%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL544+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 : n003.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 11:23:03 AM UTC 2026 % Result : Theorem 15.81s 16.20s % Output : Proof 15.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL544+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 % 0.10/0.37 % Computer : n003.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 20:16:21 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.45 %----Proving TF0_NAR, FOF, or CNF % 15.81/16.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.81/16.20 --- Run --no-e-matching --full-saturate-quant at 6... % 15.81/16.20 % SZS status Theorem % 15.81/16.20 % SZS output start Proof % 15.81/16.20 ( % 15.81/16.20 (declare-sort $$unsorted 0) % 15.81/16.20 (declare-const tptp.op_strict_implies Bool) % 15.81/16.20 (declare-const tptp.op_possibly Bool) % 15.81/16.20 (declare-const tptp.axiom_m10 Bool) % 15.81/16.20 (declare-const tptp.axiom_m9 Bool) % 15.81/16.20 (declare-const tptp.axiom_m7 Bool) % 15.81/16.20 (declare-const tptp.axiom_m6 Bool) % 15.81/16.20 (declare-const tptp.r2 Bool) % 15.81/16.20 (declare-const tptp.r1 Bool) % 15.81/16.20 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 15.81/16.20 (declare-const tptp.op_necessarily Bool) % 15.81/16.20 (declare-const tptp.kn3 Bool) % 15.81/16.20 (declare-const tptp.strict_equiv (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.cn2 Bool) % 15.81/16.20 (declare-const tptp.axiom_m3 Bool) % 15.81/16.20 (declare-const tptp.kn2 Bool) % 15.81/16.20 (declare-const tptp.cn1 Bool) % 15.81/16.20 (declare-const tptp.or_2 Bool) % 15.81/16.20 (declare-const tptp.and_3 Bool) % 15.81/16.20 (declare-const tptp.r5 Bool) % 15.81/16.20 (declare-const tptp.necessitation Bool) % 15.81/16.20 (declare-const tptp.equivalence_1 Bool) % 15.81/16.20 (declare-const tptp.implies_1 Bool) % 15.81/16.20 (declare-const tptp.equivalence_2 Bool) % 15.81/16.20 (declare-const tptp.or_3 Bool) % 15.81/16.20 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.substitution_of_equivalents Bool) % 15.81/16.20 (declare-const tptp.implies_3 Bool) % 15.81/16.20 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.axiom_m1 Bool) % 15.81/16.20 (declare-const tptp.and_1 Bool) % 15.81/16.20 (declare-const tptp.equivalence_3 Bool) % 15.81/16.20 (declare-const tptp.necessarily (-> $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.or_1 Bool) % 15.81/16.20 (declare-const tptp.op_or Bool) % 15.81/16.20 (declare-const tptp.cn3 Bool) % 15.81/16.20 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.op_strict_equiv Bool) % 15.81/16.20 (declare-const tptp.axiom_4 Bool) % 15.81/16.20 (declare-const tptp.modus_tollens Bool) % 15.81/16.20 (declare-const tptp.and_2 Bool) % 15.81/16.20 (declare-const tptp.implies_2 Bool) % 15.81/16.20 (declare-const tptp.axiom_5 Bool) % 15.81/16.20 (declare-const tptp.axiom_s2 Bool) % 15.81/16.20 (declare-const tptp.r4 Bool) % 15.81/16.20 (declare-const tptp.kn1 Bool) % 15.81/16.20 (declare-const tptp.adjunction Bool) % 15.81/16.20 (declare-const tptp.modus_ponens Bool) % 15.81/16.20 (declare-const tptp.op_and Bool) % 15.81/16.20 (declare-const tptp.axiom_M Bool) % 15.81/16.20 (declare-const tptp.possibly (-> $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.op_equiv Bool) % 15.81/16.20 (declare-const tptp.strict_implies (-> $$unsorted $$unsorted $$unsorted)) % 15.81/16.20 (declare-const tptp.axiom_m8 Bool) % 15.81/16.20 (declare-const tptp.modus_ponens_strict_implies Bool) % 15.81/16.20 (declare-const tptp.substitution_strict_equiv Bool) % 15.81/16.20 (declare-const tptp.axiom_K Bool) % 15.81/16.20 (declare-const tptp.op_implies Bool) % 15.81/16.20 (declare-const tptp.axiom_B Bool) % 15.81/16.20 (declare-const tptp.axiom_s1 Bool) % 15.81/16.20 (declare-const tptp.r3 Bool) % 15.81/16.20 (declare-const tptp.axiom_s3 Bool) % 15.81/16.20 (declare-const tptp.axiom_s4 Bool) % 15.81/16.20 (declare-const tptp.axiom_m2 Bool) % 15.81/16.20 (declare-const tptp.op_implies_and Bool) % 15.81/16.20 (declare-const tptp.axiom_m4 Bool) % 15.81/16.20 (declare-const tptp.op_implies_or Bool) % 15.81/16.20 (declare-const tptp.axiom_m5 Bool) % 15.81/16.20 (define @t1 () (@var "Y" $$unsorted)) % 15.81/16.20 (define @t2 () (tptp.is_a_theorem @t1)) % 15.81/16.20 (define @t3 () (@var "X" $$unsorted)) % 15.81/16.20 (define @t4 () (tptp.implies @t3 @t1)) % 15.81/16.20 (define @t5 () (tptp.is_a_theorem @t4)) % 15.81/16.20 (define @t6 () (tptp.is_a_theorem @t3)) % 15.81/16.20 (define @t7 () (and @t6 @t5)) % 15.81/16.20 (define @t8 () (@list @t3 @t1)) % 15.81/16.20 (define @t9 () (forall @t8 (=> @t7 @t2))) % 15.81/16.20 (define @t10 () (= tptp.modus_ponens @t9)) % 15.81/16.20 (define @t11 () (= @t3 @t1)) % 15.81/16.20 (define @t12 () (tptp.equiv @t3 @t1)) % 15.81/16.20 (define @t13 () (tptp.not @t3)) % 15.81/16.20 (define @t14 () (tptp.not @t1)) % 15.81/16.20 (define @t15 () (tptp.implies @t1 @t3)) % 15.81/16.20 (define @t16 () (@var "Z" $$unsorted)) % 15.81/16.20 (define @t17 () (tptp.implies @t3 @t16)) % 15.81/16.20 (define @t18 () (tptp.implies @t1 @t16)) % 15.81/16.20 (define @t19 () (@list @t3 @t1 @t16)) % 15.81/16.20 (define @t20 () (tptp.and @t3 @t1)) % 15.81/16.20 (define @t21 () (tptp.or @t3 @t1)) % 15.81/16.20 (define @t22 () (@var "P" $$unsorted)) % 15.81/16.20 (define @t23 () (@list @t22)) % 15.81/16.20 (define @t24 () (@var "Q" $$unsorted)) % 15.81/16.20 (define @t25 () (tptp.and @t22 @t24)) % 15.81/16.20 (define @t26 () (@list @t22 @t24)) % 15.81/16.20 (define @t27 () (@var "R" $$unsorted)) % 15.81/16.20 (define @t28 () (tptp.implies @t22 @t24)) % 15.81/16.20 (define @t29 () (@list @t22 @t24 @t27)) % 15.81/16.20 (define @t30 () (tptp.implies @t24 @t27)) % 15.81/16.20 (define @t31 () (tptp.not @t22)) % 15.81/16.20 (define @t32 () (tptp.or @t22 @t24)) % 15.81/16.20 (define @t33 () (tptp.or @t22 @t27)) % 15.81/16.20 (define @t34 () (tptp.necessarily @t3)) % 15.81/16.20 (define @t35 () (tptp.is_a_theorem @t34)) % 15.81/16.20 (define @t36 () (@list @t3)) % 15.81/16.20 (define @t37 () (forall @t36 (=> @t6 @t35))) % 15.81/16.20 (define @t38 () (= tptp.necessitation @t37)) % 15.81/16.20 (define @t39 () (tptp.strict_implies @t3 @t1)) % 15.81/16.20 (define @t40 () (tptp.strict_equiv @t3 @t1)) % 15.81/16.20 (define @t41 () (tptp.necessarily @t4)) % 15.81/16.20 (define @t42 () (tptp.necessarily @t34)) % 15.81/16.20 (define @t43 () (tptp.possibly @t3)) % 15.81/16.20 (define @t44 () (tptp.necessarily @t43)) % 15.81/16.20 (define @t45 () (tptp.possibly @t24)) % 15.81/16.20 (define @t46 () (tptp.possibly @t22)) % 15.81/16.20 (define @t47 () (tptp.possibly @t25)) % 15.81/16.20 (define @t48 () (forall @t36 (tptp.is_a_theorem (tptp.strict_implies @t3 (tptp.and @t3 @t3))))) % 15.81/16.20 (define @t49 () (forall @t8 (= @t39 @t41))) % 15.81/16.20 (define @t50 () (=> tptp.op_strict_implies @t49)) % 15.81/16.20 (define @t51 () (not tptp.axiom_m4)) % 15.81/16.20 (define @t52 () (not @t5)) % 15.81/16.20 (define @t53 () (not @t6)) % 15.81/16.20 (define @t54 () (or @t53 @t52 @t2)) % 15.81/16.20 (define @t55 () (@quantifiers_skolemize @t48 0)) % 15.81/16.21 (define @t56 () (tptp.and @t55 @t55)) % 15.81/16.21 (define @t57 () (tptp.implies @t55 @t56)) % 15.81/16.21 (define @t58 () (@list @t55 @t56)) % 15.81/16.21 (define @t59 () (tptp.is_a_theorem (tptp.necessarily @t57))) % 15.81/16.21 (define @t60 () (tptp.is_a_theorem @t57)) % 15.81/16.21 (define @t61 () (not @t60)) % 15.81/16.21 (define @t62 () (or @t61 @t59)) % 15.81/16.21 (define @t63 () (@list true false)) % 15.81/16.21 (define @t64 () (tptp.implies @t55 @t57)) % 15.81/16.21 (define @t65 () (tptp.is_a_theorem (tptp.implies @t64 @t57))) % 15.81/16.21 (define @t66 () (not @t65)) % 15.81/16.21 (define @t67 () (tptp.is_a_theorem @t64)) % 15.81/16.21 (define @t68 () (not @t67)) % 15.81/16.21 (define @t69 () (or @t68 @t66 @t60)) % 15.81/16.21 (define @t70 () (not @t69)) % 15.81/16.21 (define @t71 () (forall @t8 @t54)) % 15.81/16.21 (assume @p1 @t10) % 15.81/16.21 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t12) @t11)))) % 15.81/16.21 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t14 @t13) @t4))))) % 15.81/16.21 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t15))))) % 15.81/16.21 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 15.81/16.21 (assume @p6 (= tptp.implies_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t18 @t17)))))) % 15.81/16.21 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t3))))) % 15.81/16.21 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t1))))) % 15.81/16.21 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t20)))))) % 15.81/16.21 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t21))))) % 15.81/16.21 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t21))))) % 15.81/16.21 (assume @p12 (= tptp.or_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t17 (tptp.implies @t18 (tptp.implies @t21 @t16))))))) % 15.81/16.21 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t4))))) % 15.81/16.21 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t15))))) % 15.81/16.21 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t15 @t12)))))) % 15.81/16.21 (assume @p16 (= tptp.kn1 (forall @t23 (tptp.is_a_theorem (tptp.implies @t22 (tptp.and @t22 @t22)))))) % 15.81/16.21 (assume @p17 (= tptp.kn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 @t22))))) % 15.81/16.21 (assume @p18 (= tptp.kn3 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies (tptp.not (tptp.and @t24 @t27)) (tptp.not (tptp.and @t27 @t22)))))))) % 15.81/16.21 (assume @p19 (= tptp.cn1 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t30 (tptp.implies @t22 @t27))))))) % 15.81/16.21 (assume @p20 (= tptp.cn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t22 (tptp.implies @t31 @t24)))))) % 15.81/16.21 (assume @p21 (= tptp.cn3 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.implies @t31 @t22) @t22))))) % 15.81/16.21 (assume @p22 (= tptp.r1 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 @t22) @t22))))) % 15.81/16.21 (assume @p23 (= tptp.r2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t24 @t32))))) % 15.81/16.21 (assume @p24 (= tptp.r3 (forall @t26 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t24 @t22)))))) % 15.81/16.21 (assume @p25 (= tptp.r4 (forall @t29 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 (tptp.or @t24 @t27)) (tptp.or @t24 @t33)))))) % 15.81/16.21 (assume @p26 (= tptp.r5 (forall @t29 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies @t32 @t33)))))) % 15.81/16.21 (assume @p27 (=> tptp.op_or (forall @t8 (= @t21 (tptp.not (tptp.and @t13 @t14)))))) % 15.81/16.21 (assume @p28 (=> tptp.op_and (forall @t8 (= @t20 (tptp.not (tptp.or @t13 @t14)))))) % 15.81/16.21 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t14)))))) % 15.81/16.21 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t13 @t1))))) % 15.81/16.21 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t12 (tptp.and @t4 @t15))))) % 15.81/16.21 (assume @p32 tptp.op_or) % 15.81/16.21 (assume @p33 tptp.op_implies_and) % 15.81/16.21 (assume @p34 tptp.op_equiv) % 15.81/16.21 (assume @p35 tptp.modus_ponens) % 15.81/16.21 (assume @p36 tptp.modus_tollens) % 15.81/16.21 (assume @p37 tptp.implies_1) % 15.81/16.21 (assume @p38 tptp.implies_2) % 15.81/16.21 (assume @p39 tptp.implies_3) % 15.81/16.21 (assume @p40 tptp.and_1) % 15.81/16.21 (assume @p41 tptp.and_2) % 15.81/16.21 (assume @p42 tptp.and_3) % 15.81/16.21 (assume @p43 tptp.or_1) % 15.81/16.21 (assume @p44 tptp.or_2) % 15.81/16.21 (assume @p45 tptp.or_3) % 15.81/16.21 (assume @p46 tptp.equivalence_1) % 15.81/16.21 (assume @p47 tptp.equivalence_2) % 15.81/16.21 (assume @p48 tptp.equivalence_3) % 15.81/16.21 (assume @p49 tptp.substitution_of_equivalents) % 15.81/16.21 (assume @p50 @t38) % 15.81/16.21 (assume @p51 (= tptp.modus_ponens_strict_implies (forall @t8 (=> (and @t6 (tptp.is_a_theorem @t39)) @t2)))) % 15.81/16.21 (assume @p52 (= tptp.adjunction (forall @t8 (=> (and @t6 @t2) (tptp.is_a_theorem @t20))))) % 15.81/16.21 (assume @p53 (= tptp.substitution_strict_equiv (forall @t8 (=> (tptp.is_a_theorem @t40) @t11)))) % 15.81/16.21 (assume @p54 (= tptp.axiom_K (forall @t8 (tptp.is_a_theorem (tptp.implies @t41 (tptp.implies @t34 (tptp.necessarily @t1))))))) % 15.81/16.21 (assume @p55 (= tptp.axiom_M (forall @t36 (tptp.is_a_theorem (tptp.implies @t34 @t3))))) % 15.81/16.21 (assume @p56 (= tptp.axiom_4 (forall @t36 (tptp.is_a_theorem (tptp.implies @t34 @t42))))) % 15.81/16.21 (assume @p57 (= tptp.axiom_B (forall @t36 (tptp.is_a_theorem (tptp.implies @t3 @t44))))) % 15.81/16.21 (assume @p58 (= tptp.axiom_5 (forall @t36 (tptp.is_a_theorem (tptp.implies @t43 @t44))))) % 15.81/16.21 (assume @p59 (= tptp.axiom_s1 (forall @t19 (tptp.is_a_theorem (tptp.implies (tptp.and @t41 (tptp.necessarily @t18)) (tptp.necessarily @t17)))))) % 15.81/16.21 (assume @p60 (= tptp.axiom_s2 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t47 (tptp.and @t46 @t45)))))) % 15.81/16.21 (assume @p61 (= tptp.axiom_s3 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t39 (tptp.strict_implies (tptp.not (tptp.possibly @t1)) (tptp.not @t43))))))) % 15.81/16.21 (assume @p62 (= tptp.axiom_s4 (forall @t36 (tptp.is_a_theorem (tptp.strict_implies @t34 @t42))))) % 15.81/16.21 (assume @p63 (= tptp.axiom_m1 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 (tptp.and @t1 @t3)))))) % 15.81/16.21 (assume @p64 (= tptp.axiom_m2 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 @t3))))) % 15.81/16.21 (assume @p65 (= tptp.axiom_m3 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t20 @t16) (tptp.and @t3 (tptp.and @t1 @t16))))))) % 15.81/16.21 (assume @p66 (= tptp.axiom_m4 @t48)) % 15.81/16.21 (assume @p67 (= tptp.axiom_m5 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t39 (tptp.strict_implies @t1 @t16)) (tptp.strict_implies @t3 @t16)))))) % 15.81/16.21 (assume @p68 (= tptp.axiom_m6 (forall @t36 (tptp.is_a_theorem (tptp.strict_implies @t3 @t43))))) % 15.81/16.21 (assume @p69 (= tptp.axiom_m7 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t47 @t22))))) % 15.81/16.21 (assume @p70 (= tptp.axiom_m8 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies (tptp.strict_implies @t22 @t24) (tptp.strict_implies @t46 @t45)))))) % 15.81/16.21 (assume @p71 (= tptp.axiom_m9 (forall @t36 (tptp.is_a_theorem (tptp.strict_implies (tptp.possibly @t43) @t43))))) % 15.81/16.21 (assume @p72 (= tptp.axiom_m10 (forall @t36 (tptp.is_a_theorem (tptp.strict_implies @t43 @t44))))) % 15.81/16.21 (assume @p73 (=> tptp.op_possibly (forall @t36 (= @t43 (tptp.not (tptp.necessarily @t13)))))) % 15.81/16.21 (assume @p74 (=> tptp.op_necessarily (forall @t36 (= @t34 (tptp.not (tptp.possibly @t13)))))) % 15.81/16.21 (assume @p75 @t50) % 15.81/16.21 (assume @p76 (=> tptp.op_strict_equiv (forall @t8 (= @t40 (tptp.and @t39 (tptp.strict_implies @t1 @t3)))))) % 15.81/16.21 (assume @p77 tptp.op_possibly) % 15.81/16.21 (assume @p78 tptp.necessitation) % 15.81/16.21 (assume @p79 tptp.axiom_K) % 15.81/16.21 (assume @p80 tptp.axiom_M) % 15.81/16.21 (assume @p81 tptp.axiom_4) % 15.81/16.21 (assume @p82 tptp.axiom_B) % 15.81/16.21 (assume @p83 tptp.op_implies) % 15.81/16.21 (assume @p84 tptp.op_strict_implies) % 15.81/16.21 (assume @p85 tptp.op_strict_equiv) % 15.81/16.21 (assume @p86 @t51) % 15.81/16.21 (assume @p87 true) % 15.81/16.21 (step @p88 :rule aci_norm :args ((= (or (or @t53 @t52) @t2) @t54))) % 15.81/16.21 (step @p89 :rule refl :args (@t2)) % 15.81/16.21 (step @p90 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 15.81/16.21 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or (not @t7) @t2))) % 15.81/16.21 (step @p92 :rule trans :premises (@p91 @p88)) % 15.81/16.21 (step @p93 :rule bool-impl-elim :args (@t7 @t2)) % 15.81/16.21 (step @p94 :rule trans :premises (@p93 @p92)) % 15.81/16.21 (step @p95 :rule cong :premises (@p94) :args (@t9)) % 15.81/16.21 (step @p96 :rule refl :args (tptp.modus_ponens)) % 15.81/16.21 (step @p97 :rule cong :premises (@p96 @p95) :args (@t10)) % 15.81/16.21 (step @p98 :rule eq_resolve :premises (@p1 @p97)) % 15.81/16.21 (step @p99 :rule eq_resolve :premises (@p35 @p98)) % 15.81/16.21 (step @p100 :rule bool-impl-elim :args (@t6 @t35)) % 15.81/16.21 (step @p101 :rule cong :premises (@p100) :args (@t37)) % 15.81/16.21 (step @p102 :rule refl :args (tptp.necessitation)) % 15.81/16.21 (step @p103 :rule cong :premises (@p102 @p101) :args (@t38)) % 15.81/16.21 (step @p104 :rule eq_resolve :premises (@p50 @p103)) % 15.81/16.21 (step @p105 :rule eq_resolve :premises (@p78 @p104)) % 15.81/16.21 (step @p106 :rule instantiate :premises (@p105) :args ((@list @t57))) % 15.81/16.21 (step @p107 :rule cong :premises (@p66) :args (@t51)) % 15.81/16.21 (step @p108 :rule eq_resolve :premises (@p86 @p107)) % 15.81/16.21 (step @p109 :rule skolemize :premises (@p108)) % 15.81/16.21 (step @p110 :rule false_intro :premises (@p109)) % 15.81/16.21 (step @p111 :rule bool-impl-true2 :args (@t49)) % 15.81/16.21 (step @p112 :rule refl :args (@t49)) % 15.81/16.21 (step @p113 :rule bool-eq-true :args (tptp.op_strict_implies)) % 15.81/16.21 (step @p114 :rule symm :premises (@p113)) % 15.81/16.21 (step @p115 :rule eq_resolve :premises (@p84 @p114)) % 15.81/16.21 (step @p116 :rule cong :premises (@p115 @p112) :args (@t50)) % 15.81/16.21 (step @p117 :rule trans :premises (@p116 @p111)) % 15.81/16.21 (step @p118 :rule eq_resolve :premises (@p75 @p117)) % 15.81/16.21 (step @p119 :rule instantiate :premises (@p118) :args (@t58)) % 15.81/16.21 (step @p120 :rule symm :premises (@p119)) % 15.81/16.21 (step @p121 :rule cong :premises (@p120) :args (@t59)) % 15.81/16.21 (step @p122 :rule trans :premises (@p121 @p110)) % 15.81/16.21 (step @p123 :rule false_elim :premises (@p122)) % 15.81/16.21 (step @p124 :rule cnf_or_pos :args (@t62)) % 15.81/16.21 (step @p125 :rule reordering :premises (@p124) :args ((or @t61 @t59 (not @t62)))) % 15.81/16.21 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p106) :args (@t61 @t63 (@list @t59 @t62))) % 15.81/16.21 (step @p127 :rule eq_resolve :premises (@p38 @p5)) % 15.81/16.21 (step @p128 :rule instantiate :premises (@p127) :args (@t58)) % 15.81/16.21 (step @p129 :rule eq_resolve :premises (@p42 @p9)) % 15.81/16.21 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t55 @t55))) % 15.81/16.21 (step @p131 :rule cnf_or_pos :args (@t69)) % 15.81/16.21 (step @p132 :rule reordering :premises (@p131) :args ((or @t68 @t66 @t60 @t70))) % 15.81/16.21 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p128 @p126) :args (@t70 (@list false false true) (@list @t67 @t65 @t60))) % 15.81/16.21 (assume-push @p140 @t71) % 15.81/16.21 (step @p135 :rule instantiate :premises (@p99) :args ((@list @t64 @t57))) % 15.81/16.21 (step-pop @p141 :rule scope :premises (@p135)) % 15.81/16.21 (step @p136 :rule process_scope :premises (@p141) :args (@t69)) % 15.81/16.21 (step @p138 :rule implies_elim :premises (@p136)) % 15.81/16.21 (step @p139 false :rule chain_m_resolution :premises (@p138 @p133 @p99) :args (false @t63 (@list @t69 @t71))) % 15.81/16.21 ) % 15.81/16.21 % SZS output end Proof % 15.81/16.21 % cvc5 exiting %------------------------------------------------------------------------------