%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU174+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:50:51 AM UTC 2026 % Result : Theorem 1.52s 1.71s % Output : Proof 1.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU174+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n019.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:33:49 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 1.52/1.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.52/1.71 % SZS status Theorem % 1.52/1.71 % SZS output start Proof % 1.52/1.71 ( % 1.52/1.71 (declare-sort $$unsorted 0) % 1.52/1.71 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (declare-const tptp.empty_set $$unsorted) % 1.52/1.71 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.52/1.71 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 1.52/1.71 (define @t1 () (@var "A" $$unsorted)) % 1.52/1.71 (define @t2 () (@var "B" $$unsorted)) % 1.52/1.71 (define @t3 () (tptp.in @t2 @t1)) % 1.52/1.71 (define @t4 () (not @t3)) % 1.52/1.71 (define @t5 () (tptp.in @t1 @t2)) % 1.52/1.71 (define @t6 () (@list @t1 @t2)) % 1.52/1.71 (define @t7 () (tptp.proper_subset @t2 @t1)) % 1.52/1.71 (define @t8 () (tptp.proper_subset @t1 @t2)) % 1.52/1.71 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 1.52/1.71 (define @t10 () (tptp.set_union2 @t2 @t1)) % 1.52/1.71 (define @t11 () (tptp.set_union2 @t1 @t2)) % 1.52/1.71 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 1.52/1.71 (define @t13 () (tptp.subset @t1 @t2)) % 1.52/1.71 (define @t14 () (= @t1 @t2)) % 1.52/1.71 (define @t15 () (@var "C" $$unsorted)) % 1.52/1.71 (define @t16 () (tptp.in @t15 @t2)) % 1.52/1.71 (define @t17 () (@list @t15)) % 1.52/1.71 (define @t18 () (tptp.singleton @t1)) % 1.52/1.71 (define @t19 () (@list @t2)) % 1.52/1.71 (define @t20 () (= @t1 tptp.empty_set)) % 1.52/1.71 (define @t21 () (@list @t1)) % 1.52/1.71 (define @t22 () (tptp.powerset @t1)) % 1.52/1.71 (define @t23 () (tptp.empty @t2)) % 1.52/1.71 (define @t24 () (tptp.element @t2 @t1)) % 1.52/1.71 (define @t25 () (tptp.empty @t1)) % 1.52/1.71 (define @t26 () (not @t25)) % 1.52/1.71 (define @t27 () (@var "D" $$unsorted)) % 1.52/1.71 (define @t28 () (tptp.in @t27 @t15)) % 1.52/1.71 (define @t29 () (@list @t27)) % 1.52/1.71 (define @t30 () (@list @t1 @t2 @t15)) % 1.52/1.71 (define @t31 () (tptp.in @t27 @t2)) % 1.52/1.71 (define @t32 () (tptp.in @t27 @t1)) % 1.52/1.71 (define @t33 () (@var "F" $$unsorted)) % 1.52/1.71 (define @t34 () (@var "E" $$unsorted)) % 1.52/1.71 (define @t35 () (tptp.in @t15 @t1)) % 1.52/1.71 (define @t36 () (forall @t17 (=> @t35 @t16))) % 1.52/1.71 (define @t37 () (tptp.set_difference @t1 @t2)) % 1.52/1.71 (define @t38 () (tptp.subset_complement @t1 @t2)) % 1.52/1.71 (define @t39 () (tptp.element @t2 @t22)) % 1.52/1.71 (define @t40 () (tptp.ordered_pair @t1 @t2)) % 1.52/1.71 (define @t41 () (tptp.disjoint @t1 @t2)) % 1.52/1.71 (define @t42 () (tptp.in (tptp.subset_complement @t1 @t27) @t2)) % 1.52/1.71 (define @t43 () (= @t28 @t42)) % 1.52/1.71 (define @t44 () (tptp.element @t27 @t22)) % 1.52/1.71 (define @t45 () (forall @t29 (=> @t44 @t43))) % 1.52/1.71 (define @t46 () (tptp.complements_of_subsets @t1 @t2)) % 1.52/1.71 (define @t47 () (= @t15 @t46)) % 1.52/1.71 (define @t48 () (= @t47 @t45)) % 1.52/1.71 (define @t49 () (tptp.powerset @t22)) % 1.52/1.71 (define @t50 () (tptp.element @t15 @t49)) % 1.52/1.71 (define @t51 () (=> @t50 @t48)) % 1.52/1.71 (define @t52 () (forall @t17 @t51)) % 1.52/1.71 (define @t53 () (tptp.element @t2 @t49)) % 1.52/1.71 (define @t54 () (=> @t53 @t52)) % 1.52/1.71 (define @t55 () (forall @t6 @t54)) % 1.52/1.71 (define @t56 () (not @t14)) % 1.52/1.71 (define @t57 () (tptp.element @t46 @t49)) % 1.52/1.71 (define @t58 () (forall @t6 (=> @t53 @t57))) % 1.52/1.71 (define @t59 () (tptp.complements_of_subsets @t1 @t46)) % 1.52/1.71 (define @t60 () (=> @t53 (= @t59 @t2))) % 1.52/1.71 (define @t61 () (forall @t6 @t60)) % 1.52/1.71 (define @t62 () (tptp.disjoint @t18 @t2)) % 1.52/1.71 (define @t63 () (tptp.singleton @t2)) % 1.52/1.71 (define @t64 () (tptp.in @t1 @t15)) % 1.52/1.71 (define @t65 () (@list @t1 @t2 @t15 @t27)) % 1.52/1.71 (define @t66 () (tptp.element @t1 (tptp.powerset @t2))) % 1.52/1.71 (define @t67 () (= @t1 @t15)) % 1.52/1.71 (define @t68 () (tptp.cartesian_product2 @t1 @t15)) % 1.52/1.71 (define @t69 () (not @t16)) % 1.52/1.71 (define @t70 () (tptp.subset @t15 @t2)) % 1.52/1.71 (define @t71 () (forall @t17 (not (and @t70 (not (tptp.are_equipotent @t15 @t2)) @t69)))) % 1.52/1.71 (define @t72 () (tptp.powerset @t15)) % 1.52/1.71 (define @t73 () (forall (@list @t15 @t27) (=> (and @t16 (tptp.subset @t27 @t15)) @t31))) % 1.52/1.71 (define @t74 () (tptp.set_intersection2 @t2 @t15)) % 1.52/1.71 (define @t75 () (tptp.subset @t1 @t15)) % 1.52/1.71 (define @t76 () (tptp.element @t1 @t2)) % 1.52/1.71 (define @t77 () (or @t23 @t5)) % 1.52/1.71 (define @t78 () (forall @t6 (=> @t76 @t77))) % 1.52/1.71 (define @t79 () (tptp.in @t2 @t15)) % 1.52/1.71 (define @t80 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 1.52/1.71 (define @t81 () (tptp.set_difference @t1 tptp.empty_set)) % 1.52/1.71 (define @t82 () (forall @t21 (= @t81 @t1))) % 1.52/1.71 (define @t83 () (and @t35 @t16)) % 1.52/1.71 (define @t84 () (exists @t17 @t83)) % 1.52/1.71 (define @t85 () (and @t84 @t41)) % 1.52/1.71 (define @t86 () (not @t85)) % 1.52/1.71 (define @t87 () (forall @t17 (not @t83))) % 1.52/1.71 (define @t88 () (not @t41)) % 1.52/1.71 (define @t89 () (and @t88 @t87)) % 1.52/1.71 (define @t90 () (not @t89)) % 1.52/1.71 (define @t91 () (and @t90 @t86)) % 1.52/1.71 (define @t92 () (forall @t6 @t91)) % 1.52/1.71 (define @t93 () (tptp.subset_complement @t1 @t15)) % 1.52/1.71 (define @t94 () (tptp.disjoint @t2 @t15)) % 1.52/1.71 (define @t95 () (tptp.element @t15 @t22)) % 1.52/1.71 (define @t96 () (= @t2 tptp.empty_set)) % 1.52/1.71 (define @t97 () (not @t96)) % 1.52/1.71 (define @t98 () (and @t97 (= @t46 tptp.empty_set))) % 1.52/1.71 (define @t99 () (not @t98)) % 1.52/1.71 (define @t100 () (=> @t53 @t99)) % 1.52/1.71 (define @t101 () (forall @t6 @t100)) % 1.52/1.71 (define @t102 () (not @t101)) % 1.52/1.71 (define @t103 () (tptp.element @t2 @t72)) % 1.52/1.71 (define @t104 () (tptp.in @t15 @t12)) % 1.52/1.71 (define @t105 () (forall @t6 (not (and @t5 @t23)))) % 1.52/1.71 (define @t106 () (= @t41 (= @t37 @t1))) % 1.52/1.71 (define @t107 () (forall @t6 @t106)) % 1.52/1.71 (define @t108 () (= @t18 (tptp.unordered_pair @t2 @t15))) % 1.52/1.71 (define @t109 () (@var "BOUND_VARIABLE_8340" $$unsorted)) % 1.52/1.71 (define @t110 () (@var "BOUND_VARIABLE_8354" $$unsorted)) % 1.52/1.71 (define @t111 () (not (tptp.in @t110 @t109))) % 1.52/1.71 (define @t112 () (@var "BOUND_VARIABLE_8338" $$unsorted)) % 1.52/1.71 (define @t113 () (not (tptp.in @t110 @t112))) % 1.52/1.71 (define @t114 () (not (tptp.disjoint @t112 @t109))) % 1.52/1.71 (define @t115 () (or @t114 @t113 @t111)) % 1.52/1.71 (define @t116 () (or @t113 @t111)) % 1.52/1.71 (define @t117 () (or @t116 @t114)) % 1.52/1.71 (define @t118 () (@list @t112 @t109 @t110)) % 1.52/1.71 (define @t119 () (forall @t118 @t117)) % 1.52/1.71 (define @t120 () (@list @t110)) % 1.52/1.71 (define @t121 () (forall @t120 @t117)) % 1.52/1.71 (define @t122 () (@list @t112 @t109)) % 1.52/1.71 (define @t123 () (forall @t120 @t116)) % 1.52/1.71 (define @t124 () (@list @t15)) % 1.52/1.71 (define @t125 () (or @t123 @t114)) % 1.52/1.71 (define @t126 () (forall @t122 (or (forall @t17 (or (not (tptp.in @t15 @t112)) (not (tptp.in @t15 @t109)))) @t114))) % 1.52/1.71 (define @t127 () (@var "BOUND_VARIABLE_8325" $$unsorted)) % 1.52/1.71 (define @t128 () (@var "BOUND_VARIABLE_8323" $$unsorted)) % 1.52/1.71 (define @t129 () (forall (@list @t128 @t127) (or (tptp.disjoint @t128 @t127) (not (forall @t17 (or (not (tptp.in @t15 @t128)) (not (tptp.in @t15 @t127)))))))) % 1.52/1.71 (define @t130 () (forall @t17 (or (not @t35) @t69))) % 1.52/1.71 (define @t131 () (or @t130 @t88)) % 1.52/1.71 (define @t132 () (forall @t6 @t131)) % 1.52/1.71 (define @t133 () (@list @t1 @t2)) % 1.52/1.71 (define @t134 () (not @t130)) % 1.52/1.71 (define @t135 () (or @t41 @t134)) % 1.52/1.71 (define @t136 () (forall @t6 @t135)) % 1.52/1.71 (define @t137 () (and @t136 @t132)) % 1.52/1.71 (define @t138 () (and (not (and @t88 @t130)) (not (and @t134 @t41)))) % 1.52/1.71 (define @t139 () (not @t87)) % 1.52/1.71 (define @t140 () (@var "BOUND_VARIABLE_8062" $$unsorted)) % 1.52/1.71 (define @t141 () (tptp.in @t27 @t140)) % 1.52/1.71 (define @t142 () (not @t44)) % 1.52/1.71 (define @t143 () (or @t142 (= @t141 @t42))) % 1.52/1.71 (define @t144 () (forall @t29 @t143)) % 1.52/1.71 (define @t145 () (= (= @t140 @t46) @t144)) % 1.52/1.71 (define @t146 () (not (tptp.element @t140 @t49))) % 1.52/1.71 (define @t147 () (not @t53)) % 1.52/1.71 (define @t148 () (or @t147 @t146 @t145)) % 1.52/1.71 (define @t149 () (or @t146 @t145)) % 1.52/1.71 (define @t150 () (or @t147 @t149)) % 1.52/1.71 (define @t151 () (@list @t1 @t2 @t140)) % 1.52/1.71 (define @t152 () (forall @t151 @t150)) % 1.52/1.71 (define @t153 () (@list @t140)) % 1.52/1.71 (define @t154 () (forall @t153 @t150)) % 1.52/1.71 (define @t155 () (forall @t153 @t149)) % 1.52/1.71 (define @t156 () (or @t147 @t155)) % 1.52/1.71 (define @t157 () (= @t47 (forall @t29 (or @t142 @t43)))) % 1.52/1.71 (define @t158 () (forall @t17 (or (not @t50) @t157))) % 1.52/1.71 (define @t159 () (= tptp.empty_set @t46)) % 1.52/1.71 (define @t160 () (not @t159)) % 1.52/1.71 (define @t161 () (or @t147 @t96 @t160)) % 1.52/1.71 (define @t162 () (forall @t6 @t161)) % 1.52/1.71 (define @t163 () (@quantifiers_skolemize @t162 1)) % 1.52/1.71 (define @t164 () (@quantifiers_skolemize @t162 0)) % 1.52/1.71 (define @t165 () (tptp.complements_of_subsets @t164 @t163)) % 1.52/1.71 (define @t166 () (tptp.subset_complement @t164 @t27)) % 1.52/1.71 (define @t167 () (tptp.in @t166 @t163)) % 1.52/1.71 (define @t168 () (tptp.powerset @t164)) % 1.52/1.71 (define @t169 () (not (tptp.element @t27 @t168))) % 1.52/1.71 (define @t170 () (forall @t29 (or @t169 (= @t167 (tptp.in @t27 @t165))))) % 1.52/1.71 (define @t171 () (= (= @t165 @t165) @t170)) % 1.52/1.71 (define @t172 () (tptp.powerset @t168)) % 1.52/1.71 (define @t173 () (tptp.element @t165 @t172)) % 1.52/1.71 (define @t174 () (not @t173)) % 1.52/1.71 (define @t175 () (tptp.element @t163 @t172)) % 1.52/1.71 (define @t176 () (not @t175)) % 1.52/1.71 (define @t177 () (or @t176 @t174 @t171)) % 1.52/1.71 (define @t178 () (forall @t151 (or @t147 @t146 (= (= @t46 @t140) (forall @t29 (or @t142 (= @t42 @t141))))))) % 1.52/1.71 (define @t179 () (or @t176 @t174 @t170)) % 1.52/1.71 (define @t180 () (@list false)) % 1.52/1.71 (define @t181 () (@list @t178)) % 1.52/1.71 (define @t182 () (@list @t164 @t163)) % 1.52/1.71 (define @t183 () (not (and @t97 @t159))) % 1.52/1.71 (define @t184 () (= tptp.empty_set @t165)) % 1.52/1.71 (define @t185 () (not @t184)) % 1.52/1.71 (define @t186 () (= tptp.empty_set @t163)) % 1.52/1.71 (define @t187 () (or @t176 @t186 @t185)) % 1.52/1.71 (define @t188 () (not @t187)) % 1.52/1.71 (define @t189 () (not @t162)) % 1.52/1.71 (define @t190 () (or @t176 (= @t163 tptp.empty_set) @t185)) % 1.52/1.71 (define @t191 () (not @t190)) % 1.52/1.71 (define @t192 () (@list true)) % 1.52/1.71 (define @t193 () (@list @t187)) % 1.52/1.71 (define @t194 () (or @t176 @t173)) % 1.52/1.71 (define @t195 () (@list false false)) % 1.52/1.71 (define @t196 () (@list false false false)) % 1.52/1.71 (define @t197 () (tptp.in @t27 @t163)) % 1.52/1.71 (define @t198 () (forall @t29 (or @t169 (= @t167 @t197)))) % 1.52/1.71 (define @t199 () (@quantifiers_skolemize @t198 0)) % 1.52/1.71 (define @t200 () (@list @t199)) % 1.52/1.71 (define @t201 () (= @t163 @t165)) % 1.52/1.71 (define @t202 () (= @t165 @t163)) % 1.52/1.71 (define @t203 () (= @t202 @t198)) % 1.52/1.71 (define @t204 () (or @t176 @t176 @t203)) % 1.52/1.71 (define @t205 () (= @t198 @t201)) % 1.52/1.71 (define @t206 () (or @t176 @t176 @t205)) % 1.52/1.71 (define @t207 () (not @t198)) % 1.52/1.71 (define @t208 () (@list true false)) % 1.52/1.71 (define @t209 () (tptp.element @t199 @t168)) % 1.52/1.71 (define @t210 () (tptp.in @t199 @t163)) % 1.52/1.71 (define @t211 () (tptp.subset_complement @t164 @t199)) % 1.52/1.71 (define @t212 () (tptp.in @t211 @t163)) % 1.52/1.71 (define @t213 () (= @t212 @t210)) % 1.52/1.71 (define @t214 () (not @t209)) % 1.52/1.71 (define @t215 () (or @t214 @t213)) % 1.52/1.71 (define @t216 () (@list @t215)) % 1.52/1.71 (define @t217 () (tptp.in @t199 @t165)) % 1.52/1.71 (define @t218 () (= @t212 @t217)) % 1.52/1.71 (define @t219 () (or @t214 @t218)) % 1.52/1.71 (define @t220 () (tptp.in @t166 @t165)) % 1.52/1.71 (define @t221 () (or @t169 (= @t220 @t197))) % 1.52/1.71 (define @t222 () (forall @t29 @t221)) % 1.52/1.71 (define @t223 () (tptp.complements_of_subsets @t164 @t165)) % 1.52/1.71 (define @t224 () (= (= @t223 @t163) @t222)) % 1.52/1.71 (define @t225 () (or @t174 @t176 @t224)) % 1.52/1.71 (define @t226 () (forall @t29 (or @t169 (= @t197 @t220)))) % 1.52/1.71 (define @t227 () (= @t163 @t223)) % 1.52/1.71 (define @t228 () (= @t227 @t226)) % 1.52/1.71 (define @t229 () (or @t174 @t176 @t228)) % 1.52/1.71 (define @t230 () (= @t2 @t59)) % 1.52/1.71 (define @t231 () (or @t176 @t227)) % 1.52/1.71 (define @t232 () (tptp.in @t211 @t165)) % 1.52/1.71 (define @t233 () (= @t210 @t232)) % 1.52/1.71 (define @t234 () (or @t214 @t233)) % 1.52/1.71 (define @t235 () (tptp.empty @t165)) % 1.52/1.71 (define @t236 () (not @t235)) % 1.52/1.71 (define @t237 () (not @t232)) % 1.52/1.71 (define @t238 () (or @t237 @t236)) % 1.52/1.71 (define @t239 () (not @t210)) % 1.52/1.71 (define @t240 () (= @t168 (tptp.set_difference @t168 @t165))) % 1.52/1.71 (define @t241 () (tptp.disjoint @t168 @t165)) % 1.52/1.71 (define @t242 () (= @t241 @t240)) % 1.52/1.71 (define @t243 () (not @t76)) % 1.52/1.71 (define @t244 () (tptp.in @t199 @t168)) % 1.52/1.71 (define @t245 () (tptp.empty @t168)) % 1.52/1.71 (define @t246 () (or @t214 @t245 @t244)) % 1.52/1.71 (define @t247 () (not @t217)) % 1.52/1.71 (define @t248 () (not @t244)) % 1.52/1.71 (define @t249 () (not @t241)) % 1.52/1.71 (define @t250 () (or @t249 @t248 @t247)) % 1.52/1.71 (define @t251 () (not @t250)) % 1.52/1.71 (define @t252 () (forall @t118 @t115)) % 1.52/1.71 (assume @p1 (forall @t6 (=> @t5 @t4))) % 1.52/1.71 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 1.52/1.71 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 1.52/1.71 (assume @p4 (forall @t6 (= @t11 @t10))) % 1.52/1.71 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 1.52/1.71 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 1.52/1.71 (assume @p7 (forall @t6 (= (= @t2 @t18) (forall @t17 (= @t16 (= @t15 @t1)))))) % 1.52/1.71 (assume @p8 (forall @t21 (= @t20 (forall @t19 @t4)))) % 1.52/1.71 (assume @p9 (forall @t6 (= (= @t2 @t22) (forall @t17 (= @t16 (tptp.subset @t15 @t1)))))) % 1.52/1.71 (assume @p10 (forall @t6 (and (=> @t26 (= @t24 @t3)) (=> @t25 (= @t24 @t23))))) % 1.52/1.71 (assume @p11 (forall @t30 (= (= @t15 @t9) (forall @t29 (= @t28 (or (= @t27 @t1) (= @t27 @t2))))))) % 1.52/1.71 (assume @p12 (forall @t30 (= (= @t15 @t11) (forall @t29 (= @t28 (or @t32 @t31)))))) % 1.52/1.71 (assume @p13 (forall @t30 (= (= @t15 (tptp.cartesian_product2 @t1 @t2)) (forall @t29 (= @t28 (exists (@list @t34 @t33) (and (tptp.in @t34 @t1) (tptp.in @t33 @t2) (= @t27 (tptp.ordered_pair @t34 @t33))))))))) % 1.52/1.71 (assume @p14 (forall @t6 (= @t13 @t36))) % 1.52/1.71 (assume @p15 (forall @t30 (= (= @t15 @t12) (forall @t29 (= @t28 (and @t32 @t31)))))) % 1.52/1.71 (assume @p16 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t17 (= @t16 (exists @t29 (and (tptp.in @t15 @t27) @t32))))))) % 1.52/1.71 (assume @p17 (forall @t30 (= (= @t15 @t37) (forall @t29 (= @t28 (and @t32 (not @t31))))))) % 1.52/1.71 (assume @p18 (forall @t6 (=> @t39 (= @t38 @t37)))) % 1.52/1.71 (assume @p19 (forall @t6 (= @t40 (tptp.unordered_pair @t9 @t18)))) % 1.52/1.71 (assume @p20 (forall @t6 (= @t41 (= @t12 tptp.empty_set)))) % 1.52/1.71 (assume @p21 @t55) % 1.52/1.71 (assume @p22 (forall @t6 (= @t8 (and @t13 @t56)))) % 1.52/1.71 (assume @p23 true) % 1.52/1.71 (assume @p24 (forall @t6 (=> @t39 (tptp.element @t38 @t22)))) % 1.52/1.71 (assume @p25 @t58) % 1.52/1.71 (assume @p26 (forall @t21 (exists @t19 @t24))) % 1.52/1.71 (assume @p27 (forall @t21 (not (tptp.empty @t22)))) % 1.52/1.71 (assume @p28 (tptp.empty tptp.empty_set)) % 1.52/1.71 (assume @p29 (forall @t6 (not (tptp.empty @t40)))) % 1.52/1.71 (assume @p30 (forall @t6 (=> @t26 (not (tptp.empty @t11))))) % 1.52/1.71 (assume @p31 (forall @t6 (=> @t26 (not (tptp.empty @t10))))) % 1.52/1.71 (assume @p32 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 1.52/1.71 (assume @p33 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 1.52/1.71 (assume @p34 (forall @t6 (=> @t39 (= (tptp.subset_complement @t1 @t38) @t2)))) % 1.52/1.71 (assume @p35 @t61) % 1.52/1.71 (assume @p36 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 1.52/1.71 (assume @p37 (forall @t21 (not (= @t18 tptp.empty_set)))) % 1.52/1.71 (assume @p38 (forall @t6 (=> @t5 (= (tptp.set_union2 @t18 @t2) @t2)))) % 1.52/1.71 (assume @p39 (forall @t6 (not (and @t62 @t5)))) % 1.52/1.71 (assume @p40 (forall @t6 (=> (not @t5) @t62))) % 1.52/1.71 (assume @p41 (forall @t6 (= (tptp.subset @t18 @t2) @t5))) % 1.52/1.71 (assume @p42 (forall @t6 (= (= @t37 tptp.empty_set) @t13))) % 1.52/1.71 (assume @p43 (forall @t6 (=> @t39 (forall @t17 (=> @t16 @t35))))) % 1.52/1.71 (assume @p44 (forall @t30 (=> @t13 (or @t35 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15))))))) % 1.52/1.71 (assume @p45 (forall @t6 (= (tptp.subset @t1 @t63) (or @t20 (= @t1 @t63))))) % 1.52/1.71 (assume @p46 (forall @t6 (=> @t5 (tptp.subset @t1 (tptp.union @t2))))) % 1.52/1.71 (assume @p47 (forall @t65 (= (tptp.in @t40 (tptp.cartesian_product2 @t15 @t27)) (and @t64 (tptp.in @t2 @t27))))) % 1.52/1.71 (assume @p48 (forall @t6 (=> @t36 @t66))) % 1.52/1.71 (assume @p49 (forall @t21 (=> @t26 (exists @t19 (and @t39 (not @t23)))))) % 1.52/1.71 (assume @p50 (exists @t21 @t25)) % 1.52/1.71 (assume @p51 (forall @t21 (exists @t19 (and @t39 @t23)))) % 1.52/1.71 (assume @p52 (exists @t21 @t26)) % 1.52/1.71 (assume @p53 (forall @t6 (tptp.subset @t1 @t1))) % 1.52/1.71 (assume @p54 (forall @t6 (=> @t41 (tptp.disjoint @t2 @t1)))) % 1.52/1.71 (assume @p55 (forall @t65 (not (and (= @t9 (tptp.unordered_pair @t15 @t27)) (not @t67) (not (= @t1 @t27)))))) % 1.52/1.71 (assume @p56 (forall @t30 (=> @t13 (and (tptp.subset @t68 (tptp.cartesian_product2 @t2 @t15)) (tptp.subset (tptp.cartesian_product2 @t15 @t1) (tptp.cartesian_product2 @t15 @t2)))))) % 1.52/1.71 (assume @p57 (forall @t65 (=> (and @t13 (tptp.subset @t15 @t27)) (tptp.subset @t68 (tptp.cartesian_product2 @t2 @t27))))) % 1.52/1.71 (assume @p58 (forall @t6 (=> @t13 (= @t11 @t2)))) % 1.52/1.71 (assume @p59 (forall @t21 (exists @t19 (and @t5 @t73 (forall @t17 (=> @t16 (tptp.in @t72 @t2))) @t71)))) % 1.52/1.71 (assume @p60 (forall @t6 (tptp.subset @t12 @t1))) % 1.52/1.71 (assume @p61 (forall @t30 (=> (and @t13 @t75) (tptp.subset @t1 @t74)))) % 1.52/1.71 (assume @p62 (forall @t21 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 1.52/1.71 (assume @p63 (forall @t6 (=> @t5 @t76))) % 1.52/1.71 (assume @p64 (forall @t30 (=> (and @t13 (tptp.subset @t2 @t15)) @t75))) % 1.52/1.71 (assume @p65 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 1.52/1.71 (assume @p66 (forall @t30 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t74)))) % 1.52/1.71 (assume @p67 (forall @t6 (=> @t13 (= @t12 @t1)))) % 1.52/1.71 (assume @p68 (forall @t21 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.52/1.71 (assume @p69 @t78) % 1.52/1.71 (assume @p70 (forall @t6 (=> (forall @t17 (= @t35 @t16)) @t14))) % 1.52/1.71 (assume @p71 (forall @t21 (tptp.subset tptp.empty_set @t1))) % 1.52/1.71 (assume @p72 (forall @t30 (=> @t13 (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))))) % 1.52/1.71 (assume @p73 (forall @t65 (=> (= @t40 (tptp.ordered_pair @t15 @t27)) (and @t67 (= @t2 @t27))))) % 1.52/1.71 (assume @p74 (forall @t6 (tptp.subset @t37 @t1))) % 1.52/1.71 (assume @p75 (forall @t30 (= (tptp.subset @t9 @t15) (and @t64 @t79)))) % 1.52/1.71 (assume @p76 (forall @t6 (= @t80 @t11))) % 1.52/1.71 (assume @p77 @t82) % 1.52/1.71 (assume @p78 (forall @t6 (= @t66 @t13))) % 1.52/1.71 (assume @p79 @t92) % 1.52/1.71 (assume @p80 (forall @t21 (=> (tptp.subset @t1 tptp.empty_set) @t20))) % 1.52/1.71 (assume @p81 (forall @t6 (= (tptp.set_difference @t11 @t2) @t37))) % 1.52/1.71 (assume @p82 (forall @t6 (=> @t39 (forall @t17 (=> @t95 (= @t94 (tptp.subset @t2 @t93))))))) % 1.52/1.71 (assume @p83 (forall @t6 (=> @t13 (= @t2 @t80)))) % 1.52/1.71 (assume @p84 @t102) % 1.52/1.71 (assume @p85 (forall @t6 (= (tptp.set_difference @t1 @t37) @t12))) % 1.52/1.71 (assume @p86 (forall @t21 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 1.52/1.71 (assume @p87 (forall @t30 (=> (and @t5 @t103) (tptp.element @t1 @t15)))) % 1.52/1.71 (assume @p88 (forall @t6 (and (not (and @t88 (forall @t17 (not @t104)))) (not (and (exists @t17 @t104) @t41))))) % 1.52/1.71 (assume @p89 (forall @t21 (=> (not @t20) (forall @t19 (=> @t39 (forall @t17 (=> (tptp.element @t15 @t1) (=> @t69 (tptp.in @t15 @t38))))))))) % 1.52/1.71 (assume @p90 (forall @t30 (=> @t95 (not (and (tptp.in @t2 @t93) @t79))))) % 1.52/1.71 (assume @p91 (forall @t30 (not (and @t5 @t103 (tptp.empty @t15))))) % 1.52/1.71 (assume @p92 (forall @t6 (not (and @t13 @t7)))) % 1.52/1.71 (assume @p93 (forall @t30 (=> (and @t13 @t94) (tptp.disjoint @t1 @t15)))) % 1.52/1.71 (assume @p94 (forall @t6 (= (= (tptp.set_difference @t1 @t63) @t1) @t4))) % 1.52/1.71 (assume @p95 (forall @t21 (= (tptp.unordered_pair @t1 @t1) @t18))) % 1.52/1.71 (assume @p96 (forall @t21 (=> @t25 @t20))) % 1.52/1.71 (assume @p97 (forall @t6 (=> (tptp.subset @t18 @t63) @t14))) % 1.52/1.71 (assume @p98 @t105) % 1.52/1.71 (assume @p99 (forall @t6 (tptp.subset @t1 @t11))) % 1.52/1.71 (assume @p100 @t107) % 1.52/1.71 (assume @p101 (forall @t6 (not (and @t25 @t56 @t23)))) % 1.52/1.72 (assume @p102 (forall @t30 (=> (and @t13 @t70) (tptp.subset (tptp.set_union2 @t1 @t15) @t2)))) % 1.52/1.72 (assume @p103 (forall @t30 (=> @t108 @t14))) % 1.52/1.72 (assume @p104 (forall @t21 (= (tptp.union @t22) @t1))) % 1.52/1.72 (assume @p105 (forall @t21 (exists @t19 (and @t5 @t73 (forall @t17 (not (and @t16 (forall @t29 (not (and @t31 (forall (@list @t34) (=> (tptp.subset @t34 @t15) (tptp.in @t34 @t27))))))))) @t71)))) % 1.52/1.72 (assume @p106 (forall @t30 (=> @t108 (= @t2 @t15)))) % 1.52/1.72 (step @p107 :rule aci_norm :args ((= @t117 @t115))) % 1.52/1.72 (step @p108 :rule cong :premises (@p107) :args (@t119)) % 1.52/1.72 (step @p109 :rule quant-merge-prenex :args ((= (forall @t122 @t121) @t119))) % 1.52/1.72 (step @p110 :rule refl :args (@t114)) % 1.52/1.72 (step @p111 :rule alpha_equiv :args (@t123 (@list @t110) @t124)) % 1.52/1.72 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t125)) % 1.52/1.72 (step @p113 :rule quant-miniscope-or :args ((= @t121 @t125))) % 1.52/1.72 (step @p114 :rule trans :premises (@p113 @p112)) % 1.52/1.72 (step @p115 :rule symm :premises (@p114)) % 1.52/1.72 (step @p116 :rule cong :premises (@p115) :args (@t126)) % 1.52/1.72 (step @p117 :rule trans :premises (@p116 @p109)) % 1.52/1.72 (step @p118 :rule trans :premises (@p117 @p108)) % 1.52/1.72 (step @p119 :rule refl :args (@t129)) % 1.52/1.72 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((and @t129 @t126))) % 1.52/1.72 (step @p121 :rule alpha_equiv :args (@t132 @t133 (@list @t112 @t109))) % 1.52/1.72 (step @p122 :rule alpha_equiv :args (@t136 @t133 (@list @t128 @t127))) % 1.52/1.72 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t137)) % 1.52/1.72 (step @p124 :rule quant-miniscope-and :args ((= (forall @t6 (and @t135 @t131)) @t137))) % 1.52/1.72 (step @p125 :rule trans :premises (@p124 @p123)) % 1.52/1.72 (step @p126 :rule trans :premises (@p125 @p120)) % 1.52/1.72 (step @p127 :rule refl :args (@t88)) % 1.52/1.72 (step @p128 :rule bool-double-not-elim :args (@t130)) % 1.52/1.72 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t134) @t88))) % 1.52/1.72 (step @p130 :rule bool-and-de-morgan :args (@t134 @t41 true)) % 1.52/1.72 (step @p131 :rule trans :premises (@p130 @p129)) % 1.52/1.72 (step @p132 :rule refl :args (@t134)) % 1.52/1.72 (step @p133 :rule bool-double-not-elim :args (@t41)) % 1.52/1.72 (step @p134 :rule nary_cong :premises (@p133 @p132) :args ((or (not @t88) @t134))) % 1.52/1.72 (step @p135 :rule bool-and-de-morgan :args (@t88 @t130 true)) % 1.52/1.72 (step @p136 :rule trans :premises (@p135 @p134)) % 1.52/1.72 (step @p137 :rule nary_cong :premises (@p136 @p131) :args (@t138)) % 1.52/1.72 (step @p138 :rule cong :premises (@p137) :args ((forall @t6 @t138))) % 1.52/1.72 (step @p139 :rule trans :premises (@p138 @p126)) % 1.52/1.72 (step @p140 :rule refl :args (@t41)) % 1.52/1.72 (step @p141 :rule bool-and-de-morgan :args (@t35 @t16 true)) % 1.52/1.72 (step @p142 :rule cong :premises (@p141) :args (@t87)) % 1.52/1.72 (step @p143 :rule cong :premises (@p142) :args (@t139)) % 1.52/1.72 (step @p144 :rule exists-elim :args ((= @t84 @t139))) % 1.52/1.72 (step @p145 :rule trans :premises (@p144 @p143)) % 1.52/1.72 (step @p146 :rule nary_cong :premises (@p145 @p140) :args (@t85)) % 1.52/1.72 (step @p147 :rule cong :premises (@p146) :args (@t86)) % 1.52/1.72 (step @p148 :rule refl :args (@t88)) % 1.52/1.72 (step @p149 :rule nary_cong :premises (@p148 @p142) :args (@t89)) % 1.52/1.72 (step @p150 :rule cong :premises (@p149) :args (@t90)) % 1.52/1.72 (step @p151 :rule nary_cong :premises (@p150 @p147) :args (@t91)) % 1.52/1.72 (step @p152 :rule cong :premises (@p151) :args (@t92)) % 1.52/1.72 (step @p153 :rule trans :premises (@p152 @p139)) % 1.52/1.72 (step @p154 :rule eq_resolve :premises (@p79 @p153)) % 1.52/1.72 (step @p155 :rule and_elim :premises (@p154) :args (1)) % 1.52/1.72 (step @p156 :rule eq-symm :args (@t141 @t42)) % 1.52/1.72 (step @p157 :rule refl :args (@t142)) % 1.52/1.72 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t143)) % 1.52/1.72 (step @p159 :rule cong :premises (@p158) :args (@t144)) % 1.52/1.72 (step @p160 :rule eq-symm :args (@t140 @t46)) % 1.52/1.72 (step @p161 :rule cong :premises (@p160 @p159) :args (@t145)) % 1.52/1.72 (step @p162 :rule refl :args (@t146)) % 1.52/1.72 (step @p163 :rule refl :args (@t147)) % 1.52/1.72 (step @p164 :rule nary_cong :premises (@p163 @p162 @p161) :args (@t148)) % 1.52/1.72 (step @p165 :rule aci_norm :args ((= @t150 @t148))) % 1.52/1.72 (step @p166 :rule trans :premises (@p165 @p164)) % 1.52/1.72 (step @p167 :rule cong :premises (@p166) :args (@t152)) % 1.52/1.72 (step @p168 :rule quant-merge-prenex :args ((= (forall @t6 @t154) @t152))) % 1.52/1.72 (step @p169 :rule alpha_equiv :args (@t155 (@list @t140) @t124)) % 1.52/1.72 (step @p170 :rule refl :args (@t147)) % 1.52/1.72 (step @p171 :rule nary_cong :premises (@p170 @p169) :args (@t156)) % 1.52/1.72 (step @p172 :rule quant-miniscope-or :args ((= @t154 @t156))) % 1.52/1.72 (step @p173 :rule trans :premises (@p172 @p171)) % 1.52/1.72 (step @p174 :rule symm :premises (@p173)) % 1.52/1.72 (step @p175 :rule cong :premises (@p174) :args ((forall @t6 (or @t147 @t158)))) % 1.52/1.72 (step @p176 :rule trans :premises (@p175 @p168)) % 1.52/1.72 (step @p177 :rule trans :premises (@p176 @p167)) % 1.52/1.72 (step @p178 :rule bool-impl-elim :args (@t53 @t158)) % 1.52/1.72 (step @p179 :rule cong :premises (@p178) :args ((forall @t6 (=> @t53 @t158)))) % 1.52/1.72 (step @p180 :rule trans :premises (@p179 @p177)) % 1.52/1.72 (step @p181 :rule bool-impl-elim :args (@t50 @t157)) % 1.52/1.72 (step @p182 :rule cong :premises (@p181) :args ((forall @t17 (=> @t50 @t157)))) % 1.52/1.72 (step @p183 :rule bool-impl-elim :args (@t44 @t43)) % 1.52/1.72 (step @p184 :rule cong :premises (@p183) :args (@t45)) % 1.52/1.72 (step @p185 :rule refl :args (@t47)) % 1.52/1.72 (step @p186 :rule cong :premises (@p185 @p184) :args (@t48)) % 1.52/1.72 (step @p187 :rule refl :args (@t50)) % 1.52/1.72 (step @p188 :rule cong :premises (@p187 @p186) :args (@t51)) % 1.52/1.72 (step @p189 :rule cong :premises (@p188) :args (@t52)) % 1.52/1.72 (step @p190 :rule trans :premises (@p189 @p182)) % 1.52/1.72 (step @p191 :rule refl :args (@t53)) % 1.52/1.72 (step @p192 :rule cong :premises (@p191 @p190) :args (@t54)) % 1.52/1.72 (step @p193 :rule cong :premises (@p192) :args (@t55)) % 1.52/1.72 (step @p194 :rule trans :premises (@p193 @p180)) % 1.52/1.72 (step @p195 :rule eq_resolve :premises (@p21 @p194)) % 1.52/1.72 (step @p196 :rule bool-eq-true :args (@t170)) % 1.52/1.72 (step @p197 :rule eq-symm :args (true @t170)) % 1.52/1.72 (step @p198 :rule trans :premises (@p197 @p196)) % 1.52/1.72 (step @p199 :rule refl :args (@t170)) % 1.52/1.72 (step @p200 :rule eq-refl :args (@t165)) % 1.52/1.72 (step @p201 :rule cong :premises (@p200 @p199) :args (@t171)) % 1.52/1.72 (step @p202 :rule trans :premises (@p201 @p198)) % 1.52/1.72 (step @p203 :rule refl :args (@t174)) % 1.52/1.72 (step @p204 :rule refl :args (@t176)) % 1.52/1.72 (step @p205 :rule nary_cong :premises (@p204 @p203 @p202) :args (@t177)) % 1.52/1.72 (step @p206 :rule refl :args (@t178)) % 1.52/1.72 (step @p207 :rule cong :premises (@p206 @p205) :args ((=> @t178 @t177))) % 1.52/1.72 (assume-push @p415 @t178) % 1.52/1.72 (step @p209 :rule instantiate :premises (@p195) :args ((@list @t164 @t163 @t165))) % 1.52/1.72 (step-pop @p416 :rule scope :premises (@p209)) % 1.52/1.72 (step @p210 :rule process_scope :premises (@p416) :args (@t177)) % 1.52/1.72 (step @p212 :rule eq_resolve :premises (@p210 @p207)) % 1.52/1.72 (step @p213 :rule implies_elim :premises (@p212)) % 1.52/1.72 (step @p214 :rule chain_m_resolution :premises (@p213 @p195) :args (@t179 @t180 @t181)) % 1.52/1.72 (step @p215 :rule bool-impl-elim :args (@t53 @t57)) % 1.52/1.72 (step @p216 :rule cong :premises (@p215) :args (@t58)) % 1.52/1.72 (step @p217 :rule eq_resolve :premises (@p25 @p216)) % 1.52/1.72 (step @p218 :rule instantiate :premises (@p217) :args (@t182)) % 1.52/1.72 (step @p219 :rule aci_norm :args ((= (or @t147 (or @t96 @t160)) @t161))) % 1.52/1.72 (step @p220 :rule refl :args (@t160)) % 1.52/1.72 (step @p221 :rule bool-double-not-elim :args (@t96)) % 1.52/1.72 (step @p222 :rule nary_cong :premises (@p221 @p220) :args ((or (not @t97) @t160))) % 1.52/1.72 (step @p223 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:args (@t102)) % 1.52/1.72 (step @p238 :rule eq_resolve :premises (@p84 @p237)) % 1.52/1.72 (step @p239 :rule refl :args (@t188)) % 1.52/1.72 (step @p240 :rule bool-double-not-elim :args (@t162)) % 1.52/1.72 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or (not @t189) @t188))) % 1.52/1.72 (step @p242 :rule refl :args (@t185)) % 1.52/1.72 (step @p243 :rule eq-symm :args (@t163 tptp.empty_set)) % 1.52/1.72 (step @p244 :rule nary_cong :premises (@p204 @p243 @p242) :args (@t190)) % 1.52/1.72 (step @p245 :rule cong :premises (@p244) :args (@t191)) % 1.52/1.72 (step @p246 :rule refl :args (@t189)) % 1.52/1.72 (step @p247 :rule cong :premises (@p246 @p245) :args ((=> @t189 @t191))) % 1.52/1.72 (assume-push @p417 @t189) % 1.52/1.72 (step @p249 :rule skolemize :premises (@p238)) % 1.52/1.72 (step-pop @p418 :rule scope :premises (@p249)) % 1.52/1.72 (step @p250 :rule process_scope :premises (@p418) :args (@t191)) % 1.52/1.72 (step @p252 :rule eq_resolve :premises (@p250 @p247)) % 1.52/1.72 (step @p253 :rule implies_elim :premises (@p252)) % 1.52/1.72 (step @p254 :rule eq_resolve :premises (@p253 @p241)) % 1.52/1.72 (step @p255 :rule chain_m_resolution :premises (@p254 @p238) :args (@t188 @t192 (@list @t162))) % 1.52/1.72 (step @p256 :rule bool-double-not-elim :args (@t175)) % 1.52/1.72 (step @p257 :rule refl :args (@t187)) % 1.52/1.72 (step @p258 :rule nary_cong :premises (@p257 @p256) :args ((or @t187 (not @t176)))) % 1.52/1.72 (step @p259 :rule cnf_or_neg :args (@t187 0)) % 1.52/1.72 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 1.52/1.72 (step @p261 :rule reordering :premises (@p260) :args ((or @t175 @t187))) % 1.52/1.72 (step @p262 :rule chain_m_resolution :premises (@p261 @p255) :args (@t175 @t192 @t193)) % 1.52/1.72 (step @p263 :rule cnf_or_pos :args (@t194)) % 1.52/1.72 (step @p264 :rule reordering :premises (@p263) :args ((or @t176 @t173 (not @t194)))) % 1.52/1.72 (step @p265 :rule chain_m_resolution :premises (@p264 @p262 @p218) :args (@t173 @t195 (@list @t175 @t194))) % 1.52/1.72 (step @p266 :rule cnf_or_pos :args (@t179)) % 1.52/1.72 (step @p267 :rule reordering :premises (@p266) :args ((or @t176 @t174 @t170 (not @t179)))) % 1.52/1.72 (step @p268 :rule chain_m_resolution :premises (@p267 @p262 @p265 @p214) :args (@t170 @t196 (@list @t175 @t173 @t179))) % 1.52/1.72 (step @p269 :rule instantiate :premises (@p268) :args (@t200)) % 1.52/1.72 (step @p270 :rule eq-symm :args (@t201 @t198)) % 1.52/1.72 (step @p271 :rule refl :args (@t198)) % 1.52/1.72 (step @p272 :rule eq-symm :args (@t165 @t163)) % 1.52/1.72 (step @p273 :rule cong :premises (@p272 @p271) :args (@t203)) % 1.52/1.72 (step @p274 :rule trans :premises (@p273 @p270)) % 1.52/1.72 (step @p275 :rule nary_cong :premises (@p204 @p204 @p274) :args (@t204)) % 1.52/1.72 (step @p276 :rule cong :premises (@p206 @p275) :args ((=> @t178 @t204))) % 1.52/1.72 (assume-push @p419 @t178) % 1.52/1.72 (step @p278 :rule instantiate :premises (@p195) :args ((@list @t164 @t163 @t163))) % 1.52/1.72 (step-pop @p420 :rule scope :premises (@p278)) % 1.52/1.72 (step @p279 :rule process_scope :premises (@p420) :args (@t204)) % 1.52/1.72 (step @p281 :rule eq_resolve :premises (@p279 @p276)) % 1.52/1.72 (step @p282 :rule implies_elim :premises (@p281)) % 1.52/1.72 (step @p283 :rule chain_m_resolution :premises (@p282 @p195) :args (@t206 @t180 @t181)) % 1.52/1.72 (step @p284 :rule cnf_or_pos :args (@t206)) % 1.52/1.72 (step @p285 :rule factoring :premises (@p284)) % 1.52/1.72 (step @p286 :rule reordering :premises (@p285) :args ((or @t176 @t205 (not @t206)))) % 1.52/1.72 (step @p287 :rule chain_m_resolution :premises (@p286 @p262 @p283) :args (@t205 @t195 (@list @t175 @t206))) % 1.52/1.72 (step @p288 :rule bool-eq-false :args (@t201)) % 1.52/1.72 (step @p289 :rule symm :premises (@p288)) % 1.52/1.72 (step @p290 :rule cong :premises (@p272) :args ((not @t202))) % 1.52/1.72 (step @p291 :rule bool-eq-false :args (@t202)) % 1.52/1.72 (step @p292 :rule trans :premises (@p291 @p290)) % 1.52/1.72 (step @p293 :rule trans :premises (@p292 @p289)) % 1.52/1.72 (step @p294 :rule cnf_or_neg :args (@t187 1)) % 1.52/1.72 (step @p295 :rule chain_m_resolution :premises (@p294 @p255) :args ((not @t186) @t192 @t193)) % 1.52/1.72 (step @p296 :rule false_intro :premises (@p295)) % 1.52/1.72 (step @p297 :rule refl :args (@t163)) % 1.52/1.72 (step @p298 :rule bool-double-not-elim :args (@t184)) % 1.52/1.72 (step @p299 :rule nary_cong :premises (@p257 @p298) :args ((or @t187 (not @t185)))) % 1.52/1.72 (step @p300 :rule cnf_or_neg :args (@t187 2)) % 1.52/1.72 (step @p301 :rule eq_resolve :premises (@p300 @p299)) % 1.52/1.72 (step @p302 :rule reordering :premises (@p301) :args ((or @t184 @t187))) % 1.52/1.72 (step @p303 :rule chain_m_resolution :premises (@p302 @p255) :args (@t184 @t192 @t193)) % 1.52/1.72 (step @p304 :rule symm :premises (@p303)) % 1.52/1.72 (step @p305 :rule cong :premises (@p304 @p297) :args (@t202)) % 1.52/1.72 (step @p306 :rule trans :premises (@p305 @p296)) % 1.52/1.72 (step @p307 :rule eq_resolve :premises (@p306 @p293)) % 1.52/1.72 (step @p308 :rule false_elim :premises (@p307)) % 1.52/1.72 (step @p309 :rule cnf_equiv_pos1 :args (@t205)) % 1.52/1.72 (step @p310 :rule reordering :premises (@p309) :args ((or @t201 @t207 (not @t205)))) % 1.52/1.72 (step @p311 :rule chain_m_resolution :premises (@p310 @p308 @p287) :args (@t207 @t208 (@list @t201 @t205))) % 1.52/1.72 (step @p312 :rule skolemize :premises (@p311)) % 1.52/1.72 (step @p313 :rule bool-double-not-elim :args (@t209)) % 1.52/1.72 (step @p314 :rule refl :args (@t215)) % 1.52/1.72 (step @p315 :rule nary_cong :premises (@p314 @p313) :args ((or @t215 (not @t214)))) % 1.52/1.72 (step @p316 :rule cnf_or_neg :args (@t215 0)) % 1.52/1.72 (step @p317 :rule eq_resolve :premises (@p316 @p315)) % 1.52/1.72 (step @p318 :rule reordering :premises (@p317) :args ((or @t209 @t215))) % 1.52/1.72 (step @p319 :rule chain_m_resolution :premises (@p318 @p312) :args (@t209 @t192 @t216)) % 1.52/1.72 (step @p320 :rule cnf_or_pos :args (@t219)) % 1.52/1.72 (step @p321 :rule reordering :premises (@p320) :args ((or @t214 @t218 (not @t219)))) % 1.52/1.72 (step @p322 :rule chain_m_resolution :premises (@p321 @p319 @p269) :args (@t218 @t195 (@list @t209 @t219))) % 1.52/1.72 (step @p323 :rule cnf_or_neg :args (@t215 1)) % 1.52/1.72 (step @p324 :rule chain_m_resolution :premises (@p323 @p312) :args ((not @t213) @t192 @t216)) % 1.52/1.72 (step @p325 :rule eq-symm :args (@t220 @t197)) % 1.52/1.72 (step @p326 :rule refl :args (@t169)) % 1.52/1.72 (step @p327 :rule nary_cong :premises (@p326 @p325) :args (@t221)) % 1.52/1.72 (step @p328 :rule cong :premises (@p327) :args (@t222)) % 1.52/1.72 (step @p329 :rule eq-symm :args (@t223 @t163)) % 1.52/1.72 (step @p330 :rule cong :premises (@p329 @p328) :args (@t224)) % 1.52/1.72 (step @p331 :rule nary_cong :premises (@p203 @p204 @p330) :args (@t225)) % 1.52/1.72 (step @p332 :rule cong :premises (@p206 @p331) :args ((=> @t178 @t225))) % 1.52/1.72 (assume-push @p421 @t178) % 1.52/1.72 (step @p334 :rule instantiate :premises (@p195) :args ((@list @t164 @t165 @t163))) % 1.52/1.72 (step-pop @p422 :rule scope :premises (@p334)) % 1.52/1.72 (step @p335 :rule process_scope :premises (@p422) :args (@t225)) % 1.52/1.72 (step @p337 :rule eq_resolve :premises (@p335 @p332)) % 1.52/1.72 (step @p338 :rule implies_elim :premises (@p337)) % 1.52/1.72 (step @p339 :rule chain_m_resolution :premises (@p338 @p195) :args (@t229 @t180 @t181)) % 1.52/1.72 (step @p340 :rule cnf_or_pos :args (@t229)) % 1.52/1.72 (step @p341 :rule reordering :premises (@p340) :args ((or @t176 @t174 @t228 (not @t229)))) % 1.52/1.72 (step @p342 :rule chain_m_resolution :premises (@p341 @p262 @p265 @p339) :args (@t228 @t196 (@list @t175 @t173 @t229))) % 1.52/1.72 (step @p343 :rule bool-impl-elim :args (@t53 @t230)) % 1.52/1.72 (step @p344 :rule cong :premises (@p343) :args ((forall @t6 (=> @t53 @t230)))) % 1.52/1.72 (step @p345 :rule eq-symm :args (@t59 @t2)) % 1.52/1.72 (step @p346 :rule cong :premises (@p191 @p345) :args (@t60)) % 1.52/1.72 (step @p347 :rule cong :premises (@p346) :args (@t61)) % 1.52/1.72 (step @p348 :rule trans :premises (@p347 @p344)) % 1.52/1.72 (step @p349 :rule eq_resolve :premises (@p35 @p348)) % 1.52/1.72 (step @p350 :rule instantiate :premises (@p349) :args (@t182)) % 1.52/1.72 (step @p351 :rule cnf_or_pos :args (@t231)) % 1.52/1.72 (step @p352 :rule reordering :premises (@p351) :args ((or @t176 @t227 (not @t231)))) % 1.52/1.72 (step @p353 :rule chain_m_resolution :premises (@p352 @p262 @p350) :args (@t227 @t195 (@list @t175 @t231))) % 1.52/1.72 (step @p354 :rule cnf_equiv_pos1 :args (@t228)) % 1.52/1.72 (step @p355 :rule reordering :premises (@p354) :args ((or (not @t227) @t226 (not @t228)))) % 1.52/1.72 (step @p356 :rule chain_m_resolution :premises (@p355 @p353 @p342) :args (@t226 @t195 (@list @t227 @t228))) % 1.52/1.72 (step @p357 :rule instantiate :premises (@p356) :args (@t200)) % 1.52/1.72 (step @p358 :rule cnf_or_pos :args (@t234)) % 1.52/1.72 (step @p359 :rule reordering :premises (@p358) :args ((or @t214 @t233 (not @t234)))) % 1.52/1.72 (step @p360 :rule chain_m_resolution :premises (@p359 @p319 @p357) :args (@t233 @t195 (@list @t209 @t234))) % 1.52/1.72 (step @p361 :rule bool-and-de-morgan :args (@t5 @t23 true)) % 1.52/1.72 (step @p362 :rule cong :premises (@p361) :args (@t105)) % 1.52/1.72 (step @p363 :rule eq_resolve :premises (@p98 @p362)) % 1.52/1.72 (step @p364 :rule instantiate :premises (@p363) :args ((@list @t211 @t165))) % 1.52/1.72 (step @p365 :rule true_intro :premises (@p28)) % 1.52/1.72 (step @p366 :rule cong :premises (@p304) :args (@t235)) % 1.52/1.72 (step @p367 :rule trans :premises (@p366 @p365)) % 1.52/1.72 (step @p368 :rule true_elim :premises (@p367)) % 1.52/1.72 (step @p369 :rule cnf_or_pos :args (@t238)) % 1.52/1.72 (step @p370 :rule reordering :premises (@p369) :args ((or @t237 @t236 (not @t238)))) % 1.52/1.72 (step @p371 :rule chain_m_resolution :premises (@p370 @p368 @p364) :args (@t237 @t195 (@list @t235 @t238))) % 1.52/1.72 (step @p372 :rule cnf_equiv_pos1 :args (@t233)) % 1.52/1.72 (step @p373 :rule reordering :premises (@p372) :args ((or @t239 @t232 (not @t233)))) % 1.52/1.72 (step @p374 :rule chain_m_resolution :premises (@p373 @p371 @p360) :args (@t239 @t208 (@list @t232 @t233))) % 1.52/1.72 (step @p375 :rule cnf_equiv_neg1 :args (@t213)) % 1.52/1.72 (step @p376 :rule reordering :premises (@p375) :args ((or @t212 @t210 @t213))) % 1.52/1.72 (step @p377 :rule chain_m_resolution :premises (@p376 @p374 @p324) :args (@t212 (@list true true) (@list @t210 @t213))) % 1.52/1.72 (step @p378 :rule cnf_equiv_pos1 :args (@t218)) % 1.52/1.72 (step @p379 :rule reordering :premises (@p378) :args ((or (not @t212) @t217 (not @t218)))) % 1.52/1.72 (step @p380 :rule chain_m_resolution :premises (@p379 @p377 @p322) :args (@t217 @t195 (@list @t212 @t218))) % 1.52/1.72 (step @p381 :rule eq-symm :args (@t37 @t1)) % 1.52/1.72 (step @p382 :rule cong :premises (@p140 @p381) :args (@t106)) % 1.52/1.72 (step @p383 :rule cong :premises (@p382) :args (@t107)) % 1.52/1.72 (step @p384 :rule eq_resolve :premises (@p100 @p383)) % 1.52/1.72 (step @p385 :rule instantiate :premises (@p384) :args ((@list @t168 @t165))) % 1.52/1.72 (step @p386 :rule refl :args (@t168)) % 1.52/1.72 (step @p387 :rule cong :premises (@p386 @p303) :args ((tptp.set_difference @t168 tptp.empty_set))) % 1.52/1.72 (step @p388 :rule eq-symm :args (@t81 @t1)) % 1.52/1.72 (step @p389 :rule cong :premises (@p388) :args (@t82)) % 1.52/1.72 (step @p390 :rule eq_resolve :premises (@p77 @p389)) % 1.52/1.72 (step @p391 :rule instantiate :premises (@p390) :args ((@list @t168))) % 1.52/1.72 (step @p392 :rule trans :premises (@p391 @p387)) % 1.52/1.72 (step @p393 :rule cnf_equiv_pos2 :args (@t242)) % 1.52/1.72 (step @p394 :rule reordering :premises (@p393) :args ((or @t241 (not @t240) (not @t242)))) % 1.52/1.72 (step @p395 :rule chain_m_resolution :premises (@p394 @p392 @p385) :args (@t241 @t195 (@list @t240 @t242))) % 1.52/1.72 (step @p396 :rule aci_norm :args ((= (or @t243 @t77) (or @t243 @t23 @t5)))) % 1.52/1.72 (step @p397 :rule bool-impl-elim :args (@t76 @t77)) % 1.52/1.72 (step @p398 :rule trans :premises (@p397 @p396)) % 1.52/1.72 (step @p399 :rule cong :premises (@p398) :args (@t78)) % 1.52/1.72 (step @p400 :rule eq_resolve :premises (@p69 @p399)) % 1.52/1.72 (step @p401 :rule instantiate :premises (@p400) :args ((@list @t199 @t168))) % 1.52/1.72 (step @p402 :rule instantiate :premises (@p27) :args ((@list @t164))) % 1.52/1.72 (step @p403 :rule cnf_or_pos :args (@t246)) % 1.52/1.72 (step @p404 :rule reordering :premises (@p403) :args ((or @t245 @t214 @t244 (not @t246)))) % 1.52/1.72 (step @p405 :rule chain_m_resolution :premises (@p404 @p402 @p319 @p401) :args (@t244 (@list true false false) (@list @t245 @t209 @t246))) % 1.52/1.72 (step @p406 :rule cnf_or_pos :args (@t250)) % 1.52/1.72 (step @p407 :rule reordering :premises (@p406) :args ((or @t248 @t249 @t247 @t251))) % 1.52/1.72 (step @p408 :rule chain_m_resolution :premises (@p407 @p405 @p395 @p380) :args (@t251 @t196 (@list @t244 @t241 @t217))) % 1.52/1.72 (assume-push @p423 @t252) % 1.52/1.72 (step @p410 :rule instantiate :premises (@p155) :args ((@list @t168 @t165 @t199))) % 1.52/1.72 (step-pop @p424 :rule scope :premises (@p410)) % 1.52/1.72 (step @p411 :rule process_scope :premises (@p424) :args (@t250)) % 1.52/1.72 (step @p413 :rule implies_elim :premises (@p411)) % 1.52/1.72 (step @p414 false :rule chain_m_resolution :premises (@p413 @p408 @p155) :args (false @t208 (@list @t250 @t252))) % 1.52/1.72 ) % 1.52/1.72 % SZS output end Proof % 1.52/1.72 % cvc5 exiting %------------------------------------------------------------------------------