%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL496+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 : n004.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 11:23:00 AM UTC 2026 % Result : Theorem 2.42s 2.77s % Output : Proof 2.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL496+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 % 0.11/0.37 % Computer : n004.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sun Sep 6 01:19:44 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.45 %----Proving TF0_NAR, FOF, or CNF % 2.42/2.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.42/2.77 % SZS status Theorem % 2.42/2.77 % SZS output start Proof % 2.42/2.77 ( % 2.42/2.77 (declare-sort $$unsorted 0) % 2.42/2.77 (declare-const tptp.op_equiv Bool) % 2.42/2.77 (declare-const tptp.op_implies_or Bool) % 2.42/2.77 (declare-const tptp.op_and Bool) % 2.42/2.77 (declare-const tptp.r4 Bool) % 2.42/2.77 (declare-const tptp.r3 Bool) % 2.42/2.77 (declare-const tptp.implies_2 Bool) % 2.42/2.77 (declare-const tptp.and_2 Bool) % 2.42/2.77 (declare-const tptp.modus_tollens Bool) % 2.42/2.77 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 2.42/2.77 (declare-const tptp.op_or Bool) % 2.42/2.77 (declare-const tptp.or_1 Bool) % 2.42/2.77 (declare-const tptp.equivalence_3 Bool) % 2.42/2.77 (declare-const tptp.and_1 Bool) % 2.42/2.77 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.77 (declare-const tptp.implies_3 Bool) % 2.42/2.77 (declare-const tptp.substitution_of_equivalents Bool) % 2.42/2.77 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.77 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.77 (declare-const tptp.op_implies_and Bool) % 2.42/2.77 (declare-const tptp.or_3 Bool) % 2.42/2.77 (declare-const tptp.equivalence_2 Bool) % 2.42/2.77 (declare-const tptp.modus_ponens Bool) % 2.42/2.77 (declare-const tptp.implies_1 Bool) % 2.42/2.77 (declare-const tptp.equivalence_1 Bool) % 2.42/2.77 (declare-const tptp.op_implies Bool) % 2.42/2.77 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 2.42/2.77 (declare-const tptp.r5 Bool) % 2.42/2.77 (declare-const tptp.and_3 Bool) % 2.42/2.77 (declare-const tptp.cn3 Bool) % 2.42/2.77 (declare-const tptp.or_2 Bool) % 2.42/2.77 (declare-const tptp.kn1 Bool) % 2.42/2.77 (declare-const tptp.cn1 Bool) % 2.42/2.77 (declare-const tptp.kn2 Bool) % 2.42/2.77 (declare-const tptp.cn2 Bool) % 2.42/2.77 (declare-const tptp.kn3 Bool) % 2.42/2.77 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 2.42/2.77 (declare-const tptp.r1 Bool) % 2.42/2.77 (declare-const tptp.r2 Bool) % 2.42/2.77 (define @t1 () (@var "Y" $$unsorted)) % 2.42/2.77 (define @t2 () (tptp.is_a_theorem @t1)) % 2.42/2.77 (define @t3 () (@var "X" $$unsorted)) % 2.42/2.77 (define @t4 () (tptp.implies @t3 @t1)) % 2.42/2.77 (define @t5 () (tptp.is_a_theorem @t4)) % 2.42/2.77 (define @t6 () (tptp.is_a_theorem @t3)) % 2.42/2.77 (define @t7 () (and @t6 @t5)) % 2.42/2.77 (define @t8 () (@list @t3 @t1)) % 2.42/2.77 (define @t9 () (forall @t8 (=> @t7 @t2))) % 2.42/2.77 (define @t10 () (= tptp.modus_ponens @t9)) % 2.42/2.77 (define @t11 () (tptp.equiv @t3 @t1)) % 2.42/2.77 (define @t12 () (tptp.not @t3)) % 2.42/2.77 (define @t13 () (tptp.not @t1)) % 2.42/2.77 (define @t14 () (tptp.implies @t1 @t3)) % 2.42/2.77 (define @t15 () (@var "Z" $$unsorted)) % 2.42/2.77 (define @t16 () (tptp.implies @t3 @t15)) % 2.42/2.77 (define @t17 () (tptp.implies @t1 @t15)) % 2.42/2.77 (define @t18 () (@list @t3 @t1 @t15)) % 2.42/2.77 (define @t19 () (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16))))) % 2.42/2.77 (define @t20 () (tptp.and @t3 @t1)) % 2.42/2.77 (define @t21 () (tptp.or @t3 @t1)) % 2.42/2.77 (define @t22 () (@var "P" $$unsorted)) % 2.42/2.77 (define @t23 () (@list @t22)) % 2.42/2.77 (define @t24 () (@var "Q" $$unsorted)) % 2.42/2.77 (define @t25 () (@list @t22 @t24)) % 2.42/2.77 (define @t26 () (@var "R" $$unsorted)) % 2.42/2.77 (define @t27 () (tptp.implies @t22 @t24)) % 2.42/2.77 (define @t28 () (@list @t22 @t24 @t26)) % 2.42/2.77 (define @t29 () (tptp.implies @t24 @t26)) % 2.42/2.77 (define @t30 () (forall @t28 (tptp.is_a_theorem (tptp.implies @t27 (tptp.implies @t29 (tptp.implies @t22 @t26)))))) % 2.42/2.77 (define @t31 () (tptp.not @t22)) % 2.42/2.77 (define @t32 () (tptp.or @t22 @t24)) % 2.42/2.77 (define @t33 () (tptp.or @t22 @t26)) % 2.42/2.77 (define @t34 () (forall @t28 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 (tptp.or @t24 @t26)) (tptp.or @t24 @t33))))) % 2.42/2.77 (define @t35 () (forall @t28 (tptp.is_a_theorem (tptp.implies @t29 (tptp.implies @t32 @t33))))) % 2.42/2.77 (define @t36 () (forall @t8 (= @t4 (tptp.or @t12 @t1)))) % 2.42/2.77 (define @t37 () (@list false)) % 2.42/2.77 (define @t38 () (@quantifiers_skolemize @t19 2)) % 2.42/2.77 (define @t39 () (@quantifiers_skolemize @t19 1)) % 2.42/2.77 (define @t40 () (@quantifiers_skolemize @t19 0)) % 2.42/2.77 (define @t41 () (tptp.implies @t40 @t38)) % 2.42/2.77 (define @t42 () (tptp.implies @t40 @t39)) % 2.42/2.77 (define @t43 () (tptp.implies @t42 @t41)) % 2.42/2.77 (define @t44 () (tptp.not @t42)) % 2.42/2.77 (define @t45 () (tptp.or @t44 @t41)) % 2.42/2.77 (define @t46 () (= @t43 @t45)) % 2.42/2.77 (define @t47 () (@list @t36)) % 2.42/2.77 (define @t48 () (tptp.implies @t39 @t38)) % 2.42/2.77 (define @t49 () (tptp.implies @t48 @t45)) % 2.42/2.77 (define @t50 () (tptp.not @t48)) % 2.42/2.77 (define @t51 () (tptp.or @t50 @t45)) % 2.42/2.77 (define @t52 () (= @t49 @t51)) % 2.42/2.77 (define @t53 () (tptp.is_a_theorem @t51)) % 2.42/2.77 (define @t54 () (not @t5)) % 2.42/2.77 (define @t55 () (not @t6)) % 2.42/2.77 (define @t56 () (or @t55 @t54 @t2)) % 2.42/2.77 (define @t57 () (forall @t8 @t56)) % 2.42/2.77 (define @t58 () (tptp.or @t44 (tptp.or @t50 @t41))) % 2.42/2.77 (define @t59 () (@list true)) % 2.42/2.77 (define @t60 () (not @t19)) % 2.42/2.77 (define @t61 () (tptp.is_a_theorem @t58)) % 2.42/2.77 (define @t62 () (tptp.is_a_theorem (tptp.implies @t51 @t58))) % 2.42/2.77 (define @t63 () (not @t62)) % 2.42/2.77 (define @t64 () (not @t53)) % 2.42/2.77 (define @t65 () (or @t64 @t63 @t61)) % 2.42/2.77 (assume @p1 @t10) % 2.42/2.77 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 2.42/2.77 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 2.42/2.77 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 2.42/2.77 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 2.42/2.77 (assume @p6 (= tptp.implies_3 @t19)) % 2.42/2.77 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t3))))) % 2.42/2.77 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t1))))) % 2.42/2.77 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t20)))))) % 2.42/2.77 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t21))))) % 2.42/2.77 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t21))))) % 2.42/2.77 (assume @p12 (= tptp.or_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t21 @t15))))))) % 2.42/2.77 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 2.42/2.77 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 2.42/2.77 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 2.42/2.77 (assume @p16 (= tptp.kn1 (forall @t23 (tptp.is_a_theorem (tptp.implies @t22 (tptp.and @t22 @t22)))))) % 2.42/2.77 (assume @p17 (= tptp.kn2 (forall @t25 (tptp.is_a_theorem (tptp.implies (tptp.and @t22 @t24) @t22))))) % 2.42/2.77 (assume @p18 (= tptp.kn3 (forall @t28 (tptp.is_a_theorem (tptp.implies @t27 (tptp.implies (tptp.not (tptp.and @t24 @t26)) (tptp.not (tptp.and @t26 @t22)))))))) % 2.42/2.77 (assume @p19 (= tptp.cn1 @t30)) % 2.42/2.77 (assume @p20 (= tptp.cn2 (forall @t25 (tptp.is_a_theorem (tptp.implies @t22 (tptp.implies @t31 @t24)))))) % 2.42/2.77 (assume @p21 (= tptp.cn3 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.implies @t31 @t22) @t22))))) % 2.42/2.77 (assume @p22 (= tptp.r1 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 @t22) @t22))))) % 2.42/2.77 (assume @p23 (= tptp.r2 (forall @t25 (tptp.is_a_theorem (tptp.implies @t24 @t32))))) % 2.42/2.77 (assume @p24 (= tptp.r3 (forall @t25 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t24 @t22)))))) % 2.42/2.77 (assume @p25 (= tptp.r4 @t34)) % 2.42/2.77 (assume @p26 (= tptp.r5 @t35)) % 2.42/2.77 (assume @p27 (=> tptp.op_or (forall @t8 (= @t21 (tptp.not (tptp.and @t12 @t13)))))) % 2.42/2.77 (assume @p28 (=> tptp.op_and (forall @t8 (= @t20 (tptp.not (tptp.or @t12 @t13)))))) % 2.42/2.77 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13)))))) % 2.42/2.77 (assume @p30 (=> tptp.op_implies_or @t36)) % 2.42/2.77 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 2.42/2.77 (assume @p32 tptp.op_implies_or) % 2.42/2.77 (assume @p33 tptp.op_and) % 2.42/2.77 (assume @p34 tptp.op_equiv) % 2.42/2.77 (assume @p35 tptp.modus_ponens) % 2.42/2.77 (assume @p36 tptp.r1) % 2.42/2.77 (assume @p37 tptp.r2) % 2.42/2.77 (assume @p38 tptp.r3) % 2.42/2.77 (assume @p39 tptp.r4) % 2.42/2.77 (assume @p40 tptp.r5) % 2.42/2.77 (assume @p41 tptp.substitution_of_equivalents) % 2.42/2.77 (assume @p42 tptp.op_or) % 2.42/2.77 (assume @p43 tptp.op_implies) % 2.42/2.77 (assume @p44 (not tptp.cn1)) % 2.42/2.77 (assume @p45 true) % 2.42/2.77 (step @p46 :rule evaluate :args ((= false true))) % 2.42/2.77 (step @p47 :rule equiv_elim1 :premises (@p26)) % 2.42/2.77 (step @p48 :rule reordering :premises (@p47) :args ((or @t35 (not tptp.r5)))) % 2.42/2.77 (step @p49 :rule chain_m_resolution :premises (@p48 @p40) :args (@t35 @t37 (@list tptp.r5))) % 2.42/2.77 (step @p50 :rule instantiate :premises (@p49) :args ((@list (tptp.not @t40) @t39 @t38))) % 2.42/2.77 (step @p51 :rule true_intro :premises (@p50)) % 2.42/2.77 (step @p52 :rule implies_elim :premises (@p30)) % 2.42/2.77 (step @p53 :rule reordering :premises (@p52) :args ((or @t36 (not tptp.op_implies_or)))) % 2.42/2.77 (step @p54 :rule chain_m_resolution :premises (@p53 @p32) :args (@t36 @t37 (@list tptp.op_implies_or))) % 2.42/2.77 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t40 @t38))) % 2.42/2.77 (step @p56 :rule instantiate :premises (@p54) :args ((@list @t40 @t39))) % 2.42/2.77 (step @p57 :rule cong :premises (@p56 @p55) :args (@t43)) % 2.42/2.77 (step @p58 :rule eq-symm :args (@t43 @t45)) % 2.42/2.77 (step @p59 :rule refl :args (@t36)) % 2.42/2.77 (step @p60 :rule cong :premises (@p59 @p58) :args ((=> @t36 @t46))) % 2.42/2.77 (assume-push @p126 @t36) % 2.42/2.77 (step @p62 :rule instantiate :premises (@p54) :args ((@list @t42 @t41))) % 2.42/2.77 (step-pop @p127 :rule scope :premises (@p62)) % 2.42/2.77 (step @p63 :rule process_scope :premises (@p127) :args (@t46)) % 2.42/2.77 (step @p65 :rule eq_resolve :premises (@p63 @p60)) % 2.42/2.77 (step @p66 :rule implies_elim :premises (@p65)) % 2.42/2.77 (step @p67 :rule chain_m_resolution :premises (@p66 @p54) :args ((= @t45 @t43) @t37 @t47)) % 2.42/2.77 (step @p68 :rule trans :premises (@p67 @p57)) % 2.42/2.77 (step @p69 :rule refl :args (@t48)) % 2.42/2.77 (step @p70 :rule cong :premises (@p69 @p68) :args (@t49)) % 2.42/2.77 (step @p71 :rule eq-symm :args (@t49 @t51)) % 2.42/2.77 (step @p72 :rule cong :premises (@p59 @p71) :args ((=> @t36 @t52))) % 2.42/2.77 (assume-push @p128 @t36) % 2.42/2.77 (step @p74 :rule instantiate :premises (@p54) :args ((@list @t48 @t45))) % 2.42/2.77 (step-pop @p129 :rule scope :premises (@p74)) % 2.42/2.77 (step @p75 :rule process_scope :premises (@p129) :args (@t52)) % 2.42/2.77 (step @p77 :rule eq_resolve :premises (@p75 @p72)) % 2.42/2.77 (step @p78 :rule implies_elim :premises (@p77)) % 2.42/2.77 (step @p79 :rule chain_m_resolution :premises (@p78 @p54) :args ((= @t51 @t49) @t37 @t47)) % 2.42/2.77 (step @p80 :rule trans :premises (@p79 @p70)) % 2.42/2.77 (step @p81 :rule cong :premises (@p80) :args (@t53)) % 2.42/2.77 (step @p82 :rule aci_norm :args ((= (or (or @t55 @t54) @t2) @t56))) % 2.42/2.77 (step @p83 :rule refl :args (@t2)) % 2.42/2.77 (step @p84 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 2.42/2.77 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or (not @t7) @t2))) % 2.42/2.77 (step @p86 :rule trans :premises (@p85 @p82)) % 2.42/2.77 (step @p87 :rule bool-impl-elim :args (@t7 @t2)) % 2.42/2.77 (step @p88 :rule trans :premises (@p87 @p86)) % 2.42/2.77 (step @p89 :rule cong :premises (@p88) :args (@t9)) % 2.42/2.77 (step @p90 :rule refl :args (tptp.modus_ponens)) % 2.42/2.77 (step @p91 :rule cong :premises (@p90 @p89) :args (@t10)) % 2.42/2.77 (step @p92 :rule eq_resolve :premises (@p1 @p91)) % 2.42/2.77 (step @p93 :rule equiv_elim1 :premises (@p92)) % 2.42/2.77 (step @p94 :rule reordering :premises (@p93) :args ((or @t57 (not tptp.modus_ponens)))) % 2.42/2.77 (step @p95 :rule chain_m_resolution :premises (@p94 @p35) :args (@t57 @t37 (@list tptp.modus_ponens))) % 2.42/2.77 (step @p96 :rule instantiate :premises (@p95) :args ((@list @t51 @t58))) % 2.42/2.77 (step @p97 :rule equiv_elim2 :premises (@p19)) % 2.42/2.77 (step @p98 :rule chain_m_resolution :premises (@p97 @p44) :args ((not @t30) @t59 (@list tptp.cn1))) % 2.42/2.77 (step @p99 :rule alpha_equiv :args (@t19 (@list @t3 @t1 @t15) (@list @t22 @t24 @t26))) % 2.42/2.77 (step @p100 :rule equiv_elim1 :premises (@p99)) % 2.42/2.77 (step @p101 :rule reordering :premises (@p100) :args ((or @t30 @t60))) % 2.42/2.77 (step @p102 :rule chain_m_resolution :premises (@p101 @p98) :args (@t60 @t59 (@list @t30))) % 2.42/2.77 (step @p103 :rule skolemize :premises (@p102)) % 2.42/2.77 (step @p104 :rule false_intro :premises (@p103)) % 2.42/2.77 (step @p105 :rule instantiate :premises (@p54) :args ((@list @t42 (tptp.implies @t48 @t41)))) % 2.42/2.77 (step @p106 :rule symm :premises (@p105)) % 2.42/2.77 (step @p107 :rule instantiate :premises (@p54) :args ((@list @t48 @t41))) % 2.42/2.77 (step @p108 :rule symm :premises (@p107)) % 2.42/2.77 (step @p109 :rule refl :args (@t44)) % 2.42/2.77 (step @p110 :rule cong :premises (@p109 @p108) :args (@t58)) % 2.42/2.77 (step @p111 :rule trans :premises (@p110 @p106)) % 2.42/2.77 (step @p112 :rule cong :premises (@p111) :args (@t61)) % 2.42/2.77 (step @p113 :rule trans :premises (@p112 @p104)) % 2.42/2.77 (step @p114 :rule false_elim :premises (@p113)) % 2.42/2.77 (step @p115 :rule equiv_elim1 :premises (@p25)) % 2.42/2.77 (step @p116 :rule reordering :premises (@p115) :args ((or @t34 (not tptp.r4)))) % 2.42/2.77 (step @p117 :rule chain_m_resolution :premises (@p116 @p39) :args (@t34 @t37 (@list tptp.r4))) % 2.42/2.77 (step @p118 :rule instantiate :premises (@p117) :args ((@list @t50 @t44 @t41))) % 2.42/2.77 (step @p119 :rule cnf_or_pos :args (@t65)) % 2.42/2.77 (step @p120 :rule reordering :premises (@p119) :args ((or @t63 @t64 @t61 (not @t65)))) % 2.42/2.77 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p114 @p96) :args (@t64 (@list false true false) (@list @t62 @t61 @t65))) % 2.42/2.77 (step @p122 :rule false_intro :premises (@p121)) % 2.42/2.77 (step @p123 :rule symm :premises (@p122)) % 2.42/2.77 (step @p124 :rule trans :premises (@p123 @p81 @p51)) % 2.42/2.77 (step @p125 false :rule eq_resolve :premises (@p124 @p46)) % 2.42/2.78 ) % 2.42/2.78 % SZS output end Proof % 2.42/2.78 % cvc5 exiting %------------------------------------------------------------------------------