%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL526+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 : n029.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 11:23:02 AM UTC 2026 % Result : Theorem 33.37s 34.56s % Output : Proof 33.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL526+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 % 0.10/0.37 % Computer : n029.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 19:28:40 UTC 2026 % 0.10/0.37 % CPUTime : % 0.16/0.44 %----Proving TF0_NAR, FOF, or CNF % 33.37/34.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.37/34.56 --- Run --no-e-matching --full-saturate-quant at 6... % 33.37/34.56 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.37/34.56 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.37/34.56 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.37/34.56 % SZS status Theorem % 33.37/34.56 % SZS output start Proof % 33.37/34.56 ( % 33.37/34.56 (declare-sort $$unsorted 0) % 33.37/34.56 (declare-const tptp.op_strict_implies Bool) % 33.37/34.56 (declare-const tptp.op_possibly Bool) % 33.37/34.56 (declare-const tptp.axiom_m10 Bool) % 33.37/34.56 (declare-const tptp.axiom_m9 Bool) % 33.37/34.56 (declare-const tptp.axiom_m7 Bool) % 33.37/34.56 (declare-const tptp.axiom_m6 Bool) % 33.37/34.56 (declare-const tptp.r2 Bool) % 33.37/34.56 (declare-const tptp.r1 Bool) % 33.37/34.56 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 33.37/34.56 (declare-const tptp.op_necessarily Bool) % 33.37/34.56 (declare-const tptp.kn3 Bool) % 33.37/34.56 (declare-const tptp.strict_equiv (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.cn2 Bool) % 33.37/34.56 (declare-const tptp.axiom_m3 Bool) % 33.37/34.56 (declare-const tptp.kn2 Bool) % 33.37/34.56 (declare-const tptp.cn1 Bool) % 33.37/34.56 (declare-const tptp.or_2 Bool) % 33.37/34.56 (declare-const tptp.and_3 Bool) % 33.37/34.56 (declare-const tptp.r5 Bool) % 33.37/34.56 (declare-const tptp.necessitation Bool) % 33.37/34.56 (declare-const tptp.equivalence_1 Bool) % 33.37/34.56 (declare-const tptp.implies_1 Bool) % 33.37/34.56 (declare-const tptp.equivalence_2 Bool) % 33.37/34.56 (declare-const tptp.or_3 Bool) % 33.37/34.56 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.substitution_of_equivalents Bool) % 33.37/34.56 (declare-const tptp.implies_3 Bool) % 33.37/34.56 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.axiom_m1 Bool) % 33.37/34.56 (declare-const tptp.and_1 Bool) % 33.37/34.56 (declare-const tptp.equivalence_3 Bool) % 33.37/34.56 (declare-const tptp.necessarily (-> $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.or_1 Bool) % 33.37/34.56 (declare-const tptp.op_or Bool) % 33.37/34.56 (declare-const tptp.cn3 Bool) % 33.37/34.56 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.op_strict_equiv Bool) % 33.37/34.56 (declare-const tptp.axiom_4 Bool) % 33.37/34.56 (declare-const tptp.modus_tollens Bool) % 33.37/34.56 (declare-const tptp.and_2 Bool) % 33.37/34.56 (declare-const tptp.implies_2 Bool) % 33.37/34.56 (declare-const tptp.axiom_5 Bool) % 33.37/34.56 (declare-const tptp.axiom_s2 Bool) % 33.37/34.56 (declare-const tptp.r4 Bool) % 33.37/34.56 (declare-const tptp.kn1 Bool) % 33.37/34.56 (declare-const tptp.adjunction Bool) % 33.37/34.56 (declare-const tptp.modus_ponens Bool) % 33.37/34.56 (declare-const tptp.op_and Bool) % 33.37/34.56 (declare-const tptp.axiom_M Bool) % 33.37/34.56 (declare-const tptp.possibly (-> $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.op_equiv Bool) % 33.37/34.56 (declare-const tptp.strict_implies (-> $$unsorted $$unsorted $$unsorted)) % 33.37/34.56 (declare-const tptp.axiom_m8 Bool) % 33.37/34.56 (declare-const tptp.modus_ponens_strict_implies Bool) % 33.37/34.56 (declare-const tptp.substitution_strict_equiv Bool) % 33.37/34.56 (declare-const tptp.axiom_K Bool) % 33.37/34.56 (declare-const tptp.op_implies Bool) % 33.37/34.56 (declare-const tptp.axiom_B Bool) % 33.37/34.56 (declare-const tptp.axiom_s1 Bool) % 33.37/34.56 (declare-const tptp.r3 Bool) % 33.37/34.56 (declare-const tptp.axiom_s3 Bool) % 33.37/34.56 (declare-const tptp.axiom_s4 Bool) % 33.37/34.56 (declare-const tptp.axiom_m2 Bool) % 33.37/34.56 (declare-const tptp.op_implies_and Bool) % 33.37/34.56 (declare-const tptp.axiom_m4 Bool) % 33.37/34.56 (declare-const tptp.op_implies_or Bool) % 33.37/34.56 (declare-const tptp.axiom_m5 Bool) % 33.37/34.56 (define @t1 () (@var "Y" $$unsorted)) % 33.37/34.56 (define @t2 () (tptp.is_a_theorem @t1)) % 33.37/34.56 (define @t3 () (@var "X" $$unsorted)) % 33.37/34.56 (define @t4 () (tptp.implies @t3 @t1)) % 33.37/34.56 (define @t5 () (tptp.is_a_theorem @t4)) % 33.37/34.56 (define @t6 () (tptp.is_a_theorem @t3)) % 33.37/34.56 (define @t7 () (and @t6 @t5)) % 33.37/34.56 (define @t8 () (@list @t3 @t1)) % 33.37/34.56 (define @t9 () (forall @t8 (=> @t7 @t2))) % 33.37/34.56 (define @t10 () (= tptp.modus_ponens @t9)) % 33.37/34.56 (define @t11 () (= @t3 @t1)) % 33.37/34.56 (define @t12 () (tptp.equiv @t3 @t1)) % 33.37/34.56 (define @t13 () (tptp.is_a_theorem @t12)) % 33.37/34.56 (define @t14 () (forall @t8 (=> @t13 @t11))) % 33.37/34.56 (define @t15 () (= tptp.substitution_of_equivalents @t14)) % 33.37/34.56 (define @t16 () (tptp.not @t3)) % 33.37/34.56 (define @t17 () (tptp.not @t1)) % 33.37/34.56 (define @t18 () (tptp.implies @t1 @t3)) % 33.37/34.56 (define @t19 () (@var "Z" $$unsorted)) % 33.37/34.56 (define @t20 () (tptp.implies @t3 @t19)) % 33.37/34.56 (define @t21 () (tptp.implies @t1 @t19)) % 33.37/34.56 (define @t22 () (@list @t3 @t1 @t19)) % 33.37/34.56 (define @t23 () (tptp.and @t3 @t1)) % 33.37/34.56 (define @t24 () (tptp.or @t3 @t1)) % 33.37/34.56 (define @t25 () (@var "P" $$unsorted)) % 33.37/34.56 (define @t26 () (@list @t25)) % 33.37/34.56 (define @t27 () (@var "Q" $$unsorted)) % 33.37/34.56 (define @t28 () (tptp.and @t25 @t27)) % 33.37/34.56 (define @t29 () (@list @t25 @t27)) % 33.37/34.56 (define @t30 () (@var "R" $$unsorted)) % 33.37/34.56 (define @t31 () (tptp.implies @t25 @t27)) % 33.37/34.56 (define @t32 () (@list @t25 @t27 @t30)) % 33.37/34.56 (define @t33 () (tptp.implies @t27 @t30)) % 33.37/34.56 (define @t34 () (tptp.not @t25)) % 33.37/34.56 (define @t35 () (tptp.or @t25 @t27)) % 33.37/34.56 (define @t36 () (tptp.or @t25 @t30)) % 33.37/34.56 (define @t37 () (tptp.necessarily @t3)) % 33.37/34.56 (define @t38 () (@list @t3)) % 33.37/34.56 (define @t39 () (tptp.strict_implies @t3 @t1)) % 33.37/34.56 (define @t40 () (tptp.strict_equiv @t3 @t1)) % 33.37/34.56 (define @t41 () (tptp.is_a_theorem @t40)) % 33.37/34.56 (define @t42 () (forall @t8 (=> @t41 @t11))) % 33.37/34.56 (define @t43 () (= tptp.substitution_strict_equiv @t42)) % 33.37/34.56 (define @t44 () (tptp.necessarily @t4)) % 33.37/34.56 (define @t45 () (tptp.necessarily @t37)) % 33.37/34.56 (define @t46 () (tptp.possibly @t3)) % 33.37/34.56 (define @t47 () (tptp.necessarily @t46)) % 33.37/34.56 (define @t48 () (tptp.possibly @t27)) % 33.37/34.56 (define @t49 () (tptp.possibly @t25)) % 33.37/34.56 (define @t50 () (tptp.possibly @t28)) % 33.37/34.56 (define @t51 () (forall @t8 (= @t39 @t44))) % 33.37/34.56 (define @t52 () (=> tptp.op_strict_implies @t51)) % 33.37/34.56 (define @t53 () (forall @t8 (= @t40 (tptp.and @t39 (tptp.strict_implies @t1 @t3))))) % 33.37/34.56 (define @t54 () (=> tptp.op_strict_equiv @t53)) % 33.37/34.56 (define @t55 () (not tptp.substitution_strict_equiv)) % 33.37/34.56 (define @t56 () (not @t5)) % 33.37/34.56 (define @t57 () (not @t6)) % 33.37/34.56 (define @t58 () (forall @t8 (or (not @t41) @t11))) % 33.37/34.56 (define @t59 () (@quantifiers_skolemize @t58 0)) % 33.37/34.56 (define @t60 () (@quantifiers_skolemize @t58 1)) % 33.37/34.56 (define @t61 () (tptp.implies @t60 @t59)) % 33.37/34.56 (define @t62 () (tptp.necessarily @t61)) % 33.37/34.56 (define @t63 () (tptp.strict_implies @t60 @t59)) % 33.37/34.56 (define @t64 () (tptp.strict_implies @t59 @t60)) % 33.37/34.56 (define @t65 () (tptp.and @t64 @t63)) % 33.37/34.56 (define @t66 () (tptp.is_a_theorem (tptp.strict_equiv @t59 @t60))) % 33.37/34.56 (define @t67 () (= @t59 @t60)) % 33.37/34.56 (define @t68 () (not @t66)) % 33.37/34.56 (define @t69 () (or @t68 @t67)) % 33.37/34.56 (define @t70 () (@list true)) % 33.37/34.56 (define @t71 () (@list @t69)) % 33.37/34.56 (define @t72 () (@list @t59 @t60)) % 33.37/34.56 (define @t73 () (tptp.is_a_theorem @t65)) % 33.37/34.56 (define @t74 () (@list @t64 @t63)) % 33.37/34.56 (define @t75 () (tptp.is_a_theorem @t63)) % 33.37/34.56 (define @t76 () (tptp.is_a_theorem (tptp.implies @t65 @t63))) % 33.37/34.56 (define @t77 () (not @t76)) % 33.37/34.56 (define @t78 () (not @t73)) % 33.37/34.56 (define @t79 () (or @t78 @t77 @t75)) % 33.37/34.56 (define @t80 () (@list false false false)) % 33.37/34.56 (define @t81 () (tptp.is_a_theorem @t62)) % 33.37/34.56 (define @t82 () (tptp.is_a_theorem @t61)) % 33.37/34.56 (define @t83 () (tptp.is_a_theorem (tptp.implies @t62 @t61))) % 33.37/34.56 (define @t84 () (not @t83)) % 33.37/34.56 (define @t85 () (not @t81)) % 33.37/34.56 (define @t86 () (or @t85 @t84 @t82)) % 33.37/34.56 (define @t87 () (tptp.equiv @t59 @t60)) % 33.37/34.56 (define @t88 () (tptp.is_a_theorem @t87)) % 33.37/34.56 (define @t89 () (not @t88)) % 33.37/34.56 (define @t90 () (or @t89 @t67)) % 33.37/34.56 (define @t91 () (tptp.implies @t61 @t87)) % 33.37/34.56 (define @t92 () (tptp.implies @t59 @t60)) % 33.37/34.56 (define @t93 () (tptp.necessarily @t92)) % 33.37/34.56 (define @t94 () (tptp.is_a_theorem @t64)) % 33.37/34.56 (define @t95 () (tptp.is_a_theorem (tptp.implies @t65 @t64))) % 33.37/34.56 (define @t96 () (not @t95)) % 33.37/34.56 (define @t97 () (or @t78 @t96 @t94)) % 33.37/34.56 (define @t98 () (tptp.is_a_theorem @t93)) % 33.37/34.56 (define @t99 () (tptp.is_a_theorem @t92)) % 33.37/34.56 (define @t100 () (tptp.is_a_theorem (tptp.implies @t93 @t92))) % 33.37/34.56 (define @t101 () (not @t100)) % 33.37/34.56 (define @t102 () (not @t98)) % 33.37/34.56 (define @t103 () (or @t102 @t101 @t99)) % 33.37/34.56 (define @t104 () (tptp.is_a_theorem @t91)) % 33.37/34.56 (define @t105 () (tptp.is_a_theorem (tptp.implies @t92 @t91))) % 33.37/34.56 (define @t106 () (not @t105)) % 33.37/34.56 (define @t107 () (not @t99)) % 33.37/34.56 (define @t108 () (or @t107 @t106 @t104)) % 33.37/34.56 (define @t109 () (not @t104)) % 33.37/34.56 (define @t110 () (not @t82)) % 33.37/34.56 (define @t111 () (or @t110 @t109 @t88)) % 33.37/34.56 (assume @p1 @t10) % 33.37/34.56 (assume @p2 @t15) % 33.37/34.56 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t17 @t16) @t4))))) % 33.37/34.56 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t18))))) % 33.37/34.56 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 33.37/34.56 (assume @p6 (= tptp.implies_3 (forall @t22 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t21 @t20)))))) % 33.37/34.56 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t23 @t3))))) % 33.37/34.56 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t23 @t1))))) % 33.37/34.56 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t23)))))) % 33.37/34.56 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t24))))) % 33.37/34.56 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t24))))) % 33.37/34.56 (assume @p12 (= tptp.or_3 (forall @t22 (tptp.is_a_theorem (tptp.implies @t20 (tptp.implies @t21 (tptp.implies @t24 @t19))))))) % 33.37/34.56 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t4))))) % 33.37/34.56 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t18))))) % 33.37/34.56 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t18 @t12)))))) % 33.37/34.56 (assume @p16 (= tptp.kn1 (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 (tptp.and @t25 @t25)))))) % 33.37/34.56 (assume @p17 (= tptp.kn2 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 @t25))))) % 33.37/34.56 (assume @p18 (= tptp.kn3 (forall @t32 (tptp.is_a_theorem (tptp.implies @t31 (tptp.implies (tptp.not (tptp.and @t27 @t30)) (tptp.not (tptp.and @t30 @t25)))))))) % 33.37/34.56 (assume @p19 (= tptp.cn1 (forall @t32 (tptp.is_a_theorem (tptp.implies @t31 (tptp.implies @t33 (tptp.implies @t25 @t30))))))) % 33.37/34.56 (assume @p20 (= tptp.cn2 (forall @t29 (tptp.is_a_theorem (tptp.implies @t25 (tptp.implies @t34 @t27)))))) % 33.37/34.56 (assume @p21 (= tptp.cn3 (forall @t26 (tptp.is_a_theorem (tptp.implies (tptp.implies @t34 @t25) @t25))))) % 33.37/34.56 (assume @p22 (= tptp.r1 (forall @t26 (tptp.is_a_theorem (tptp.implies (tptp.or @t25 @t25) @t25))))) % 33.37/34.56 (assume @p23 (= tptp.r2 (forall @t29 (tptp.is_a_theorem (tptp.implies @t27 @t35))))) % 33.37/34.56 (assume @p24 (= tptp.r3 (forall @t29 (tptp.is_a_theorem (tptp.implies @t35 (tptp.or @t27 @t25)))))) % 33.37/34.56 (assume @p25 (= tptp.r4 (forall @t32 (tptp.is_a_theorem (tptp.implies (tptp.or @t25 (tptp.or @t27 @t30)) (tptp.or @t27 @t36)))))) % 33.37/34.56 (assume @p26 (= tptp.r5 (forall @t32 (tptp.is_a_theorem (tptp.implies @t33 (tptp.implies @t35 @t36)))))) % 33.37/34.56 (assume @p27 (=> tptp.op_or (forall @t8 (= @t24 (tptp.not (tptp.and @t16 @t17)))))) % 33.37/34.56 (assume @p28 (=> tptp.op_and (forall @t8 (= @t23 (tptp.not (tptp.or @t16 @t17)))))) % 33.37/34.56 (assume @p29 (=> tptp.op_implies_and (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t17)))))) % 33.37/34.56 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t16 @t1))))) % 33.37/34.56 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t12 (tptp.and @t4 @t18))))) % 33.37/34.56 (assume @p32 tptp.op_or) % 33.37/34.56 (assume @p33 tptp.op_implies_and) % 33.37/34.56 (assume @p34 tptp.op_equiv) % 33.37/34.56 (assume @p35 tptp.modus_ponens) % 33.37/34.56 (assume @p36 tptp.modus_tollens) % 33.37/34.56 (assume @p37 tptp.implies_1) % 33.37/34.56 (assume @p38 tptp.implies_2) % 33.37/34.56 (assume @p39 tptp.implies_3) % 33.37/34.56 (assume @p40 tptp.and_1) % 33.37/34.56 (assume @p41 tptp.and_2) % 33.37/34.56 (assume @p42 tptp.and_3) % 33.37/34.56 (assume @p43 tptp.or_1) % 33.37/34.56 (assume @p44 tptp.or_2) % 33.37/34.56 (assume @p45 tptp.or_3) % 33.37/34.56 (assume @p46 tptp.equivalence_1) % 33.37/34.56 (assume @p47 tptp.equivalence_2) % 33.37/34.56 (assume @p48 tptp.equivalence_3) % 33.37/34.56 (assume @p49 tptp.substitution_of_equivalents) % 33.37/34.56 (assume @p50 (= tptp.necessitation (forall @t38 (=> @t6 (tptp.is_a_theorem @t37))))) % 33.37/34.56 (assume @p51 (= tptp.modus_ponens_strict_implies (forall @t8 (=> (and @t6 (tptp.is_a_theorem @t39)) @t2)))) % 33.37/34.56 (assume @p52 (= tptp.adjunction (forall @t8 (=> (and @t6 @t2) (tptp.is_a_theorem @t23))))) % 33.37/34.56 (assume @p53 @t43) % 33.37/34.56 (assume @p54 (= tptp.axiom_K (forall @t8 (tptp.is_a_theorem (tptp.implies @t44 (tptp.implies @t37 (tptp.necessarily @t1))))))) % 33.37/34.56 (assume @p55 (= tptp.axiom_M (forall @t38 (tptp.is_a_theorem (tptp.implies @t37 @t3))))) % 33.37/34.56 (assume @p56 (= tptp.axiom_4 (forall @t38 (tptp.is_a_theorem (tptp.implies @t37 @t45))))) % 33.37/34.56 (assume @p57 (= tptp.axiom_B (forall @t38 (tptp.is_a_theorem (tptp.implies @t3 @t47))))) % 33.37/34.56 (assume @p58 (= tptp.axiom_5 (forall @t38 (tptp.is_a_theorem (tptp.implies @t46 @t47))))) % 33.37/34.56 (assume @p59 (= tptp.axiom_s1 (forall @t22 (tptp.is_a_theorem (tptp.implies (tptp.and @t44 (tptp.necessarily @t21)) (tptp.necessarily @t20)))))) % 33.37/34.56 (assume @p60 (= tptp.axiom_s2 (forall @t29 (tptp.is_a_theorem (tptp.strict_implies @t50 (tptp.and @t49 @t48)))))) % 33.37/34.56 (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 @t46))))))) % 33.37/34.56 (assume @p62 (= tptp.axiom_s4 (forall @t38 (tptp.is_a_theorem (tptp.strict_implies @t37 @t45))))) % 33.37/34.56 (assume @p63 (= tptp.axiom_m1 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t23 (tptp.and @t1 @t3)))))) % 33.37/34.56 (assume @p64 (= tptp.axiom_m2 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t23 @t3))))) % 33.37/34.56 (assume @p65 (= tptp.axiom_m3 (forall @t22 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t23 @t19) (tptp.and @t3 (tptp.and @t1 @t19))))))) % 33.37/34.56 (assume @p66 (= tptp.axiom_m4 (forall @t38 (tptp.is_a_theorem (tptp.strict_implies @t3 (tptp.and @t3 @t3)))))) % 33.37/34.56 (assume @p67 (= tptp.axiom_m5 (forall @t22 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t39 (tptp.strict_implies @t1 @t19)) (tptp.strict_implies @t3 @t19)))))) % 33.37/34.56 (assume @p68 (= tptp.axiom_m6 (forall @t38 (tptp.is_a_theorem (tptp.strict_implies @t3 @t46))))) % 33.37/34.56 (assume @p69 (= tptp.axiom_m7 (forall @t29 (tptp.is_a_theorem (tptp.strict_implies @t50 @t25))))) % 33.37/34.56 (assume @p70 (= tptp.axiom_m8 (forall @t29 (tptp.is_a_theorem (tptp.strict_implies (tptp.strict_implies @t25 @t27) (tptp.strict_implies @t49 @t48)))))) % 33.37/34.56 (assume @p71 (= tptp.axiom_m9 (forall @t38 (tptp.is_a_theorem (tptp.strict_implies (tptp.possibly @t46) @t46))))) % 33.37/34.56 (assume @p72 (= tptp.axiom_m10 (forall @t38 (tptp.is_a_theorem (tptp.strict_implies @t46 @t47))))) % 33.37/34.56 (assume @p73 (=> tptp.op_possibly (forall @t38 (= @t46 (tptp.not (tptp.necessarily @t16)))))) % 33.37/34.56 (assume @p74 (=> tptp.op_necessarily (forall @t38 (= @t37 (tptp.not (tptp.possibly @t16)))))) % 33.37/34.56 (assume @p75 @t52) % 33.37/34.56 (assume @p76 @t54) % 33.37/34.56 (assume @p77 tptp.op_possibly) % 33.37/34.56 (assume @p78 tptp.necessitation) % 33.37/34.56 (assume @p79 tptp.axiom_K) % 33.37/34.56 (assume @p80 tptp.axiom_M) % 33.37/34.56 (assume @p81 tptp.axiom_5) % 33.37/34.56 (assume @p82 tptp.op_implies) % 33.37/34.56 (assume @p83 tptp.op_strict_implies) % 33.37/34.56 (assume @p84 tptp.op_strict_equiv) % 33.37/34.56 (assume @p85 @t55) % 33.37/34.56 (assume @p86 true) % 33.37/34.56 (step @p87 :rule aci_norm :args ((= (or (or @t57 @t56) @t2) (or @t57 @t56 @t2)))) % 33.37/34.56 (step @p88 :rule refl :args (@t2)) % 33.37/34.56 (step @p89 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 33.37/34.56 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t7) @t2))) % 33.37/34.56 (step @p91 :rule trans :premises (@p90 @p87)) % 33.37/34.56 (step @p92 :rule bool-impl-elim :args (@t7 @t2)) % 33.37/34.56 (step @p93 :rule trans :premises (@p92 @p91)) % 33.37/34.56 (step @p94 :rule cong :premises (@p93) :args (@t9)) % 33.37/34.56 (step @p95 :rule refl :args (tptp.modus_ponens)) % 33.37/34.56 (step @p96 :rule cong :premises (@p95 @p94) :args (@t10)) % 33.37/34.56 (step @p97 :rule eq_resolve :premises (@p1 @p96)) % 33.37/34.56 (step @p98 :rule eq_resolve :premises (@p35 @p97)) % 33.37/34.56 (step @p99 :rule instantiate :premises (@p98) :args ((@list @t62 @t61))) % 33.37/34.56 (step @p100 :rule eq_resolve :premises (@p80 @p55)) % 33.37/34.56 (step @p101 :rule instantiate :premises (@p100) :args ((@list @t61))) % 33.37/34.56 (step @p102 :rule instantiate :premises (@p98) :args ((@list @t65 @t63))) % 33.37/34.56 (step @p103 :rule bool-impl-elim :args (@t41 @t11)) % 33.37/34.56 (step @p104 :rule cong :premises (@p103) :args (@t42)) % 33.37/34.56 (step @p105 :rule refl :args (tptp.substitution_strict_equiv)) % 33.37/34.56 (step @p106 :rule cong :premises (@p105 @p104) :args (@t43)) % 33.37/34.56 (step @p107 :rule eq_resolve :premises (@p53 @p106)) % 33.37/34.56 (step @p108 :rule cong :premises (@p107) :args (@t55)) % 33.37/34.56 (step @p109 :rule eq_resolve :premises (@p85 @p108)) % 33.37/34.56 (step @p110 :rule skolemize :premises (@p109)) % 33.37/34.56 (step @p111 :rule bool-double-not-elim :args (@t66)) % 33.37/34.56 (step @p112 :rule refl :args (@t69)) % 33.37/34.56 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or @t69 (not @t68)))) % 33.37/34.56 (step @p114 :rule cnf_or_neg :args (@t69 0)) % 33.37/34.56 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 33.37/34.56 (step @p116 :rule reordering :premises (@p115) :args ((or @t66 @t69))) % 33.37/34.56 (step @p117 :rule chain_m_resolution :premises (@p116 @p110) :args (@t66 @t70 @t71)) % 33.37/34.56 (step @p118 :rule true_intro :premises (@p117)) % 33.37/34.56 (step @p119 :rule bool-impl-true2 :args (@t53)) % 33.37/34.56 (step @p120 :rule refl :args (@t53)) % 33.37/34.56 (step @p121 :rule bool-eq-true :args (tptp.op_strict_equiv)) % 33.37/34.56 (step @p122 :rule symm :premises (@p121)) % 33.37/34.56 (step @p123 :rule eq_resolve :premises (@p84 @p122)) % 33.37/34.56 (step @p124 :rule cong :premises (@p123 @p120) :args (@t54)) % 33.37/34.56 (step @p125 :rule trans :premises (@p124 @p119)) % 33.37/34.56 (step @p126 :rule eq_resolve :premises (@p76 @p125)) % 33.37/34.56 (step @p127 :rule instantiate :premises (@p126) :args (@t72)) % 33.37/34.56 (step @p128 :rule symm :premises (@p127)) % 33.37/34.56 (step @p129 :rule cong :premises (@p128) :args (@t73)) % 33.37/34.56 (step @p130 :rule trans :premises (@p129 @p118)) % 33.37/34.56 (step @p131 :rule true_elim :premises (@p130)) % 33.37/34.56 (step @p132 :rule eq_resolve :premises (@p41 @p8)) % 33.37/34.56 (step @p133 :rule instantiate :premises (@p132) :args (@t74)) % 33.37/34.56 (step @p134 :rule cnf_or_pos :args (@t79)) % 33.37/34.56 (step @p135 :rule reordering :premises (@p134) :args ((or @t77 @t78 @t75 (not @t79)))) % 33.37/34.56 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p131 @p102) :args (@t75 @t80 (@list @t76 @t73 @t79))) % 33.37/34.56 (step @p137 :rule true_intro :premises (@p136)) % 33.37/34.56 (step @p138 :rule bool-impl-true2 :args (@t51)) % 33.37/34.56 (step @p139 :rule refl :args (@t51)) % 33.37/34.56 (step @p140 :rule bool-eq-true :args (tptp.op_strict_implies)) % 33.37/34.56 (step @p141 :rule symm :premises (@p140)) % 33.37/34.56 (step @p142 :rule eq_resolve :premises (@p83 @p141)) % 33.37/34.56 (step @p143 :rule cong :premises (@p142 @p139) :args (@t52)) % 33.37/34.56 (step @p144 :rule trans :premises (@p143 @p138)) % 33.37/34.56 (step @p145 :rule eq_resolve :premises (@p75 @p144)) % 33.37/34.56 (step @p146 :rule instantiate :premises (@p145) :args ((@list @t60 @t59))) % 33.37/34.56 (step @p147 :rule symm :premises (@p146)) % 33.37/34.56 (step @p148 :rule cong :premises (@p147) :args (@t81)) % 33.37/34.56 (step @p149 :rule trans :premises (@p148 @p137)) % 33.37/34.56 (step @p150 :rule true_elim :premises (@p149)) % 33.37/34.56 (step @p151 :rule cnf_or_pos :args (@t86)) % 33.37/34.56 (step @p152 :rule reordering :premises (@p151) :args ((or @t82 @t85 @t84 (not @t86)))) % 33.37/34.56 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p101 @p99) :args (@t82 @t80 (@list @t81 @t83 @t86))) % 33.37/34.56 (step @p154 :rule bool-impl-elim :args (@t13 @t11)) % 33.37/34.56 (step @p155 :rule cong :premises (@p154) :args (@t14)) % 33.37/34.56 (step @p156 :rule refl :args (tptp.substitution_of_equivalents)) % 33.37/34.56 (step @p157 :rule cong :premises (@p156 @p155) :args (@t15)) % 33.37/34.56 (step @p158 :rule eq_resolve :premises (@p2 @p157)) % 33.37/34.56 (step @p159 :rule eq_resolve :premises (@p49 @p158)) % 33.37/34.56 (step @p160 :rule instantiate :premises (@p159) :args (@t72)) % 33.37/34.56 (step @p161 :rule cnf_or_neg :args (@t69 1)) % 33.37/34.56 (step @p162 :rule chain_m_resolution :premises (@p161 @p110) :args ((not @t67) @t70 @t71)) % 33.37/34.56 (step @p163 :rule cnf_or_pos :args (@t90)) % 33.37/34.56 (step @p164 :rule reordering :premises (@p163) :args ((or @t67 @t89 (not @t90)))) % 33.37/34.56 (step @p165 :rule chain_m_resolution :premises (@p164 @p162 @p160) :args (@t89 (@list true false) (@list @t67 @t90))) % 33.37/34.56 (step @p166 :rule instantiate :premises (@p98) :args ((@list @t61 @t87))) % 33.37/34.56 (step @p167 :rule instantiate :premises (@p98) :args ((@list @t92 @t91))) % 33.37/34.56 (step @p168 :rule eq_resolve :premises (@p48 @p15)) % 33.37/34.56 (step @p169 :rule instantiate :premises (@p168) :args (@t72)) % 33.37/34.56 (step @p170 :rule instantiate :premises (@p98) :args ((@list @t93 @t92))) % 33.37/34.56 (step @p171 :rule instantiate :premises (@p100) :args ((@list @t92))) % 33.37/34.56 (step @p172 :rule instantiate :premises (@p98) :args ((@list @t65 @t64))) % 33.37/34.56 (step @p173 :rule eq_resolve :premises (@p40 @p7)) % 33.37/34.56 (step @p174 :rule instantiate :premises (@p173) :args (@t74)) % 33.37/34.56 (step @p175 :rule cnf_or_pos :args (@t97)) % 33.37/34.56 (step @p176 :rule reordering :premises (@p175) :args ((or @t96 @t78 @t94 (not @t97)))) % 33.37/34.56 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p131 @p172) :args (@t94 @t80 (@list @t95 @t73 @t97))) % 33.37/34.56 (step @p178 :rule true_intro :premises (@p177)) % 33.37/34.56 (step @p179 :rule instantiate :premises (@p145) :args (@t72)) % 33.37/34.56 (step @p180 :rule symm :premises (@p179)) % 33.37/34.56 (step @p181 :rule cong :premises (@p180) :args (@t98)) % 33.37/34.56 (step @p182 :rule trans :premises (@p181 @p178)) % 33.37/34.56 (step @p183 :rule true_elim :premises (@p182)) % 33.37/34.56 (step @p184 :rule cnf_or_pos :args (@t103)) % 33.37/34.56 (step @p185 :rule reordering :premises (@p184) :args ((or @t99 @t102 @t101 (not @t103)))) % 33.37/34.56 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p171 @p170) :args (@t99 @t80 (@list @t98 @t100 @t103))) % 33.37/34.56 (step @p187 :rule cnf_or_pos :args (@t108)) % 33.37/34.56 (step @p188 :rule reordering :premises (@p187) :args ((or @t107 @t106 @t104 (not @t108)))) % 33.37/34.56 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p169 @p167) :args (@t104 @t80 (@list @t99 @t105 @t108))) % 33.37/34.56 (step @p190 :rule cnf_or_pos :args (@t111)) % 33.37/34.56 (step @p191 :rule reordering :premises (@p190) :args ((or @t110 @t88 @t109 (not @t111)))) % 33.37/34.56 (step @p192 false :rule chain_m_resolution :premises (@p191 @p189 @p166 @p165 @p153) :args (false (@list false false true false) (@list @t104 @t111 @t88 @t82))) % 33.37/34.56 ) % 33.37/34.56 % SZS output end Proof % 33.37/34.56 % cvc5 exiting %------------------------------------------------------------------------------