%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n007.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 11:22:56 AM UTC 2026 % Result : Theorem 0.43s 0.71s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.12/0.38 % Computer : n007.cluster.edu % 0.12/0.38 % Model : x86_64 x86_64 % 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.38 % Memory : 8046.5625MB % 0.12/0.38 % OS : Linux 6.8.0-71-generic % 0.12/0.39 % CPULimit : 300 % 0.12/0.39 % WCLimit : 300 % 0.12/0.39 % DateTime : Fri Sep 4 18:41:09 UTC 2026 % 0.12/0.39 % CPUTime : % 0.22/0.47 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.71 % SZS status Theorem % 0.43/0.71 % SZS output start Proof % 0.43/0.71 ( % 0.43/0.71 (declare-sort $$unsorted 0) % 0.43/0.71 (declare-const tptp.op_equiv Bool) % 0.43/0.71 (declare-const tptp.op_implies_or Bool) % 0.43/0.71 (declare-const tptp.op_and Bool) % 0.43/0.71 (declare-const tptp.r4 Bool) % 0.43/0.71 (declare-const tptp.r3 Bool) % 0.43/0.71 (declare-const tptp.implies_2 Bool) % 0.43/0.71 (declare-const tptp.and_2 Bool) % 0.43/0.71 (declare-const tptp.modus_tollens Bool) % 0.43/0.71 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 0.43/0.71 (declare-const tptp.op_or Bool) % 0.43/0.71 (declare-const tptp.or_1 Bool) % 0.43/0.71 (declare-const tptp.equivalence_3 Bool) % 0.43/0.71 (declare-const tptp.and_1 Bool) % 0.43/0.71 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.71 (declare-const tptp.implies_3 Bool) % 0.43/0.71 (declare-const tptp.substitution_of_equivalents Bool) % 0.43/0.71 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.71 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.71 (declare-const tptp.op_implies_and Bool) % 0.43/0.71 (declare-const tptp.or_3 Bool) % 0.43/0.71 (declare-const tptp.equivalence_2 Bool) % 0.43/0.71 (declare-const tptp.modus_ponens Bool) % 0.43/0.71 (declare-const tptp.implies_1 Bool) % 0.43/0.71 (declare-const tptp.equivalence_1 Bool) % 0.43/0.71 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.71 (declare-const tptp.r5 Bool) % 0.43/0.71 (declare-const tptp.and_3 Bool) % 0.43/0.71 (declare-const tptp.cn3 Bool) % 0.43/0.71 (declare-const tptp.or_2 Bool) % 0.43/0.71 (declare-const tptp.kn1 Bool) % 0.43/0.71 (declare-const tptp.cn1 Bool) % 0.43/0.71 (declare-const tptp.kn2 Bool) % 0.43/0.71 (declare-const tptp.cn2 Bool) % 0.43/0.71 (declare-const tptp.kn3 Bool) % 0.43/0.71 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 0.43/0.71 (declare-const tptp.r1 Bool) % 0.43/0.71 (declare-const tptp.r2 Bool) % 0.43/0.71 (define @t1 () (@var "Y" $$unsorted)) % 0.43/0.71 (define @t2 () (tptp.is_a_theorem @t1)) % 0.43/0.71 (define @t3 () (@var "X" $$unsorted)) % 0.43/0.71 (define @t4 () (tptp.implies @t3 @t1)) % 0.43/0.71 (define @t5 () (tptp.is_a_theorem @t4)) % 0.43/0.71 (define @t6 () (tptp.is_a_theorem @t3)) % 0.43/0.71 (define @t7 () (and @t6 @t5)) % 0.43/0.71 (define @t8 () (@list @t3 @t1)) % 0.43/0.71 (define @t9 () (forall @t8 (=> @t7 @t2))) % 0.43/0.71 (define @t10 () (= tptp.modus_ponens @t9)) % 0.43/0.71 (define @t11 () (tptp.equiv @t3 @t1)) % 0.43/0.71 (define @t12 () (tptp.not @t3)) % 0.43/0.71 (define @t13 () (tptp.not @t1)) % 0.43/0.71 (define @t14 () (tptp.implies @t1 @t3)) % 0.43/0.71 (define @t15 () (@var "Z" $$unsorted)) % 0.43/0.71 (define @t16 () (tptp.implies @t3 @t15)) % 0.43/0.71 (define @t17 () (tptp.implies @t1 @t15)) % 0.43/0.71 (define @t18 () (@list @t3 @t1 @t15)) % 0.43/0.71 (define @t19 () (tptp.and @t3 @t1)) % 0.43/0.71 (define @t20 () (tptp.or @t3 @t1)) % 0.43/0.71 (define @t21 () (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t20)))) % 0.43/0.71 (define @t22 () (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t20)))) % 0.43/0.71 (define @t23 () (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t20 @t15)))))) % 0.43/0.71 (define @t24 () (@var "P" $$unsorted)) % 0.43/0.71 (define @t25 () (@list @t24)) % 0.43/0.71 (define @t26 () (@var "Q" $$unsorted)) % 0.43/0.71 (define @t27 () (@list @t24 @t26)) % 0.43/0.71 (define @t28 () (@var "R" $$unsorted)) % 0.43/0.71 (define @t29 () (tptp.implies @t24 @t26)) % 0.43/0.71 (define @t30 () (@list @t24 @t26 @t28)) % 0.43/0.71 (define @t31 () (tptp.implies @t26 @t28)) % 0.43/0.71 (define @t32 () (tptp.not @t24)) % 0.43/0.71 (define @t33 () (tptp.or @t24 @t26)) % 0.43/0.71 (define @t34 () (forall @t27 (tptp.is_a_theorem (tptp.implies @t33 (tptp.or @t26 @t24))))) % 0.43/0.71 (define @t35 () (tptp.or @t24 @t28)) % 0.43/0.71 (define @t36 () (@list false)) % 0.43/0.71 (define @t37 () (@quantifiers_skolemize @t34 0)) % 0.43/0.71 (define @t38 () (@quantifiers_skolemize @t34 1)) % 0.43/0.71 (define @t39 () (@list @t38 @t37)) % 0.43/0.71 (define @t40 () (tptp.or @t38 @t37)) % 0.43/0.71 (define @t41 () (not @t5)) % 0.43/0.71 (define @t42 () (not @t6)) % 0.43/0.71 (define @t43 () (or @t42 @t41 @t2)) % 0.43/0.71 (define @t44 () (forall @t8 @t43)) % 0.43/0.71 (define @t45 () (tptp.implies (tptp.or @t37 @t38) @t40)) % 0.43/0.71 (define @t46 () (tptp.implies @t38 @t40)) % 0.43/0.71 (define @t47 () (tptp.implies @t46 @t45)) % 0.43/0.71 (define @t48 () (tptp.implies @t37 @t40)) % 0.43/0.71 (define @t49 () (tptp.is_a_theorem @t45)) % 0.43/0.71 (define @t50 () (tptp.is_a_theorem @t47)) % 0.43/0.71 (define @t51 () (not @t50)) % 0.43/0.71 (define @t52 () (tptp.is_a_theorem @t46)) % 0.43/0.71 (define @t53 () (not @t52)) % 0.43/0.71 (define @t54 () (or @t53 @t51 @t49)) % 0.43/0.71 (define @t55 () (tptp.is_a_theorem (tptp.implies @t48 @t47))) % 0.43/0.71 (define @t56 () (not @t55)) % 0.43/0.71 (define @t57 () (tptp.is_a_theorem @t48)) % 0.43/0.71 (define @t58 () (not @t57)) % 0.43/0.71 (define @t59 () (or @t58 @t56 @t50)) % 0.43/0.71 (assume @p1 @t10) % 0.43/0.71 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 0.43/0.71 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 0.43/0.71 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 0.43/0.71 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 0.43/0.71 (assume @p6 (= tptp.implies_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16)))))) % 0.43/0.71 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t3))))) % 0.43/0.71 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t1))))) % 0.43/0.71 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t19)))))) % 0.43/0.71 (assume @p10 (= tptp.or_1 @t21)) % 0.43/0.71 (assume @p11 (= tptp.or_2 @t22)) % 0.43/0.71 (assume @p12 (= tptp.or_3 @t23)) % 0.43/0.71 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 0.43/0.71 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 0.43/0.71 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 0.43/0.71 (assume @p16 (= tptp.kn1 (forall @t25 (tptp.is_a_theorem (tptp.implies @t24 (tptp.and @t24 @t24)))))) % 0.43/0.71 (assume @p17 (= tptp.kn2 (forall @t27 (tptp.is_a_theorem (tptp.implies (tptp.and @t24 @t26) @t24))))) % 0.43/0.71 (assume @p18 (= tptp.kn3 (forall @t30 (tptp.is_a_theorem (tptp.implies @t29 (tptp.implies (tptp.not (tptp.and @t26 @t28)) (tptp.not (tptp.and @t28 @t24)))))))) % 0.43/0.71 (assume @p19 (= tptp.cn1 (forall @t30 (tptp.is_a_theorem (tptp.implies @t29 (tptp.implies @t31 (tptp.implies @t24 @t28))))))) % 0.43/0.71 (assume @p20 (= tptp.cn2 (forall @t27 (tptp.is_a_theorem (tptp.implies @t24 (tptp.implies @t32 @t26)))))) % 0.43/0.71 (assume @p21 (= tptp.cn3 (forall @t25 (tptp.is_a_theorem (tptp.implies (tptp.implies @t32 @t24) @t24))))) % 0.43/0.71 (assume @p22 (= tptp.r1 (forall @t25 (tptp.is_a_theorem (tptp.implies (tptp.or @t24 @t24) @t24))))) % 0.43/0.71 (assume @p23 (= tptp.r2 (forall @t27 (tptp.is_a_theorem (tptp.implies @t26 @t33))))) % 0.43/0.71 (assume @p24 (= tptp.r3 @t34)) % 0.43/0.71 (assume @p25 (= tptp.r4 (forall @t30 (tptp.is_a_theorem (tptp.implies (tptp.or @t24 (tptp.or @t26 @t28)) (tptp.or @t26 @t35)))))) % 0.43/0.71 (assume @p26 (= tptp.r5 (forall @t30 (tptp.is_a_theorem (tptp.implies @t31 (tptp.implies @t33 @t35)))))) % 0.43/0.71 (assume @p27 (=> tptp.op_or (forall @t8 (= @t20 (tptp.not (tptp.and @t12 @t13)))))) % 0.43/0.71 (assume @p28 (=> tptp.op_and (forall @t8 (= @t19 (tptp.not (tptp.or @t12 @t13)))))) % 0.43/0.71 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13)))))) % 0.43/0.71 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t12 @t1))))) % 0.43/0.71 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 0.43/0.71 (assume @p32 tptp.op_or) % 0.43/0.71 (assume @p33 tptp.op_implies_and) % 0.43/0.71 (assume @p34 tptp.op_equiv) % 0.43/0.71 (assume @p35 tptp.modus_ponens) % 0.43/0.71 (assume @p36 tptp.modus_tollens) % 0.43/0.71 (assume @p37 tptp.implies_1) % 0.43/0.71 (assume @p38 tptp.implies_2) % 0.43/0.71 (assume @p39 tptp.implies_3) % 0.43/0.71 (assume @p40 tptp.and_1) % 0.43/0.71 (assume @p41 tptp.and_2) % 0.43/0.71 (assume @p42 tptp.and_3) % 0.43/0.71 (assume @p43 tptp.or_1) % 0.43/0.71 (assume @p44 tptp.or_2) % 0.43/0.71 (assume @p45 tptp.or_3) % 0.43/0.71 (assume @p46 tptp.equivalence_1) % 0.43/0.71 (assume @p47 tptp.equivalence_2) % 0.43/0.71 (assume @p48 tptp.equivalence_3) % 0.43/0.71 (assume @p49 tptp.substitution_of_equivalents) % 0.43/0.71 (assume @p50 tptp.op_implies_or) % 0.43/0.71 (assume @p51 tptp.op_and) % 0.43/0.71 (assume @p52 (not tptp.r3)) % 0.43/0.71 (assume @p53 true) % 0.43/0.71 (step @p54 :rule equiv_elim1 :premises (@p11)) % 0.43/0.71 (step @p55 :rule reordering :premises (@p54) :args ((or @t22 (not tptp.or_2)))) % 0.43/0.71 (step @p56 :rule chain_m_resolution :premises (@p55 @p44) :args (@t22 @t36 (@list tptp.or_2))) % 0.43/0.71 (step @p57 :rule instantiate :premises (@p56) :args (@t39)) % 0.43/0.71 (step @p58 :rule equiv_elim1 :premises (@p12)) % 0.43/0.71 (step @p59 :rule reordering :premises (@p58) :args ((or @t23 (not tptp.or_3)))) % 0.43/0.71 (step @p60 :rule chain_m_resolution :premises (@p59 @p45) :args (@t23 @t36 (@list tptp.or_3))) % 0.43/0.71 (step @p61 :rule instantiate :premises (@p60) :args ((@list @t37 @t38 @t40))) % 0.43/0.71 (step @p62 :rule aci_norm :args ((= (or (or @t42 @t41) @t2) @t43))) % 0.43/0.71 (step @p63 :rule refl :args (@t2)) % 0.43/0.71 (step @p64 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 0.43/0.71 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or (not @t7) @t2))) % 0.43/0.71 (step @p66 :rule trans :premises (@p65 @p62)) % 0.43/0.71 (step @p67 :rule bool-impl-elim :args (@t7 @t2)) % 0.43/0.71 (step @p68 :rule trans :premises (@p67 @p66)) % 0.43/0.71 (step @p69 :rule cong :premises (@p68) :args (@t9)) % 0.43/0.71 (step @p70 :rule refl :args (tptp.modus_ponens)) % 0.43/0.71 (step @p71 :rule cong :premises (@p70 @p69) :args (@t10)) % 0.43/0.71 (step @p72 :rule eq_resolve :premises (@p1 @p71)) % 0.43/0.71 (step @p73 :rule equiv_elim1 :premises (@p72)) % 0.43/0.71 (step @p74 :rule reordering :premises (@p73) :args ((or @t44 (not tptp.modus_ponens)))) % 0.43/0.71 (step @p75 :rule chain_m_resolution :premises (@p74 @p35) :args (@t44 @t36 (@list tptp.modus_ponens))) % 0.43/0.71 (step @p76 :rule instantiate :premises (@p75) :args ((@list @t48 @t47))) % 0.43/0.71 (step @p77 :rule instantiate :premises (@p75) :args ((@list @t46 @t45))) % 0.43/0.71 (step @p78 :rule equiv_elim1 :premises (@p10)) % 0.43/0.71 (step @p79 :rule reordering :premises (@p78) :args ((or @t21 (not tptp.or_1)))) % 0.43/0.71 (step @p80 :rule chain_m_resolution :premises (@p79 @p43) :args (@t21 @t36 (@list tptp.or_1))) % 0.43/0.71 (step @p81 :rule instantiate :premises (@p80) :args (@t39)) % 0.43/0.71 (step @p82 :rule equiv_elim2 :premises (@p24)) % 0.43/0.71 (step @p83 :rule chain_m_resolution :premises (@p82 @p52) :args ((not @t34) (@list true) (@list tptp.r3))) % 0.43/0.71 (step @p84 :rule skolemize :premises (@p83)) % 0.43/0.71 (step @p85 :rule cnf_or_pos :args (@t54)) % 0.43/0.71 (step @p86 :rule reordering :premises (@p85) :args ((or @t49 @t53 @t51 (not @t54)))) % 0.43/0.71 (step @p87 :rule chain_m_resolution :premises (@p86 @p84 @p81 @p77) :args (@t51 (@list true false false) (@list @t49 @t52 @t54))) % 0.43/0.71 (step @p88 :rule cnf_or_pos :args (@t59)) % 0.43/0.71 (step @p89 :rule reordering :premises (@p88) :args ((or @t58 @t56 @t50 (not @t59)))) % 0.43/0.71 (step @p90 false :rule chain_m_resolution :premises (@p89 @p87 @p76 @p61 @p57) :args (false (@list true false false false) (@list @t50 @t59 @t55 @t57))) % 0.43/0.71 ) % 0.43/0.71 % SZS output end Proof % 0.43/0.71 % cvc5 exiting %------------------------------------------------------------------------------