%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU199+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:50:55 AM UTC 2026 % Result : Theorem 4.01s 4.23s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU199+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:36:46 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.52 %----Proving TF0_NAR, FOF, or CNF % 4.01/4.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 4.01/4.23 % SZS status Theorem % 4.01/4.23 % SZS output start Proof % 4.01/4.23 ( % 4.01/4.23 (declare-sort $$unsorted 0) % 4.01/4.23 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.empty_set $$unsorted) % 4.01/4.23 (declare-const tptp.empty (-> $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.relation (-> $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 4.01/4.23 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 4.01/4.23 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 4.01/4.23 (define @t1 () (@var "A" $$unsorted)) % 4.01/4.23 (define @t2 () (@var "B" $$unsorted)) % 4.01/4.23 (define @t3 () (tptp.in @t2 @t1)) % 4.01/4.23 (define @t4 () (not @t3)) % 4.01/4.23 (define @t5 () (tptp.in @t1 @t2)) % 4.01/4.23 (define @t6 () (@list @t1 @t2)) % 4.01/4.23 (define @t7 () (tptp.proper_subset @t2 @t1)) % 4.01/4.23 (define @t8 () (tptp.proper_subset @t1 @t2)) % 4.01/4.23 (define @t9 () (tptp.relation @t1)) % 4.01/4.23 (define @t10 () (tptp.empty @t1)) % 4.01/4.23 (define @t11 () (@list @t1)) % 4.01/4.23 (define @t12 () (tptp.unordered_pair @t1 @t2)) % 4.01/4.23 (define @t13 () (tptp.set_union2 @t2 @t1)) % 4.01/4.23 (define @t14 () (tptp.set_union2 @t1 @t2)) % 4.01/4.23 (define @t15 () (tptp.set_intersection2 @t1 @t2)) % 4.01/4.23 (define @t16 () (@var "D" $$unsorted)) % 4.01/4.23 (define @t17 () (@var "C" $$unsorted)) % 4.01/4.23 (define @t18 () (tptp.in @t17 @t1)) % 4.01/4.23 (define @t19 () (tptp.ordered_pair @t17 @t16)) % 4.01/4.23 (define @t20 () (tptp.in @t19 @t2)) % 4.01/4.23 (define @t21 () (@list @t17 @t16)) % 4.01/4.23 (define @t22 () (tptp.identity_relation @t1)) % 4.01/4.23 (define @t23 () (tptp.relation @t2)) % 4.01/4.23 (define @t24 () (tptp.subset @t1 @t2)) % 4.01/4.23 (define @t25 () (= @t1 @t2)) % 4.01/4.23 (define @t26 () (@var "E" $$unsorted)) % 4.01/4.23 (define @t27 () (tptp.ordered_pair @t16 @t26)) % 4.01/4.23 (define @t28 () (tptp.in @t16 @t2)) % 4.01/4.23 (define @t29 () (tptp.in @t27 @t17)) % 4.01/4.23 (define @t30 () (@list @t16 @t26)) % 4.01/4.23 (define @t31 () (tptp.relation_dom_restriction @t1 @t2)) % 4.01/4.23 (define @t32 () (tptp.relation @t17)) % 4.01/4.23 (define @t33 () (@list @t2 @t17)) % 4.01/4.23 (define @t34 () (tptp.in @t26 @t1)) % 4.01/4.23 (define @t35 () (and @t34 (tptp.in @t27 @t2))) % 4.01/4.23 (define @t36 () (tptp.relation_rng_restriction @t1 @t2)) % 4.01/4.23 (define @t37 () (= (= @t17 @t36) (forall @t30 (= @t29 @t35)))) % 4.01/4.23 (define @t38 () (@list @t17)) % 4.01/4.23 (define @t39 () (forall @t38 (=> @t32 @t37))) % 4.01/4.23 (define @t40 () (=> @t23 @t39)) % 4.01/4.23 (define @t41 () (forall @t6 @t40)) % 4.01/4.23 (define @t42 () (@list @t2)) % 4.01/4.23 (define @t43 () (= @t2 tptp.empty_set)) % 4.01/4.23 (define @t44 () (= @t2 (tptp.set_meet @t1))) % 4.01/4.23 (define @t45 () (= @t1 tptp.empty_set)) % 4.01/4.23 (define @t46 () (tptp.in @t17 @t16)) % 4.01/4.23 (define @t47 () (tptp.in @t16 @t1)) % 4.01/4.23 (define @t48 () (@list @t16)) % 4.01/4.23 (define @t49 () (tptp.in @t17 @t2)) % 4.01/4.23 (define @t50 () (not @t45)) % 4.01/4.23 (define @t51 () (tptp.singleton @t1)) % 4.01/4.23 (define @t52 () (tptp.powerset @t1)) % 4.01/4.23 (define @t53 () (tptp.in @t19 @t1)) % 4.01/4.23 (define @t54 () (tptp.empty @t2)) % 4.01/4.23 (define @t55 () (tptp.element @t2 @t1)) % 4.01/4.23 (define @t56 () (not @t10)) % 4.01/4.23 (define @t57 () (tptp.in @t16 @t17)) % 4.01/4.23 (define @t58 () (@list @t1 @t2 @t17)) % 4.01/4.23 (define @t59 () (@var "F" $$unsorted)) % 4.01/4.23 (define @t60 () (tptp.cartesian_product2 @t1 @t2)) % 4.01/4.23 (define @t61 () (forall @t21 (=> @t53 @t20))) % 4.01/4.23 (define @t62 () (= @t24 @t61)) % 4.01/4.23 (define @t63 () (=> @t23 @t62)) % 4.01/4.23 (define @t64 () (forall @t42 @t63)) % 4.01/4.23 (define @t65 () (=> @t9 @t64)) % 4.01/4.23 (define @t66 () (forall @t11 @t65)) % 4.01/4.23 (define @t67 () (forall @t38 (=> @t18 @t49))) % 4.01/4.23 (define @t68 () (tptp.relation_dom @t1)) % 4.01/4.23 (define @t69 () (tptp.cast_to_subset @t1)) % 4.01/4.23 (define @t70 () (tptp.set_difference @t1 @t2)) % 4.01/4.23 (define @t71 () (tptp.in (tptp.ordered_pair @t16 @t17) @t1)) % 4.01/4.23 (define @t72 () (tptp.relation_rng @t1)) % 4.01/4.23 (define @t73 () (tptp.subset_complement @t1 @t2)) % 4.01/4.23 (define @t74 () (tptp.element @t2 @t52)) % 4.01/4.23 (define @t75 () (tptp.ordered_pair @t1 @t2)) % 4.01/4.23 (define @t76 () (tptp.relation_inverse @t1)) % 4.01/4.23 (define @t77 () (tptp.disjoint @t1 @t2)) % 4.01/4.23 (define @t78 () (tptp.relation_composition @t1 @t2)) % 4.01/4.23 (define @t79 () (tptp.complements_of_subsets @t1 @t2)) % 4.01/4.23 (define @t80 () (tptp.powerset @t52)) % 4.01/4.23 (define @t81 () (tptp.element @t2 @t80)) % 4.01/4.23 (define @t82 () (not @t25)) % 4.01/4.23 (define @t83 () (tptp.relation @t78)) % 4.01/4.23 (define @t84 () (and @t9 @t23)) % 4.01/4.23 (define @t85 () (tptp.union_of_subsets @t1 @t2)) % 4.01/4.23 (define @t86 () (tptp.meet_of_subsets @t1 @t2)) % 4.01/4.23 (define @t87 () (tptp.subset_difference @t1 @t2 @t17)) % 4.01/4.23 (define @t88 () (tptp.element @t17 @t52)) % 4.01/4.23 (define @t89 () (and @t74 @t88)) % 4.01/4.23 (define @t90 () (tptp.relation @t36)) % 4.01/4.23 (define @t91 () (forall @t6 (=> @t23 @t90))) % 4.01/4.23 (define @t92 () (tptp.relation_composition @t2 @t1)) % 4.01/4.23 (define @t93 () (and @t10 @t23)) % 4.01/4.23 (define @t94 () (tptp.empty tptp.empty_set)) % 4.01/4.23 (define @t95 () (not @t54)) % 4.01/4.23 (define @t96 () (tptp.empty @t68)) % 4.01/4.23 (define @t97 () (and @t56 @t9)) % 4.01/4.23 (define @t98 () (tptp.empty @t72)) % 4.01/4.23 (define @t99 () (tptp.disjoint @t51 @t2)) % 4.01/4.23 (define @t100 () (tptp.singleton @t2)) % 4.01/4.23 (define @t101 () (tptp.union @t2)) % 4.01/4.23 (define @t102 () (tptp.in @t1 @t17)) % 4.01/4.23 (define @t103 () (@list @t1 @t2 @t17 @t16)) % 4.01/4.23 (define @t104 () (tptp.element @t1 (tptp.powerset @t2))) % 4.01/4.23 (define @t105 () (tptp.set_difference @t2 @t17)) % 4.01/4.23 (define @t106 () (= @t1 @t17)) % 4.01/4.23 (define @t107 () (tptp.relation_rng @t17)) % 4.01/4.23 (define @t108 () (tptp.subset @t36 @t2)) % 4.01/4.23 (define @t109 () (forall @t6 (=> @t23 @t108))) % 4.01/4.23 (define @t110 () (not @t109)) % 4.01/4.23 (define @t111 () (tptp.cartesian_product2 @t1 @t17)) % 4.01/4.23 (define @t112 () (not @t49)) % 4.01/4.23 (define @t113 () (tptp.subset @t17 @t2)) % 4.01/4.23 (define @t114 () (forall @t38 (not (and @t113 (not (tptp.are_equipotent @t17 @t2)) @t112)))) % 4.01/4.23 (define @t115 () (tptp.powerset @t17)) % 4.01/4.23 (define @t116 () (forall @t21 (=> (and @t49 (tptp.subset @t16 @t17)) @t28))) % 4.01/4.23 (define @t117 () (tptp.set_intersection2 @t2 @t17)) % 4.01/4.23 (define @t118 () (tptp.subset @t1 @t17)) % 4.01/4.23 (define @t119 () (tptp.element @t1 @t2)) % 4.01/4.23 (define @t120 () (tptp.in @t1 (tptp.relation_dom @t17))) % 4.01/4.23 (define @t121 () (tptp.in @t75 @t17)) % 4.01/4.23 (define @t122 () (tptp.relation_rng @t2)) % 4.01/4.23 (define @t123 () (tptp.relation_dom @t2)) % 4.01/4.23 (define @t124 () (tptp.relation_field @t17)) % 4.01/4.23 (define @t125 () (tptp.in @t2 @t17)) % 4.01/4.23 (define @t126 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 4.01/4.23 (define @t127 () (and @t18 @t49)) % 4.01/4.23 (define @t128 () (not @t77)) % 4.01/4.23 (define @t129 () (tptp.subset_complement @t1 @t17)) % 4.01/4.23 (define @t130 () (tptp.disjoint @t2 @t17)) % 4.01/4.23 (define @t131 () (tptp.relation_dom @t78)) % 4.01/4.23 (define @t132 () (not @t43)) % 4.01/4.23 (define @t133 () (tptp.element @t2 @t115)) % 4.01/4.23 (define @t134 () (tptp.in @t17 @t15)) % 4.01/4.23 (define @t135 () (= @t72 tptp.empty_set)) % 4.01/4.23 (define @t136 () (= @t68 tptp.empty_set)) % 4.01/4.23 (define @t137 () (tptp.relation_dom_restriction @t2 @t1)) % 4.01/4.23 (define @t138 () (= @t51 (tptp.unordered_pair @t2 @t17))) % 4.01/4.23 (define @t139 () (@var "BOUND_VARIABLE_8589" $$unsorted)) % 4.01/4.23 (define @t140 () (not @t53)) % 4.01/4.23 (define @t141 () (= (tptp.subset @t1 @t139) (forall @t21 (or @t140 (tptp.in @t19 @t139))))) % 4.01/4.23 (define @t142 () (not (tptp.relation @t139))) % 4.01/4.23 (define @t143 () (not @t9)) % 4.01/4.23 (define @t144 () (or @t142 @t141)) % 4.01/4.23 (define @t145 () (or @t143 @t144)) % 4.01/4.23 (define @t146 () (forall (@list @t1 @t139) @t145)) % 4.01/4.23 (define @t147 () (@list @t139)) % 4.01/4.23 (define @t148 () (forall @t147 @t145)) % 4.01/4.23 (define @t149 () (forall @t147 @t144)) % 4.01/4.23 (define @t150 () (or @t143 @t149)) % 4.01/4.23 (define @t151 () (= @t24 (forall @t21 (or @t140 @t20)))) % 4.01/4.23 (define @t152 () (not @t23)) % 4.01/4.23 (define @t153 () (forall @t42 (or @t152 @t151))) % 4.01/4.23 (define @t154 () (forall @t6 (or @t152 @t108))) % 4.01/4.23 (define @t155 () (@quantifiers_skolemize @t154 1)) % 4.01/4.23 (define @t156 () (@quantifiers_skolemize @t154 0)) % 4.01/4.23 (define @t157 () (tptp.relation_rng_restriction @t156 @t155)) % 4.01/4.23 (define @t158 () (tptp.relation @t155)) % 4.01/4.23 (define @t159 () (tptp.subset @t157 @t155)) % 4.01/4.23 (define @t160 () (not @t158)) % 4.01/4.23 (define @t161 () (or @t160 @t159)) % 4.01/4.23 (define @t162 () (@list true)) % 4.01/4.23 (define @t163 () (@list @t161)) % 4.01/4.23 (define @t164 () (tptp.relation @t157)) % 4.01/4.23 (define @t165 () (or @t160 @t164)) % 4.01/4.23 (define @t166 () (forall @t21 (or (not (tptp.in @t19 @t157)) (tptp.in @t19 @t155)))) % 4.01/4.23 (define @t167 () (= @t159 @t166)) % 4.01/4.23 (define @t168 () (not @t164)) % 4.01/4.23 (define @t169 () (or @t168 @t160 @t167)) % 4.01/4.23 (define @t170 () (@list false false false)) % 4.01/4.23 (define @t171 () (not @t166)) % 4.01/4.23 (define @t172 () (@quantifiers_skolemize @t166 1)) % 4.01/4.23 (define @t173 () (@quantifiers_skolemize @t166 0)) % 4.01/4.23 (define @t174 () (tptp.ordered_pair @t173 @t172)) % 4.01/4.23 (define @t175 () (tptp.in @t174 @t157)) % 4.01/4.23 (define @t176 () (tptp.in @t174 @t155)) % 4.01/4.23 (define @t177 () (not @t175)) % 4.01/4.23 (define @t178 () (or @t177 @t176)) % 4.01/4.23 (define @t179 () (@list @t178)) % 4.01/4.23 (define @t180 () (and (tptp.in @t172 @t156) @t176)) % 4.01/4.23 (define @t181 () (not @t180)) % 4.01/4.23 (define @t182 () (@var "BOUND_VARIABLE_8388" $$unsorted)) % 4.01/4.23 (define @t183 () (tptp.in @t27 @t182)) % 4.01/4.23 (define @t184 () (forall @t30 (= @t183 @t35))) % 4.01/4.23 (define @t185 () (= (= @t182 @t36) @t184)) % 4.01/4.23 (define @t186 () (not (tptp.relation @t182))) % 4.01/4.23 (define @t187 () (or @t152 @t186 @t185)) % 4.01/4.23 (define @t188 () (or @t186 @t185)) % 4.01/4.23 (define @t189 () (or @t152 @t188)) % 4.01/4.23 (define @t190 () (@list @t1 @t2 @t182)) % 4.01/4.23 (define @t191 () (forall @t190 @t189)) % 4.01/4.23 (define @t192 () (@list @t182)) % 4.01/4.23 (define @t193 () (forall @t192 @t189)) % 4.01/4.23 (define @t194 () (forall @t192 @t188)) % 4.01/4.23 (define @t195 () (or @t152 @t194)) % 4.01/4.23 (define @t196 () (forall @t38 (or (not @t32) @t37))) % 4.01/4.23 (define @t197 () (forall @t30 (= (and (tptp.in @t26 @t156) (tptp.in @t27 @t155)) (tptp.in @t27 @t157)))) % 4.01/4.23 (define @t198 () (= (= @t157 @t157) @t197)) % 4.01/4.23 (define @t199 () (or @t160 @t168 @t198)) % 4.01/4.23 (define @t200 () (forall @t190 (or @t152 @t186 (= (= @t36 @t182) (forall @t30 (= @t35 @t183)))))) % 4.01/4.23 (define @t201 () (or @t160 @t168 @t197)) % 4.01/4.23 (define @t202 () (@list false)) % 4.01/4.23 (define @t203 () (= @t180 @t175)) % 4.01/4.23 (define @t204 () (= @t175 @t180)) % 4.01/4.23 (assume @p1 (forall @t6 (=> @t5 @t4))) % 4.01/4.23 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 4.01/4.23 (assume @p3 (forall @t11 (=> @t10 @t9))) % 4.01/4.23 (assume @p4 (forall @t6 (= @t12 (tptp.unordered_pair @t2 @t1)))) % 4.01/4.23 (assume @p5 (forall @t6 (= @t14 @t13))) % 4.01/4.23 (assume @p6 (forall @t6 (= @t15 (tptp.set_intersection2 @t2 @t1)))) % 4.01/4.23 (assume @p7 (forall @t6 (=> @t23 (= (= @t2 @t22) (forall @t21 (= @t20 (and @t18 (= @t17 @t16)))))))) % 4.01/4.23 (assume @p8 (forall @t6 (= @t25 (and @t24 (tptp.subset @t2 @t1))))) % 4.01/4.23 (assume @p9 (forall @t11 (=> @t9 (forall @t33 (=> @t32 (= (= @t17 @t31) (forall @t30 (= @t29 (and @t28 (tptp.in @t27 @t1)))))))))) % 4.01/4.23 (assume @p10 @t41) % 4.01/4.23 (assume @p11 (forall @t11 (= @t9 (forall @t42 (not (and @t3 (forall @t21 (not (= @t2 @t19))))))))) % 4.01/4.23 (assume @p12 (forall @t6 (and (=> @t50 (= @t44 (forall @t38 (= @t49 (forall @t48 (=> @t47 @t46)))))) (=> @t45 (= @t44 @t43))))) % 4.01/4.23 (assume @p13 (forall @t6 (= (= @t2 @t51) (forall @t38 (= @t49 (= @t17 @t1)))))) % 4.01/4.23 (assume @p14 (forall @t11 (= @t45 (forall @t42 @t4)))) % 4.01/4.23 (assume @p15 (forall @t6 (= (= @t2 @t52) (forall @t38 (= @t49 (tptp.subset @t17 @t1)))))) % 4.01/4.23 (assume @p16 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= @t25 (forall @t21 (= @t53 @t20)))))))) % 4.01/4.23 (assume @p17 (forall @t6 (and (=> @t56 (= @t55 @t3)) (=> @t10 (= @t55 @t54))))) % 4.01/4.23 (assume @p18 (forall @t58 (= (= @t17 @t12) (forall @t48 (= @t57 (or (= @t16 @t1) (= @t16 @t2))))))) % 4.01/4.23 (assume @p19 (forall @t58 (= (= @t17 @t14) (forall @t48 (= @t57 (or @t47 @t28)))))) % 4.01/4.23 (assume @p20 (forall @t58 (= (= @t17 @t60) (forall @t48 (= @t57 (exists (@list @t26 @t59) (and @t34 (tptp.in @t59 @t2) (= @t16 (tptp.ordered_pair @t26 @t59))))))))) % 4.01/4.23 (assume @p21 @t66) % 4.01/4.23 (assume @p22 (forall @t6 (= @t24 @t67))) % 4.01/4.23 (assume @p23 (forall @t58 (= (= @t17 @t15) (forall @t48 (= @t57 (and @t47 @t28)))))) % 4.01/4.23 (assume @p24 (forall @t11 (=> @t9 (forall @t42 (= (= @t2 @t68) (forall @t38 (= @t49 (exists @t48 @t53)))))))) % 4.01/4.23 (assume @p25 (forall @t11 (= @t69 @t1))) % 4.01/4.23 (assume @p26 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t38 (= @t49 (exists @t48 (and @t46 @t47))))))) % 4.01/4.23 (assume @p27 (forall @t58 (= (= @t17 @t70) (forall @t48 (= @t57 (and @t47 (not @t28))))))) % 4.01/4.23 (assume @p28 (forall @t11 (=> @t9 (forall @t42 (= (= @t2 @t72) (forall @t38 (= @t49 (exists @t48 @t71)))))))) % 4.01/4.23 (assume @p29 (forall @t6 (=> @t74 (= @t73 @t70)))) % 4.01/4.23 (assume @p30 (forall @t6 (= @t75 (tptp.unordered_pair @t12 @t51)))) % 4.01/4.23 (assume @p31 (forall @t11 (=> @t9 (= (tptp.relation_field @t1) (tptp.set_union2 @t68 @t72))))) % 4.01/4.23 (assume @p32 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= (= @t2 @t76) (forall @t21 (= @t20 @t71)))))))) % 4.01/4.23 (assume @p33 (forall @t6 (= @t77 (= @t15 tptp.empty_set)))) % 4.01/4.23 (assume @p34 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (forall @t38 (=> @t32 (= (= @t17 @t78) (forall @t30 (= @t29 (exists (@list @t59) (and (tptp.in (tptp.ordered_pair @t16 @t59) @t1) (tptp.in (tptp.ordered_pair @t59 @t26) @t2))))))))))))) % 4.01/4.23 (assume @p35 (forall @t6 (=> @t81 (forall @t38 (=> (tptp.element @t17 @t80) (= (= @t17 @t79) (forall @t48 (=> (tptp.element @t16 @t52) (= @t57 (tptp.in (tptp.subset_complement @t1 @t16) @t2)))))))))) % 4.01/4.23 (assume @p36 (forall @t6 (= @t8 (and @t24 @t82)))) % 4.01/4.23 (assume @p37 true) % 4.01/4.23 (assume @p38 (forall @t11 (tptp.element @t69 @t52))) % 4.01/4.23 (assume @p39 (forall @t6 (=> @t74 (tptp.element @t73 @t52)))) % 4.01/4.23 (assume @p40 (forall @t11 (=> @t9 (tptp.relation @t76)))) % 4.01/4.23 (assume @p41 (forall @t6 (=> @t84 @t83))) % 4.01/4.23 (assume @p42 (forall @t6 (=> @t81 (tptp.element @t85 @t52)))) % 4.01/4.23 (assume @p43 (forall @t11 (tptp.relation @t22))) % 4.01/4.23 (assume @p44 (forall @t6 (=> @t81 (tptp.element @t86 @t52)))) % 4.01/4.23 (assume @p45 (forall @t58 (=> @t89 (tptp.element @t87 @t52)))) % 4.01/4.23 (assume @p46 (forall @t6 (=> @t9 (tptp.relation @t31)))) % 4.01/4.23 (assume @p47 (forall @t6 (=> @t81 (tptp.element @t79 @t80)))) % 4.01/4.23 (assume @p48 @t91) % 4.01/4.23 (assume @p49 (forall @t11 (exists @t42 @t55))) % 4.01/4.23 (assume @p50 (forall @t6 (=> @t93 (and (tptp.empty @t92) (tptp.relation @t92))))) % 4.01/4.23 (assume @p51 (forall @t6 (=> @t84 (tptp.relation @t15)))) % 4.01/4.23 (assume @p52 (forall @t11 (not (tptp.empty @t52)))) % 4.01/4.23 (assume @p53 @t94) % 4.01/4.23 (assume @p54 (forall @t6 (not (tptp.empty @t75)))) % 4.01/4.23 (assume @p55 (forall @t6 (=> @t84 (tptp.relation @t14)))) % 4.01/4.23 (assume @p56 (forall @t11 (not (tptp.empty @t51)))) % 4.01/4.23 (assume @p57 (forall @t6 (=> @t56 (not (tptp.empty @t14))))) % 4.01/4.23 (assume @p58 (forall @t6 (not (tptp.empty @t12)))) % 4.01/4.23 (assume @p59 (forall @t6 (=> @t56 (not (tptp.empty @t13))))) % 4.01/4.23 (assume @p60 (and @t94 (tptp.relation tptp.empty_set))) % 4.01/4.23 (assume @p61 (forall @t6 (=> (and @t56 @t95) (not (tptp.empty @t60))))) % 4.01/4.23 (assume @p62 (forall @t11 (=> @t97 (not @t96)))) % 4.01/4.23 (assume @p63 (forall @t11 (=> @t97 (not @t98)))) % 4.01/4.23 (assume @p64 (forall @t11 (=> @t10 (and @t96 (tptp.relation @t68))))) % 4.01/4.23 (assume @p65 (forall @t11 (=> @t10 (and @t98 (tptp.relation @t72))))) % 4.01/4.23 (assume @p66 (forall @t6 (=> @t93 (and (tptp.empty @t78) @t83)))) % 4.01/4.23 (assume @p67 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 4.01/4.23 (assume @p68 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 4.01/4.23 (assume @p69 (forall @t6 (=> @t74 (= (tptp.subset_complement @t1 @t73) @t2)))) % 4.01/4.23 (assume @p70 (forall @t11 (=> @t9 (= (tptp.relation_inverse @t76) @t1)))) % 4.01/4.23 (assume @p71 (forall @t6 (=> @t81 (= (tptp.complements_of_subsets @t1 @t79) @t2)))) % 4.01/4.23 (assume @p72 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 4.01/4.23 (assume @p73 (forall @t11 (not (= @t51 tptp.empty_set)))) % 4.01/4.23 (assume @p74 (forall @t6 (=> @t5 (= (tptp.set_union2 @t51 @t2) @t2)))) % 4.01/4.23 (assume @p75 (forall @t6 (not (and @t99 @t5)))) % 4.01/4.23 (assume @p76 (forall @t6 (=> (not @t5) @t99))) % 4.01/4.23 (assume @p77 (forall @t6 (= (tptp.subset @t51 @t2) @t5))) % 4.01/4.23 (assume @p78 (forall @t6 (= (= @t70 tptp.empty_set) @t24))) % 4.01/4.23 (assume @p79 (forall @t6 (=> @t74 (forall @t38 (=> @t49 @t18))))) % 4.01/4.23 (assume @p80 (forall @t58 (=> @t24 (or @t18 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t17))))))) % 4.01/4.23 (assume @p81 (forall @t6 (= (tptp.subset @t1 @t100) (or @t45 (= @t1 @t100))))) % 4.01/4.23 (assume @p82 (forall @t6 (=> @t5 (tptp.subset @t1 @t101)))) % 4.01/4.23 (assume @p83 (forall @t103 (= (tptp.in @t75 (tptp.cartesian_product2 @t17 @t16)) (and @t102 (tptp.in @t2 @t16))))) % 4.01/4.23 (assume @p84 (forall @t6 (=> @t67 @t104))) % 4.01/4.23 (assume @p85 (exists @t11 (and @t10 @t9))) % 4.01/4.23 (assume @p86 (forall @t11 (=> @t56 (exists @t42 (and @t74 @t95))))) % 4.01/4.23 (assume @p87 (exists @t11 @t10)) % 4.01/4.23 (assume @p88 (exists @t11 @t97)) % 4.01/4.23 (assume @p89 (forall @t11 (exists @t42 (and @t74 @t54)))) % 4.01/4.23 (assume @p90 (exists @t11 @t56)) % 4.01/4.23 (assume @p91 (forall @t6 (=> @t81 (= @t85 @t101)))) % 4.01/4.23 (assume @p92 (forall @t6 (=> @t81 (= @t86 (tptp.set_meet @t2))))) % 4.01/4.23 (assume @p93 (forall @t58 (=> @t89 (= @t87 @t105)))) % 4.01/4.23 (assume @p94 (forall @t6 (tptp.subset @t1 @t1))) % 4.01/4.23 (assume @p95 (forall @t6 (=> @t77 (tptp.disjoint @t2 @t1)))) % 4.01/4.23 (assume @p96 (forall @t103 (not (and (= @t12 (tptp.unordered_pair @t17 @t16)) (not @t106) (not (= @t1 @t16)))))) % 4.01/4.23 (assume @p97 (forall @t58 (=> @t32 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t17))) (and @t5 (tptp.in @t1 @t107)))))) % 4.01/4.23 (assume @p98 (forall @t6 (=> @t23 (tptp.subset (tptp.relation_rng @t36) @t1)))) % 4.01/4.23 (assume @p99 @t110) % 4.01/4.23 (assume @p100 (forall @t58 (=> @t24 (and (tptp.subset @t111 (tptp.cartesian_product2 @t2 @t17)) (tptp.subset (tptp.cartesian_product2 @t17 @t1) (tptp.cartesian_product2 @t17 @t2)))))) % 4.01/4.23 (assume @p101 (forall @t103 (=> (and @t24 (tptp.subset @t17 @t16)) (tptp.subset @t111 (tptp.cartesian_product2 @t2 @t16))))) % 4.01/4.23 (assume @p102 (forall @t6 (=> @t24 (= @t14 @t2)))) % 4.01/4.23 (assume @p103 (forall @t11 (exists @t42 (and @t5 @t116 (forall @t38 (=> @t49 (tptp.in @t115 @t2))) @t114)))) % 4.01/4.23 (assume @p104 (forall @t6 (tptp.subset @t15 @t1))) % 4.01/4.23 (assume @p105 (forall @t58 (=> (and @t24 @t118) (tptp.subset @t1 @t117)))) % 4.01/4.23 (assume @p106 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 4.01/4.23 (assume @p107 (forall @t6 (=> @t5 @t119))) % 4.01/4.23 (assume @p108 (forall @t58 (=> (and @t24 (tptp.subset @t2 @t17)) @t118))) % 4.01/4.23 (assume @p109 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 4.01/4.23 (assume @p110 (forall @t58 (=> @t32 (=> @t121 (and @t120 (tptp.in @t2 @t107)))))) % 4.01/4.23 (assume @p111 (forall @t11 (=> @t9 (tptp.subset @t1 (tptp.cartesian_product2 @t68 @t72))))) % 4.01/4.23 (assume @p112 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> @t24 (and (tptp.subset @t68 @t123) (tptp.subset @t72 @t122)))))))) % 4.01/4.23 (assume @p113 (forall @t58 (=> @t24 (tptp.subset (tptp.set_intersection2 @t1 @t17) @t117)))) % 4.01/4.23 (assume @p114 (forall @t6 (=> @t24 (= @t15 @t1)))) % 4.01/4.23 (assume @p115 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 4.01/4.23 (assume @p116 (forall @t6 (=> @t119 (or @t54 @t5)))) % 4.01/4.23 (assume @p117 (forall @t6 (=> (forall @t38 (= @t18 @t49)) @t25))) % 4.01/4.23 (assume @p118 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 4.01/4.23 (assume @p119 (forall @t58 (=> @t32 (=> @t121 (and (tptp.in @t1 @t124) (tptp.in @t2 @t124)))))) % 4.01/4.23 (assume @p120 (forall @t58 (=> @t24 (tptp.subset (tptp.set_difference @t1 @t17) @t105)))) % 4.01/4.23 (assume @p121 (forall @t103 (=> (= @t75 @t19) (and @t106 (= @t2 @t16))))) % 4.01/4.23 (assume @p122 (forall @t6 (tptp.subset @t70 @t1))) % 4.01/4.23 (assume @p123 (forall @t11 (=> @t9 (and (= @t72 (tptp.relation_dom @t76)) (= @t68 (tptp.relation_rng @t76)))))) % 4.01/4.23 (assume @p124 (forall @t58 (= (tptp.subset @t12 @t17) (and @t102 @t125)))) % 4.01/4.23 (assume @p125 (forall @t6 (= @t126 @t14))) % 4.01/4.23 (assume @p126 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 4.01/4.23 (assume @p127 (forall @t6 (= @t104 @t24))) % 4.01/4.23 (assume @p128 (forall @t6 (and (not (and @t128 (forall @t38 (not @t127)))) (not (and (exists @t38 @t127) @t77))))) % 4.01/4.23 (assume @p129 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t45))) % 4.01/4.23 (assume @p130 (forall @t6 (= (tptp.set_difference @t14 @t2) @t70))) % 4.01/4.23 (assume @p131 (forall @t6 (=> @t74 (forall @t38 (=> @t88 (= @t130 (tptp.subset @t2 @t129))))))) % 4.01/4.23 (assume @p132 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (tptp.subset @t131 @t68)))))) % 4.01/4.23 (assume @p133 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (tptp.subset (tptp.relation_rng @t78) @t122)))))) % 4.01/4.23 (assume @p134 (forall @t6 (=> @t24 (= @t2 @t126)))) % 4.01/4.23 (assume @p135 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> (tptp.subset @t72 @t123) (= @t131 @t68))))))) % 4.01/4.23 (assume @p136 (forall @t6 (=> @t81 (not (and @t132 (= @t79 tptp.empty_set)))))) % 4.01/4.23 (assume @p137 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> (tptp.subset @t68 @t122) (= (tptp.relation_rng @t92) @t72))))))) % 4.01/4.23 (assume @p138 (forall @t6 (=> @t81 (=> @t132 (= (tptp.subset_difference @t1 @t69 @t85) (tptp.meet_of_subsets @t1 @t79)))))) % 4.01/4.23 (assume @p139 (forall @t6 (=> @t81 (=> @t132 (= (tptp.union_of_subsets @t1 @t79) (tptp.subset_difference @t1 @t69 @t86)))))) % 4.01/4.23 (assume @p140 (forall @t6 (= (tptp.set_difference @t1 @t70) @t15))) % 4.01/4.23 (assume @p141 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 4.01/4.23 (assume @p142 (forall @t58 (=> (and @t5 @t133) (tptp.element @t1 @t17)))) % 4.01/4.23 (assume @p143 (forall @t6 (and (not (and @t128 (forall @t38 (not @t134)))) (not (and (exists @t38 @t134) @t77))))) % 4.01/4.23 (assume @p144 (forall @t11 (=> @t50 (forall @t42 (=> @t74 (forall @t38 (=> (tptp.element @t17 @t1) (=> @t112 (tptp.in @t17 @t73))))))))) % 4.01/4.23 (assume @p145 (forall @t58 (=> @t88 (not (and (tptp.in @t2 @t129) @t125))))) % 4.01/4.23 (assume @p146 (forall @t11 (=> @t9 (=> (forall @t33 (not (tptp.in (tptp.ordered_pair @t2 @t17) @t1))) @t45)))) % 4.01/4.23 (assume @p147 (forall @t58 (not (and @t5 @t133 (tptp.empty @t17))))) % 4.01/4.23 (assume @p148 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 4.01/4.23 (assume @p149 (forall @t6 (not (and @t24 @t7)))) % 4.01/4.23 (assume @p150 (forall @t58 (=> (and @t24 @t130) (tptp.disjoint @t1 @t17)))) % 4.01/4.23 (assume @p151 (forall @t11 (=> @t9 (=> (or @t136 @t135) @t45)))) % 4.01/4.23 (assume @p152 (forall @t11 (=> @t9 (= @t136 @t135)))) % 4.01/4.23 (assume @p153 (forall @t6 (= (= (tptp.set_difference @t1 @t100) @t1) @t4))) % 4.01/4.23 (assume @p154 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t51))) % 4.01/4.23 (assume @p155 (forall @t11 (=> @t10 @t45))) % 4.01/4.23 (assume @p156 (forall @t6 (=> (tptp.subset @t51 @t100) @t25))) % 4.01/4.23 (assume @p157 (forall @t11 (and (= (tptp.relation_dom @t22) @t1) (= (tptp.relation_rng @t22) @t1)))) % 4.01/4.23 (assume @p158 (forall @t103 (=> (tptp.relation @t16) (= (tptp.in @t75 (tptp.relation_composition (tptp.identity_relation @t17) @t16)) (and @t102 (tptp.in @t75 @t16)))))) % 4.01/4.23 (assume @p159 (forall @t6 (not (and @t5 @t54)))) % 4.01/4.23 (assume @p160 (forall @t6 (tptp.subset @t1 @t14))) % 4.01/4.23 (assume @p161 (forall @t6 (= @t77 (= @t70 @t1)))) % 4.01/4.23 (assume @p162 (forall @t58 (=> @t32 (= (tptp.in @t1 (tptp.relation_dom (tptp.relation_dom_restriction @t17 @t2))) (and @t5 @t120))))) % 4.01/4.23 (assume @p163 (forall @t6 (=> @t23 (tptp.subset @t137 @t2)))) % 4.01/4.23 (assume @p164 (forall @t6 (not (and @t10 @t82 @t54)))) % 4.01/4.23 (assume @p165 (forall @t58 (=> (and @t24 @t113) (tptp.subset (tptp.set_union2 @t1 @t17) @t2)))) % 4.01/4.23 (assume @p166 (forall @t58 (=> @t138 @t25))) % 4.01/4.23 (assume @p167 (forall @t6 (=> @t23 (= (tptp.relation_dom @t137) (tptp.set_intersection2 @t123 @t1))))) % 4.01/4.23 (assume @p168 (forall @t6 (=> @t23 (= @t137 (tptp.relation_composition @t22 @t2))))) % 4.01/4.23 (assume @p169 (forall @t6 (=> @t23 (tptp.subset (tptp.relation_rng @t137) @t122)))) % 4.01/4.23 (assume @p170 (forall @t11 (= (tptp.union @t52) @t1))) % 4.01/4.23 (assume @p171 (forall @t11 (exists @t42 (and @t5 @t116 (forall @t38 (not (and @t49 (forall @t48 (not (and @t28 (forall (@list @t26) (=> (tptp.subset @t26 @t17) (tptp.in @t26 @t16))))))))) @t114)))) % 4.01/4.23 (assume @p172 (forall @t58 (=> @t138 (= @t2 @t17)))) % 4.01/4.23 (step @p173 :rule aci_norm :args ((= @t145 (or @t143 @t142 @t141)))) % 4.01/4.23 (step @p174 :rule cong :premises (@p173) :args (@t146)) % 4.01/4.23 (step @p175 :rule quant-merge-prenex :args ((= (forall @t11 @t148) @t146))) % 4.01/4.23 (step @p176 :rule alpha_equiv :args (@t149 (@list @t139) (@list @t2))) % 4.01/4.23 (step @p177 :rule refl :args (@t143)) % 4.01/4.23 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t150)) % 4.01/4.23 (step @p179 :rule quant-miniscope-or :args ((= @t148 @t150))) % 4.01/4.23 (step @p180 :rule trans :premises (@p179 @p178)) % 4.01/4.23 (step @p181 :rule symm :premises (@p180)) % 4.01/4.23 (step @p182 :rule cong :premises (@p181) :args ((forall @t11 (or @t143 @t153)))) % 4.01/4.23 (step @p183 :rule trans :premises (@p182 @p175)) % 4.01/4.23 (step @p184 :rule trans :premises (@p183 @p174)) % 4.01/4.23 (step @p185 :rule bool-impl-elim :args (@t9 @t153)) % 4.01/4.23 (step @p186 :rule cong :premises (@p185) :args ((forall @t11 (=> @t9 @t153)))) % 4.01/4.23 (step @p187 :rule trans :premises (@p186 @p184)) % 4.01/4.23 (step @p188 :rule bool-impl-elim :args (@t23 @t151)) % 4.01/4.23 (step @p189 :rule cong :premises (@p188) :args ((forall @t42 (=> @t23 @t151)))) % 4.01/4.23 (step @p190 :rule bool-impl-elim :args (@t53 @t20)) % 4.01/4.23 (step @p191 :rule cong :premises (@p190) :args (@t61)) % 4.01/4.23 (step @p192 :rule refl :args (@t24)) % 4.01/4.23 (step @p193 :rule cong :premises (@p192 @p191) :args (@t62)) % 4.01/4.23 (step @p194 :rule refl :args (@t23)) % 4.01/4.23 (step @p195 :rule cong :premises (@p194 @p193) :args (@t63)) % 4.01/4.23 (step @p196 :rule cong :premises (@p195) :args (@t64)) % 4.01/4.23 (step @p197 :rule trans :premises (@p196 @p189)) % 4.01/4.23 (step @p198 :rule refl :args (@t9)) % 4.01/4.23 (step @p199 :rule cong :premises (@p198 @p197) :args (@t65)) % 4.01/4.23 (step @p200 :rule cong :premises (@p199) :args (@t66)) % 4.01/4.23 (step @p201 :rule trans :premises (@p200 @p187)) % 4.01/4.23 (step @p202 :rule eq_resolve :premises (@p21 @p201)) % 4.01/4.23 (step @p203 :rule instantiate :premises (@p202) :args ((@list @t157 @t155))) % 4.01/4.23 (step @p204 :rule bool-impl-elim :args (@t23 @t90)) % 4.01/4.23 (step @p205 :rule cong :premises (@p204) :args (@t91)) % 4.01/4.23 (step @p206 :rule eq_resolve :premises (@p48 @p205)) % 4.01/4.23 (step @p207 :rule instantiate :premises (@p206) :args ((@list @t156 @t155))) % 4.01/4.23 (step @p208 :rule bool-impl-elim :args (@t23 @t108)) % 4.01/4.23 (step @p209 :rule cong :premises (@p208) :args (@t109)) % 4.01/4.23 (step @p210 :rule cong :premises (@p209) :args (@t110)) % 4.01/4.23 (step @p211 :rule eq_resolve :premises (@p99 @p210)) % 4.01/4.23 (step @p212 :rule skolemize :premises (@p211)) % 4.01/4.23 (step @p213 :rule bool-double-not-elim :args (@t158)) % 4.01/4.23 (step @p214 :rule refl :args (@t161)) % 4.01/4.23 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t161 (not @t160)))) % 4.01/4.23 (step @p216 :rule cnf_or_neg :args (@t161 0)) % 4.01/4.23 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 4.01/4.23 (step @p218 :rule reordering :premises (@p217) :args ((or @t158 @t161))) % 4.01/4.23 (step @p219 :rule chain_m_resolution :premises (@p218 @p212) :args (@t158 @t162 @t163)) % 4.01/4.23 (step @p220 :rule cnf_or_pos :args (@t165)) % 4.01/4.23 (step @p221 :rule reordering :premises (@p220) :args ((or @t160 @t164 (not @t165)))) % 4.01/4.23 (step @p222 :rule chain_m_resolution :premises (@p221 @p219 @p207) :args (@t164 (@list false false) (@list @t158 @t165))) % 4.01/4.23 (step @p223 :rule cnf_or_pos :args (@t169)) % 4.01/4.23 (step @p224 :rule reordering :premises (@p223) :args ((or @t160 @t168 @t167 (not @t169)))) % 4.01/4.23 (step @p225 :rule chain_m_resolution :premises (@p224 @p219 @p222 @p203) :args (@t167 @t170 (@list @t158 @t164 @t169))) % 4.01/4.23 (step @p226 :rule cnf_or_neg :args (@t161 1)) % 4.01/4.23 (step @p227 :rule chain_m_resolution :premises (@p226 @p212) :args ((not @t159) @t162 @t163)) % 4.01/4.23 (step @p228 :rule cnf_equiv_pos2 :args (@t167)) % 4.01/4.23 (step @p229 :rule reordering :premises (@p228) :args ((or @t159 @t171 (not @t167)))) % 4.01/4.23 (step @p230 :rule chain_m_resolution :premises (@p229 @p227 @p225) :args (@t171 (@list true false) (@list @t159 @t167))) % 4.01/4.23 (step @p231 :rule skolemize :premises (@p230)) % 4.01/4.23 (step @p232 :rule bool-double-not-elim :args (@t175)) % 4.01/4.23 (step @p233 :rule refl :args (@t178)) % 4.01/4.23 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t178 (not @t177)))) % 4.01/4.23 (step @p235 :rule cnf_or_neg :args (@t178 0)) % 4.01/4.23 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 4.01/4.23 (step @p237 :rule reordering :premises (@p236) :args ((or @t175 @t178))) % 4.01/4.23 (step @p238 :rule chain_m_resolution :premises (@p237 @p231) :args (@t175 @t162 @t179)) % 4.01/4.23 (step @p239 :rule cnf_or_neg :args (@t178 1)) % 4.01/4.23 (step @p240 :rule chain_m_resolution :premises (@p239 @p231) :args ((not @t176) @t162 @t179)) % 4.01/4.23 (step @p241 :rule cnf_and_pos :args (@t180 1)) % 4.01/4.23 (step @p242 :rule reordering :premises (@p241) :args ((or @t176 @t181))) % 4.01/4.23 (step @p243 :rule chain_m_resolution :premises (@p242 @p240) :args (@t181 @t162 (@list @t176))) % 4.01/4.23 (step @p244 :rule eq-symm :args (@t183 @t35)) % 4.01/4.23 (step @p245 :rule cong :premises (@p244) :args (@t184)) % 4.01/4.23 (step @p246 :rule eq-symm :args (@t182 @t36)) % 4.01/4.23 (step @p247 :rule cong :premises (@p246 @p245) :args (@t185)) % 4.01/4.23 (step @p248 :rule refl :args (@t186)) % 4.01/4.25 (step @p249 :rule refl :args (@t152)) % 4.01/4.25 (step @p250 :rule nary_cong :premises (@p249 @p248 @p247) :args (@t187)) % 4.01/4.25 (step @p251 :rule aci_norm :args ((= @t189 @t187))) % 4.01/4.25 (step @p252 :rule trans :premises (@p251 @p250)) % 4.01/4.25 (step @p253 :rule cong :premises (@p252) :args (@t191)) % 4.01/4.25 (step @p254 :rule quant-merge-prenex :args ((= (forall @t6 @t193) @t191))) % 4.01/4.25 (step @p255 :rule alpha_equiv :args (@t194 (@list @t182) (@list @t17))) % 4.01/4.25 (step @p256 :rule refl :args (@t152)) % 4.01/4.25 (step @p257 :rule nary_cong :premises (@p256 @p255) :args (@t195)) % 4.01/4.25 (step @p258 :rule quant-miniscope-or :args ((= @t193 @t195))) % 4.01/4.25 (step @p259 :rule trans :premises (@p258 @p257)) % 4.01/4.25 (step @p260 :rule symm :premises (@p259)) % 4.01/4.25 (step @p261 :rule cong :premises (@p260) :args ((forall @t6 (or @t152 @t196)))) % 4.01/4.25 (step @p262 :rule trans :premises (@p261 @p254)) % 4.01/4.25 (step @p263 :rule trans :premises (@p262 @p253)) % 4.01/4.25 (step @p264 :rule bool-impl-elim :args (@t23 @t196)) % 4.01/4.25 (step @p265 :rule cong :premises (@p264) :args ((forall @t6 (=> @t23 @t196)))) % 4.01/4.25 (step @p266 :rule trans :premises (@p265 @p263)) % 4.01/4.25 (step @p267 :rule bool-impl-elim :args (@t32 @t37)) % 4.01/4.25 (step @p268 :rule cong :premises (@p267) :args (@t39)) % 4.01/4.25 (step @p269 :rule cong :premises (@p194 @p268) :args (@t40)) % 4.01/4.25 (step @p270 :rule cong :premises (@p269) :args (@t41)) % 4.01/4.25 (step @p271 :rule trans :premises (@p270 @p266)) % 4.01/4.25 (step @p272 :rule eq_resolve :premises (@p10 @p271)) % 4.01/4.25 (step @p273 :rule bool-eq-true :args (@t197)) % 4.01/4.25 (step @p274 :rule eq-symm :args (true @t197)) % 4.01/4.25 (step @p275 :rule trans :premises (@p274 @p273)) % 4.01/4.25 (step @p276 :rule refl :args (@t197)) % 4.01/4.25 (step @p277 :rule eq-refl :args (@t157)) % 4.01/4.25 (step @p278 :rule cong :premises (@p277 @p276) :args (@t198)) % 4.01/4.25 (step @p279 :rule trans :premises (@p278 @p275)) % 4.01/4.25 (step @p280 :rule refl :args (@t168)) % 4.01/4.25 (step @p281 :rule refl :args (@t160)) % 4.01/4.25 (step @p282 :rule nary_cong :premises (@p281 @p280 @p279) :args (@t199)) % 4.01/4.25 (step @p283 :rule refl :args (@t200)) % 4.01/4.25 (step @p284 :rule cong :premises (@p283 @p282) :args ((=> @t200 @t199))) % 4.01/4.25 (assume-push @p307 @t200) % 4.01/4.25 (step @p286 :rule instantiate :premises (@p272) :args ((@list @t156 @t155 @t157))) % 4.01/4.25 (step-pop @p308 :rule scope :premises (@p286)) % 4.01/4.25 (step @p287 :rule process_scope :premises (@p308) :args (@t199)) % 4.01/4.25 (step @p289 :rule eq_resolve :premises (@p287 @p284)) % 4.01/4.25 (step @p290 :rule implies_elim :premises (@p289)) % 4.01/4.25 (step @p291 :rule chain_m_resolution :premises (@p290 @p272) :args (@t201 @t202 (@list @t200))) % 4.01/4.25 (step @p292 :rule cnf_or_pos :args (@t201)) % 4.01/4.25 (step @p293 :rule reordering :premises (@p292) :args ((or @t160 @t168 @t197 (not @t201)))) % 4.01/4.25 (step @p294 :rule chain_m_resolution :premises (@p293 @p219 @p222 @p291) :args (@t197 @t170 (@list @t158 @t164 @t201))) % 4.01/4.25 (step @p295 :rule eq-symm :args (@t180 @t175)) % 4.01/4.25 (step @p296 :rule cong :premises (@p276 @p295) :args ((=> @t197 @t203))) % 4.01/4.25 (assume-push @p309 @t197) % 4.01/4.25 (step @p298 :rule instantiate :premises (@p294) :args ((@list @t173 @t172))) % 4.01/4.25 (step-pop @p310 :rule scope :premises (@p298)) % 4.01/4.25 (step @p299 :rule process_scope :premises (@p310) :args (@t203)) % 4.01/4.25 (step @p301 :rule eq_resolve :premises (@p299 @p296)) % 4.01/4.25 (step @p302 :rule implies_elim :premises (@p301)) % 4.01/4.25 (step @p303 :rule chain_m_resolution :premises (@p302 @p294) :args (@t204 @t202 (@list @t197))) % 4.01/4.25 (step @p304 :rule cnf_equiv_pos1 :args (@t204)) % 4.01/4.25 (step @p305 :rule reordering :premises (@p304) :args ((or @t177 @t180 (not @t204)))) % 4.01/4.25 (step @p306 false :rule chain_m_resolution :premises (@p305 @p303 @p243 @p238) :args (false (@list false true false) (@list @t204 @t180 @t175))) % 4.01/4.25 ) % 4.01/4.25 % SZS output end Proof % 4.01/4.25 % cvc5 exiting %------------------------------------------------------------------------------