%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL488+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 : n031.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 11:22:59 AM UTC 2026 % Result : Theorem 4.93s 5.28s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL488+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 : n031.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 07:16:09 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.44 %----Proving TF0_NAR, FOF, or CNF % 4.93/5.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 4.93/5.28 % SZS status Theorem % 4.93/5.28 % SZS output start Proof % 4.93/5.28 ( % 4.93/5.28 (declare-sort $$unsorted 0) % 4.93/5.28 (declare-const tptp.op_equiv Bool) % 4.93/5.28 (declare-const tptp.op_implies_or Bool) % 4.93/5.28 (declare-const tptp.op_and Bool) % 4.93/5.28 (declare-const tptp.r4 Bool) % 4.93/5.28 (declare-const tptp.r3 Bool) % 4.93/5.28 (declare-const tptp.implies_2 Bool) % 4.93/5.28 (declare-const tptp.and_2 Bool) % 4.93/5.28 (declare-const tptp.modus_tollens Bool) % 4.93/5.28 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 4.93/5.28 (declare-const tptp.op_or Bool) % 4.93/5.28 (declare-const tptp.or_1 Bool) % 4.93/5.28 (declare-const tptp.equivalence_3 Bool) % 4.93/5.28 (declare-const tptp.and_1 Bool) % 4.93/5.28 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 4.93/5.28 (declare-const tptp.implies_3 Bool) % 4.93/5.28 (declare-const tptp.substitution_of_equivalents Bool) % 4.93/5.28 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 4.93/5.28 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 4.93/5.28 (declare-const tptp.op_implies_and Bool) % 4.93/5.28 (declare-const tptp.or_3 Bool) % 4.93/5.28 (declare-const tptp.equivalence_2 Bool) % 4.93/5.28 (declare-const tptp.modus_ponens Bool) % 4.93/5.28 (declare-const tptp.implies_1 Bool) % 4.93/5.28 (declare-const tptp.equivalence_1 Bool) % 4.93/5.28 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 4.93/5.28 (declare-const tptp.r5 Bool) % 4.93/5.28 (declare-const tptp.and_3 Bool) % 4.93/5.28 (declare-const tptp.cn3 Bool) % 4.93/5.28 (declare-const tptp.or_2 Bool) % 4.93/5.28 (declare-const tptp.kn1 Bool) % 4.93/5.28 (declare-const tptp.cn1 Bool) % 4.93/5.28 (declare-const tptp.kn2 Bool) % 4.93/5.28 (declare-const tptp.cn2 Bool) % 4.93/5.28 (declare-const tptp.kn3 Bool) % 4.93/5.28 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 4.93/5.28 (declare-const tptp.r1 Bool) % 4.93/5.28 (declare-const tptp.r2 Bool) % 4.93/5.28 (define @t1 () (@var "Y" $$unsorted)) % 4.93/5.28 (define @t2 () (tptp.is_a_theorem @t1)) % 4.93/5.28 (define @t3 () (@var "X" $$unsorted)) % 4.93/5.28 (define @t4 () (tptp.implies @t3 @t1)) % 4.93/5.28 (define @t5 () (tptp.is_a_theorem @t4)) % 4.93/5.28 (define @t6 () (tptp.is_a_theorem @t3)) % 4.93/5.28 (define @t7 () (and @t6 @t5)) % 4.93/5.28 (define @t8 () (@list @t3 @t1)) % 4.93/5.28 (define @t9 () (forall @t8 (=> @t7 @t2))) % 4.93/5.28 (define @t10 () (= tptp.modus_ponens @t9)) % 4.93/5.28 (define @t11 () (tptp.equiv @t3 @t1)) % 4.93/5.28 (define @t12 () (tptp.not @t3)) % 4.93/5.28 (define @t13 () (tptp.not @t1)) % 4.93/5.28 (define @t14 () (tptp.implies @t1 @t3)) % 4.93/5.28 (define @t15 () (@var "Z" $$unsorted)) % 4.93/5.28 (define @t16 () (tptp.implies @t3 @t15)) % 4.93/5.28 (define @t17 () (tptp.implies @t1 @t15)) % 4.93/5.28 (define @t18 () (@list @t3 @t1 @t15)) % 4.93/5.28 (define @t19 () (tptp.and @t3 @t1)) % 4.93/5.28 (define @t20 () (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t1)))) % 4.93/5.28 (define @t21 () (tptp.or @t3 @t1)) % 4.93/5.28 (define @t22 () (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t21)))) % 4.93/5.28 (define @t23 () (@var "P" $$unsorted)) % 4.93/5.28 (define @t24 () (@list @t23)) % 4.93/5.28 (define @t25 () (@var "Q" $$unsorted)) % 4.93/5.28 (define @t26 () (@list @t23 @t25)) % 4.93/5.28 (define @t27 () (@var "R" $$unsorted)) % 4.93/5.28 (define @t28 () (tptp.implies @t23 @t25)) % 4.93/5.28 (define @t29 () (@list @t23 @t25 @t27)) % 4.93/5.28 (define @t30 () (tptp.implies @t25 @t27)) % 4.93/5.28 (define @t31 () (tptp.not @t23)) % 4.93/5.28 (define @t32 () (tptp.or @t23 @t25)) % 4.93/5.28 (define @t33 () (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 @t32)))) % 4.93/5.28 (define @t34 () (forall @t26 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t25 @t23))))) % 4.93/5.28 (define @t35 () (tptp.or @t23 @t27)) % 4.93/5.28 (define @t36 () (forall @t8 (= @t21 (tptp.not (tptp.and @t12 @t13))))) % 4.93/5.28 (define @t37 () (forall @t8 (= @t19 (tptp.not (tptp.or @t12 @t13))))) % 4.93/5.28 (define @t38 () (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t13))))) % 4.93/5.28 (define @t39 () (@list false)) % 4.93/5.28 (define @t40 () (@quantifiers_skolemize @t20 1)) % 4.93/5.28 (define @t41 () (tptp.not @t40)) % 4.93/5.28 (define @t42 () (@quantifiers_skolemize @t20 0)) % 4.93/5.28 (define @t43 () (tptp.not @t42)) % 4.93/5.28 (define @t44 () (tptp.or @t43 @t41)) % 4.93/5.28 (define @t45 () (@list @t40 @t44)) % 4.93/5.28 (define @t46 () (not @t5)) % 4.93/5.28 (define @t47 () (not @t6)) % 4.93/5.28 (define @t48 () (or @t47 @t46 @t2)) % 4.93/5.28 (define @t49 () (forall @t8 @t48)) % 4.93/5.28 (define @t50 () (tptp.or @t44 @t40)) % 4.93/5.28 (define @t51 () (tptp.or @t40 @t44)) % 4.93/5.28 (define @t52 () (tptp.and (tptp.not @t44) @t41)) % 4.93/5.28 (define @t53 () (tptp.is_a_theorem @t50)) % 4.93/5.28 (define @t54 () (tptp.is_a_theorem @t51)) % 4.93/5.28 (define @t55 () (tptp.is_a_theorem (tptp.implies @t51 @t50))) % 4.93/5.28 (define @t56 () (not @t55)) % 4.93/5.28 (define @t57 () (not @t54)) % 4.93/5.28 (define @t58 () (or @t57 @t56 @t53)) % 4.93/5.28 (assume @p1 @t10) % 4.93/5.28 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t11) (= @t3 @t1))))) % 4.93/5.28 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t13 @t12) @t4))))) % 4.93/5.28 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t14))))) % 4.93/5.28 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 4.93/5.28 (assume @p6 (= tptp.implies_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t17 @t16)))))) % 4.93/5.28 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t19 @t3))))) % 4.93/5.28 (assume @p8 (= tptp.and_2 @t20)) % 4.93/5.28 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t19)))))) % 4.93/5.28 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t21))))) % 4.93/5.28 (assume @p11 (= tptp.or_2 @t22)) % 4.93/5.28 (assume @p12 (= tptp.or_3 (forall @t18 (tptp.is_a_theorem (tptp.implies @t16 (tptp.implies @t17 (tptp.implies @t21 @t15))))))) % 4.93/5.28 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t4))))) % 4.93/5.28 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t11 @t14))))) % 4.93/5.28 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t14 @t11)))))) % 4.93/5.28 (assume @p16 (= tptp.kn1 (forall @t24 (tptp.is_a_theorem (tptp.implies @t23 (tptp.and @t23 @t23)))))) % 4.93/5.28 (assume @p17 (= tptp.kn2 (forall @t26 (tptp.is_a_theorem (tptp.implies (tptp.and @t23 @t25) @t23))))) % 4.93/5.28 (assume @p18 (= tptp.kn3 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies (tptp.not (tptp.and @t25 @t27)) (tptp.not (tptp.and @t27 @t23)))))))) % 4.93/5.28 (assume @p19 (= tptp.cn1 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t30 (tptp.implies @t23 @t27))))))) % 4.93/5.28 (assume @p20 (= tptp.cn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t23 (tptp.implies @t31 @t25)))))) % 4.93/5.28 (assume @p21 (= tptp.cn3 (forall @t24 (tptp.is_a_theorem (tptp.implies (tptp.implies @t31 @t23) @t23))))) % 4.93/5.28 (assume @p22 (= tptp.r1 (forall @t24 (tptp.is_a_theorem (tptp.implies (tptp.or @t23 @t23) @t23))))) % 4.93/5.28 (assume @p23 (= tptp.r2 @t33)) % 4.93/5.28 (assume @p24 (= tptp.r3 @t34)) % 4.93/5.28 (assume @p25 (= tptp.r4 (forall @t29 (tptp.is_a_theorem (tptp.implies (tptp.or @t23 (tptp.or @t25 @t27)) (tptp.or @t25 @t35)))))) % 4.93/5.28 (assume @p26 (= tptp.r5 (forall @t29 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies @t32 @t35)))))) % 4.93/5.28 (assume @p27 (=> tptp.op_or @t36)) % 4.93/5.28 (assume @p28 (=> tptp.op_and @t37)) % 4.93/5.28 (assume @p29 (=> tptp.op_implies_and @t38)) % 4.93/5.28 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t12 @t1))))) % 4.93/5.28 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t11 (tptp.and @t4 @t14))))) % 4.93/5.28 (assume @p32 tptp.op_implies_or) % 4.93/5.28 (assume @p33 tptp.op_and) % 4.93/5.28 (assume @p34 tptp.op_equiv) % 4.93/5.28 (assume @p35 tptp.modus_ponens) % 4.93/5.28 (assume @p36 tptp.r1) % 4.93/5.28 (assume @p37 tptp.r2) % 4.93/5.28 (assume @p38 tptp.r3) % 4.93/5.28 (assume @p39 tptp.r4) % 4.93/5.28 (assume @p40 tptp.r5) % 4.93/5.28 (assume @p41 tptp.substitution_of_equivalents) % 4.93/5.28 (assume @p42 tptp.op_or) % 4.93/5.28 (assume @p43 tptp.op_implies_and) % 4.93/5.28 (assume @p44 (not tptp.and_2)) % 4.93/5.28 (assume @p45 true) % 4.93/5.28 (step @p46 :rule equiv_elim1 :premises (@p24)) % 4.93/5.28 (step @p47 :rule reordering :premises (@p46) :args ((or @t34 (not tptp.r3)))) % 4.93/5.28 (step @p48 :rule chain_m_resolution :premises (@p47 @p38) :args (@t34 @t39 (@list tptp.r3))) % 4.93/5.28 (step @p49 :rule instantiate :premises (@p48) :args (@t45)) % 4.93/5.28 (step @p50 :rule aci_norm :args ((= (or (or @t47 @t46) @t2) @t48))) % 4.93/5.28 (step @p51 :rule refl :args (@t2)) % 4.93/5.28 (step @p52 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 4.93/5.28 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or (not @t7) @t2))) % 4.93/5.28 (step @p54 :rule trans :premises (@p53 @p50)) % 4.93/5.28 (step @p55 :rule bool-impl-elim :args (@t7 @t2)) % 4.93/5.28 (step @p56 :rule trans :premises (@p55 @p54)) % 4.93/5.28 (step @p57 :rule cong :premises (@p56) :args (@t9)) % 4.93/5.28 (step @p58 :rule refl :args (tptp.modus_ponens)) % 4.93/5.28 (step @p59 :rule cong :premises (@p58 @p57) :args (@t10)) % 4.93/5.28 (step @p60 :rule eq_resolve :premises (@p1 @p59)) % 4.93/5.28 (step @p61 :rule equiv_elim1 :premises (@p60)) % 4.93/5.28 (step @p62 :rule reordering :premises (@p61) :args ((or @t49 (not tptp.modus_ponens)))) % 4.93/5.28 (step @p63 :rule chain_m_resolution :premises (@p62 @p35) :args (@t49 @t39 (@list tptp.modus_ponens))) % 0.20/5.30 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t51 @t50))) % 0.20/5.30 (step @p65 :rule equiv_elim2 :premises (@p8)) % 0.20/5.30 (step @p66 :rule chain_m_resolution :premises (@p65 @p44) :args ((not @t20) (@list true) (@list tptp.and_2))) % 0.20/5.30 (step @p67 :rule skolemize :premises (@p66)) % 0.20/5.30 (step @p68 :rule false_intro :premises (@p67)) % 0.20/5.30 (step @p69 :rule implies_elim :premises (@p29)) % 0.20/5.30 (step @p70 :rule reordering :premises (@p69) :args ((or @t38 (not tptp.op_implies_and)))) % 0.20/5.30 (step @p71 :rule chain_m_resolution :premises (@p70 @p43) :args (@t38 @t39 (@list tptp.op_implies_and))) % 0.20/5.30 (step @p72 :rule instantiate :premises (@p71) :args ((@list (tptp.and @t42 @t40) @t40))) % 0.20/5.30 (step @p73 :rule symm :premises (@p72)) % 0.20/5.30 (step @p74 :rule refl :args (@t41)) % 0.20/5.30 (step @p75 :rule implies_elim :premises (@p28)) % 0.20/5.30 (step @p76 :rule reordering :premises (@p75) :args ((or @t37 (not tptp.op_and)))) % 0.20/5.30 (step @p77 :rule chain_m_resolution :premises (@p76 @p33) :args (@t37 @t39 (@list tptp.op_and))) % 0.20/5.30 (step @p78 :rule instantiate :premises (@p77) :args ((@list @t42 @t40))) % 0.20/5.30 (step @p79 :rule symm :premises (@p78)) % 0.20/5.30 (step @p80 :rule cong :premises (@p79 @p74) :args (@t52)) % 0.20/5.30 (step @p81 :rule cong :premises (@p80) :args ((tptp.not @t52))) % 0.20/5.30 (step @p82 :rule implies_elim :premises (@p27)) % 0.20/5.30 (step @p83 :rule reordering :premises (@p82) :args ((or @t36 (not tptp.op_or)))) % 0.20/5.30 (step @p84 :rule chain_m_resolution :premises (@p83 @p42) :args (@t36 @t39 (@list tptp.op_or))) % 0.20/5.30 (step @p85 :rule instantiate :premises (@p84) :args ((@list @t44 @t40))) % 0.20/5.30 (step @p86 :rule trans :premises (@p85 @p81 @p73)) % 0.20/5.30 (step @p87 :rule cong :premises (@p86) :args (@t53)) % 0.20/5.30 (step @p88 :rule trans :premises (@p87 @p68)) % 0.20/5.30 (step @p89 :rule false_elim :premises (@p88)) % 0.20/5.30 (step @p90 :rule equiv_elim1 :premises (@p23)) % 0.20/5.30 (step @p91 :rule reordering :premises (@p90) :args ((or @t33 (not tptp.r2)))) % 0.20/5.30 (step @p92 :rule chain_m_resolution :premises (@p91 @p37) :args (@t33 @t39 (@list tptp.r2))) % 0.20/5.30 (step @p93 :rule alpha_equiv :args (@t22 (@list @t1 @t3) (@list @t25 @t23))) % 0.20/5.30 (step @p94 :rule equiv_elim2 :premises (@p93)) % 0.20/5.30 (step @p95 :rule chain_m_resolution :premises (@p94 @p92) :args (@t22 @t39 (@list @t33))) % 0.20/5.30 (step @p96 :rule instantiate :premises (@p95) :args ((@list @t43 @t41))) % 0.20/5.30 (step @p97 :rule true_intro :premises (@p96)) % 0.20/5.30 (step @p98 :rule instantiate :premises (@p71) :args ((@list @t41 @t44))) % 0.20/5.30 (step @p99 :rule symm :premises (@p98)) % 0.20/5.30 (step @p100 :rule instantiate :premises (@p84) :args (@t45)) % 0.20/5.30 (step @p101 :rule trans :premises (@p100 @p99)) % 0.20/5.30 (step @p102 :rule cong :premises (@p101) :args (@t54)) % 0.20/5.30 (step @p103 :rule trans :premises (@p102 @p97)) % 0.20/5.30 (step @p104 :rule true_elim :premises (@p103)) % 0.20/5.30 (step @p105 :rule cnf_or_pos :args (@t58)) % 0.20/5.30 (step @p106 :rule reordering :premises (@p105) :args ((or @t56 @t57 @t53 (not @t58)))) % 0.20/5.30 (step @p107 false :rule chain_m_resolution :premises (@p106 @p104 @p89 @p64 @p49) :args (false (@list false true false false) (@list @t54 @t53 @t58 @t55))) % 0.20/5.30 ) % 0.20/5.30 % SZS output end Proof % 0.20/5.30 % cvc5 exiting %------------------------------------------------------------------------------