%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL512+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 : n006.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 11:23:01 AM UTC 2026 % Result : Theorem 0.28s 0.62s % Output : Proof 0.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n006.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 17:14:31 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.44 %----Proving TF0_NAR, FOF, or CNF % 0.28/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.28/0.62 % SZS status Theorem % 0.28/0.62 % SZS output start Proof % 0.28/0.62 ( % 0.28/0.62 (declare-sort $$unsorted 0) % 0.28/0.62 (declare-const tptp.op_equiv Bool) % 0.28/0.62 (declare-const tptp.op_implies_or Bool) % 0.28/0.62 (declare-const tptp.op_and Bool) % 0.28/0.62 (declare-const tptp.r4 Bool) % 0.28/0.62 (declare-const tptp.r3 Bool) % 0.28/0.62 (declare-const tptp.implies_2 Bool) % 0.28/0.62 (declare-const tptp.and_2 Bool) % 0.28/0.62 (declare-const tptp.modus_tollens Bool) % 0.28/0.62 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 0.28/0.62 (declare-const tptp.op_or Bool) % 0.28/0.62 (declare-const tptp.or_1 Bool) % 0.28/0.62 (declare-const tptp.equivalence_3 Bool) % 0.28/0.62 (declare-const tptp.and_1 Bool) % 0.28/0.62 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 0.28/0.62 (declare-const tptp.implies_3 Bool) % 0.28/0.62 (declare-const tptp.substitution_of_equivalents Bool) % 0.28/0.62 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 0.28/0.62 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 0.28/0.62 (declare-const tptp.op_implies_and Bool) % 0.28/0.62 (declare-const tptp.or_3 Bool) % 0.28/0.62 (declare-const tptp.equivalence_2 Bool) % 0.28/0.62 (declare-const tptp.modus_ponens Bool) % 0.28/0.62 (declare-const tptp.implies_1 Bool) % 0.28/0.62 (declare-const tptp.equivalence_1 Bool) % 0.28/0.62 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 0.28/0.62 (declare-const tptp.r5 Bool) % 0.28/0.62 (declare-const tptp.and_3 Bool) % 0.28/0.62 (declare-const tptp.cn3 Bool) % 0.28/0.62 (declare-const tptp.or_2 Bool) % 0.28/0.62 (declare-const tptp.kn1 Bool) % 0.28/0.62 (declare-const tptp.cn1 Bool) % 0.28/0.62 (declare-const tptp.kn2 Bool) % 0.28/0.62 (declare-const tptp.cn2 Bool) % 0.28/0.62 (declare-const tptp.kn3 Bool) % 0.28/0.62 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 0.28/0.62 (declare-const tptp.r1 Bool) % 0.28/0.62 (declare-const tptp.r2 Bool) % 0.28/0.62 (define @t1 () (@var "Y" $$unsorted)) % 0.28/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.28/0.62 (define @t3 () (tptp.implies @t2 @t1)) % 0.28/0.62 (define @t4 () (@list @t2 @t1)) % 0.28/0.62 (define @t5 () (tptp.equiv @t2 @t1)) % 0.28/0.62 (define @t6 () (tptp.not @t2)) % 0.28/0.62 (define @t7 () (tptp.not @t1)) % 0.28/0.62 (define @t8 () (tptp.implies @t1 @t2)) % 0.28/0.62 (define @t9 () (@var "Z" $$unsorted)) % 0.28/0.62 (define @t10 () (tptp.implies @t2 @t9)) % 0.28/0.62 (define @t11 () (tptp.implies @t1 @t9)) % 0.28/0.62 (define @t12 () (@list @t2 @t1 @t9)) % 0.28/0.62 (define @t13 () (tptp.and @t2 @t1)) % 0.28/0.62 (define @t14 () (forall @t4 (tptp.is_a_theorem (tptp.implies @t13 @t2)))) % 0.28/0.62 (define @t15 () (tptp.or @t2 @t1)) % 0.28/0.62 (define @t16 () (forall @t4 (tptp.is_a_theorem (tptp.implies @t5 @t3)))) % 0.28/0.62 (define @t17 () (@var "P" $$unsorted)) % 0.28/0.62 (define @t18 () (@list @t17)) % 0.28/0.62 (define @t19 () (@var "Q" $$unsorted)) % 0.28/0.62 (define @t20 () (@list @t17 @t19)) % 0.28/0.62 (define @t21 () (forall @t20 (tptp.is_a_theorem (tptp.implies (tptp.and @t17 @t19) @t17)))) % 0.28/0.62 (define @t22 () (@var "R" $$unsorted)) % 0.28/0.62 (define @t23 () (tptp.implies @t17 @t19)) % 0.28/0.62 (define @t24 () (@list @t17 @t19 @t22)) % 0.28/0.62 (define @t25 () (tptp.implies @t19 @t22)) % 0.28/0.62 (define @t26 () (tptp.not @t17)) % 0.28/0.62 (define @t27 () (tptp.or @t17 @t19)) % 0.28/0.62 (define @t28 () (tptp.or @t17 @t22)) % 0.28/0.62 (define @t29 () (forall @t4 (= @t5 (tptp.and @t3 @t8)))) % 0.28/0.62 (define @t30 () (@list false)) % 0.28/0.62 (define @t31 () (@quantifiers_skolemize @t16 0)) % 0.28/0.62 (define @t32 () (@quantifiers_skolemize @t16 1)) % 0.28/0.62 (define @t33 () (tptp.implies @t31 @t32)) % 0.28/0.62 (define @t34 () (tptp.implies (tptp.equiv @t31 @t32) @t33)) % 0.28/0.62 (assume @p1 (= tptp.modus_ponens (forall @t4 (=> (and (tptp.is_a_theorem @t2) (tptp.is_a_theorem @t3)) (tptp.is_a_theorem @t1))))) % 0.28/0.62 (assume @p2 (= tptp.substitution_of_equivalents (forall @t4 (=> (tptp.is_a_theorem @t5) (= @t2 @t1))))) % 0.28/0.62 (assume @p3 (= tptp.modus_tollens (forall @t4 (tptp.is_a_theorem (tptp.implies (tptp.implies @t7 @t6) @t3))))) % 0.28/0.62 (assume @p4 (= tptp.implies_1 (forall @t4 (tptp.is_a_theorem (tptp.implies @t2 @t8))))) % 0.28/0.62 (assume @p5 (= tptp.implies_2 (forall @t4 (tptp.is_a_theorem (tptp.implies (tptp.implies @t2 @t3) @t3))))) % 0.28/0.62 (assume @p6 (= tptp.implies_3 (forall @t12 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t11 @t10)))))) % 0.28/0.62 (assume @p7 (= tptp.and_1 @t14)) % 0.28/0.62 (assume @p8 (= tptp.and_2 (forall @t4 (tptp.is_a_theorem (tptp.implies @t13 @t1))))) % 0.28/0.62 (assume @p9 (= tptp.and_3 (forall @t4 (tptp.is_a_theorem (tptp.implies @t2 (tptp.implies @t1 @t13)))))) % 0.28/0.62 (assume @p10 (= tptp.or_1 (forall @t4 (tptp.is_a_theorem (tptp.implies @t2 @t15))))) % 0.28/0.62 (assume @p11 (= tptp.or_2 (forall @t4 (tptp.is_a_theorem (tptp.implies @t1 @t15))))) % 0.28/0.62 (assume @p12 (= tptp.or_3 (forall @t12 (tptp.is_a_theorem (tptp.implies @t10 (tptp.implies @t11 (tptp.implies @t15 @t9))))))) % 0.28/0.62 (assume @p13 (= tptp.equivalence_1 @t16)) % 0.28/0.62 (assume @p14 (= tptp.equivalence_2 (forall @t4 (tptp.is_a_theorem (tptp.implies @t5 @t8))))) % 0.28/0.62 (assume @p15 (= tptp.equivalence_3 (forall @t4 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t8 @t5)))))) % 0.28/0.62 (assume @p16 (= tptp.kn1 (forall @t18 (tptp.is_a_theorem (tptp.implies @t17 (tptp.and @t17 @t17)))))) % 0.28/0.62 (assume @p17 (= tptp.kn2 @t21)) % 0.28/0.62 (assume @p18 (= tptp.kn3 (forall @t24 (tptp.is_a_theorem (tptp.implies @t23 (tptp.implies (tptp.not (tptp.and @t19 @t22)) (tptp.not (tptp.and @t22 @t17)))))))) % 0.28/0.62 (assume @p19 (= tptp.cn1 (forall @t24 (tptp.is_a_theorem (tptp.implies @t23 (tptp.implies @t25 (tptp.implies @t17 @t22))))))) % 0.28/0.62 (assume @p20 (= tptp.cn2 (forall @t20 (tptp.is_a_theorem (tptp.implies @t17 (tptp.implies @t26 @t19)))))) % 0.28/0.62 (assume @p21 (= tptp.cn3 (forall @t18 (tptp.is_a_theorem (tptp.implies (tptp.implies @t26 @t17) @t17))))) % 0.28/0.62 (assume @p22 (= tptp.r1 (forall @t18 (tptp.is_a_theorem (tptp.implies (tptp.or @t17 @t17) @t17))))) % 0.28/0.62 (assume @p23 (= tptp.r2 (forall @t20 (tptp.is_a_theorem (tptp.implies @t19 @t27))))) % 0.28/0.62 (assume @p24 (= tptp.r3 (forall @t20 (tptp.is_a_theorem (tptp.implies @t27 (tptp.or @t19 @t17)))))) % 0.28/0.62 (assume @p25 (= tptp.r4 (forall @t24 (tptp.is_a_theorem (tptp.implies (tptp.or @t17 (tptp.or @t19 @t22)) (tptp.or @t19 @t28)))))) % 0.28/0.62 (assume @p26 (= tptp.r5 (forall @t24 (tptp.is_a_theorem (tptp.implies @t25 (tptp.implies @t27 @t28)))))) % 0.28/0.62 (assume @p27 (=> tptp.op_or (forall @t4 (= @t15 (tptp.not (tptp.and @t6 @t7)))))) % 0.28/0.62 (assume @p28 (=> tptp.op_and (forall @t4 (= @t13 (tptp.not (tptp.or @t6 @t7)))))) % 0.28/0.62 (assume @p29 (=> tptp.op_implies_and (forall @t4 (= @t3 (tptp.not (tptp.and @t2 @t7)))))) % 0.28/0.62 (assume @p30 (=> tptp.op_implies_or (forall @t4 (= @t3 (tptp.or @t6 @t1))))) % 0.28/0.62 (assume @p31 (=> tptp.op_equiv @t29)) % 0.28/0.62 (assume @p32 tptp.op_or) % 0.28/0.62 (assume @p33 tptp.op_implies_and) % 0.28/0.62 (assume @p34 tptp.op_equiv) % 0.28/0.62 (assume @p35 tptp.modus_ponens) % 0.28/0.62 (assume @p36 tptp.kn1) % 0.28/0.62 (assume @p37 tptp.kn2) % 0.28/0.62 (assume @p38 tptp.kn3) % 0.28/0.62 (assume @p39 tptp.substitution_of_equivalents) % 0.28/0.62 (assume @p40 (not tptp.equivalence_1)) % 0.28/0.62 (assume @p41 true) % 0.28/0.62 (step @p42 :rule evaluate :args ((= false true))) % 0.28/0.62 (step @p43 :rule equiv_elim1 :premises (@p17)) % 0.28/0.62 (step @p44 :rule reordering :premises (@p43) :args ((or @t21 (not tptp.kn2)))) % 0.28/0.62 (step @p45 :rule chain_m_resolution :premises (@p44 @p37) :args (@t21 @t30 (@list tptp.kn2))) % 0.28/0.62 (step @p46 :rule alpha_equiv :args (@t14 (@list @t2 @t1) (@list @t17 @t19))) % 0.28/0.62 (step @p47 :rule equiv_elim2 :premises (@p46)) % 0.28/0.62 (step @p48 :rule chain_m_resolution :premises (@p47 @p45) :args (@t14 @t30 (@list @t21))) % 0.28/0.62 (step @p49 :rule instantiate :premises (@p48) :args ((@list @t33 (tptp.implies @t32 @t31)))) % 0.28/0.62 (step @p50 :rule true_intro :premises (@p49)) % 0.28/0.62 (step @p51 :rule refl :args (@t33)) % 0.28/0.62 (step @p52 :rule implies_elim :premises (@p31)) % 0.28/0.62 (step @p53 :rule reordering :premises (@p52) :args ((or @t29 (not tptp.op_equiv)))) % 0.28/0.62 (step @p54 :rule chain_m_resolution :premises (@p53 @p34) :args (@t29 @t30 (@list tptp.op_equiv))) % 0.28/0.62 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t31 @t32))) % 0.28/0.62 (step @p56 :rule cong :premises (@p55 @p51) :args (@t34)) % 0.28/0.62 (step @p57 :rule cong :premises (@p56) :args ((tptp.is_a_theorem @t34))) % 0.28/0.62 (step @p58 :rule equiv_elim2 :premises (@p13)) % 0.28/0.62 (step @p59 :rule chain_m_resolution :premises (@p58 @p40) :args ((not @t16) (@list true) (@list tptp.equivalence_1))) % 0.28/0.62 (step @p60 :rule skolemize :premises (@p59)) % 0.28/0.62 (step @p61 :rule false_intro :premises (@p60)) % 0.28/0.62 (step @p62 :rule symm :premises (@p61)) % 0.28/0.62 (step @p63 :rule trans :premises (@p62 @p57 @p50)) % 0.28/0.62 (step @p64 false :rule eq_resolve :premises (@p63 @p42)) % 0.28/0.62 ) % 0.28/0.62 % SZS output end Proof % 0.28/0.62 % cvc5 exiting %------------------------------------------------------------------------------