%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL520+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 : n001.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 164.85s 166.63s % Output : Proof 164.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL520+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 % 0.11/0.37 % Computer : n001.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Fri Sep 4 13:30:29 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.45 %----Proving TF0_NAR, FOF, or CNF % 164.85/166.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 164.85/166.63 --- Run --no-e-matching --full-saturate-quant at 6... % 164.85/166.63 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 164.85/166.63 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 164.85/166.63 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 164.85/166.63 --- Run --trigger-sel=max --full-saturate-quant at 15... % 164.85/166.63 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 164.85/166.63 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 164.85/166.63 --- Run --prenex-quant=none --full-saturate-quant at 30... % 164.85/166.63 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 164.85/166.63 % SZS status Theorem % 164.85/166.63 % SZS output start Proof % 164.85/166.63 ( % 164.85/166.63 (declare-sort $$unsorted 0) % 164.85/166.63 (declare-const tptp.op_equiv Bool) % 164.85/166.63 (declare-const tptp.op_implies_or Bool) % 164.85/166.63 (declare-const tptp.op_and Bool) % 164.85/166.63 (declare-const tptp.r4 Bool) % 164.85/166.63 (declare-const tptp.r3 Bool) % 164.85/166.63 (declare-const tptp.implies_2 Bool) % 164.85/166.63 (declare-const tptp.and_2 Bool) % 164.85/166.63 (declare-const tptp.modus_tollens Bool) % 164.85/166.63 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 164.85/166.63 (declare-const tptp.op_or Bool) % 164.85/166.63 (declare-const tptp.or_1 Bool) % 164.85/166.63 (declare-const tptp.equivalence_3 Bool) % 164.85/166.63 (declare-const tptp.and_1 Bool) % 164.85/166.63 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 164.85/166.63 (declare-const tptp.implies_3 Bool) % 164.85/166.63 (declare-const tptp.substitution_of_equivalents Bool) % 164.85/166.63 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 164.85/166.63 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 164.85/166.63 (declare-const tptp.op_implies_and Bool) % 164.85/166.63 (declare-const tptp.or_3 Bool) % 164.85/166.63 (declare-const tptp.equivalence_2 Bool) % 164.85/166.63 (declare-const tptp.modus_ponens Bool) % 164.85/166.63 (declare-const tptp.implies_1 Bool) % 164.85/166.63 (declare-const tptp.equivalence_1 Bool) % 164.85/166.63 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 164.85/166.63 (declare-const tptp.r5 Bool) % 164.85/166.63 (declare-const tptp.and_3 Bool) % 164.85/166.63 (declare-const tptp.cn3 Bool) % 164.85/166.63 (declare-const tptp.or_2 Bool) % 164.85/166.63 (declare-const tptp.kn1 Bool) % 164.85/166.63 (declare-const tptp.cn1 Bool) % 164.85/166.63 (declare-const tptp.kn2 Bool) % 164.85/166.63 (declare-const tptp.cn2 Bool) % 164.85/166.63 (declare-const tptp.kn3 Bool) % 164.85/166.63 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 164.85/166.63 (declare-const tptp.r1 Bool) % 164.85/166.63 (declare-const tptp.r2 Bool) % 164.85/166.63 (define @t1 () (@var "Y" $$unsorted)) % 164.85/166.63 (define @t2 () (tptp.is_a_theorem @t1)) % 164.85/166.63 (define @t3 () (@var "X" $$unsorted)) % 164.85/166.63 (define @t4 () (tptp.implies @t3 @t1)) % 164.85/166.63 (define @t5 () (tptp.is_a_theorem @t4)) % 164.85/166.63 (define @t6 () (tptp.is_a_theorem @t3)) % 164.85/166.63 (define @t7 () (and @t6 @t5)) % 164.85/166.63 (define @t8 () (@list @t3 @t1)) % 164.85/166.63 (define @t9 () (forall @t8 (=> @t7 @t2))) % 164.85/166.63 (define @t10 () (= tptp.modus_ponens @t9)) % 164.85/166.63 (define @t11 () (= @t3 @t1)) % 164.85/166.63 (define @t12 () (tptp.equiv @t3 @t1)) % 164.85/166.63 (define @t13 () (tptp.is_a_theorem @t12)) % 164.85/166.63 (define @t14 () (forall @t8 (=> @t13 @t11))) % 164.85/166.63 (define @t15 () (= tptp.substitution_of_equivalents @t14)) % 164.85/166.63 (define @t16 () (tptp.not @t3)) % 164.85/166.63 (define @t17 () (tptp.not @t1)) % 164.85/166.63 (define @t18 () (tptp.implies @t1 @t3)) % 164.85/166.63 (define @t19 () (@var "Z" $$unsorted)) % 164.85/166.63 (define @t20 () (tptp.implies @t3 @t19)) % 164.85/166.63 (define @t21 () (tptp.implies @t1 @t19)) % 164.85/166.63 (define @t22 () (@list @t3 @t1 @t19)) % 164.85/166.63 (define @t23 () (tptp.and @t3 @t1)) % 164.85/166.63 (define @t24 () (tptp.or @t3 @t1)) % 164.85/166.63 (define @t25 () (@var "P" $$unsorted)) % 164.85/166.63 (define @t26 () (@list @t25)) % 164.85/166.63 (define @t27 () (@var "Q" $$unsorted)) % 164.85/166.63 (define @t28 () (@list @t25 @t27)) % 164.85/166.63 (define @t29 () (@var "R" $$unsorted)) % 164.85/166.63 (define @t30 () (tptp.implies @t25 @t27)) % 164.85/166.63 (define @t31 () (@list @t25 @t27 @t29)) % 164.85/166.63 (define @t32 () (tptp.implies @t27 @t29)) % 164.85/166.63 (define @t33 () (tptp.not @t25)) % 164.85/166.63 (define @t34 () (tptp.or @t25 @t27)) % 164.85/166.63 (define @t35 () (forall @t28 (tptp.is_a_theorem (tptp.implies @t34 (tptp.or @t27 @t25))))) % 164.85/166.63 (define @t36 () (tptp.or @t25 @t29)) % 164.85/166.63 (define @t37 () (forall @t8 (= @t24 (tptp.not (tptp.and @t16 @t17))))) % 164.85/166.63 (define @t38 () (=> tptp.op_or @t37)) % 164.85/166.63 (define @t39 () (forall @t8 (= @t23 (tptp.not (tptp.or @t16 @t17))))) % 164.85/166.63 (define @t40 () (=> tptp.op_and @t39)) % 164.85/166.63 (define @t41 () (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t17))))) % 164.85/166.63 (define @t42 () (=> tptp.op_implies_and @t41)) % 164.85/166.63 (define @t43 () (forall @t8 (= @t4 (tptp.or @t16 @t1)))) % 164.85/166.63 (define @t44 () (=> tptp.op_implies_or @t43)) % 164.85/166.63 (define @t45 () (forall @t8 (= @t12 (tptp.and @t4 @t18)))) % 164.85/166.63 (define @t46 () (=> tptp.op_equiv @t45)) % 164.85/166.63 (define @t47 () (not tptp.r3)) % 164.85/166.63 (define @t48 () (not @t5)) % 164.85/166.63 (define @t49 () (not @t6)) % 164.85/166.63 (define @t50 () (@quantifiers_skolemize @t35 0)) % 164.85/166.63 (define @t51 () (tptp.not @t50)) % 164.85/166.63 (define @t52 () (@quantifiers_skolemize @t35 1)) % 164.85/166.63 (define @t53 () (tptp.not @t52)) % 164.85/166.63 (define @t54 () (tptp.implies (tptp.not (tptp.and @t51 @t53)) (tptp.not (tptp.and @t53 @t51)))) % 164.85/166.63 (define @t55 () (tptp.implies @t51 @t51)) % 164.85/166.63 (define @t56 () (tptp.is_a_theorem @t54)) % 164.85/166.63 (define @t57 () (tptp.is_a_theorem (tptp.implies @t55 @t54))) % 164.85/166.63 (define @t58 () (not @t57)) % 164.85/166.63 (define @t59 () (not (tptp.is_a_theorem @t55))) % 164.85/166.63 (define @t60 () (or @t59 @t58 @t56)) % 164.85/166.63 (define @t61 () (@list @t51 @t51)) % 164.85/166.63 (define @t62 () (tptp.not @t51)) % 164.85/166.63 (define @t63 () (tptp.not (tptp.and @t51 @t62))) % 164.85/166.63 (define @t64 () (tptp.is_a_theorem @t63)) % 164.85/166.63 (define @t65 () (tptp.and @t50 @t50)) % 164.85/166.63 (define @t66 () (tptp.and @t65 @t51)) % 164.85/166.63 (define @t67 () (tptp.not @t66)) % 164.85/166.63 (define @t68 () (@list @t62 @t62)) % 164.85/166.63 (define @t69 () (tptp.and @t62 @t62)) % 164.85/166.63 (define @t70 () (tptp.not @t62)) % 164.85/166.63 (define @t71 () (tptp.or @t51 @t51)) % 164.85/166.63 (define @t72 () (@list @t50 @t50)) % 164.85/166.63 (define @t73 () (tptp.and @t65 @t70)) % 164.85/166.63 (define @t74 () (@list @t50 @t51)) % 164.85/166.63 (define @t75 () (tptp.and @t50 @t62)) % 164.85/166.63 (define @t76 () (tptp.not @t75)) % 164.85/166.63 (define @t77 () (@list @t50 @t62)) % 164.85/166.63 (define @t78 () (tptp.implies @t50 @t50)) % 164.85/166.63 (define @t79 () (tptp.and @t78 @t78)) % 164.85/166.63 (define @t80 () (tptp.not (tptp.and @t62 @t51))) % 164.85/166.63 (define @t81 () (tptp.and @t51 @t51)) % 164.85/166.63 (define @t82 () (tptp.not (tptp.and @t81 @t62))) % 164.85/166.63 (define @t83 () (tptp.implies @t82 @t80)) % 164.85/166.63 (define @t84 () (tptp.implies @t51 @t81)) % 164.85/166.63 (define @t85 () (tptp.is_a_theorem @t83)) % 164.85/166.63 (define @t86 () (tptp.is_a_theorem (tptp.implies @t84 @t83))) % 164.85/166.63 (define @t87 () (not @t86)) % 164.85/166.63 (define @t88 () (tptp.is_a_theorem @t84)) % 164.85/166.63 (define @t89 () (not @t88)) % 164.85/166.63 (define @t90 () (or @t89 @t87 @t85)) % 164.85/166.63 (define @t91 () (@list false false false)) % 164.85/166.63 (define @t92 () (tptp.is_a_theorem @t82)) % 164.85/166.63 (define @t93 () (tptp.is_a_theorem @t80)) % 164.85/166.63 (define @t94 () (not @t85)) % 164.85/166.63 (define @t95 () (not @t92)) % 164.85/166.63 (define @t96 () (or @t95 @t94 @t93)) % 164.85/166.63 (define @t97 () (tptp.is_a_theorem @t78)) % 164.85/166.63 (define @t98 () (tptp.is_a_theorem @t79)) % 164.85/166.63 (define @t99 () (tptp.is_a_theorem (tptp.implies @t78 @t79))) % 164.85/166.63 (define @t100 () (not @t99)) % 164.85/166.63 (define @t101 () (not @t97)) % 164.85/166.63 (define @t102 () (or @t101 @t100 @t98)) % 164.85/166.63 (define @t103 () (tptp.not @t78)) % 164.85/166.63 (define @t104 () (@list @t78 @t103)) % 164.85/166.63 (define @t105 () (tptp.not @t103)) % 164.85/166.63 (define @t106 () (tptp.and @t50 @t51)) % 164.85/166.63 (define @t107 () (tptp.and (tptp.not @t106) @t105)) % 164.85/166.63 (define @t108 () (tptp.implies @t62 @t50)) % 164.85/166.63 (define @t109 () (tptp.not @t108)) % 164.85/166.63 (define @t110 () (tptp.implies @t62 @t62)) % 164.85/166.63 (define @t111 () (tptp.or @t70 @t62)) % 164.85/166.63 (define @t112 () (= @t110 @t111)) % 164.85/166.63 (define @t113 () (tptp.implies @t50 @t62)) % 164.85/166.63 (define @t114 () (tptp.not @t113)) % 164.85/166.63 (define @t115 () (tptp.or @t114 @t109)) % 164.85/166.63 (define @t116 () (tptp.is_a_theorem (tptp.equiv @t50 @t62))) % 164.85/166.63 (define @t117 () (= @t50 @t62)) % 164.85/166.63 (define @t118 () (not @t116)) % 164.85/166.63 (define @t119 () (or @t118 @t117)) % 164.85/166.63 (define @t120 () (tptp.is_a_theorem @t67)) % 164.85/166.63 (define @t121 () (tptp.implies @t67 @t63)) % 164.85/166.63 (define @t122 () (tptp.implies @t62 @t65)) % 164.85/166.63 (define @t123 () (tptp.and @t62 @t76)) % 164.85/166.63 (define @t124 () (tptp.is_a_theorem @t122)) % 164.85/166.63 (define @t125 () (tptp.is_a_theorem @t121)) % 164.85/166.63 (define @t126 () (tptp.is_a_theorem (tptp.implies @t122 @t121))) % 164.85/166.63 (define @t127 () (not @t126)) % 164.85/166.63 (define @t128 () (not @t124)) % 164.85/166.63 (define @t129 () (or @t128 @t127 @t125)) % 164.85/166.63 (define @t130 () (not @t125)) % 164.85/166.63 (define @t131 () (not @t120)) % 164.85/166.63 (define @t132 () (or @t131 @t130 @t64)) % 164.85/166.63 (assume @p1 @t10) % 164.85/166.63 (assume @p2 @t15) % 164.85/166.63 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t17 @t16) @t4))))) % 164.85/166.63 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t18))))) % 164.85/166.63 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 164.85/166.63 (assume @p6 (= tptp.implies_3 (forall @t22 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t21 @t20)))))) % 164.85/166.63 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t23 @t3))))) % 164.85/166.63 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t23 @t1))))) % 164.85/166.63 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t23)))))) % 164.85/166.63 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t24))))) % 164.85/166.63 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t24))))) % 164.85/166.63 (assume @p12 (= tptp.or_3 (forall @t22 (tptp.is_a_theorem (tptp.implies @t20 (tptp.implies @t21 (tptp.implies @t24 @t19))))))) % 164.85/166.63 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t4))))) % 164.85/166.63 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t18))))) % 164.85/166.63 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t18 @t12)))))) % 164.85/166.63 (assume @p16 (= tptp.kn1 (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 (tptp.and @t25 @t25)))))) % 164.85/166.63 (assume @p17 (= tptp.kn2 (forall @t28 (tptp.is_a_theorem (tptp.implies (tptp.and @t25 @t27) @t25))))) % 164.85/166.63 (assume @p18 (= tptp.kn3 (forall @t31 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies (tptp.not (tptp.and @t27 @t29)) (tptp.not (tptp.and @t29 @t25)))))))) % 164.85/166.63 (assume @p19 (= tptp.cn1 (forall @t31 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies @t32 (tptp.implies @t25 @t29))))))) % 164.85/166.63 (assume @p20 (= tptp.cn2 (forall @t28 (tptp.is_a_theorem (tptp.implies @t25 (tptp.implies @t33 @t27)))))) % 164.85/166.63 (assume @p21 (= tptp.cn3 (forall @t26 (tptp.is_a_theorem (tptp.implies (tptp.implies @t33 @t25) @t25))))) % 164.85/166.63 (assume @p22 (= tptp.r1 (forall @t26 (tptp.is_a_theorem (tptp.implies (tptp.or @t25 @t25) @t25))))) % 164.85/166.63 (assume @p23 (= tptp.r2 (forall @t28 (tptp.is_a_theorem (tptp.implies @t27 @t34))))) % 164.85/166.63 (assume @p24 (= tptp.r3 @t35)) % 164.85/166.63 (assume @p25 (= tptp.r4 (forall @t31 (tptp.is_a_theorem (tptp.implies (tptp.or @t25 (tptp.or @t27 @t29)) (tptp.or @t27 @t36)))))) % 164.85/166.63 (assume @p26 (= tptp.r5 (forall @t31 (tptp.is_a_theorem (tptp.implies @t32 (tptp.implies @t34 @t36)))))) % 164.85/166.63 (assume @p27 @t38) % 164.85/166.63 (assume @p28 @t40) % 164.85/166.63 (assume @p29 @t42) % 164.85/166.63 (assume @p30 @t44) % 164.85/166.63 (assume @p31 @t46) % 164.85/166.63 (assume @p32 tptp.op_or) % 164.85/166.63 (assume @p33 tptp.op_implies_and) % 164.85/166.63 (assume @p34 tptp.op_equiv) % 164.85/166.63 (assume @p35 tptp.modus_ponens) % 164.85/166.63 (assume @p36 tptp.kn1) % 164.85/166.63 (assume @p37 tptp.kn2) % 164.85/166.63 (assume @p38 tptp.kn3) % 164.85/166.63 (assume @p39 tptp.substitution_of_equivalents) % 164.85/166.63 (assume @p40 tptp.op_implies_or) % 164.85/166.63 (assume @p41 tptp.op_and) % 164.85/166.63 (assume @p42 @t47) % 164.85/166.63 (assume @p43 true) % 164.85/166.63 (step @p44 :rule aci_norm :args ((= (or (or @t49 @t48) @t2) (or @t49 @t48 @t2)))) % 164.85/166.63 (step @p45 :rule refl :args (@t2)) % 164.85/166.63 (step @p46 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 164.85/166.63 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t7) @t2))) % 164.85/166.63 (step @p48 :rule trans :premises (@p47 @p44)) % 164.85/166.63 (step @p49 :rule bool-impl-elim :args (@t7 @t2)) % 164.85/166.63 (step @p50 :rule trans :premises (@p49 @p48)) % 164.85/166.63 (step @p51 :rule cong :premises (@p50) :args (@t9)) % 164.85/166.63 (step @p52 :rule refl :args (tptp.modus_ponens)) % 164.85/166.63 (step @p53 :rule cong :premises (@p52 @p51) :args (@t10)) % 164.85/166.63 (step @p54 :rule eq_resolve :premises (@p1 @p53)) % 164.85/166.63 (step @p55 :rule eq_resolve :premises (@p35 @p54)) % 164.85/166.63 (step @p56 :rule instantiate :premises (@p55) :args ((@list @t55 @t54))) % 164.85/166.63 (step @p57 :rule cong :premises (@p24) :args (@t47)) % 164.85/166.63 (step @p58 :rule eq_resolve :premises (@p42 @p57)) % 164.85/166.63 (step @p59 :rule skolemize :premises (@p58)) % 164.85/166.63 (step @p60 :rule false_intro :premises (@p59)) % 164.85/166.63 (step @p61 :rule bool-impl-true2 :args (@t37)) % 164.85/166.63 (step @p62 :rule refl :args (@t37)) % 164.85/166.63 (step @p63 :rule bool-eq-true :args (tptp.op_or)) % 164.85/166.63 (step @p64 :rule symm :premises (@p63)) % 164.85/166.63 (step @p65 :rule eq_resolve :premises (@p32 @p64)) % 164.85/166.63 (step @p66 :rule cong :premises (@p65 @p62) :args (@t38)) % 164.85/166.63 (step @p67 :rule trans :premises (@p66 @p61)) % 164.85/166.63 (step @p68 :rule eq_resolve :premises (@p27 @p67)) % 164.85/166.63 (step @p69 :rule instantiate :premises (@p68) :args ((@list @t52 @t50))) % 164.85/166.63 (step @p70 :rule symm :premises (@p69)) % 164.85/166.63 (step @p71 :rule instantiate :premises (@p68) :args ((@list @t50 @t52))) % 164.85/166.63 (step @p72 :rule symm :premises (@p71)) % 164.85/166.63 (step @p73 :rule cong :premises (@p72 @p70) :args (@t54)) % 164.85/166.63 (step @p74 :rule cong :premises (@p73) :args (@t56)) % 164.85/166.63 (step @p75 :rule trans :premises (@p74 @p60)) % 164.85/166.63 (step @p76 :rule false_elim :premises (@p75)) % 164.85/166.63 (step @p77 :rule eq_resolve :premises (@p38 @p18)) % 164.85/166.63 (step @p78 :rule instantiate :premises (@p77) :args ((@list @t51 @t51 @t53))) % 164.85/166.63 (step @p79 :rule cnf_or_pos :args (@t60)) % 164.85/166.63 (step @p80 :rule reordering :premises (@p79) :args ((or @t58 @t59 @t56 (not @t60)))) % 164.85/166.63 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p76 @p56) :args (@t59 (@list false true false) (@list @t57 @t56 @t60))) % 164.85/166.63 (step @p82 :rule false_intro :premises (@p81)) % 164.85/166.63 (step @p83 :rule bool-impl-true2 :args (@t41)) % 164.85/166.63 (step @p84 :rule refl :args (@t41)) % 164.85/166.63 (step @p85 :rule bool-eq-true :args (tptp.op_implies_and)) % 164.85/166.63 (step @p86 :rule symm :premises (@p85)) % 164.85/166.63 (step @p87 :rule eq_resolve :premises (@p33 @p86)) % 164.85/166.63 (step @p88 :rule cong :premises (@p87 @p84) :args (@t42)) % 164.85/166.63 (step @p89 :rule trans :premises (@p88 @p83)) % 164.85/166.63 (step @p90 :rule eq_resolve :premises (@p29 @p89)) % 164.85/166.63 (step @p91 :rule instantiate :premises (@p90) :args (@t61)) % 164.85/166.63 (step @p92 :rule symm :premises (@p91)) % 164.85/166.63 (step @p93 :rule cong :premises (@p92) :args (@t64)) % 164.85/166.63 (step @p94 :rule trans :premises (@p93 @p82)) % 164.85/166.63 (step @p95 :rule false_elim :premises (@p94)) % 164.85/166.63 (step @p96 :rule instantiate :premises (@p55) :args ((@list @t67 @t63))) % 164.85/166.63 (step @p97 :rule eq_resolve :premises (@p37 @p17)) % 164.85/166.63 (step @p98 :rule instantiate :premises (@p97) :args (@t68)) % 164.85/166.63 (step @p99 :rule true_intro :premises (@p98)) % 164.85/166.63 (step @p100 :rule bool-impl-true2 :args (@t43)) % 164.85/166.63 (step @p101 :rule refl :args (@t43)) % 164.85/166.63 (step @p102 :rule bool-eq-true :args (tptp.op_implies_or)) % 164.85/166.63 (step @p103 :rule symm :premises (@p102)) % 164.85/166.63 (step @p104 :rule eq_resolve :premises (@p40 @p103)) % 164.85/166.63 (step @p105 :rule cong :premises (@p104 @p101) :args (@t44)) % 164.85/166.63 (step @p106 :rule trans :premises (@p105 @p100)) % 164.85/166.63 (step @p107 :rule eq_resolve :premises (@p30 @p106)) % 164.85/166.63 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t69 @t62))) % 164.85/166.63 (step @p109 :rule symm :premises (@p108)) % 164.85/166.63 (step @p110 :rule instantiate :premises (@p68) :args ((@list (tptp.not @t69) @t62))) % 164.85/166.63 (step @p111 :rule symm :premises (@p110)) % 164.85/166.63 (step @p112 :rule refl :args (@t70)) % 164.85/166.63 (step @p113 :rule instantiate :premises (@p68) :args (@t61)) % 164.85/166.63 (step @p114 :rule cong :premises (@p113) :args ((tptp.not @t71))) % 164.85/166.63 (step @p115 :rule bool-impl-true2 :args (@t39)) % 164.85/166.63 (step @p116 :rule refl :args (@t39)) % 164.85/166.63 (step @p117 :rule bool-eq-true :args (tptp.op_and)) % 164.85/166.63 (step @p118 :rule symm :premises (@p117)) % 164.85/166.63 (step @p119 :rule eq_resolve :premises (@p41 @p118)) % 164.85/166.63 (step @p120 :rule cong :premises (@p119 @p116) :args (@t40)) % 164.85/166.63 (step @p121 :rule trans :premises (@p120 @p115)) % 164.85/166.63 (step @p122 :rule eq_resolve :premises (@p28 @p121)) % 164.85/166.63 (step @p123 :rule instantiate :premises (@p122) :args (@t72)) % 164.85/166.63 (step @p124 :rule trans :premises (@p123 @p114)) % 164.85/166.63 (step @p125 :rule cong :premises (@p124 @p112) :args (@t73)) % 164.85/166.63 (step @p126 :rule cong :premises (@p125) :args ((tptp.not @t73))) % 164.85/166.63 (step @p127 :rule instantiate :premises (@p90) :args ((@list @t65 @t62))) % 164.85/166.63 (step @p128 :rule trans :premises (@p127 @p126 @p111 @p109)) % 164.85/166.63 (step @p129 :rule cong :premises (@p128) :args ((tptp.is_a_theorem (tptp.implies @t65 @t62)))) % 164.85/166.63 (step @p130 :rule symm :premises (@p127)) % 164.85/166.63 (step @p131 :rule symm :premises (@p126)) % 164.85/166.63 (step @p132 :rule refl :args (@t62)) % 164.85/166.63 (step @p133 :rule instantiate :premises (@p107) :args (@t74)) % 164.85/166.63 (step @p134 :rule instantiate :premises (@p90) :args (@t74)) % 164.85/166.63 (step @p135 :rule symm :premises (@p134)) % 164.85/166.63 (step @p136 :rule trans :premises (@p135 @p133)) % 164.85/166.63 (step @p137 :rule trans :premises (@p136 @p113)) % 164.85/166.63 (step @p138 :rule cong :premises (@p137 @p132) :args ((tptp.or @t76 @t62))) % 164.85/166.63 (step @p139 :rule bool-impl-elim :args (@t13 @t11)) % 164.85/166.63 (step @p140 :rule cong :premises (@p139) :args (@t14)) % 164.85/166.63 (step @p141 :rule refl :args (tptp.substitution_of_equivalents)) % 164.85/166.63 (step @p142 :rule cong :premises (@p141 @p140) :args (@t15)) % 164.85/166.63 (step @p143 :rule eq_resolve :premises (@p2 @p142)) % 164.85/166.63 (step @p144 :rule eq_resolve :premises (@p39 @p143)) % 164.85/166.63 (step @p145 :rule instantiate :premises (@p144) :args (@t77)) % 164.85/166.63 (step @p146 :rule instantiate :premises (@p55) :args ((@list @t78 @t79))) % 164.85/166.63 (step @p147 :rule eq_resolve :premises (@p36 @p16)) % 164.85/166.63 (step @p148 :rule instantiate :premises (@p147) :args ((@list @t78))) % 164.85/166.63 (step @p149 :rule instantiate :premises (@p55) :args ((@list @t82 @t80))) % 164.85/166.63 (step @p150 :rule instantiate :premises (@p55) :args ((@list @t84 @t83))) % 164.85/166.63 (step @p151 :rule instantiate :premises (@p77) :args ((@list @t51 @t81 @t62))) % 164.85/166.63 (step @p152 :rule instantiate :premises (@p147) :args ((@list @t51))) % 164.85/166.63 (step @p153 :rule cnf_or_pos :args (@t90)) % 164.85/166.63 (step @p154 :rule reordering :premises (@p153) :args ((or @t89 @t87 @t85 (not @t90)))) % 164.85/166.63 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p151 @p150) :args (@t85 @t91 (@list @t88 @t86 @t90))) % 164.85/166.63 (step @p156 :rule instantiate :premises (@p97) :args (@t61)) % 164.85/166.63 (step @p157 :rule true_intro :premises (@p156)) % 164.85/166.63 (step @p158 :rule instantiate :premises (@p90) :args ((@list @t81 @t51))) % 164.85/166.63 (step @p159 :rule symm :premises (@p158)) % 164.85/166.63 (step @p160 :rule cong :premises (@p159) :args (@t92)) % 164.85/166.63 (step @p161 :rule trans :premises (@p160 @p157)) % 164.85/166.63 (step @p162 :rule true_elim :premises (@p161)) % 164.85/166.63 (step @p163 :rule cnf_or_pos :args (@t96)) % 164.85/166.63 (step @p164 :rule reordering :premises (@p163) :args ((or @t95 @t94 @t93 (not @t96)))) % 164.85/166.63 (step @p165 :rule chain_m_resolution :premises (@p164 @p162 @p155 @p149) :args (@t93 @t91 (@list @t92 @t85 @t96))) % 164.85/166.63 (step @p166 :rule true_intro :premises (@p165)) % 164.85/166.63 (step @p167 :rule instantiate :premises (@p68) :args ((@list @t51 @t50))) % 164.85/166.63 (step @p168 :rule instantiate :premises (@p107) :args (@t72)) % 164.85/166.63 (step @p169 :rule trans :premises (@p168 @p167)) % 164.85/166.63 (step @p170 :rule cong :premises (@p169) :args (@t97)) % 164.85/166.63 (step @p171 :rule trans :premises (@p170 @p166)) % 164.85/166.63 (step @p172 :rule true_elim :premises (@p171)) % 164.85/166.63 (step @p173 :rule cnf_or_pos :args (@t102)) % 164.85/166.63 (step @p174 :rule reordering :premises (@p173) :args ((or @t101 @t100 @t98 (not @t102)))) % 164.85/166.63 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p148 @p146) :args (@t98 @t91 (@list @t97 @t99 @t102))) % 164.85/166.63 (step @p176 :rule true_intro :premises (@p175)) % 164.85/166.63 (step @p177 :rule instantiate :premises (@p122) :args ((@list @t78 @t78))) % 164.85/166.63 (step @p178 :rule symm :premises (@p177)) % 164.85/166.63 (step @p179 :rule instantiate :premises (@p107) :args (@t104)) % 164.85/166.63 (step @p180 :rule instantiate :premises (@p90) :args (@t104)) % 164.85/166.63 (step @p181 :rule symm :premises (@p180)) % 164.85/166.63 (step @p182 :rule refl :args (@t105)) % 164.85/166.63 (step @p183 :rule instantiate :premises (@p90) :args (@t72)) % 164.85/166.63 (step @p184 :rule symm :premises (@p183)) % 164.85/166.63 (step @p185 :rule cong :premises (@p184 @p182) :args (@t107)) % 164.85/166.63 (step @p186 :rule cong :premises (@p185) :args ((tptp.not @t107))) % 164.85/166.63 (step @p187 :rule instantiate :premises (@p68) :args ((@list @t106 @t103))) % 164.85/166.63 (step @p188 :rule symm :premises (@p168)) % 164.85/166.63 (step @p189 :rule symm :premises (@p167)) % 164.85/166.63 (step @p190 :rule instantiate :premises (@p90) :args ((@list @t62 @t50))) % 164.85/166.63 (step @p191 :rule trans :premises (@p190 @p189 @p188)) % 164.85/166.63 (step @p192 :rule cong :premises (@p191) :args (@t109)) % 164.85/166.63 (step @p193 :rule instantiate :premises (@p122) :args (@t74)) % 164.85/166.63 (step @p194 :rule symm :premises (@p193)) % 164.85/166.63 (step @p195 :rule instantiate :premises (@p68) :args ((@list @t51 @t62))) % 164.85/166.63 (step @p196 :rule symm :premises (@p195)) % 164.85/166.63 (step @p197 :rule instantiate :premises (@p90) :args (@t68)) % 164.85/166.63 (step @p198 :rule eq-symm :args (@t110 @t111)) % 164.85/166.63 (step @p199 :rule cong :premises (@p101 @p198) :args ((=> @t43 @t112))) % 164.85/166.63 (assume-push @p272 @t43) % 164.85/166.63 (step @p201 :rule instantiate :premises (@p107) :args (@t68)) % 164.85/166.63 (step-pop @p273 :rule scope :premises (@p201)) % 164.85/166.63 (step @p202 :rule process_scope :premises (@p273) :args (@t112)) % 164.85/166.63 (step @p204 :rule eq_resolve :premises (@p202 @p199)) % 164.85/166.63 (step @p205 :rule implies_elim :premises (@p204)) % 164.85/166.63 (step @p206 :rule chain_m_resolution :premises (@p205 @p107) :args ((= @t111 @t110) (@list false) (@list @t43))) % 164.85/166.63 (step @p207 :rule trans :premises (@p206 @p197 @p196)) % 164.85/166.63 (step @p208 :rule cong :premises (@p207) :args ((tptp.not @t111))) % 164.85/166.63 (step @p209 :rule instantiate :premises (@p122) :args ((@list @t62 @t51))) % 164.85/166.63 (step @p210 :rule trans :premises (@p209 @p208 @p194)) % 164.85/166.63 (step @p211 :rule symm :premises (@p209)) % 164.85/166.63 (step @p212 :rule symm :premises (@p208)) % 164.85/166.63 (step @p213 :rule instantiate :premises (@p107) :args (@t77)) % 164.85/166.63 (step @p214 :rule cong :premises (@p213) :args (@t114)) % 164.85/166.63 (step @p215 :rule trans :premises (@p214 @p212 @p211)) % 164.85/166.63 (step @p216 :rule trans :premises (@p215 @p210)) % 164.85/166.63 (step @p217 :rule cong :premises (@p216 @p192) :args (@t115)) % 164.85/166.63 (step @p218 :rule trans :premises (@p217 @p187 @p186 @p181 @p179)) % 164.85/166.65 (step @p219 :rule cong :premises (@p218) :args ((tptp.not @t115))) % 164.85/166.65 (step @p220 :rule instantiate :premises (@p122) :args ((@list @t113 @t108))) % 164.85/166.65 (step @p221 :rule bool-impl-true2 :args (@t45)) % 164.85/166.65 (step @p222 :rule refl :args (@t45)) % 164.85/166.65 (step @p223 :rule bool-eq-true :args (tptp.op_equiv)) % 164.85/166.65 (step @p224 :rule symm :premises (@p223)) % 164.85/166.65 (step @p225 :rule eq_resolve :premises (@p34 @p224)) % 164.85/166.65 (step @p226 :rule cong :premises (@p225 @p222) :args (@t46)) % 164.85/166.65 (step @p227 :rule trans :premises (@p226 @p221)) % 164.85/166.65 (step @p228 :rule eq_resolve :premises (@p31 @p227)) % 164.85/166.65 (step @p229 :rule instantiate :premises (@p228) :args (@t77)) % 164.85/166.65 (step @p230 :rule trans :premises (@p229 @p220 @p219 @p178)) % 164.85/166.65 (step @p231 :rule cong :premises (@p230) :args (@t116)) % 164.85/166.65 (step @p232 :rule trans :premises (@p231 @p176)) % 164.85/166.65 (step @p233 :rule true_elim :premises (@p232)) % 164.85/166.65 (step @p234 :rule cnf_or_pos :args (@t119)) % 164.85/166.65 (step @p235 :rule reordering :premises (@p234) :args ((or @t118 @t117 (not @t119)))) % 164.85/166.65 (step @p236 :rule chain_m_resolution :premises (@p235 @p233 @p145) :args (@t117 (@list false false) (@list @t116 @t119))) % 164.85/166.65 (step @p237 :rule refl :args (@t76)) % 164.85/166.65 (step @p238 :rule cong :premises (@p237 @p236) :args ((tptp.or @t76 @t50))) % 164.85/166.65 (step @p239 :rule refl :args (@t50)) % 164.85/166.65 (step @p240 :rule symm :premises (@p136)) % 164.85/166.65 (step @p241 :rule cong :premises (@p240 @p239) :args ((tptp.or @t71 @t50))) % 164.85/166.65 (step @p242 :rule instantiate :premises (@p68) :args ((@list @t71 @t50))) % 164.85/166.65 (step @p243 :rule symm :premises (@p242)) % 164.85/166.65 (step @p244 :rule refl :args (@t51)) % 164.85/166.65 (step @p245 :rule cong :premises (@p123 @p244) :args (@t66)) % 164.85/166.65 (step @p246 :rule cong :premises (@p245) :args (@t67)) % 164.85/166.65 (step @p247 :rule trans :premises (@p246 @p243 @p241 @p238 @p138 @p110 @p131 @p130)) % 164.85/166.65 (step @p248 :rule cong :premises (@p247) :args (@t120)) % 164.85/166.65 (step @p249 :rule trans :premises (@p248 @p129 @p99)) % 164.85/166.65 (step @p250 :rule true_elim :premises (@p249)) % 164.85/166.65 (step @p251 :rule instantiate :premises (@p55) :args ((@list @t122 @t121))) % 164.85/166.65 (step @p252 :rule instantiate :premises (@p147) :args ((@list @t62))) % 164.85/166.65 (step @p253 :rule true_intro :premises (@p252)) % 164.85/166.65 (step @p254 :rule instantiate :premises (@p90) :args ((@list @t62 @t69))) % 164.85/166.65 (step @p255 :rule symm :premises (@p254)) % 164.85/166.65 (step @p256 :rule cong :premises (@p132 @p137) :args (@t123)) % 164.85/166.65 (step @p257 :rule cong :premises (@p256) :args ((tptp.not @t123))) % 164.85/166.65 (step @p258 :rule instantiate :premises (@p90) :args ((@list @t62 @t75))) % 164.85/166.65 (step @p259 :rule cong :premises (@p239 @p236) :args (@t65)) % 164.85/166.65 (step @p260 :rule cong :premises (@p132 @p259) :args (@t122)) % 164.85/166.65 (step @p261 :rule trans :premises (@p260 @p258 @p257 @p255)) % 164.85/166.65 (step @p262 :rule cong :premises (@p261) :args (@t124)) % 164.85/166.65 (step @p263 :rule trans :premises (@p262 @p253)) % 164.85/166.65 (step @p264 :rule true_elim :premises (@p263)) % 164.85/166.65 (step @p265 :rule instantiate :premises (@p77) :args ((@list @t62 @t65 @t51))) % 164.85/166.65 (step @p266 :rule cnf_or_pos :args (@t129)) % 164.85/166.65 (step @p267 :rule reordering :premises (@p266) :args ((or @t127 @t125 @t128 (not @t129)))) % 164.85/166.65 (step @p268 :rule chain_m_resolution :premises (@p267 @p265 @p264 @p251) :args (@t125 @t91 (@list @t126 @t124 @t129))) % 164.85/166.65 (step @p269 :rule cnf_or_pos :args (@t132)) % 164.85/166.65 (step @p270 :rule reordering :premises (@p269) :args ((or @t64 @t131 @t130 (not @t132)))) % 164.85/166.65 (step @p271 false :rule chain_m_resolution :premises (@p270 @p268 @p250 @p96 @p95) :args (false (@list false false false true) (@list @t125 @t120 @t132 @t64))) % 164.85/166.65 ) % 164.85/166.65 % SZS output end Proof % 164.85/166.65 % cvc5 exiting %------------------------------------------------------------------------------