%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU072+1 : TPTP v9.2.1. Released v3.2.0. % 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:32 AM UTC 2026 % Result : Theorem 33.98s 34.38s % Output : Proof 33.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU072+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.36 % Computer : n001.cluster.edu % 0.18/0.36 % Model : x86_64 x86_64 % 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.36 % Memory : 8042.1875MB % 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.36 % CPULimit : 300 % 0.18/0.36 % WCLimit : 300 % 0.18/0.36 % DateTime : Tue Jun 2 16:26:05 EDT 2026 % 0.18/0.36 % CPUTime : % 0.26/0.52 %----Proving TF0_NAR, FOF, or CNF % 33.98/34.38 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.98/34.38 --- Run --no-e-matching --full-saturate-quant at 6... % 33.98/34.38 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.98/34.38 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.98/34.38 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.98/34.38 % SZS status Theorem % 33.98/34.38 % SZS output start Proof % 33.98/34.38 ( % 33.98/34.38 (declare-sort $$unsorted 0) % 33.98/34.38 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.empty_set $$unsorted) % 33.98/34.38 (declare-const tptp.function (-> $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.empty (-> $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.relation (-> $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 33.98/34.38 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 33.98/34.38 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 33.98/34.38 (define @t1 () (@var "A" $$unsorted)) % 33.98/34.38 (define @t2 () (@var "B" $$unsorted)) % 33.98/34.38 (define @t3 () (tptp.in @t1 @t2)) % 33.98/34.38 (define @t4 () (@list @t1 @t2)) % 33.98/34.38 (define @t5 () (tptp.function @t1)) % 33.98/34.38 (define @t6 () (tptp.empty @t1)) % 33.98/34.38 (define @t7 () (@list @t1)) % 33.98/34.38 (define @t8 () (tptp.relation @t1)) % 33.98/34.38 (define @t9 () (tptp.one_to_one @t1)) % 33.98/34.38 (define @t10 () (and @t8 @t5 @t9)) % 33.98/34.38 (define @t11 () (and @t8 @t6 @t5)) % 33.98/34.38 (define @t12 () (@var "D" $$unsorted)) % 33.98/34.38 (define @t13 () (@var "C" $$unsorted)) % 33.98/34.38 (define @t14 () (= @t13 (tptp.apply @t1 @t12))) % 33.98/34.38 (define @t15 () (tptp.relation_dom @t1)) % 33.98/34.38 (define @t16 () (tptp.in @t12 @t15)) % 33.98/34.38 (define @t17 () (and @t16 @t14)) % 33.98/34.38 (define @t18 () (@list @t12)) % 33.98/34.38 (define @t19 () (exists @t18 @t17)) % 33.98/34.38 (define @t20 () (tptp.in @t13 @t2)) % 33.98/34.38 (define @t21 () (= @t20 @t19)) % 33.98/34.38 (define @t22 () (@list @t13)) % 33.98/34.38 (define @t23 () (forall @t22 @t21)) % 33.98/34.38 (define @t24 () (tptp.relation_rng @t1)) % 33.98/34.38 (define @t25 () (= @t2 @t24)) % 33.98/34.38 (define @t26 () (= @t25 @t23)) % 33.98/34.38 (define @t27 () (@list @t2)) % 33.98/34.38 (define @t28 () (forall @t27 @t26)) % 33.98/34.38 (define @t29 () (and @t8 @t5)) % 33.98/34.38 (define @t30 () (=> @t29 @t28)) % 33.98/34.38 (define @t31 () (forall @t7 @t30)) % 33.98/34.38 (define @t32 () (= @t2 @t13)) % 33.98/34.38 (define @t33 () (= (tptp.apply @t1 @t2) (tptp.apply @t1 @t13))) % 33.98/34.38 (define @t34 () (tptp.in @t13 @t15)) % 33.98/34.38 (define @t35 () (tptp.in @t2 @t15)) % 33.98/34.38 (define @t36 () (and @t35 @t34 @t33)) % 33.98/34.38 (define @t37 () (@list @t2 @t13)) % 33.98/34.38 (define @t38 () (forall @t37 (=> @t36 @t32))) % 33.98/34.38 (define @t39 () (= @t9 @t38)) % 33.98/34.38 (define @t40 () (=> @t29 @t39)) % 33.98/34.38 (define @t41 () (forall @t7 @t40)) % 33.98/34.38 (define @t42 () (tptp.relation tptp.empty_set)) % 33.98/34.38 (define @t43 () (tptp.empty tptp.empty_set)) % 33.98/34.38 (define @t44 () (tptp.powerset @t1)) % 33.98/34.38 (define @t45 () (tptp.singleton @t1)) % 33.98/34.38 (define @t46 () (tptp.empty @t15)) % 33.98/34.38 (define @t47 () (not @t6)) % 33.98/34.38 (define @t48 () (and @t47 @t8)) % 33.98/34.38 (define @t49 () (tptp.empty @t24)) % 33.98/34.38 (define @t50 () (tptp.empty @t2)) % 33.98/34.38 (define @t51 () (tptp.element @t2 @t44)) % 33.98/34.38 (define @t52 () (= (tptp.relation_image @t2 @t45) (tptp.singleton (tptp.apply @t2 @t1)))) % 33.98/34.38 (define @t53 () (tptp.in @t1 (tptp.relation_dom @t2))) % 33.98/34.38 (define @t54 () (=> @t53 @t52)) % 33.98/34.38 (define @t55 () (tptp.function @t2)) % 33.98/34.38 (define @t56 () (tptp.relation @t2)) % 33.98/34.38 (define @t57 () (and @t56 @t55)) % 33.98/34.38 (define @t58 () (forall @t4 (=> @t57 @t54))) % 33.98/34.38 (define @t59 () (tptp.relation_inverse_image @t2 @t45)) % 33.98/34.38 (define @t60 () (not (= @t59 tptp.empty_set))) % 33.98/34.38 (define @t61 () (tptp.in @t1 (tptp.relation_rng @t2))) % 33.98/34.38 (define @t62 () (= @t61 @t60)) % 33.98/34.38 (define @t63 () (=> @t56 @t62)) % 33.98/34.38 (define @t64 () (forall @t4 @t63)) % 33.98/34.38 (define @t65 () (forall @t27 (tptp.subset (tptp.relation_inverse_image @t1 (tptp.relation_image @t1 @t2)) @t2))) % 33.98/34.38 (define @t66 () (=> @t65 @t9)) % 33.98/34.38 (define @t67 () (forall @t7 (=> @t29 @t66))) % 33.98/34.38 (define @t68 () (not @t67)) % 33.98/34.38 (define @t69 () (tptp.element @t1 @t2)) % 33.98/34.38 (define @t70 () (tptp.singleton @t2)) % 33.98/34.38 (define @t71 () (= @t1 tptp.empty_set)) % 33.98/34.38 (define @t72 () (forall @t4 (= (tptp.subset @t1 @t70) (or @t71 (= @t1 @t70))))) % 33.98/34.38 (define @t73 () (tptp.element @t2 (tptp.powerset @t13))) % 33.98/34.38 (define @t74 () (@list @t1 @t2 @t13)) % 33.98/34.38 (define @t75 () (= @t1 @t2)) % 33.98/34.38 (define @t76 () (tptp.subset @t45 @t70)) % 33.98/34.38 (define @t77 () (forall @t4 (=> @t76 @t75))) % 33.98/34.38 (define @t78 () (not @t33)) % 33.98/34.38 (define @t79 () (not @t34)) % 33.98/34.38 (define @t80 () (not @t35)) % 33.98/34.38 (define @t81 () (or @t80 @t79 @t78 @t32)) % 33.98/34.38 (define @t82 () (= @t9 (forall @t37 @t81))) % 33.98/34.38 (define @t83 () (not @t5)) % 33.98/34.38 (define @t84 () (not @t8)) % 33.98/34.38 (define @t85 () (or @t84 @t83)) % 33.98/34.38 (define @t86 () (not @t29)) % 33.98/34.38 (define @t87 () (or @t80 @t79 @t78)) % 33.98/34.38 (define @t88 () (not @t65)) % 33.98/34.38 (define @t89 () (or @t84 @t83 @t88 @t9)) % 33.98/34.38 (define @t90 () (@quantifiers_skolemize (forall @t7 @t89) 0)) % 33.98/34.38 (define @t91 () (tptp.function @t90)) % 33.98/34.38 (define @t92 () (tptp.one_to_one @t90)) % 33.98/34.38 (define @t93 () (forall @t27 (tptp.subset (tptp.relation_inverse_image @t90 (tptp.relation_image @t90 @t2)) @t2))) % 33.98/34.38 (define @t94 () (not @t93)) % 33.98/34.38 (define @t95 () (not @t91)) % 33.98/34.38 (define @t96 () (tptp.relation @t90)) % 33.98/34.38 (define @t97 () (not @t96)) % 33.98/34.38 (define @t98 () (or @t97 @t95 @t94 @t92)) % 33.98/34.38 (define @t99 () (@list true)) % 33.98/34.38 (define @t100 () (@list @t98)) % 33.98/34.38 (define @t101 () (tptp.relation_dom @t90)) % 33.98/34.38 (define @t102 () (forall @t37 (or (not (tptp.in @t2 @t101)) (not (tptp.in @t13 @t101)) (not (= (tptp.apply @t90 @t2) (tptp.apply @t90 @t13))) @t32))) % 33.98/34.38 (define @t103 () (= @t92 @t102)) % 33.98/34.38 (define @t104 () (or @t97 @t95 @t103)) % 33.98/34.38 (define @t105 () (@list false false false)) % 33.98/34.38 (define @t106 () (not @t102)) % 33.98/34.38 (define @t107 () (@list true false)) % 33.98/34.38 (define @t108 () (@quantifiers_skolemize @t102 1)) % 33.98/34.38 (define @t109 () (tptp.apply @t90 @t108)) % 33.98/34.38 (define @t110 () (@quantifiers_skolemize @t102 0)) % 33.98/34.38 (define @t111 () (tptp.apply @t90 @t110)) % 33.98/34.38 (define @t112 () (= @t111 @t109)) % 33.98/34.38 (define @t113 () (= @t110 @t108)) % 33.98/34.38 (define @t114 () (not @t112)) % 33.98/34.38 (define @t115 () (tptp.in @t108 @t101)) % 33.98/34.38 (define @t116 () (not @t115)) % 33.98/34.38 (define @t117 () (tptp.in @t110 @t101)) % 33.98/34.38 (define @t118 () (not @t117)) % 33.98/34.38 (define @t119 () (or @t118 @t116 @t114 @t113)) % 33.98/34.38 (define @t120 () (@list @t119)) % 33.98/34.38 (define @t121 () (not @t53)) % 33.98/34.38 (define @t122 () (not @t55)) % 33.98/34.38 (define @t123 () (not @t56)) % 33.98/34.38 (define @t124 () (tptp.singleton @t111)) % 33.98/34.38 (define @t125 () (tptp.singleton @t110)) % 33.98/34.38 (define @t126 () (tptp.relation_image @t90 @t125)) % 33.98/34.38 (define @t127 () (= @t126 @t124)) % 33.98/34.38 (define @t128 () (or @t97 @t95 @t118 @t127)) % 33.98/34.38 (define @t129 () (@list false false false false)) % 33.98/34.38 (define @t130 () (tptp.singleton @t109)) % 33.98/34.38 (define @t131 () (tptp.singleton @t108)) % 33.98/34.38 (define @t132 () (tptp.relation_image @t90 @t131)) % 33.98/34.38 (define @t133 () (= @t132 @t130)) % 33.98/34.38 (define @t134 () (or @t97 @t95 @t116 @t133)) % 33.98/34.38 (define @t135 () (tptp.relation_inverse_image @t90 @t126)) % 33.98/34.38 (define @t136 () (or (= @t135 tptp.empty_set) (= @t135 @t125))) % 33.98/34.38 (define @t137 () (tptp.subset @t135 @t125)) % 33.98/34.38 (define @t138 () (= @t137 @t136)) % 33.98/34.38 (define @t139 () (= @t125 @t135)) % 33.98/34.38 (define @t140 () (= tptp.empty_set @t135)) % 33.98/34.38 (define @t141 () (or @t140 @t139)) % 33.98/34.38 (define @t142 () (= @t137 @t141)) % 33.98/34.38 (define @t143 () (@list false)) % 33.98/34.38 (define @t144 () (@list @t72)) % 33.98/34.38 (define @t145 () (not @t137)) % 33.98/34.38 (define @t146 () (@list false false)) % 33.98/34.38 (define @t147 () (= @t61 (not (= tptp.empty_set @t59)))) % 33.98/34.38 (define @t148 () (= tptp.empty_set (tptp.relation_inverse_image @t90 @t130))) % 33.98/34.38 (define @t149 () (not @t148)) % 33.98/34.38 (define @t150 () (tptp.relation_rng @t90)) % 33.98/34.38 (define @t151 () (tptp.in @t109 @t150)) % 33.98/34.38 (define @t152 () (= @t151 @t149)) % 33.98/34.38 (define @t153 () (or @t97 @t152)) % 33.98/34.38 (define @t154 () (@var "BOUND_VARIABLE_7644" $$unsorted)) % 33.98/34.38 (define @t155 () (tptp.in @t13 @t154)) % 33.98/34.38 (define @t156 () (not (forall @t18 (or (not @t16) (not @t14))))) % 33.98/34.38 (define @t157 () (forall @t22 (= @t155 @t156))) % 33.98/34.38 (define @t158 () (= (= @t154 @t24) @t157)) % 33.98/34.38 (define @t159 () (or @t84 @t83 @t158)) % 33.98/34.38 (define @t160 () (@list @t1 @t154)) % 33.98/34.38 (define @t161 () (forall @t160 @t159)) % 33.98/34.38 (define @t162 () (@list @t154)) % 33.98/34.38 (define @t163 () (forall @t162 @t159)) % 33.98/34.38 (define @t164 () (forall @t162 @t158)) % 33.98/34.38 (define @t165 () (or @t84 @t83 @t164)) % 33.98/34.38 (define @t166 () (forall @t27 (= @t25 (forall @t22 (= @t20 @t156))))) % 33.98/34.38 (define @t167 () (or @t84 @t83 @t166)) % 33.98/34.38 (define @t168 () (forall @t18 (not @t17))) % 33.98/34.38 (define @t169 () (not @t168)) % 33.98/34.38 (define @t170 () (tptp.apply @t90 @t12)) % 33.98/34.38 (define @t171 () (not (tptp.in @t12 @t101))) % 33.98/34.38 (define @t172 () (forall @t22 (= (not (forall @t18 (or @t171 (not (= @t13 @t170))))) (tptp.in @t13 @t150)))) % 33.98/34.38 (define @t173 () (= (= @t150 @t150) @t172)) % 33.98/34.38 (define @t174 () (or @t97 @t95 @t173)) % 33.98/34.38 (define @t175 () (forall @t160 (or @t84 @t83 (= (= @t24 @t154) (forall @t22 (= @t156 @t155)))))) % 33.98/34.38 (define @t176 () (or @t97 @t95 @t172)) % 33.98/34.38 (define @t177 () (forall @t18 (or @t171 (not (= @t109 @t170))))) % 33.98/34.38 (define @t178 () (not @t177)) % 33.98/34.38 (define @t179 () (= @t178 @t151)) % 33.98/34.38 (define @t180 () (= @t151 @t178)) % 33.98/34.38 (define @t181 () (or @t118 @t114)) % 33.98/34.38 (define @t182 () (not @t181)) % 33.98/34.38 (define @t183 () (not (= @t109 @t111))) % 33.98/34.38 (define @t184 () (or @t118 @t183)) % 33.98/34.38 (define @t185 () (not @t180)) % 33.98/34.38 (define @t186 () (not @t140)) % 33.98/34.38 (define @t187 () (not @t127)) % 33.98/34.38 (define @t188 () (not @t149)) % 33.98/34.38 (define @t189 () (and @t112 @t127 @t149)) % 33.98/34.38 (define @t190 () (tptp.relation_inverse_image @t90 @t132)) % 33.98/34.38 (define @t191 () (or (= @t190 tptp.empty_set) (= @t190 @t131))) % 33.98/34.38 (define @t192 () (tptp.subset @t190 @t131)) % 33.98/34.38 (define @t193 () (= @t192 @t191)) % 33.98/34.38 (define @t194 () (= @t131 @t190)) % 33.98/34.38 (define @t195 () (= tptp.empty_set @t190)) % 33.98/34.38 (define @t196 () (or @t195 @t194)) % 33.98/34.38 (define @t197 () (= @t192 @t196)) % 33.98/34.38 (define @t198 () (not @t195)) % 33.98/34.38 (define @t199 () (not @t133)) % 33.98/34.38 (define @t200 () (and @t112 @t127 @t133 @t149)) % 33.98/34.38 (define @t201 () (tptp.subset @t125 @t131)) % 33.98/34.38 (define @t202 () (not @t201)) % 33.98/34.38 (define @t203 () (or @t202 @t113)) % 33.98/34.38 (define @t204 () (not @t194)) % 33.98/34.38 (define @t205 () (not @t139)) % 33.98/34.38 (define @t206 () (and @t202 @t139 @t127 @t112 @t133 @t194 @t137)) % 33.98/34.38 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 33.98/34.38 (assume @p2 (forall @t7 (=> @t6 @t5))) % 33.98/34.38 (assume @p3 (forall @t7 (=> @t6 @t8))) % 33.98/34.38 (assume @p4 (forall @t7 (=> @t11 @t10))) % 33.98/34.38 (assume @p5 @t31) % 33.98/34.38 (assume @p6 @t41) % 33.98/34.38 (assume @p7 (forall @t7 (exists @t27 (tptp.element @t2 @t1)))) % 33.98/34.38 (assume @p8 (and @t43 @t42 (tptp.relation_empty_yielding tptp.empty_set))) % 33.98/34.38 (assume @p9 (forall @t7 (not (tptp.empty @t44)))) % 33.98/34.38 (assume @p10 @t43) % 33.98/34.38 (assume @p11 (forall @t7 (not (tptp.empty @t45)))) % 33.98/34.38 (assume @p12 (and @t43 @t42)) % 33.98/34.38 (assume @p13 (forall @t7 (=> @t48 (not @t46)))) % 33.98/34.38 (assume @p14 (forall @t7 (=> @t48 (not @t49)))) % 33.98/34.38 (assume @p15 (forall @t7 (=> @t6 (and @t46 (tptp.relation @t15))))) % 33.98/34.38 (assume @p16 (forall @t7 (=> @t6 (and @t49 (tptp.relation @t24))))) % 33.98/34.38 (assume @p17 (exists @t7 @t29)) % 33.98/34.38 (assume @p18 (exists @t7 (and @t6 @t8))) % 33.98/34.38 (assume @p19 (forall @t7 (=> @t47 (exists @t27 (and @t51 (not @t50)))))) % 33.98/34.38 (assume @p20 (exists @t7 @t6)) % 33.98/34.38 (assume @p21 (exists @t7 @t11)) % 33.98/34.38 (assume @p22 (exists @t7 @t48)) % 33.98/34.38 (assume @p23 (forall @t7 (exists @t27 (and @t51 @t50)))) % 33.98/34.38 (assume @p24 (exists @t7 @t47)) % 33.98/34.38 (assume @p25 (exists @t7 @t10)) % 33.98/34.38 (assume @p26 (exists @t7 (and @t8 (tptp.relation_empty_yielding @t1)))) % 33.98/34.38 (assume @p27 (forall @t4 (tptp.subset @t1 @t1))) % 33.98/34.38 (assume @p28 @t58) % 33.98/34.38 (assume @p29 @t64) % 33.98/34.38 (assume @p30 @t68) % 33.98/34.38 (assume @p31 (forall @t4 (=> @t3 @t69))) % 33.98/34.38 (assume @p32 (forall @t4 (=> @t69 (or @t50 @t3)))) % 33.98/34.38 (assume @p33 @t72) % 33.98/34.38 (assume @p34 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 33.98/34.38 (assume @p35 (forall @t74 (=> (and @t3 @t73) (tptp.element @t1 @t13)))) % 33.98/34.38 (assume @p36 (forall @t74 (not (and @t3 @t73 (tptp.empty @t13))))) % 33.98/34.38 (assume @p37 (forall @t7 (=> @t6 @t71))) % 33.98/34.38 (assume @p38 @t77) % 33.98/34.38 (assume @p39 (forall @t4 (not (and @t3 @t50)))) % 33.98/34.38 (assume @p40 (forall @t4 (not (and @t6 (not @t75) @t50)))) % 33.98/34.38 (assume @p41 true) % 33.98/34.38 (step @p42 :rule aci_norm :args ((= (or @t85 @t82) (or @t84 @t83 @t82)))) % 33.98/34.38 (step @p43 :rule refl :args (@t82)) % 33.98/34.38 (step @p44 :rule bool-and-de-morgan :args (@t8 @t5 true)) % 33.98/34.38 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or @t86 @t82))) % 33.98/34.38 (step @p46 :rule trans :premises (@p45 @p42)) % 33.98/34.38 (step @p47 :rule bool-impl-elim :args (@t29 @t82)) % 33.98/34.38 (step @p48 :rule trans :premises (@p47 @p46)) % 33.98/34.38 (step @p49 :rule cong :premises (@p48) :args ((forall @t7 (=> @t29 @t82)))) % 33.98/34.38 (step @p50 :rule aci_norm :args ((= (or @t87 @t32) @t81))) % 33.98/34.38 (step @p51 :rule refl :args (@t32)) % 33.98/34.38 (step @p52 :rule aci_norm :args ((= (or @t80 (or @t79 @t78)) @t87))) % 33.98/34.38 (step @p53 :rule bool-and-de-morgan :args (@t34 @t33 true)) % 33.98/34.38 (step @p54 :rule refl :args (@t80)) % 33.98/34.38 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t80 (not (and @t34 @t33))))) % 33.98/34.38 (step @p56 :rule bool-and-de-morgan :args (@t35 @t34 (and @t33))) % 33.98/34.38 (step @p57 :rule trans :premises (@p56 @p55)) % 33.98/34.38 (step @p58 :rule trans :premises (@p57 @p52)) % 33.98/34.38 (step @p59 :rule nary_cong :premises (@p58 @p51) :args ((or (not @t36) @t32))) % 33.98/34.38 (step @p60 :rule trans :premises (@p59 @p50)) % 33.98/34.38 (step @p61 :rule bool-impl-elim :args (@t36 @t32)) % 33.98/34.38 (step @p62 :rule trans :premises (@p61 @p60)) % 33.98/34.38 (step @p63 :rule cong :premises (@p62) :args (@t38)) % 33.98/34.38 (step @p64 :rule refl :args (@t9)) % 33.98/34.38 (step @p65 :rule cong :premises (@p64 @p63) :args (@t39)) % 33.98/34.38 (step @p66 :rule refl :args (@t29)) % 33.98/34.38 (step @p67 :rule cong :premises (@p66 @p65) :args (@t40)) % 33.98/34.38 (step @p68 :rule cong :premises (@p67) :args (@t41)) % 33.98/34.38 (step @p69 :rule trans :premises (@p68 @p49)) % 33.98/34.38 (step @p70 :rule eq_resolve :premises (@p6 @p69)) % 33.98/34.38 (step @p71 :rule instantiate :premises (@p70) :args ((@list @t90))) % 33.98/34.38 (step @p72 :rule aci_norm :args ((= (or @t85 (or @t88 @t9)) @t89))) % 33.98/34.38 (step @p73 :rule bool-impl-elim :args (@t65 @t9)) % 33.98/34.38 (step @p74 :rule nary_cong :premises (@p44 @p73) :args ((or @t86 @t66))) % 33.98/34.38 (step @p75 :rule trans :premises (@p74 @p72)) % 33.98/34.38 (step @p76 :rule bool-impl-elim :args (@t29 @t66)) % 33.98/34.38 (step @p77 :rule trans :premises (@p76 @p75)) % 33.98/34.38 (step @p78 :rule cong :premises (@p77) :args (@t67)) % 33.98/34.38 (step @p79 :rule cong :premises (@p78) :args (@t68)) % 33.98/34.38 (step @p80 :rule eq_resolve :premises (@p30 @p79)) % 33.98/34.38 (step @p81 :rule skolemize :premises (@p80)) % 33.98/34.38 (step @p82 :rule bool-double-not-elim :args (@t91)) % 33.98/34.38 (step @p83 :rule refl :args (@t98)) % 33.98/34.38 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t98 (not @t95)))) % 33.98/34.38 (step @p85 :rule 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@t96 @t91 @t104))) % 33.98/34.38 (step @p98 :rule cnf_or_neg :args (@t98 3)) % 33.98/34.38 (step @p99 :rule chain_m_resolution :premises (@p98 @p81) :args ((not @t92) @t99 @t100)) % 33.98/34.38 (step @p100 :rule cnf_equiv_pos2 :args (@t103)) % 33.98/34.38 (step @p101 :rule reordering :premises (@p100) :args ((or @t92 @t106 (not @t103)))) % 33.98/34.38 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p97) :args (@t106 @t107 (@list @t92 @t103))) % 33.98/34.38 (step @p103 :rule skolemize :premises (@p102)) % 33.98/34.38 (step @p104 :rule bool-double-not-elim :args (@t112)) % 33.98/34.38 (step @p105 :rule refl :args (@t119)) % 33.98/34.38 (step @p106 :rule nary_cong :premises (@p105 @p104) :args ((or @t119 (not @t114)))) % 33.98/34.38 (step @p107 :rule cnf_or_neg :args (@t119 2)) % 33.98/34.38 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 33.98/34.38 (step @p109 :rule reordering :premises (@p108) :args ((or @t112 @t119))) % 33.98/34.38 (step @p110 :rule chain_m_resolution :premises (@p109 @p103) :args (@t112 @t99 @t120)) % 33.98/34.38 (step @p111 :rule aci_norm :args ((= (or (or @t123 @t122) (or @t121 @t52)) (or @t123 @t122 @t121 @t52)))) % 33.98/34.38 (step @p112 :rule bool-impl-elim :args (@t53 @t52)) % 33.98/34.38 (step @p113 :rule bool-and-de-morgan :args (@t56 @t55 true)) % 33.98/34.38 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or (not @t57) @t54))) % 33.98/34.38 (step @p115 :rule trans :premises (@p114 @p111)) % 33.98/34.38 (step @p116 :rule bool-impl-elim :args (@t57 @t54)) % 33.98/34.38 (step @p117 :rule trans :premises (@p116 @p115)) % 33.98/34.38 (step @p118 :rule cong :premises (@p117) :args (@t58)) % 33.98/34.38 (step @p119 :rule eq_resolve :premises (@p28 @p118)) % 33.98/34.38 (step @p120 :rule instantiate :premises (@p119) :args ((@list @t110 @t90))) % 33.98/34.38 (step @p121 :rule bool-double-not-elim :args (@t117)) % 33.98/34.38 (step @p122 :rule nary_cong :premises (@p105 @p121) :args ((or @t119 (not @t118)))) % 33.98/34.38 (step @p123 :rule cnf_or_neg :args (@t119 0)) % 33.98/34.38 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 33.98/34.38 (step @p125 :rule reordering :premises (@p124) :args ((or @t117 @t119))) % 33.98/34.38 (step @p126 :rule chain_m_resolution :premises (@p125 @p103) :args (@t117 @t99 @t120)) % 33.98/34.38 (step @p127 :rule cnf_or_pos :args (@t128)) % 33.98/34.38 (step @p128 :rule reordering :premises (@p127) :args ((or @t97 @t95 @t118 @t127 (not @t128)))) % 33.98/34.38 (step @p129 :rule chain_m_resolution :premises (@p128 @p94 @p88 @p126 @p120) :args (@t127 @t129 (@list @t96 @t91 @t117 @t128))) % 33.98/34.38 (step @p130 :rule instantiate :premises (@p119) :args ((@list @t108 @t90))) % 33.98/34.38 (step @p131 :rule bool-double-not-elim :args (@t115)) % 33.98/34.38 (step @p132 :rule nary_cong :premises (@p105 @p131) :args ((or @t119 (not @t116)))) % 33.98/34.38 (step @p133 :rule cnf_or_neg :args (@t119 1)) % 33.98/34.38 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 33.98/34.38 (step @p135 :rule reordering :premises (@p134) :args ((or @t115 @t119))) % 33.98/34.38 (step @p136 :rule chain_m_resolution :premises (@p135 @p103) :args (@t115 @t99 @t120)) % 33.98/34.38 (step @p137 :rule cnf_or_pos :args (@t134)) % 33.98/34.38 (step @p138 :rule reordering :premises (@p137) :args ((or @t97 @t95 @t116 @t133 (not @t134)))) % 33.98/34.38 (step @p139 :rule chain_m_resolution :premises (@p138 @p94 @p88 @p136 @p130) :args (@t133 @t129 (@list @t96 @t91 @t115 @t134))) % 33.98/34.38 (step @p140 :rule bool-double-not-elim :args (@t93)) % 33.98/34.38 (step @p141 :rule nary_cong :premises (@p83 @p140) :args ((or @t98 (not @t94)))) % 33.98/34.38 (step @p142 :rule cnf_or_neg :args (@t98 2)) % 33.98/34.38 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 33.98/34.38 (step @p144 :rule reordering :premises (@p143) :args ((or @t93 @t98))) % 33.98/34.38 (step @p145 :rule chain_m_resolution :premises (@p144 @p81) :args (@t93 @t99 @t100)) % 33.98/34.38 (step @p146 :rule instantiate :premises (@p145) :args ((@list @t125))) % 33.98/34.38 (step @p147 :rule eq-symm :args (@t135 @t125)) % 33.98/34.38 (step @p148 :rule eq-symm :args (@t135 tptp.empty_set)) % 33.98/34.38 (step @p149 :rule nary_cong :premises (@p148 @p147) :args (@t136)) % 33.98/34.38 (step @p150 :rule refl :args (@t137)) % 33.98/34.38 (step @p151 :rule cong :premises (@p150 @p149) :args (@t138)) % 33.98/34.38 (step @p152 :rule refl :args (@t72)) % 33.98/34.38 (step @p153 :rule cong :premises (@p152 @p151) :args ((=> @t72 @t138))) % 33.98/34.38 (assume-push @p439 @t72) % 33.98/34.38 (step @p155 :rule instantiate :premises (@p33) :args ((@list @t135 @t110))) % 33.98/34.38 (step-pop @p440 :rule scope :premises (@p155)) % 33.98/34.38 (step @p156 :rule process_scope :premises (@p440) :args (@t138)) % 33.98/34.38 (step @p158 :rule eq_resolve :premises (@p156 @p153)) % 33.98/34.38 (step @p159 :rule implies_elim :premises (@p158)) % 33.98/34.38 (step @p160 :rule chain_m_resolution :premises (@p159 @p33) :args (@t142 @t143 @t144)) % 33.98/34.38 (step @p161 :rule cnf_equiv_pos1 :args (@t142)) % 33.98/34.38 (step @p162 :rule reordering :premises (@p161) :args ((or @t145 @t141 (not @t142)))) % 33.98/34.38 (step @p163 :rule chain_m_resolution :premises (@p162 @p146 @p160) :args (@t141 @t146 (@list @t137 @t142))) % 33.98/34.38 (step @p164 :rule bool-impl-elim :args (@t56 @t147)) % 33.98/34.38 (step @p165 :rule cong :premises (@p164) :args ((forall @t4 (=> @t56 @t147)))) % 33.98/34.38 (step @p166 :rule eq-symm :args (@t59 tptp.empty_set)) % 33.98/34.38 (step @p167 :rule cong :premises (@p166) :args (@t60)) % 33.98/34.38 (step @p168 :rule refl :args (@t61)) % 33.98/34.38 (step @p169 :rule cong :premises (@p168 @p167) :args (@t62)) % 33.98/34.38 (step @p170 :rule refl :args (@t56)) % 33.98/34.38 (step @p171 :rule cong :premises (@p170 @p169) :args (@t63)) % 33.98/34.38 (step @p172 :rule cong :premises (@p171) :args (@t64)) % 33.98/34.38 (step @p173 :rule trans :premises (@p172 @p165)) % 33.98/34.38 (step @p174 :rule eq_resolve :premises (@p29 @p173)) % 33.98/34.38 (step @p175 :rule instantiate :premises (@p174) :args ((@list @t109 @t90))) % 33.98/34.38 (step @p176 :rule cnf_or_pos :args (@t153)) % 33.98/34.38 (step @p177 :rule reordering :premises (@p176) :args ((or @t97 @t152 (not @t153)))) % 33.98/34.38 (step @p178 :rule chain_m_resolution :premises (@p177 @p94 @p175) :args (@t152 @t146 (@list @t96 @t153))) % 33.98/34.38 (step @p179 :rule eq-symm :args (@t155 @t156)) % 33.98/34.38 (step @p180 :rule cong :premises (@p179) :args (@t157)) % 33.98/34.38 (step @p181 :rule eq-symm :args (@t154 @t24)) % 33.98/34.38 (step @p182 :rule cong :premises (@p181 @p180) :args (@t158)) % 33.98/34.38 (step @p183 :rule refl :args (@t83)) % 33.98/34.38 (step @p184 :rule refl :args (@t84)) % 33.98/34.38 (step @p185 :rule nary_cong :premises (@p184 @p183 @p182) :args (@t159)) % 33.98/34.38 (step @p186 :rule cong :premises (@p185) :args (@t161)) % 33.98/34.38 (step @p187 :rule quant-merge-prenex :args ((= (forall @t7 @t163) @t161))) % 33.98/34.38 (step @p188 :rule alpha_equiv :args (@t164 (@list @t154) (@list @t2))) % 33.98/34.38 (step @p189 :rule refl :args (@t83)) % 33.98/34.38 (step @p190 :rule refl :args (@t84)) % 33.98/34.38 (step @p191 :rule nary_cong :premises (@p190 @p189 @p188) :args (@t165)) % 33.98/34.38 (step @p192 :rule quant-miniscope-or :args ((= @t163 @t165))) % 33.98/34.38 (step @p193 :rule trans :premises (@p192 @p191)) % 33.98/34.38 (step @p194 :rule symm :premises (@p193)) % 33.98/34.38 (step @p195 :rule cong :premises (@p194) :args ((forall @t7 @t167))) % 33.98/34.38 (step @p196 :rule trans :premises (@p195 @p187)) % 33.98/34.38 (step @p197 :rule trans :premises (@p196 @p186)) % 33.98/34.38 (step @p198 :rule aci_norm :args ((= (or @t85 @t166) @t167))) % 33.98/34.38 (step @p199 :rule refl :args (@t166)) % 33.98/34.38 (step @p200 :rule nary_cong :premises (@p44 @p199) :args ((or @t86 @t166))) % 33.98/34.38 (step @p201 :rule trans :premises (@p200 @p198)) % 33.98/34.38 (step @p202 :rule bool-impl-elim :args (@t29 @t166)) % 33.98/34.38 (step @p203 :rule trans :premises (@p202 @p201)) % 33.98/34.38 (step @p204 :rule cong :premises (@p203) :args ((forall @t7 (=> @t29 @t166)))) % 33.98/34.38 (step @p205 :rule trans :premises (@p204 @p197)) % 33.98/34.38 (step @p206 :rule bool-and-de-morgan :args (@t16 @t14 true)) % 33.98/34.38 (step @p207 :rule cong :premises (@p206) :args (@t168)) % 33.98/34.38 (step @p208 :rule cong :premises (@p207) :args (@t169)) % 33.98/34.38 (step @p209 :rule exists-elim :args ((= @t19 @t169))) % 33.98/34.38 (step @p210 :rule trans :premises (@p209 @p208)) % 33.98/34.38 (step @p211 :rule refl :args (@t20)) % 33.98/34.38 (step @p212 :rule cong :premises (@p211 @p210) :args (@t21)) % 33.98/34.38 (step @p213 :rule cong :premises (@p212) :args (@t23)) % 33.98/34.38 (step @p214 :rule refl :args (@t25)) % 33.98/34.38 (step @p215 :rule cong :premises (@p214 @p213) :args (@t26)) % 33.98/34.38 (step @p216 :rule cong :premises (@p215) :args (@t28)) % 33.98/34.38 (step @p217 :rule cong :premises (@p66 @p216) :args (@t30)) % 33.98/34.38 (step @p218 :rule cong :premises (@p217) :args (@t31)) % 33.98/34.38 (step @p219 :rule trans :premises (@p218 @p205)) % 33.98/34.38 (step @p220 :rule eq_resolve :premises (@p5 @p219)) % 33.98/34.38 (step @p221 :rule bool-eq-true :args (@t172)) % 33.98/34.38 (step @p222 :rule eq-symm :args (true @t172)) % 33.98/34.38 (step @p223 :rule trans :premises (@p222 @p221)) % 33.98/34.38 (step @p224 :rule refl :args (@t172)) % 33.98/34.38 (step @p225 :rule eq-refl :args (@t150)) % 33.98/34.38 (step @p226 :rule cong :premises (@p225 @p224) :args (@t173)) % 33.98/34.38 (step @p227 :rule trans :premises (@p226 @p223)) % 33.98/34.38 (step @p228 :rule refl :args (@t95)) % 33.98/34.38 (step @p229 :rule refl :args (@t97)) % 33.98/34.38 (step @p230 :rule nary_cong :premises (@p229 @p228 @p227) :args (@t174)) % 33.98/34.38 (step @p231 :rule refl :args (@t175)) % 33.98/34.38 (step @p232 :rule cong :premises (@p231 @p230) :args ((=> @t175 @t174))) % 33.98/34.38 (assume-push @p441 @t175) % 33.98/34.38 (step @p234 :rule instantiate :premises (@p220) :args ((@list @t90 @t150))) % 33.98/34.38 (step-pop @p442 :rule scope :premises (@p234)) % 33.98/34.38 (step @p235 :rule process_scope :premises (@p442) :args (@t174)) % 33.98/34.38 (step @p237 :rule eq_resolve :premises (@p235 @p232)) % 33.98/34.38 (step @p238 :rule implies_elim :premises (@p237)) % 33.98/34.38 (step @p239 :rule chain_m_resolution :premises (@p238 @p220) :args (@t176 @t143 (@list @t175))) % 33.98/34.38 (step @p240 :rule cnf_or_pos :args (@t176)) % 33.98/34.38 (step @p241 :rule reordering :premises (@p240) :args ((or @t97 @t95 @t172 (not @t176)))) % 33.98/34.38 (step @p242 :rule chain_m_resolution :premises (@p241 @p94 @p88 @p239) :args (@t172 @t105 (@list @t96 @t91 @t176))) % 33.98/34.38 (step @p243 :rule eq-symm :args (@t178 @t151)) % 33.98/34.38 (step @p244 :rule cong :premises (@p224 @p243) :args ((=> @t172 @t179))) % 33.98/34.38 (assume-push @p443 @t172) % 33.98/34.38 (step @p246 :rule instantiate :premises (@p242) :args ((@list @t109))) % 33.98/34.38 (step-pop @p444 :rule scope :premises (@p246)) % 33.98/34.38 (step @p247 :rule process_scope :premises (@p444) :args (@t179)) % 33.98/34.38 (step @p249 :rule eq_resolve :premises (@p247 @p244)) % 33.98/34.38 (step @p250 :rule implies_elim :premises (@p249)) % 33.98/34.38 (step @p251 :rule chain_m_resolution :premises (@p250 @p242) :args (@t180 @t143 (@list @t172))) % 33.98/34.38 (step @p252 :rule cnf_or_pos :args (@t181)) % 33.98/34.38 (step @p253 :rule reordering :premises (@p252) :args ((or @t118 @t114 @t182))) % 33.98/34.38 (step @p254 :rule chain_m_resolution :premises (@p253 @p126 @p110) :args (@t182 @t146 (@list @t117 @t112))) % 33.98/34.38 (step @p255 :rule eq-symm :args (@t109 @t111)) % 33.98/34.38 (step @p256 :rule cong :premises (@p255) :args (@t183)) % 33.98/34.38 (step @p257 :rule refl :args (@t118)) % 33.98/34.38 (step @p258 :rule nary_cong :premises (@p257 @p256) :args (@t184)) % 33.98/34.38 (step @p259 :rule refl :args (@t177)) % 33.98/34.38 (step @p260 :rule cong :premises (@p259 @p258) :args ((=> @t177 @t184))) % 33.98/34.38 (assume-push @p445 @t177) % 33.98/34.38 (step @p262 :rule instantiate :premises (@p445) :args ((@list @t110))) % 33.98/34.38 (step-pop @p446 :rule scope :premises (@p262)) % 33.98/34.38 (step @p263 :rule process_scope :premises (@p446) :args (@t184)) % 33.98/34.38 (step @p265 :rule eq_resolve :premises (@p263 @p260)) % 33.98/34.38 (step @p266 :rule implies_elim :premises (@p265)) % 33.98/34.38 (step @p267 :rule chain_m_resolution :premises (@p266 @p254) :args (@t178 @t99 (@list @t181))) % 33.98/34.38 (step @p268 :rule bool-double-not-elim :args (@t177)) % 33.98/34.38 (step @p269 :rule refl :args (@t151)) % 33.98/34.38 (step @p270 :rule refl :args (@t185)) % 33.98/34.38 (step @p271 :rule nary_cong :premises (@p270 @p269 @p268) :args ((or @t185 @t151 (not @t178)))) % 33.98/34.38 (step @p272 :rule cnf_equiv_pos2 :args (@t180)) % 33.98/34.38 (step @p273 :rule eq_resolve :premises (@p272 @p271)) % 33.98/34.38 (step @p274 :rule reordering :premises (@p273) :args ((or @t151 @t177 @t185))) % 33.98/34.38 (step @p275 :rule chain_m_resolution :premises (@p274 @p267 @p251) :args (@t151 @t107 (@list @t177 @t180))) % 33.98/34.38 (step @p276 :rule cnf_equiv_pos1 :args (@t152)) % 33.98/34.38 (step @p277 :rule reordering :premises (@p276) :args ((or @t149 (not @t151) (not @t152)))) % 33.98/34.38 (step @p278 :rule chain_m_resolution :premises (@p277 @p275 @p178) :args (@t149 @t146 (@list @t151 @t152))) % 33.98/34.38 (step @p279 :rule refl :args (@t186)) % 33.98/34.38 (step @p280 :rule bool-double-not-elim :args (@t148)) % 33.98/34.38 (step @p281 :rule refl :args (@t187)) % 33.98/34.38 (step @p282 :rule refl :args (@t114)) % 33.98/34.38 (step @p283 :rule nary_cong :premises (@p282 @p281 @p280 @p279) :args ((or @t114 @t187 @t188 @t186))) % 33.98/34.38 (assume-push @p447 @t112) % 33.98/34.38 (assume-push @p448 @t127) % 33.98/34.38 (assume-push @p449 @t149) % 33.98/34.38 (assume-push @p450 @t127) % 33.98/34.38 (assume-push @p451 @t112) % 33.98/34.38 (assume-push @p452 @t149) % 33.98/34.38 (step @p290 :rule false_intro :premises (@p449)) % 33.98/34.38 (step @p291 :rule cong :premises (@p110) :args (@t124)) % 33.98/34.38 (step @p292 :rule trans :premises (@p129 @p291)) % 33.98/34.38 (step @p293 :rule refl :args (@t90)) % 33.98/34.38 (step @p294 :rule cong :premises (@p293 @p292) :args (@t135)) % 33.98/34.38 (step @p295 :rule refl :args (tptp.empty_set)) % 33.98/34.38 (step @p296 :rule cong :premises (@p295 @p294) :args (@t140)) % 33.98/34.38 (step @p297 :rule trans :premises (@p296 @p290)) % 33.98/34.38 (step @p298 :rule false_elim :premises (@p297)) % 33.98/34.38 (step-pop @p453 :rule scope :premises (@p298)) % 33.98/34.38 (step-pop @p454 :rule scope :premises (@p453)) % 33.98/34.38 (step-pop @p455 :rule scope :premises (@p454)) % 33.98/34.38 (step @p299 :rule process_scope :premises (@p455) :args (@t186)) % 33.98/34.38 (step @p303 :rule and_intro :premises (@p129 @p110 @p449)) % 33.98/34.38 (step @p304 :rule modus_ponens :premises (@p303 @p299)) % 33.98/34.38 (step-pop @p456 :rule scope :premises (@p304)) % 33.98/34.38 (step-pop @p457 :rule scope :premises (@p456)) % 33.98/34.38 (step-pop @p458 :rule scope :premises (@p457)) % 33.98/34.38 (step @p305 :rule process_scope :premises (@p458) :args (@t186)) % 33.98/34.38 (step @p309 :rule implies_elim :premises (@p305)) % 33.98/34.38 (step @p310 :rule cnf_and_neg :args (@t189)) % 33.98/34.38 (step @p311 :rule resolution :premises (@p310 @p309) :args (true @t189)) % 33.98/34.38 (step @p312 :rule eq_resolve :premises (@p311 @p283)) % 33.98/34.38 (step @p313 :rule reordering :premises (@p312) :args ((or @t114 @t187 @t186 @t148))) % 33.98/34.38 (step @p314 :rule chain_m_resolution :premises (@p313 @p110 @p129 @p278) :args (@t186 (@list false false true) (@list @t112 @t127 @t148))) % 33.98/34.38 (step @p315 :rule cnf_or_pos :args (@t141)) % 33.98/34.38 (step @p316 :rule reordering :premises (@p315) :args ((or @t140 @t139 (not @t141)))) % 33.98/34.38 (step @p317 :rule chain_m_resolution :premises (@p316 @p314 @p163) :args (@t139 @t107 (@list @t140 @t141))) % 33.98/34.38 (step @p318 :rule eq-symm :args (@t190 @t131)) % 33.98/34.38 (step @p319 :rule eq-symm :args (@t190 tptp.empty_set)) % 33.98/34.38 (step @p320 :rule nary_cong :premises (@p319 @p318) :args (@t191)) % 33.98/34.38 (step @p321 :rule refl :args (@t192)) % 33.98/34.38 (step @p322 :rule cong :premises (@p321 @p320) :args (@t193)) % 33.98/34.38 (step @p323 :rule cong :premises (@p152 @p322) :args ((=> @t72 @t193))) % 33.98/34.38 (assume-push @p459 @t72) % 33.98/34.38 (step @p325 :rule instantiate :premises (@p33) :args ((@list @t190 @t108))) % 33.98/34.38 (step-pop @p460 :rule scope :premises (@p325)) % 33.98/34.38 (step @p326 :rule process_scope :premises (@p460) :args (@t193)) % 33.98/34.38 (step @p328 :rule eq_resolve :premises (@p326 @p323)) % 33.98/34.38 (step @p329 :rule implies_elim :premises (@p328)) % 33.98/34.38 (step @p330 :rule chain_m_resolution :premises (@p329 @p33) :args (@t197 @t143 @t144)) % 33.98/34.38 (step @p331 :rule instantiate :premises (@p145) :args ((@list @t131))) % 33.98/34.38 (step @p332 :rule cnf_equiv_pos1 :args (@t197)) % 33.98/34.38 (step @p333 :rule reordering :premises (@p332) :args ((or (not @t192) @t196 (not @t197)))) % 33.98/34.38 (step @p334 :rule chain_m_resolution :premises (@p333 @p331 @p330) :args (@t196 @t146 (@list @t192 @t197))) % 33.98/34.38 (step @p335 :rule refl :args (@t198)) % 33.98/34.38 (step @p336 :rule refl :args (@t199)) % 33.98/34.38 (step @p337 :rule nary_cong :premises (@p282 @p281 @p336 @p280 @p335) :args ((or @t114 @t187 @t199 @t188 @t198))) % 33.98/34.38 (assume-push @p461 @t112) % 33.98/34.38 (assume-push @p462 @t127) % 33.98/34.38 (assume-push @p463 @t133) % 33.98/34.38 (assume-push @p464 @t149) % 33.98/34.38 (assume-push @p465 @t149) % 33.98/34.38 (assume-push @p466 @t112) % 33.98/34.38 (assume-push @p467 @t127) % 33.98/34.38 (assume-push @p468 @t133) % 33.98/34.38 (step @p346 :rule false_intro :premises (@p464)) % 33.98/34.38 (step @p291 :rule cong :premises (@p110) :args (@t124)) % 33.98/34.38 (step @p292 :rule trans :premises (@p129 @p291)) % 33.98/34.38 (step @p293 :rule refl :args (@t90)) % 33.98/34.38 (step @p294 :rule cong :premises (@p293 @p292) :args (@t135)) % 33.98/34.38 (step @p347 :rule symm :premises (@p129)) % 33.98/34.38 (step @p348 :rule symm :premises (@p291)) % 33.98/34.38 (step @p349 :rule trans :premises (@p139 @p348 @p347)) % 33.98/34.38 (step @p350 :rule cong :premises (@p293 @p349) :args (@t190)) % 33.98/34.38 (step @p351 :rule trans :premises (@p350 @p294)) % 33.98/34.38 (step @p295 :rule refl :args (tptp.empty_set)) % 33.98/34.38 (step @p352 :rule cong :premises (@p295 @p351) :args (@t195)) % 33.98/34.38 (step @p353 :rule trans :premises (@p352 @p346)) % 33.98/34.38 (step @p354 :rule false_elim :premises (@p353)) % 33.98/34.38 (step-pop @p469 :rule scope :premises (@p354)) % 33.98/34.38 (step-pop @p470 :rule scope :premises (@p469)) % 33.98/34.38 (step-pop @p471 :rule scope :premises (@p470)) % 33.98/34.38 (step-pop @p472 :rule scope :premises (@p471)) % 33.98/34.38 (step @p355 :rule process_scope :premises (@p472) :args (@t198)) % 33.98/34.38 (step @p360 :rule and_intro :premises (@p464 @p110 @p129 @p139)) % 33.98/34.38 (step @p361 :rule modus_ponens :premises (@p360 @p355)) % 33.98/34.38 (step-pop @p473 :rule scope :premises (@p361)) % 33.98/34.38 (step-pop @p474 :rule scope :premises (@p473)) % 33.98/34.38 (step-pop @p475 :rule scope :premises (@p474)) % 33.98/34.38 (step-pop @p476 :rule scope :premises (@p475)) % 33.98/34.38 (step @p362 :rule process_scope :premises (@p476) :args (@t198)) % 33.98/34.38 (step @p367 :rule implies_elim :premises (@p362)) % 33.98/34.38 (step @p368 :rule cnf_and_neg :args (@t200)) % 33.98/34.38 (step @p369 :rule resolution :premises (@p368 @p367) :args (true @t200)) % 33.98/34.38 (step @p370 :rule eq_resolve :premises (@p369 @p337)) % 33.98/34.38 (step @p371 :rule reordering :premises (@p370) :args ((or @t114 @t187 @t199 @t198 @t148))) % 33.98/34.38 (step @p372 :rule chain_m_resolution :premises (@p371 @p110 @p129 @p139 @p278) :args (@t198 (@list false false false true) (@list @t112 @t127 @t133 @t148))) % 33.98/34.38 (step @p373 :rule cnf_or_pos :args (@t196)) % 33.98/34.38 (step @p374 :rule reordering :premises (@p373) :args ((or @t195 @t194 (not @t196)))) % 33.98/34.38 (step @p375 :rule chain_m_resolution :premises (@p374 @p372 @p334) :args (@t194 @t107 (@list @t195 @t196))) % 33.98/34.38 (step @p376 :rule bool-impl-elim :args (@t76 @t75)) % 33.98/34.38 (step @p377 :rule cong :premises (@p376) :args (@t77)) % 33.98/34.38 (step @p378 :rule eq_resolve :premises (@p38 @p377)) % 33.98/34.38 (step @p379 :rule instantiate :premises (@p378) :args ((@list @t110 @t108))) % 33.98/34.38 (step @p380 :rule cnf_or_neg :args (@t119 3)) % 33.98/34.38 (step @p381 :rule chain_m_resolution :premises (@p380 @p103) :args ((not @t113) @t99 @t120)) % 33.98/34.38 (step @p382 :rule cnf_or_pos :args (@t203)) % 33.98/34.38 (step @p383 :rule reordering :premises (@p382) :args ((or @t113 @t202 (not @t203)))) % 33.98/34.38 (step @p384 :rule chain_m_resolution :premises (@p383 @p381 @p379) :args (@t202 @t107 (@list @t113 @t203))) % 33.98/34.38 (step @p385 :rule bool-double-not-elim :args (@t201)) % 33.98/34.38 (step @p386 :rule refl :args (@t204)) % 33.98/34.38 (step @p387 :rule refl :args (@t205)) % 33.98/34.38 (step @p388 :rule refl :args (@t145)) % 33.98/34.38 (step @p389 :rule nary_cong :premises (@p282 @p281 @p336 @p388 @p387 @p386 @p385) :args ((or @t114 @t187 @t199 @t145 @t205 @t204 (not @t202)))) % 33.98/34.38 (assume-push @p477 @t202) % 33.98/34.38 (assume-push @p478 @t139) % 33.98/34.38 (assume-push @p479 @t127) % 33.98/34.38 (assume-push @p480 @t112) % 33.98/34.38 (assume-push @p481 @t133) % 33.98/34.38 (assume-push @p482 @t194) % 33.98/34.38 (assume-push @p483 @t137) % 33.98/34.38 (step @p397 :rule evaluate :args ((= true false))) % 33.98/34.38 (step @p398 :rule false_intro :premises (@p384)) % 33.98/34.38 (step @p399 :rule symm :premises (@p482)) % 33.98/34.38 (step @p400 :rule symm :premises (@p139)) % 33.98/34.38 (step @p291 :rule cong :premises (@p110) :args (@t124)) % 33.98/34.38 (step @p401 :rule trans :premises (@p129 @p291 @p400)) % 33.98/34.38 (step @p293 :rule refl :args (@t90)) % 33.98/34.38 (step @p402 :rule cong :premises (@p293 @p401) :args (@t135)) % 33.98/34.38 (step @p403 :rule trans :premises (@p478 @p402 @p399)) % 33.98/34.38 (step @p404 :rule symm :premises (@p478)) % 33.98/34.38 (step @p405 :rule cong :premises (@p404 @p403) :args (@t137)) % 33.98/34.38 (step @p406 :rule true_intro :premises (@p146)) % 33.98/34.38 (step @p407 :rule symm :premises (@p406)) % 33.98/34.38 (step @p408 :rule trans :premises (@p407 @p405 @p398)) % 33.98/34.38 (step @p409 false :rule eq_resolve :premises (@p408 @p397)) % 33.98/34.38 (step-pop @p484 :rule scope :premises (@p409)) % 33.98/34.38 (step-pop @p485 :rule scope :premises (@p484)) % 33.98/34.38 (step-pop @p486 :rule scope :premises (@p485)) % 33.98/34.38 (step-pop @p487 :rule scope :premises (@p486)) % 33.98/34.38 (step-pop @p488 :rule scope :premises (@p487)) % 33.98/34.38 (step-pop @p489 :rule scope :premises (@p488)) % 33.98/34.38 (step-pop @p490 :rule scope :premises (@p489)) % 33.98/34.38 (step @p410 :rule process_scope :premises (@p490) :args (false)) % 33.98/34.38 (assume-push @p491 @t112) % 33.98/34.38 (assume-push @p492 @t127) % 33.98/34.38 (assume-push @p493 @t133) % 33.98/34.38 (assume-push @p494 @t137) % 33.98/34.38 (assume-push @p495 @t139) % 33.98/34.38 (assume-push @p496 @t194) % 33.98/34.38 (assume-push @p497 @t202) % 33.98/34.38 (step @p425 :rule and_intro :premises (@p384 @p495 @p129 @p110 @p139 @p496 @p146)) % 33.98/34.38 (step-pop @p498 :rule scope :premises (@p425)) % 33.98/34.38 (step-pop @p499 :rule scope :premises (@p498)) % 33.98/34.38 (step-pop @p500 :rule scope :premises (@p499)) % 33.98/34.38 (step-pop @p501 :rule scope :premises (@p500)) % 33.98/34.38 (step-pop @p502 :rule scope :premises (@p501)) % 33.98/34.38 (step-pop @p503 :rule scope :premises (@p502)) % 33.98/34.38 (step-pop @p504 :rule scope :premises (@p503)) % 33.98/34.38 (step @p426 :rule process_scope :premises (@p504) :args (@t206)) % 33.98/34.38 (step @p434 :rule implies_elim :premises (@p426)) % 33.98/34.38 (step @p435 :rule resolution :premises (@p434 @p410) :args (true @t206)) % 33.98/34.38 (step @p436 :rule not_and :premises (@p435)) % 33.98/34.38 (step @p437 :rule eq_resolve :premises (@p436 @p389)) % 33.98/34.38 (step @p438 false :rule chain_m_resolution :premises (@p437 @p384 @p375 @p317 @p146 @p139 @p129 @p110) :args (false (@list true false false false false false false) (@list @t201 @t194 @t139 @t137 @t133 @t127 @t112))) % 33.98/34.38 ) % 33.98/34.38 % SZS output end Proof % 33.98/34.38 % cvc5 exiting %------------------------------------------------------------------------------