)))))))) % 15.31/15.96 (assume @p19 (= tptp.cn1 (forall @t27 (tptp.is_a_theorem (tptp.implies @t26 (tptp.implies @t28 (tptp.implies @t21 @t25))))))) % 15.31/15.96 (assume @p20 (= tptp.cn2 (forall @t24 (tptp.is_a_theorem (tptp.implies @t21 (tptp.implies @t29 @t23)))))) % 15.31/15.96 (assume @p21 (= tptp.cn3 (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.implies @t29 @t21) @t21))))) % 15.31/15.96 (assume @p22 (= tptp.r1 @t30)) % 15.31/15.96 (assume @p23 (= tptp.r2 (forall @t24 (tptp.is_a_theorem (tptp.implies @t23 @t31))))) % 15.31/15.96 (assume @p24 (= tptp.r3 (forall @t24 (tptp.is_a_theorem (tptp.implies @t31 (tptp.or @t23 @t21)))))) % 15.31/15.96 (assume @p25 (= tptp.r4 (forall @t27 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 (tptp.or @t23 @t25)) (tptp.or @t23 @t32)))))) % 15.31/15.96 (assume @p26 (= tptp.r5 (forall @t27 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t31 @t32)))))) % 15.31/15.96 (assume @p27 (=> tptp.op_or (forall @t8 (= @t20 (tptp.not (tptp.and @t12 @t13)))))) % 15.31/15.96 (assume @p28 (=> tptp.op_and (forall @t8 (= @t19 (tptp.not (tptp.or @t12 @t13)))))) % 15.31/15.96 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13)))))) % 15.31/15.96 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t12 @t1))))) % 15.31/15.96 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 15.31/15.96 (assume @p32 tptp.op_or) % 15.31/15.96 (assume @p33 tptp.op_implies_and) % 15.31/15.96 (assume @p34 tptp.op_equiv) % 15.31/15.96 (assume @p35 tptp.modus_ponens) % 15.31/15.96 (assume @p36 tptp.modus_tollens) % 15.31/15.96 (assume @p37 tptp.implies_1) % 15.31/15.96 (assume @p38 tptp.implies_2) % 15.31/15.96 (assume @p39 tptp.implies_3) % 15.31/15.96 (assume @p40 tptp.and_1) % 15.31/15.96 (assume @p41 tptp.and_2) % 15.31/15.96 (assume @p42 tptp.and_3) % 15.31/15.96 (assume @p43 tptp.or_1) % 15.31/15.96 (assume @p44 tptp.or_2) % 15.31/15.96 (assume @p45 tptp.or_3) % 15.31/15.96 (assume @p46 tptp.equivalence_1) % 15.31/15.96 (assume @p47 tptp.equivalence_2) % 15.31/15.96 (assume @p48 tptp.equivalence_3) % 15.31/15.96 (assume @p49 tptp.substitution_of_equivalents) % 15.31/15.96 (assume @p50 tptp.op_implies_or) % 15.31/15.96 (assume @p51 tptp.op_and) % 15.31/15.96 (assume @p52 @t33) % 15.31/15.96 (assume @p53 true) % 15.31/15.96 (step @p54 :rule aci_norm :args ((= (or (or @t35 @t34) @t2) @t36))) % 15.31/15.96 (step @p55 :rule refl :args (@t2)) % 15.31/15.96 (step @p56 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 15.31/15.96 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or (not @t7) @t2))) % 15.31/15.96 (step @p58 :rule trans :premises (@p57 @p54)) % 15.31/15.96 (step @p59 :rule bool-impl-elim :args (@t7 @t2)) % 15.31/15.96 (step @p60 :rule trans :premises (@p59 @p58)) % 15.31/15.96 (step @p61 :rule cong :premises (@p60) :args (@t9)) % 15.31/15.96 (step @p62 :rule refl :args (tptp.modus_ponens)) % 15.31/15.96 (step @p63 :rule cong :premises (@p62 @p61) :args (@t10)) % 15.31/15.96 (step @p64 :rule eq_resolve :premises (@p1 @p63)) % 15.31/15.96 (step @p65 :rule eq_resolve :premises (@p35 @p64)) % 15.31/15.96 (step @p66 :rule instantiate :premises (@p65) :args ((@list @t39 @t38))) % 15.31/15.96 (step @p67 :rule instantiate :premises (@p65) :args ((@list @t40 @t39))) % 15.31/15.96 (step @p68 :rule eq_resolve :premises (@p38 @p5)) % 15.31/15.96 (step @p69 :rule instantiate :premises (@p68) :args (@t41)) % 15.31/15.96 (step @p70 :rule eq_resolve :premises (@p37 @p4)) % 15.31/15.96 (step @p71 :rule instantiate :premises (@p70) :args (@t41)) % 15.31/15.96 (step @p72 :rule cnf_or_pos :args (@t47)) % 15.31/15.96 (step @p73 :rule reordering :premises (@p72) :args ((or @t42 @t46 @t44 (not @t47)))) % 15.31/15.96 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p69 @p67) :args (@t42 (@list false false false) (@list @t45 @t43 @t47))) % 15.31/15.96 (step @p75 :rule cong :premises (@p22) :args (@t33)) % 15.31/15.96 (step @p76 :rule eq_resolve :premises (@p52 @p75)) % 15.31/15.96 (step @p77 :rule skolemize :premises (@p76)) % 15.31/15.96 (step @p78 :rule cnf_or_pos :args (@t53)) % 15.31/15.96 (step @p79 :rule reordering :premises (@p78) :args ((or @t48 @t52 @t51 (not @t53)))) % 15.31/15.96 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p74 @p66) :args (@t51 (@list true false false) (@list @t48 @t42 @t53))) % 15.31/15.96 (step @p81 :rule eq_resolve :premises (@p45 @p12)) % 15.31/15.96 (step @p82 :rule instantiate :premises (@p81) :args ((@list @t37 @t37 @t37))) % 15.31/15.96 (step @p83 :rule cnf_or_pos :args (@t56)) % 15.31/15.96 (step @p84 :rule reordering :premises (@p83) :args ((or @t52 @t55 @t50 @t57))) % 15.31/15.96 (step @p85 :rule chain_m_resolution :premises (@p84 @p74 @p82 @p80) :args (@t57 (@list false false true) (@list @t42 @t54 @t50))) % 15.31/15.96 (assume-push @p92 @t58) % 15.31/15.96 (step @p87 :rule instantiate :premises (@p65) :args ((@list @t39 @t49))) % 15.31/15.96 (step-pop @p93 :rule scope :premises (@p87)) % 15.31/15.96 (step @p88 :rule process_scope :premises (@p93) :args (@t56)) % 15.31/15.96 (step @p90 :rule implies_elim :premises (@p88)) % 15.31/15.96 (step @p91 false :rule chain_m_resolution :premises (@p90 @p85 @p65) :args (false (@list true false) (@list @t56 @t58))) % 15.31/15.96 ) % 15.31/15.96 % SZS output end Proof % 15.31/15.96 % cvc5 exiting %------------------------------------------------------------------------------