%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL499+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 : n027.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 0.93s 1.23s % Output : Proof 0.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL499+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 : n027.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 02:56:13 UTC 2026 % 0.10/0.38 % CPUTime : % 0.10/0.45 %----Proving TF0_NAR, FOF, or CNF % 0.93/1.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.93/1.23 % SZS status Theorem % 0.93/1.23 % SZS output start Proof % 0.93/1.23 ( % 0.93/1.23 (declare-sort $$unsorted 0) % 0.93/1.23 (declare-const tptp.op_equiv Bool) % 0.93/1.23 (declare-const tptp.op_implies_or Bool) % 0.93/1.23 (declare-const tptp.op_and Bool) % 0.93/1.23 (declare-const tptp.r4 Bool) % 0.93/1.23 (declare-const tptp.r3 Bool) % 0.93/1.23 (declare-const tptp.implies_2 Bool) % 0.93/1.23 (declare-const tptp.and_2 Bool) % 0.93/1.23 (declare-const tptp.modus_tollens Bool) % 0.93/1.23 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 0.93/1.23 (declare-const tptp.op_or Bool) % 0.93/1.23 (declare-const tptp.or_1 Bool) % 0.93/1.23 (declare-const tptp.equivalence_3 Bool) % 0.93/1.23 (declare-const tptp.and_1 Bool) % 0.93/1.23 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.23 (declare-const tptp.implies_3 Bool) % 0.93/1.23 (declare-const tptp.substitution_of_equivalents Bool) % 0.93/1.23 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.23 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.23 (declare-const tptp.op_implies_and Bool) % 0.93/1.23 (declare-const tptp.or_3 Bool) % 0.93/1.23 (declare-const tptp.equivalence_2 Bool) % 0.93/1.23 (declare-const tptp.modus_ponens Bool) % 0.93/1.23 (declare-const tptp.implies_1 Bool) % 0.93/1.23 (declare-const tptp.equivalence_1 Bool) % 0.93/1.23 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.23 (declare-const tptp.r5 Bool) % 0.93/1.23 (declare-const tptp.and_3 Bool) % 0.93/1.23 (declare-const tptp.cn3 Bool) % 0.93/1.23 (declare-const tptp.or_2 Bool) % 0.93/1.23 (declare-const tptp.kn1 Bool) % 0.93/1.23 (declare-const tptp.cn1 Bool) % 0.93/1.23 (declare-const tptp.kn2 Bool) % 0.93/1.23 (declare-const tptp.cn2 Bool) % 0.93/1.23 (declare-const tptp.kn3 Bool) % 0.93/1.23 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 0.93/1.23 (declare-const tptp.r1 Bool) % 0.93/1.23 (declare-const tptp.r2 Bool) % 0.93/1.23 (define @t1 () (@var "Y" $$unsorted)) % 0.93/1.23 (define @t2 () (tptp.is_a_theorem @t1)) % 0.93/1.23 (define @t3 () (@var "X" $$unsorted)) % 0.93/1.23 (define @t4 () (tptp.implies @t3 @t1)) % 0.93/1.23 (define @t5 () (tptp.is_a_theorem @t4)) % 0.93/1.23 (define @t6 () (tptp.is_a_theorem @t3)) % 0.93/1.23 (define @t7 () (and @t6 @t5)) % 0.93/1.23 (define @t8 () (@list @t3 @t1)) % 0.93/1.23 (define @t9 () (forall @t8 (=> @t7 @t2))) % 0.93/1.23 (define @t10 () (= tptp.modus_ponens @t9)) % 0.93/1.23 (define @t11 () (tptp.equiv @t3 @t1)) % 0.93/1.23 (define @t12 () (tptp.not @t3)) % 0.93/1.23 (define @t13 () (tptp.not @t1)) % 0.93/1.23 (define @t14 () (tptp.implies @t1 @t3)) % 0.93/1.23 (define @t15 () (@var "Z" $$unsorted)) % 0.93/1.23 (define @t16 () (tptp.implies @t3 @t15)) % 0.93/1.23 (define @t17 () (tptp.implies @t1 @t15)) % 0.93/1.23 (define @t18 () (@list @t3 @t1 @t15)) % 0.93/1.23 (define @t19 () (tptp.and @t3 @t1)) % 0.93/1.23 (define @t20 () (tptp.or @t3 @t1)) % 0.93/1.23 (define @t21 () (@var "P" $$unsorted)) % 0.93/1.23 (define @t22 () (@list @t21)) % 0.93/1.23 (define @t23 () (forall @t22 (tptp.is_a_theorem (tptp.implies @t21 (tptp.and @t21 @t21))))) % 0.93/1.23 (define @t24 () (@var "Q" $$unsorted)) % 0.93/1.23 (define @t25 () (@list @t21 @t24)) % 0.93/1.23 (define @t26 () (@var "R" $$unsorted)) % 0.93/1.23 (define @t27 () (tptp.implies @t21 @t24)) % 0.93/1.23 (define @t28 () (@list @t21 @t24 @t26)) % 0.93/1.23 (define @t29 () (tptp.implies @t24 @t26)) % 0.93/1.23 (define @t30 () (tptp.not @t21)) % 0.93/1.23 (define @t31 () (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 @t21) @t21)))) % 0.93/1.23 (define @t32 () (tptp.or @t21 @t24)) % 0.93/1.23 (define @t33 () (forall @t25 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t24 @t21))))) % 0.93/1.23 (define @t34 () (tptp.or @t21 @t26)) % 0.93/1.23 (define @t35 () (forall @t8 (= @t19 (tptp.not (tptp.or @t12 @t13))))) % 0.93/1.23 (define @t36 () (forall @t8 (= @t4 (tptp.or @t12 @t1)))) % 0.93/1.23 (define @t37 () (@list false)) % 0.93/1.23 (define @t38 () (@quantifiers_skolemize @t23 0)) % 0.93/1.23 (define @t39 () (tptp.not @t38)) % 0.93/1.23 (define @t40 () (tptp.and @t38 @t38)) % 0.93/1.23 (define @t41 () (not @t5)) % 0.93/1.23 (define @t42 () (not @t6)) % 0.93/1.23 (define @t43 () (or @t42 @t41 @t2)) % 0.93/1.23 (define @t44 () (forall @t8 @t43)) % 0.93/1.23 (define @t45 () (tptp.or @t39 @t40)) % 0.93/1.23 (define @t46 () (tptp.or @t40 @t39)) % 0.93/1.23 (define @t47 () (tptp.is_a_theorem @t45)) % 0.93/1.23 (define @t48 () (tptp.is_a_theorem @t46)) % 0.93/1.23 (define @t49 () (tptp.is_a_theorem (tptp.implies @t46 @t45))) % 0.93/1.23 (define @t50 () (not @t49)) % 0.93/1.23 (define @t51 () (not @t48)) % 0.93/1.23 (define @t52 () (or @t51 @t50 @t47)) % 0.93/1.23 (assume @p1 @t10) % 0.93/1.23 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 0.93/1.23 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 0.93/1.23 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 0.93/1.23 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 0.93/1.23 (assume @p6 (= tptp.implies_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16)))))) % 0.93/1.23 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t3))))) % 0.93/1.23 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t1))))) % 0.93/1.23 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t19)))))) % 0.93/1.23 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t20))))) % 0.93/1.23 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t20))))) % 0.93/1.23 (assume @p12 (= tptp.or_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t20 @t15))))))) % 0.93/1.23 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 0.93/1.23 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 0.93/1.23 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 0.93/1.23 (assume @p16 (= tptp.kn1 @t23)) % 0.93/1.23 (assume @p17 (= tptp.kn2 (forall @t25 (tptp.is_a_theorem (tptp.implies (tptp.and @t21 @t24) @t21))))) % 0.93/1.23 (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 @t21)))))))) % 0.93/1.23 (assume @p19 (= tptp.cn1 (forall @t28 (tptp.is_a_theorem (tptp.implies @t27 (tptp.implies @t29 (tptp.implies @t21 @t26))))))) % 0.93/1.23 (assume @p20 (= tptp.cn2 (forall @t25 (tptp.is_a_theorem (tptp.implies @t21 (tptp.implies @t30 @t24)))))) % 0.93/1.23 (assume @p21 (= tptp.cn3 (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.implies @t30 @t21) @t21))))) % 0.93/1.23 (assume @p22 (= tptp.r1 @t31)) % 0.93/1.23 (assume @p23 (= tptp.r2 (forall @t25 (tptp.is_a_theorem (tptp.implies @t24 @t32))))) % 0.93/1.23 (assume @p24 (= tptp.r3 @t33)) % 0.93/1.23 (assume @p25 (= tptp.r4 (forall @t28 (tptp.is_a_theorem (tptp.implies (tptp.or @t21 (tptp.or @t24 @t26)) (tptp.or @t24 @t34)))))) % 0.93/1.23 (assume @p26 (= tptp.r5 (forall @t28 (tptp.is_a_theorem (tptp.implies @t29 (tptp.implies @t32 @t34)))))) % 0.93/1.23 (assume @p27 (=> tptp.op_or (forall @t8 (= @t20 (tptp.not (tptp.and @t12 @t13)))))) % 0.93/1.23 (assume @p28 (=> tptp.op_and @t35)) % 0.93/1.23 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13)))))) % 0.93/1.23 (assume @p30 (=> tptp.op_implies_or @t36)) % 0.93/1.23 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 0.93/1.23 (assume @p32 tptp.op_implies_or) % 0.93/1.23 (assume @p33 tptp.op_and) % 0.93/1.23 (assume @p34 tptp.op_equiv) % 0.93/1.23 (assume @p35 tptp.modus_ponens) % 0.93/1.23 (assume @p36 tptp.r1) % 0.93/1.23 (assume @p37 tptp.r2) % 0.93/1.23 (assume @p38 tptp.r3) % 0.93/1.23 (assume @p39 tptp.r4) % 0.93/1.23 (assume @p40 tptp.r5) % 0.93/1.23 (assume @p41 tptp.substitution_of_equivalents) % 0.93/1.23 (assume @p42 tptp.op_or) % 0.93/1.23 (assume @p43 tptp.op_implies_and) % 0.93/1.23 (assume @p44 (not tptp.kn1)) % 0.93/1.23 (assume @p45 true) % 0.93/1.23 (step @p46 :rule equiv_elim1 :premises (@p24)) % 0.93/1.23 (step @p47 :rule reordering :premises (@p46) :args ((or @t33 (not tptp.r3)))) % 0.93/1.23 (step @p48 :rule chain_m_resolution :premises (@p47 @p38) :args (@t33 @t37 (@list tptp.r3))) % 0.93/1.23 (step @p49 :rule instantiate :premises (@p48) :args ((@list @t40 @t39))) % 0.93/1.23 (step @p50 :rule aci_norm :args ((= (or (or @t42 @t41) @t2) @t43))) % 0.93/1.23 (step @p51 :rule refl :args (@t2)) % 0.93/1.23 (step @p52 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 0.93/1.23 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or (not @t7) @t2))) % 0.93/1.23 (step @p54 :rule trans :premises (@p53 @p50)) % 0.93/1.23 (step @p55 :rule bool-impl-elim :args (@t7 @t2)) % 0.93/1.23 (step @p56 :rule trans :premises (@p55 @p54)) % 0.93/1.23 (step @p57 :rule cong :premises (@p56) :args (@t9)) % 0.93/1.23 (step @p58 :rule refl :args (tptp.modus_ponens)) % 0.93/1.23 (step @p59 :rule cong :premises (@p58 @p57) :args (@t10)) % 0.93/1.23 (step @p60 :rule eq_resolve :premises (@p1 @p59)) % 0.93/1.23 (step @p61 :rule equiv_elim1 :premises (@p60)) % 0.93/1.23 (step @p62 :rule reordering :premises (@p61) :args ((or @t44 (not tptp.modus_ponens)))) % 0.93/1.23 (step @p63 :rule chain_m_resolution :premises (@p62 @p35) :args (@t44 @t37 (@list tptp.modus_ponens))) % 0.93/1.23 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t46 @t45))) % 0.93/1.23 (step @p65 :rule equiv_elim2 :premises (@p16)) % 0.93/1.23 (step @p66 :rule chain_m_resolution :premises (@p65 @p44) :args ((not @t23) (@list true) (@list tptp.kn1))) % 0.93/1.24 (step @p67 :rule skolemize :premises (@p66)) % 0.93/1.24 (step @p68 :rule false_intro :premises (@p67)) % 0.93/1.24 (step @p69 :rule implies_elim :premises (@p30)) % 0.93/1.24 (step @p70 :rule reordering :premises (@p69) :args ((or @t36 (not tptp.op_implies_or)))) % 0.93/1.24 (step @p71 :rule chain_m_resolution :premises (@p70 @p32) :args (@t36 @t37 (@list tptp.op_implies_or))) % 0.93/1.24 (step @p72 :rule instantiate :premises (@p71) :args ((@list @t38 @t40))) % 0.93/1.24 (step @p73 :rule symm :premises (@p72)) % 0.93/1.24 (step @p74 :rule cong :premises (@p73) :args (@t47)) % 0.93/1.24 (step @p75 :rule trans :premises (@p74 @p68)) % 0.93/1.24 (step @p76 :rule false_elim :premises (@p75)) % 0.93/1.24 (step @p77 :rule equiv_elim1 :premises (@p22)) % 0.93/1.24 (step @p78 :rule reordering :premises (@p77) :args ((or @t31 (not tptp.r1)))) % 0.93/1.24 (step @p79 :rule chain_m_resolution :premises (@p78 @p36) :args (@t31 @t37 (@list tptp.r1))) % 0.93/1.24 (step @p80 :rule instantiate :premises (@p79) :args ((@list @t39))) % 0.93/1.24 (step @p81 :rule true_intro :premises (@p80)) % 0.93/1.24 (step @p82 :rule instantiate :premises (@p71) :args ((@list (tptp.or @t39 @t39) @t39))) % 0.93/1.24 (step @p83 :rule symm :premises (@p82)) % 0.93/1.24 (step @p84 :rule refl :args (@t39)) % 0.93/1.24 (step @p85 :rule implies_elim :premises (@p28)) % 0.93/1.24 (step @p86 :rule reordering :premises (@p85) :args ((or @t35 (not tptp.op_and)))) % 0.93/1.24 (step @p87 :rule chain_m_resolution :premises (@p86 @p33) :args (@t35 @t37 (@list tptp.op_and))) % 0.93/1.24 (step @p88 :rule instantiate :premises (@p87) :args ((@list @t38 @t38))) % 0.93/1.24 (step @p89 :rule cong :premises (@p88 @p84) :args (@t46)) % 0.93/1.24 (step @p90 :rule trans :premises (@p89 @p83)) % 0.93/1.24 (step @p91 :rule cong :premises (@p90) :args (@t48)) % 0.93/1.24 (step @p92 :rule trans :premises (@p91 @p81)) % 0.93/1.24 (step @p93 :rule true_elim :premises (@p92)) % 0.93/1.24 (step @p94 :rule cnf_or_pos :args (@t52)) % 0.93/1.24 (step @p95 :rule reordering :premises (@p94) :args ((or @t50 @t51 @t47 (not @t52)))) % 0.93/1.24 (step @p96 false :rule chain_m_resolution :premises (@p95 @p93 @p76 @p64 @p49) :args (false (@list false true false false) (@list @t48 @t47 @t52 @t49))) % 0.93/1.24 ) % 0.93/1.24 % SZS output end Proof % 0.93/1.24 % cvc5 exiting %------------------------------------------------------------------------------