%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU219+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 : 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 08:51:00 AM UTC 2026 % Result : Theorem 0.37s 0.73s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU219+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:40:31 EDT 2026 % 0.15/0.35 % CPUTime : % 0.28/0.54 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.73 % SZS status Theorem % 0.37/0.73 % SZS output start Proof % 0.37/0.73 ( % 0.37/0.73 (declare-sort $$unsorted 0) % 0.37/0.73 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.function_inverse (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.empty_set $$unsorted) % 0.37/0.73 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.73 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.73 (define @t3 () (tptp.in @t2 @t1)) % 0.37/0.73 (define @t4 () (not @t3)) % 0.37/0.73 (define @t5 () (tptp.in @t1 @t2)) % 0.37/0.73 (define @t6 () (@list @t1 @t2)) % 0.37/0.73 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.37/0.74 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.37/0.74 (define @t9 () (tptp.function @t1)) % 0.37/0.74 (define @t10 () (tptp.empty @t1)) % 0.37/0.74 (define @t11 () (@list @t1)) % 0.37/0.74 (define @t12 () (tptp.relation @t1)) % 0.37/0.74 (define @t13 () (tptp.one_to_one @t1)) % 0.37/0.74 (define @t14 () (and @t12 @t9 @t13)) % 0.37/0.74 (define @t15 () (and @t12 @t10 @t9)) % 0.37/0.74 (define @t16 () (tptp.unordered_pair @t1 @t2)) % 0.37/0.74 (define @t17 () (tptp.set_union2 @t2 @t1)) % 0.37/0.74 (define @t18 () (tptp.set_union2 @t1 @t2)) % 0.37/0.74 (define @t19 () (tptp.set_intersection2 @t1 @t2)) % 0.37/0.74 (define @t20 () (@var "D" $$unsorted)) % 0.37/0.74 (define @t21 () (@var "C" $$unsorted)) % 0.37/0.74 (define @t22 () (tptp.in @t21 @t1)) % 0.37/0.74 (define @t23 () (tptp.ordered_pair @t21 @t20)) % 0.37/0.74 (define @t24 () (tptp.in @t23 @t2)) % 0.37/0.74 (define @t25 () (@list @t21 @t20)) % 0.37/0.74 (define @t26 () (tptp.identity_relation @t1)) % 0.37/0.74 (define @t27 () (= @t2 @t26)) % 0.37/0.74 (define @t28 () (tptp.relation @t2)) % 0.37/0.74 (define @t29 () (tptp.subset @t1 @t2)) % 0.37/0.74 (define @t30 () (= @t1 @t2)) % 0.37/0.74 (define @t31 () (@var "E" $$unsorted)) % 0.37/0.74 (define @t32 () (tptp.ordered_pair @t20 @t31)) % 0.37/0.74 (define @t33 () (tptp.in @t32 @t1)) % 0.37/0.74 (define @t34 () (tptp.in @t20 @t2)) % 0.37/0.74 (define @t35 () (tptp.in @t32 @t21)) % 0.37/0.74 (define @t36 () (@list @t20 @t31)) % 0.37/0.74 (define @t37 () (tptp.relation_dom_restriction @t1 @t2)) % 0.37/0.74 (define @t38 () (tptp.relation @t21)) % 0.37/0.74 (define @t39 () (@list @t2 @t21)) % 0.37/0.74 (define @t40 () (tptp.in @t31 @t1)) % 0.37/0.74 (define @t41 () (tptp.relation_rng_restriction @t1 @t2)) % 0.37/0.74 (define @t42 () (@list @t21)) % 0.37/0.74 (define @t43 () (tptp.in @t31 @t2)) % 0.37/0.74 (define @t44 () (@list @t31)) % 0.37/0.74 (define @t45 () (tptp.in @t20 @t21)) % 0.37/0.74 (define @t46 () (@list @t20)) % 0.37/0.74 (define @t47 () (@list @t2)) % 0.37/0.74 (define @t48 () (= @t2 tptp.empty_set)) % 0.37/0.74 (define @t49 () (= @t2 (tptp.set_meet @t1))) % 0.37/0.74 (define @t50 () (= @t1 tptp.empty_set)) % 0.37/0.74 (define @t51 () (tptp.in @t21 @t20)) % 0.37/0.74 (define @t52 () (tptp.in @t20 @t1)) % 0.37/0.74 (define @t53 () (tptp.in @t21 @t2)) % 0.37/0.74 (define @t54 () (not @t50)) % 0.37/0.74 (define @t55 () (tptp.singleton @t1)) % 0.37/0.74 (define @t56 () (tptp.powerset @t1)) % 0.37/0.74 (define @t57 () (tptp.in @t23 @t1)) % 0.37/0.74 (define @t58 () (tptp.empty @t2)) % 0.37/0.74 (define @t59 () (tptp.element @t2 @t1)) % 0.37/0.74 (define @t60 () (not @t10)) % 0.37/0.74 (define @t61 () (@list @t1 @t2 @t21)) % 0.37/0.74 (define @t62 () (@var "F" $$unsorted)) % 0.37/0.74 (define @t63 () (tptp.cartesian_product2 @t1 @t2)) % 0.37/0.74 (define @t64 () (forall @t42 (=> @t22 @t53))) % 0.37/0.74 (define @t65 () (= @t21 (tptp.apply @t1 @t2))) % 0.37/0.74 (define @t66 () (tptp.relation_dom @t1)) % 0.37/0.74 (define @t67 () (tptp.in @t2 @t66)) % 0.37/0.74 (define @t68 () (tptp.in (tptp.ordered_pair @t2 @t21) @t1)) % 0.37/0.74 (define @t69 () (and @t12 @t9)) % 0.37/0.74 (define @t70 () (tptp.cast_to_subset @t1)) % 0.37/0.74 (define @t71 () (tptp.set_difference @t1 @t2)) % 0.37/0.74 (define @t72 () (tptp.in (tptp.ordered_pair @t20 @t21) @t1)) % 0.37/0.74 (define @t73 () (tptp.relation_rng @t1)) % 0.37/0.74 (define @t74 () (tptp.subset_complement @t1 @t2)) % 0.37/0.74 (define @t75 () (tptp.element @t2 @t56)) % 0.37/0.74 (define @t76 () (tptp.ordered_pair @t1 @t2)) % 0.37/0.74 (define @t77 () (tptp.relation_inverse @t1)) % 0.37/0.74 (define @t78 () (tptp.disjoint @t1 @t2)) % 0.37/0.74 (define @t79 () (tptp.relation_composition @t1 @t2)) % 0.37/0.74 (define @t80 () (tptp.complements_of_subsets @t1 @t2)) % 0.37/0.74 (define @t81 () (tptp.powerset @t56)) % 0.37/0.74 (define @t82 () (tptp.element @t2 @t81)) % 0.37/0.74 (define @t83 () (not @t30)) % 0.37/0.74 (define @t84 () (tptp.function_inverse @t1)) % 0.37/0.74 (define @t85 () (=> @t13 (= @t84 @t77))) % 0.37/0.74 (define @t86 () (=> @t69 @t85)) % 0.37/0.74 (define @t87 () (forall @t11 @t86)) % 0.37/0.74 (define @t88 () (tptp.relation @t77)) % 0.37/0.74 (define @t89 () (tptp.relation @t79)) % 0.37/0.74 (define @t90 () (and @t12 @t28)) % 0.37/0.74 (define @t91 () (tptp.union_of_subsets @t1 @t2)) % 0.37/0.74 (define @t92 () (tptp.relation @t26)) % 0.37/0.74 (define @t93 () (tptp.meet_of_subsets @t1 @t2)) % 0.37/0.74 (define @t94 () (tptp.subset_difference @t1 @t2 @t21)) % 0.37/0.74 (define @t95 () (tptp.element @t21 @t56)) % 0.37/0.74 (define @t96 () (and @t75 @t95)) % 0.37/0.74 (define @t97 () (tptp.relation_composition @t2 @t1)) % 0.37/0.74 (define @t98 () (and @t10 @t28)) % 0.37/0.74 (define @t99 () (tptp.relation tptp.empty_set)) % 0.37/0.74 (define @t100 () (tptp.empty tptp.empty_set)) % 0.37/0.74 (define @t101 () (tptp.function @t2)) % 0.37/0.74 (define @t102 () (not @t58)) % 0.37/0.74 (define @t103 () (tptp.empty @t66)) % 0.37/0.74 (define @t104 () (and @t60 @t12)) % 0.37/0.74 (define @t105 () (tptp.empty @t73)) % 0.37/0.74 (define @t106 () (tptp.disjoint @t55 @t2)) % 0.37/0.74 (define @t107 () (tptp.singleton @t2)) % 0.37/0.74 (define @t108 () (tptp.union @t2)) % 0.37/0.74 (define @t109 () (tptp.in @t1 @t21)) % 0.37/0.74 (define @t110 () (@list @t1 @t2 @t21 @t20)) % 0.37/0.74 (define @t111 () (tptp.element @t1 (tptp.powerset @t2))) % 0.37/0.74 (define @t112 () (tptp.set_difference @t2 @t21)) % 0.37/0.74 (define @t113 () (= @t1 @t21)) % 0.37/0.74 (define @t114 () (tptp.relation_rng @t21)) % 0.37/0.74 (define @t115 () (tptp.relation_rng @t41)) % 0.37/0.74 (define @t116 () (tptp.relation_rng @t2)) % 0.37/0.74 (define @t117 () (tptp.cartesian_product2 @t1 @t21)) % 0.37/0.74 (define @t118 () (not @t53)) % 0.37/0.74 (define @t119 () (tptp.subset @t21 @t2)) % 0.37/0.74 (define @t120 () (forall @t42 (not (and @t119 (not (tptp.are_equipotent @t21 @t2)) @t118)))) % 0.37/0.74 (define @t121 () (tptp.powerset @t21)) % 0.37/0.74 (define @t122 () (forall @t25 (=> (and @t53 (tptp.subset @t20 @t21)) @t34))) % 0.37/0.74 (define @t123 () (tptp.relation_dom_restriction @t21 @t2)) % 0.37/0.74 (define @t124 () (tptp.relation_dom @t21)) % 0.37/0.74 (define @t125 () (tptp.relation_image @t2 @t1)) % 0.37/0.74 (define @t126 () (tptp.relation_dom @t2)) % 0.37/0.74 (define @t127 () (tptp.set_intersection2 @t126 @t1)) % 0.37/0.74 (define @t128 () (tptp.relation_rng @t79)) % 0.37/0.74 (define @t129 () (tptp.relation_inverse_image @t21 @t2)) % 0.37/0.74 (define @t130 () (tptp.relation_inverse_image @t2 @t1)) % 0.37/0.74 (define @t131 () (tptp.set_intersection2 @t2 @t21)) % 0.37/0.74 (define @t132 () (tptp.subset @t1 @t21)) % 0.37/0.74 (define @t133 () (tptp.element @t1 @t2)) % 0.37/0.74 (define @t134 () (tptp.in @t1 @t124)) % 0.37/0.74 (define @t135 () (tptp.in @t76 @t21)) % 0.37/0.74 (define @t136 () (tptp.apply @t21 @t1)) % 0.37/0.74 (define @t137 () (tptp.relation_composition @t21 @t2)) % 0.37/0.74 (define @t138 () (tptp.in @t1 (tptp.relation_dom @t137))) % 0.37/0.74 (define @t139 () (and @t38 (tptp.function @t21))) % 0.37/0.74 (define @t140 () (and @t28 @t101)) % 0.37/0.74 (define @t141 () (tptp.relation_field @t21)) % 0.37/0.74 (define @t142 () (tptp.apply @t2 @t21)) % 0.37/0.74 (define @t143 () (and (= @t73 (tptp.relation_dom @t77)) (= @t66 (tptp.relation_rng @t77)))) % 0.37/0.74 (define @t144 () (forall @t11 (=> @t12 @t143))) % 0.37/0.74 (define @t145 () (tptp.in @t2 @t21)) % 0.37/0.74 (define @t146 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.37/0.74 (define @t147 () (and @t22 @t53)) % 0.37/0.74 (define @t148 () (not @t78)) % 0.37/0.74 (define @t149 () (tptp.subset_complement @t1 @t21)) % 0.37/0.74 (define @t150 () (tptp.disjoint @t2 @t21)) % 0.37/0.74 (define @t151 () (tptp.relation_dom @t79)) % 0.37/0.74 (define @t152 () (not @t48)) % 0.37/0.74 (define @t153 () (tptp.element @t2 @t121)) % 0.37/0.74 (define @t154 () (tptp.in @t21 @t19)) % 0.37/0.74 (define @t155 () (and (tptp.in @t21 @t73) (= @t20 @t142))) % 0.37/0.74 (define @t156 () (and (tptp.in @t20 @t66) (= @t21 (tptp.apply @t1 @t20)))) % 0.37/0.74 (define @t157 () (and (= @t73 (tptp.relation_dom @t84)) (= @t66 (tptp.relation_rng @t84)))) % 0.37/0.74 (define @t158 () (=> @t13 @t157)) % 0.37/0.74 (define @t159 () (forall @t11 (=> @t69 @t158))) % 0.37/0.74 (define @t160 () (not @t159)) % 0.37/0.74 (define @t161 () (= @t73 tptp.empty_set)) % 0.37/0.74 (define @t162 () (= @t66 tptp.empty_set)) % 0.37/0.74 (define @t163 () (tptp.relation_dom_restriction @t2 @t1)) % 0.37/0.74 (define @t164 () (= @t55 (tptp.unordered_pair @t2 @t21))) % 0.37/0.74 (define @t165 () (not @t13)) % 0.37/0.74 (define @t166 () (not @t9)) % 0.37/0.74 (define @t167 () (not @t12)) % 0.37/0.74 (define @t168 () (or @t167 @t166 @t165 @t157)) % 0.37/0.74 (define @t169 () (or @t167 @t166)) % 0.37/0.74 (define @t170 () (not @t69)) % 0.37/0.74 (define @t171 () (@quantifiers_skolemize (forall @t11 @t168) 0)) % 0.37/0.74 (define @t172 () (tptp.function_inverse @t171)) % 0.37/0.74 (define @t173 () (tptp.relation_dom @t171)) % 0.37/0.74 (define @t174 () (= @t173 (tptp.relation_rng @t172))) % 0.37/0.74 (define @t175 () (tptp.relation_rng @t171)) % 0.37/0.74 (define @t176 () (= @t175 (tptp.relation_dom @t172))) % 0.37/0.74 (define @t177 () (and @t176 @t174)) % 0.37/0.74 (define @t178 () (tptp.one_to_one @t171)) % 0.37/0.74 (define @t179 () (not @t178)) % 0.37/0.74 (define @t180 () (tptp.function @t171)) % 0.37/0.74 (define @t181 () (not @t180)) % 0.37/0.74 (define @t182 () (tptp.relation @t171)) % 0.37/0.74 (define @t183 () (not @t182)) % 0.37/0.74 (define @t184 () (or @t183 @t181 @t179 @t177)) % 0.37/0.74 (define @t185 () (@list true)) % 0.37/0.74 (define @t186 () (@list @t184)) % 0.37/0.74 (define @t187 () (= @t77 @t84)) % 0.37/0.74 (define @t188 () (or @t167 @t166 @t165 @t187)) % 0.37/0.74 (define @t189 () (=> @t13 @t187)) % 0.37/0.74 (define @t190 () (tptp.relation_inverse @t171)) % 0.37/0.74 (define @t191 () (or @t183 @t181 @t179 (= @t190 @t172))) % 0.37/0.74 (define @t192 () (forall @t11 @t188)) % 0.37/0.74 (define @t193 () (@list @t171)) % 0.37/0.74 (define @t194 () (= @t172 @t190)) % 0.37/0.74 (define @t195 () (or @t183 @t181 @t179 @t194)) % 0.37/0.74 (define @t196 () (@list false)) % 0.37/0.74 (define @t197 () (tptp.relation_dom @t190)) % 0.37/0.74 (define @t198 () (tptp.relation_rng @t190)) % 0.37/0.74 (define @t199 () (= @t173 @t198)) % 0.37/0.74 (define @t200 () (= @t175 @t197)) % 0.37/0.74 (define @t201 () (and @t200 @t199)) % 0.37/0.74 (define @t202 () (or @t183 @t201)) % 0.37/0.74 (define @t203 () (not @t201)) % 0.37/0.74 (define @t204 () (@list @t201)) % 0.37/0.74 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.37/0.74 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.37/0.74 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.37/0.74 (assume @p4 (forall @t11 (=> @t10 @t12))) % 0.37/0.74 (assume @p5 (forall @t11 (=> @t15 @t14))) % 0.37/0.74 (assume @p6 (forall @t6 (= @t16 (tptp.unordered_pair @t2 @t1)))) % 0.37/0.74 (assume @p7 (forall @t6 (= @t18 @t17))) % 0.37/0.74 (assume @p8 (forall @t6 (= @t19 (tptp.set_intersection2 @t2 @t1)))) % 0.37/0.74 (assume @p9 (forall @t6 (=> @t28 (= @t27 (forall @t25 (= @t24 (and @t22 (= @t21 @t20)))))))) % 0.37/0.74 (assume @p10 (forall @t6 (= @t30 (and @t29 (tptp.subset @t2 @t1))))) % 0.37/0.74 (assume @p11 (forall @t11 (=> @t12 (forall @t39 (=> @t38 (= (= @t21 @t37) (forall @t36 (= @t35 (and @t34 @t33))))))))) % 0.37/0.74 (assume @p12 (forall @t6 (=> @t28 (forall @t42 (=> @t38 (= (= @t21 @t41) (forall @t36 (= @t35 (and @t40 (tptp.in @t32 @t2)))))))))) % 0.37/0.74 (assume @p13 (forall @t11 (=> @t12 (forall @t39 (= (= @t21 (tptp.relation_image @t1 @t2)) (forall @t46 (= @t45 (exists @t44 (and (tptp.in (tptp.ordered_pair @t31 @t20) @t1) @t43))))))))) % 0.37/0.74 (assume @p14 (forall @t11 (=> @t12 (forall @t39 (= (= @t21 (tptp.relation_inverse_image @t1 @t2)) (forall @t46 (= @t45 (exists @t44 (and @t33 @t43))))))))) % 0.37/0.74 (assume @p15 (forall @t11 (= @t12 (forall @t47 (not (and @t3 (forall @t25 (not (= @t2 @t23))))))))) % 0.37/0.74 (assume @p16 (forall @t6 (and (=> @t54 (= @t49 (forall @t42 (= @t53 (forall @t46 (=> @t52 @t51)))))) (=> @t50 (= @t49 @t48))))) % 0.37/0.74 (assume @p17 (forall @t6 (= (= @t2 @t55) (forall @t42 (= @t53 (= @t21 @t1)))))) % 0.37/0.74 (assume @p18 (forall @t11 (= @t50 (forall @t47 @t4)))) % 0.37/0.74 (assume @p19 (forall @t6 (= (= @t2 @t56) (forall @t42 (= @t53 (tptp.subset @t21 @t1)))))) % 0.37/0.74 (assume @p20 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t30 (forall @t25 (= @t57 @t24)))))))) % 0.37/0.74 (assume @p21 (forall @t6 (and (=> @t60 (= @t59 @t3)) (=> @t10 (= @t59 @t58))))) % 0.37/0.74 (assume @p22 (forall @t61 (= (= @t21 @t16) (forall @t46 (= @t45 (or (= @t20 @t1) (= @t20 @t2))))))) % 0.37/0.74 (assume @p23 (forall @t61 (= (= @t21 @t18) (forall @t46 (= @t45 (or @t52 @t34)))))) % 0.37/0.74 (assume @p24 (forall @t61 (= (= @t21 @t63) (forall @t46 (= @t45 (exists (@list @t31 @t62) (and @t40 (tptp.in @t62 @t2) (= @t20 (tptp.ordered_pair @t31 @t62))))))))) % 0.37/0.74 (assume @p25 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t29 (forall @t25 (=> @t57 @t24)))))))) % 0.37/0.74 (assume @p26 (forall @t6 (= @t29 @t64))) % 0.37/0.74 (assume @p27 (forall @t61 (= (= @t21 @t19) (forall @t46 (= @t45 (and @t52 @t34)))))) % 0.37/0.74 (assume @p28 (forall @t11 (=> @t69 (forall @t39 (and (=> @t67 (= @t65 @t68)) (=> (not @t67) (= @t65 (= @t21 tptp.empty_set)))))))) % 0.37/0.74 (assume @p29 (forall @t11 (=> @t12 (forall @t47 (= (= @t2 @t66) (forall @t42 (= @t53 (exists @t46 @t57)))))))) % 0.37/0.74 (assume @p30 (forall @t11 (= @t70 @t1))) % 0.37/0.74 (assume @p31 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t42 (= @t53 (exists @t46 (and @t51 @t52))))))) % 0.37/0.74 (assume @p32 (forall @t61 (= (= @t21 @t71) (forall @t46 (= @t45 (and @t52 (not @t34))))))) % 0.37/0.74 (assume @p33 (forall @t11 (=> @t12 (forall @t47 (= (= @t2 @t73) (forall @t42 (= @t53 (exists @t46 @t72)))))))) % 0.37/0.74 (assume @p34 (forall @t6 (=> @t75 (= @t74 @t71)))) % 0.37/0.74 (assume @p35 (forall @t6 (= @t76 (tptp.unordered_pair @t16 @t55)))) % 0.37/0.74 (assume @p36 (forall @t11 (=> @t12 (= (tptp.relation_field @t1) (tptp.set_union2 @t66 @t73))))) % 0.37/0.74 (assume @p37 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= (= @t2 @t77) (forall @t25 (= @t24 @t72)))))))) % 0.37/0.74 (assume @p38 (forall @t6 (= @t78 (= @t19 tptp.empty_set)))) % 0.37/0.74 (assume @p39 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (forall @t42 (=> @t38 (= (= @t21 @t79) (forall @t36 (= @t35 (exists (@list @t62) (and (tptp.in (tptp.ordered_pair @t20 @t62) @t1) (tptp.in (tptp.ordered_pair @t62 @t31) @t2))))))))))))) % 0.37/0.74 (assume @p40 (forall @t6 (=> @t82 (forall @t42 (=> (tptp.element @t21 @t81) (= (= @t21 @t80) (forall @t46 (=> (tptp.element @t20 @t56) (= @t45 (tptp.in (tptp.subset_complement @t1 @t20) @t2)))))))))) % 0.37/0.74 (assume @p41 (forall @t6 (= @t8 (and @t29 @t83)))) % 0.37/0.74 (assume @p42 @t87) % 0.37/0.74 (assume @p43 true) % 0.37/0.74 (assume @p44 (forall @t11 (=> @t69 (and (tptp.relation @t84) (tptp.function @t84))))) % 0.37/0.74 (assume @p45 (forall @t11 (tptp.element @t70 @t56))) % 0.37/0.74 (assume @p46 (forall @t6 (=> @t75 (tptp.element @t74 @t56)))) % 0.37/0.74 (assume @p47 (forall @t11 (=> @t12 @t88))) % 0.37/0.74 (assume @p48 (forall @t6 (=> @t90 @t89))) % 0.37/0.74 (assume @p49 (forall @t6 (=> @t82 (tptp.element @t91 @t56)))) % 0.37/0.74 (assume @p50 (forall @t11 @t92)) % 0.37/0.74 (assume @p51 (forall @t6 (=> @t82 (tptp.element @t93 @t56)))) % 0.37/0.74 (assume @p52 (forall @t61 (=> @t96 (tptp.element @t94 @t56)))) % 0.37/0.74 (assume @p53 (forall @t6 (=> @t12 (tptp.relation @t37)))) % 0.37/0.74 (assume @p54 (forall @t6 (=> @t82 (tptp.element @t80 @t81)))) % 0.37/0.74 (assume @p55 (forall @t6 (=> @t28 (tptp.relation @t41)))) % 0.37/0.74 (assume @p56 (forall @t11 (exists @t47 @t59))) % 0.37/0.74 (assume @p57 (forall @t6 (=> @t98 (and (tptp.empty @t97) (tptp.relation @t97))))) % 0.37/0.74 (assume @p58 (forall @t11 (=> @t10 (and (tptp.empty @t77) @t88)))) % 0.37/0.74 (assume @p59 (and @t100 @t99 (tptp.relation_empty_yielding tptp.empty_set))) % 0.37/0.74 (assume @p60 (forall @t6 (=> (and @t12 @t9 @t28 @t101) (and @t89 (tptp.function @t79))))) % 0.37/0.74 (assume @p61 (forall @t6 (=> @t90 (tptp.relation @t19)))) % 0.37/0.74 (assume @p62 (forall @t11 (not (tptp.empty @t56)))) % 0.37/0.74 (assume @p63 @t100) % 0.37/0.74 (assume @p64 (forall @t6 (not (tptp.empty @t76)))) % 0.37/0.74 (assume @p65 (forall @t11 (and @t92 (tptp.function @t26)))) % 0.37/0.74 (assume @p66 (forall @t6 (=> @t90 (tptp.relation @t18)))) % 0.37/0.74 (assume @p67 (forall @t11 (not (tptp.empty @t55)))) % 0.37/0.74 (assume @p68 (forall @t6 (=> @t60 (not (tptp.empty @t18))))) % 0.37/0.74 (assume @p69 (forall @t11 (=> @t14 (and @t88 (tptp.function @t77))))) % 0.37/0.74 (assume @p70 (forall @t6 (not (tptp.empty @t16)))) % 0.37/0.74 (assume @p71 (forall @t6 (=> @t60 (not (tptp.empty @t17))))) % 0.37/0.74 (assume @p72 (and @t100 @t99)) % 0.37/0.74 (assume @p73 (forall @t6 (=> (and @t60 @t102) (not (tptp.empty @t63))))) % 0.37/0.74 (assume @p74 (forall @t11 (=> @t104 (not @t103)))) % 0.37/0.74 (assume @p75 (forall @t11 (=> @t104 (not @t105)))) % 0.37/0.74 (assume @p76 (forall @t11 (=> @t10 (and @t103 (tptp.relation @t66))))) % 0.37/0.74 (assume @p77 (forall @t11 (=> @t10 (and @t105 (tptp.relation @t73))))) % 0.37/0.74 (assume @p78 (forall @t6 (=> @t98 (and (tptp.empty @t79) @t89)))) % 0.37/0.74 (assume @p79 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.37/0.74 (assume @p80 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.37/0.74 (assume @p81 (forall @t6 (=> @t75 (= (tptp.subset_complement @t1 @t74) @t2)))) % 0.37/0.74 (assume @p82 (forall @t11 (=> @t12 (= (tptp.relation_inverse @t77) @t1)))) % 0.37/0.74 (assume @p83 (forall @t6 (=> @t82 (= (tptp.complements_of_subsets @t1 @t80) @t2)))) % 0.37/0.74 (assume @p84 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.37/0.74 (assume @p85 (forall @t11 (not (= @t55 tptp.empty_set)))) % 0.37/0.74 (assume @p86 (forall @t6 (=> @t5 (= (tptp.set_union2 @t55 @t2) @t2)))) % 0.37/0.74 (assume @p87 (forall @t6 (not (and @t106 @t5)))) % 0.37/0.74 (assume @p88 (forall @t6 (=> (not @t5) @t106))) % 0.37/0.74 (assume @p89 (forall @t6 (= (tptp.subset @t55 @t2) @t5))) % 0.37/0.74 (assume @p90 (forall @t6 (= (= @t71 tptp.empty_set) @t29))) % 0.37/0.74 (assume @p91 (forall @t6 (=> @t75 (forall @t42 (=> @t53 @t22))))) % 0.37/0.74 (assume @p92 (forall @t61 (=> @t29 (or @t22 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t21))))))) % 0.37/0.74 (assume @p93 (forall @t6 (= (tptp.subset @t1 @t107) (or @t50 (= @t1 @t107))))) % 0.37/0.74 (assume @p94 (forall @t6 (=> @t5 (tptp.subset @t1 @t108)))) % 0.37/0.74 (assume @p95 (forall @t110 (= (tptp.in @t76 (tptp.cartesian_product2 @t21 @t20)) (and @t109 (tptp.in @t2 @t20))))) % 0.37/0.74 (assume @p96 (forall @t6 (=> @t64 @t111))) % 0.37/0.74 (assume @p97 (exists @t11 @t69)) % 0.37/0.74 (assume @p98 (exists @t11 (and @t10 @t12))) % 0.37/0.74 (assume @p99 (forall @t11 (=> @t60 (exists @t47 (and @t75 @t102))))) % 0.37/0.74 (assume @p100 (exists @t11 @t10)) % 0.37/0.74 (assume @p101 (exists @t11 @t15)) % 0.37/0.74 (assume @p102 (exists @t11 @t104)) % 0.37/0.74 (assume @p103 (forall @t11 (exists @t47 (and @t75 @t58)))) % 0.37/0.74 (assume @p104 (exists @t11 @t60)) % 0.37/0.74 (assume @p105 (exists @t11 @t14)) % 0.37/0.74 (assume @p106 (exists @t11 (and @t12 (tptp.relation_empty_yielding @t1)))) % 0.37/0.74 (assume @p107 (forall @t6 (=> @t82 (= @t91 @t108)))) % 0.37/0.74 (assume @p108 (forall @t6 (=> @t82 (= @t93 (tptp.set_meet @t2))))) % 0.37/0.74 (assume @p109 (forall @t61 (=> @t96 (= @t94 @t112)))) % 0.37/0.74 (assume @p110 (forall @t6 (tptp.subset @t1 @t1))) % 0.37/0.74 (assume @p111 (forall @t6 (=> @t78 (tptp.disjoint @t2 @t1)))) % 0.37/0.74 (assume @p112 (forall @t110 (not (and (= @t16 (tptp.unordered_pair @t21 @t20)) (not @t113) (not (= @t1 @t20)))))) % 0.37/0.74 (assume @p113 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t21))) (and @t5 (tptp.in @t1 @t114)))))) % 0.37/0.74 (assume @p114 (forall @t6 (=> @t28 (tptp.subset @t115 @t1)))) % 0.37/0.74 (assume @p115 (forall @t6 (=> @t28 (tptp.subset @t41 @t2)))) % 0.37/0.74 (assume @p116 (forall @t6 (=> @t28 (tptp.subset @t115 @t116)))) % 0.37/0.74 (assume @p117 (forall @t61 (=> @t29 (and (tptp.subset @t117 (tptp.cartesian_product2 @t2 @t21)) (tptp.subset (tptp.cartesian_product2 @t21 @t1) (tptp.cartesian_product2 @t21 @t2)))))) % 0.37/0.74 (assume @p118 (forall @t6 (=> @t28 (= @t115 (tptp.set_intersection2 @t116 @t1))))) % 0.37/0.74 (assume @p119 (forall @t110 (=> (and @t29 (tptp.subset @t21 @t20)) (tptp.subset @t117 (tptp.cartesian_product2 @t2 @t20))))) % 0.37/0.74 (assume @p120 (forall @t6 (=> @t29 (= @t18 @t2)))) % 0.37/0.74 (assume @p121 (forall @t11 (exists @t47 (and @t5 @t122 (forall @t42 (=> @t53 (tptp.in @t121 @t2))) @t120)))) % 0.37/0.74 (assume @p122 (forall @t61 (=> @t38 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t21) @t2) (tptp.relation_rng_restriction @t1 @t123))))) % 0.37/0.74 (assume @p123 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_image @t21 @t2)) (exists @t46 (and (tptp.in @t20 @t124) (tptp.in (tptp.ordered_pair @t20 @t1) @t21) @t34)))))) % 0.37/0.74 (assume @p124 (forall @t6 (=> @t28 (tptp.subset @t125 @t116)))) % 0.37/0.74 (assume @p125 (forall @t6 (=> @t28 (= @t125 (tptp.relation_image @t2 @t127))))) % 0.37/0.74 (assume @p126 (forall @t11 (=> @t12 (= (tptp.relation_image @t1 @t66) @t73)))) % 0.37/0.74 (assume @p127 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t128 (tptp.relation_image @t2 @t73))))))) % 0.37/0.74 (assume @p128 (forall @t61 (=> @t38 (= (tptp.in @t1 @t129) (exists @t46 (and (tptp.in @t20 @t114) (tptp.in (tptp.ordered_pair @t1 @t20) @t21) @t34)))))) % 0.37/0.74 (assume @p129 (forall @t6 (=> @t28 (tptp.subset @t130 @t126)))) % 0.37/0.74 (assume @p130 (forall @t6 (=> @t28 (not (and @t54 (tptp.subset @t1 @t116) (= @t130 tptp.empty_set)))))) % 0.37/0.74 (assume @p131 (forall @t61 (=> @t38 (=> @t29 (tptp.subset (tptp.relation_inverse_image @t21 @t1) @t129))))) % 0.37/0.74 (assume @p132 (forall @t6 (tptp.subset @t19 @t1))) % 0.37/0.74 (assume @p133 (forall @t61 (=> (and @t29 @t132) (tptp.subset @t1 @t131)))) % 0.37/0.74 (assume @p134 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.37/0.74 (assume @p135 (forall @t6 (=> @t5 @t133))) % 0.37/0.74 (assume @p136 (forall @t61 (=> (and @t29 (tptp.subset @t2 @t21)) @t132))) % 0.37/0.74 (assume @p137 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.37/0.74 (assume @p138 (forall @t61 (=> @t38 (=> @t135 (and @t134 (tptp.in @t2 @t114)))))) % 0.37/0.74 (assume @p139 (forall @t6 (=> @t140 (forall @t42 (=> @t139 (= @t138 (and @t134 (tptp.in @t136 @t126)))))))) % 0.37/0.74 (assume @p140 (forall @t11 (=> @t12 (tptp.subset @t1 (tptp.cartesian_product2 @t66 @t73))))) % 0.37/0.74 (assume @p141 (forall @t6 (=> @t140 (forall @t42 (=> @t139 (=> @t138 (= (tptp.apply @t137 @t1) (tptp.apply @t2 @t136)))))))) % 0.37/0.74 (assume @p142 (forall @t6 (=> @t140 (forall @t42 (=> @t139 (=> (tptp.in @t1 @t126) (= (tptp.apply (tptp.relation_composition @t2 @t21) @t1) (tptp.apply @t21 (tptp.apply @t2 @t1))))))))) % 0.37/0.74 (assume @p143 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> @t29 (and (tptp.subset @t66 @t126) (tptp.subset @t73 @t116)))))))) % 0.37/0.74 (assume @p144 (forall @t61 (=> @t29 (tptp.subset (tptp.set_intersection2 @t1 @t21) @t131)))) % 0.37/0.74 (assume @p145 (forall @t6 (=> @t29 (= @t19 @t1)))) % 0.37/0.74 (assume @p146 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.37/0.74 (assume @p147 (forall @t6 (=> @t133 (or @t58 @t5)))) % 0.37/0.74 (assume @p148 (forall @t6 (=> (forall @t42 (= @t22 @t53)) @t30))) % 0.37/0.74 (assume @p149 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.37/0.74 (assume @p150 (forall @t61 (=> @t38 (=> @t135 (and (tptp.in @t1 @t141) (tptp.in @t2 @t141)))))) % 0.37/0.74 (assume @p151 (forall @t61 (=> @t29 (tptp.subset (tptp.set_difference @t1 @t21) @t112)))) % 0.37/0.74 (assume @p152 (forall @t110 (=> (= @t76 @t23) (and @t113 (= @t2 @t20))))) % 0.37/0.74 (assume @p153 (forall @t6 (=> @t140 (= @t27 (and (= @t126 @t1) (forall @t42 (=> @t22 (= @t142 @t21)))))))) % 0.37/0.74 (assume @p154 (forall @t6 (=> @t3 (= (tptp.apply @t26 @t2) @t2)))) % 0.37/0.74 (assume @p155 (forall @t6 (tptp.subset @t71 @t1))) % 0.37/0.74 (assume @p156 @t144) % 0.37/0.74 (assume @p157 (forall @t61 (= (tptp.subset @t16 @t21) (and @t109 @t145)))) % 0.37/0.74 (assume @p158 (forall @t6 (= @t146 @t18))) % 0.37/0.74 (assume @p159 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.37/0.74 (assume @p160 (forall @t6 (= @t111 @t29))) % 0.37/0.74 (assume @p161 (forall @t6 (and (not (and @t148 (forall @t42 (not @t147)))) (not (and (exists @t42 @t147) @t78))))) % 0.37/0.74 (assume @p162 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t50))) % 0.37/0.74 (assume @p163 (forall @t6 (= (tptp.set_difference @t18 @t2) @t71))) % 0.37/0.74 (assume @p164 (forall @t6 (=> @t75 (forall @t42 (=> @t95 (= @t150 (tptp.subset @t2 @t149))))))) % 0.37/0.74 (assume @p165 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (tptp.subset @t151 @t66)))))) % 0.37/0.74 (assume @p166 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (tptp.subset @t128 @t116)))))) % 0.37/0.74 (assume @p167 (forall @t6 (=> @t29 (= @t2 @t146)))) % 0.37/0.74 (assume @p168 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> (tptp.subset @t73 @t126) (= @t151 @t66))))))) % 0.37/0.74 (assume @p169 (forall @t6 (=> @t82 (not (and @t152 (= @t80 tptp.empty_set)))))) % 0.37/0.74 (assume @p170 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> (tptp.subset @t66 @t116) (= (tptp.relation_rng @t97) @t73))))))) % 0.37/0.74 (assume @p171 (forall @t6 (=> @t82 (=> @t152 (= (tptp.subset_difference @t1 @t70 @t91) (tptp.meet_of_subsets @t1 @t80)))))) % 0.37/0.74 (assume @p172 (forall @t6 (=> @t82 (=> @t152 (= (tptp.union_of_subsets @t1 @t80) (tptp.subset_difference @t1 @t70 @t93)))))) % 0.37/0.74 (assume @p173 (forall @t6 (= (tptp.set_difference @t1 @t71) @t19))) % 0.37/0.74 (assume @p174 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.37/0.74 (assume @p175 (forall @t61 (=> (and @t5 @t153) (tptp.element @t1 @t21)))) % 0.37/0.74 (assume @p176 (forall @t6 (and (not (and @t148 (forall @t42 (not @t154)))) (not (and (exists @t42 @t154) @t78))))) % 0.37/0.74 (assume @p177 (forall @t11 (=> @t54 (forall @t47 (=> @t75 (forall @t42 (=> (tptp.element @t21 @t1) (=> @t118 (tptp.in @t21 @t74))))))))) % 0.37/0.74 (assume @p178 (forall @t11 (=> @t69 (=> @t13 (forall @t47 (=> @t140 (= (= @t2 @t84) (and (= @t126 @t73) (forall @t25 (and (=> @t155 @t156) (=> @t156 @t155))))))))))) % 0.37/0.74 (assume @p179 (forall @t61 (=> @t95 (not (and (tptp.in @t2 @t149) @t145))))) % 0.37/0.74 (assume @p180 @t160) % 0.37/0.74 (assume @p181 (forall @t11 (=> @t12 (=> (forall @t39 (not @t68)) @t50)))) % 0.37/0.74 (assume @p182 (forall @t61 (not (and @t5 @t153 (tptp.empty @t21))))) % 0.37/0.74 (assume @p183 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 0.37/0.74 (assume @p184 (forall @t6 (not (and @t29 @t7)))) % 0.37/0.74 (assume @p185 (forall @t61 (=> (and @t29 @t150) (tptp.disjoint @t1 @t21)))) % 0.37/0.74 (assume @p186 (forall @t11 (=> @t12 (=> (or @t162 @t161) @t50)))) % 0.37/0.74 (assume @p187 (forall @t11 (=> @t12 (= @t162 @t161)))) % 0.37/0.74 (assume @p188 (forall @t6 (= (= (tptp.set_difference @t1 @t107) @t1) @t4))) % 0.37/0.74 (assume @p189 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t55))) % 0.37/0.74 (assume @p190 (forall @t11 (=> @t10 @t50))) % 0.37/0.74 (assume @p191 (forall @t6 (=> (tptp.subset @t55 @t107) @t30))) % 0.37/0.74 (assume @p192 (forall @t11 (and (= (tptp.relation_dom @t26) @t1) (= (tptp.relation_rng @t26) @t1)))) % 0.37/0.74 (assume @p193 (forall @t110 (=> (tptp.relation @t20) (= (tptp.in @t76 (tptp.relation_composition (tptp.identity_relation @t21) @t20)) (and @t109 (tptp.in @t76 @t20)))))) % 0.37/0.74 (assume @p194 (forall @t6 (not (and @t5 @t58)))) % 0.37/0.74 (assume @p195 (forall @t6 (tptp.subset @t1 @t18))) % 0.37/0.74 (assume @p196 (forall @t6 (= @t78 (= @t71 @t1)))) % 0.37/0.74 (assume @p197 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_dom @t123)) (and @t5 @t134))))) % 0.37/0.74 (assume @p198 (forall @t6 (=> @t28 (tptp.subset @t163 @t2)))) % 0.37/0.74 (assume @p199 (forall @t6 (not (and @t10 @t83 @t58)))) % 0.37/0.74 (assume @p200 (forall @t61 (=> @t139 (= @t135 (and @t134 (= @t2 @t136)))))) % 0.37/0.74 (assume @p201 (forall @t61 (=> (and @t29 @t119) (tptp.subset (tptp.set_union2 @t1 @t21) @t2)))) % 0.37/0.74 (assume @p202 (forall @t61 (=> @t164 @t30))) % 0.37/0.74 (assume @p203 (forall @t6 (=> @t28 (= (tptp.relation_dom @t163) @t127)))) % 0.37/0.74 (assume @p204 (forall @t6 (=> @t28 (= @t163 (tptp.relation_composition @t26 @t2))))) % 0.37/0.74 (assume @p205 (forall @t6 (=> @t28 (tptp.subset (tptp.relation_rng @t163) @t116)))) % 0.37/0.74 (assume @p206 (forall @t11 (= (tptp.union @t56) @t1))) % 0.37/0.74 (assume @p207 (forall @t11 (exists @t47 (and @t5 @t122 (forall @t42 (not (and @t53 (forall @t46 (not (and @t34 (forall @t44 (=> (tptp.subset @t31 @t21) (tptp.in @t31 @t20))))))))) @t120)))) % 0.37/0.74 (assume @p208 (forall @t61 (=> @t164 (= @t2 @t21)))) % 0.37/0.74 (step @p209 :rule aci_norm :args ((= (or @t169 (or @t165 @t157)) @t168))) % 0.37/0.74 (step @p210 :rule bool-impl-elim :args (@t13 @t157)) % 0.37/0.74 (step @p211 :rule bool-and-de-morgan :args (@t12 @t9 true)) % 0.37/0.74 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or @t170 @t158))) % 0.37/0.74 (step @p213 :rule trans :premises (@p212 @p209)) % 0.37/0.74 (step @p214 :rule bool-impl-elim :args (@t69 @t158)) % 0.37/0.74 (step @p215 :rule trans :premises (@p214 @p213)) % 0.37/0.74 (step @p216 :rule cong :premises (@p215) :args (@t159)) % 0.37/0.74 (step @p217 :rule cong :premises (@p216) :args (@t160)) % 0.37/0.74 (step @p218 :rule eq_resolve :premises (@p180 @p217)) % 0.37/0.74 (step @p219 :rule skolemize :premises (@p218)) % 0.37/0.74 (step @p220 :rule cnf_or_neg :args (@t184 3)) % 0.37/0.74 (step @p221 :rule chain_m_resolution :premises (@p220 @p219) :args ((not @t177) @t185 @t186)) % 0.37/0.74 (step @p222 :rule aci_norm :args ((= (or @t169 (or @t165 @t187)) @t188))) % 0.37/0.74 (step @p223 :rule bool-impl-elim :args (@t13 @t187)) % 0.37/0.74 (step @p224 :rule nary_cong :premises (@p211 @p223) :args ((or @t170 @t189))) % 0.37/0.74 (step @p225 :rule trans :premises (@p224 @p222)) % 0.37/0.74 (step @p226 :rule bool-impl-elim :args (@t69 @t189)) % 0.37/0.74 (step @p227 :rule trans :premises (@p226 @p225)) % 0.37/0.74 (step @p228 :rule cong :premises (@p227) :args ((forall @t11 (=> @t69 @t189)))) % 0.37/0.74 (step @p229 :rule eq-symm :args (@t84 @t77)) % 0.37/0.74 (step @p230 :rule refl :args (@t13)) % 0.37/0.74 (step @p231 :rule cong :premises (@p230 @p229) :args (@t85)) % 0.37/0.74 (step @p232 :rule refl :args (@t69)) % 0.37/0.74 (step @p233 :rule cong :premises (@p232 @p231) :args (@t86)) % 0.37/0.74 (step @p234 :rule cong :premises (@p233) :args (@t87)) % 0.37/0.74 (step @p235 :rule trans :premises (@p234 @p228)) % 0.37/0.74 (step @p236 :rule eq_resolve :premises (@p42 @p235)) % 0.37/0.74 (step @p237 :rule eq-symm :args (@t190 @t172)) % 0.37/0.74 (step @p238 :rule refl :args (@t179)) % 0.37/0.74 (step @p239 :rule refl :args (@t181)) % 0.37/0.74 (step @p240 :rule refl :args (@t183)) % 0.37/0.74 (step @p241 :rule nary_cong :premises (@p240 @p239 @p238 @p237) :args (@t191)) % 0.37/0.74 (step @p242 :rule refl :args (@t192)) % 0.37/0.74 (step @p243 :rule cong :premises (@p242 @p241) :args ((=> @t192 @t191))) % 0.37/0.74 (assume-push @p293 @t192) % 0.37/0.74 (step @p245 :rule instantiate :premises (@p236) :args (@t193)) % 0.37/0.74 (step-pop @p294 :rule scope :premises (@p245)) % 0.37/0.74 (step @p246 :rule process_scope :premises (@p294) :args (@t191)) % 0.37/0.74 (step @p248 :rule eq_resolve :premises (@p246 @p243)) % 0.37/0.74 (step @p249 :rule implies_elim :premises (@p248)) % 0.37/0.74 (step @p250 :rule chain_m_resolution :premises (@p249 @p236) :args (@t195 @t196 (@list @t192))) % 0.37/0.74 (step @p251 :rule bool-double-not-elim :args (@t178)) % 0.37/0.74 (step @p252 :rule refl :args (@t184)) % 0.37/0.74 (step @p253 :rule nary_cong :premises (@p252 @p251) :args ((or @t184 (not @t179)))) % 0.37/0.74 (step @p254 :rule cnf_or_neg :args (@t184 2)) % 0.37/0.74 (step @p255 :rule eq_resolve :premises (@p254 @p253)) % 0.37/0.74 (step @p256 :rule reordering :premises (@p255) :args ((or @t178 @t184))) % 0.37/0.74 (step @p257 :rule chain_m_resolution :premises (@p256 @p219) :args (@t178 @t185 @t186)) % 0.37/0.74 (step @p258 :rule bool-double-not-elim :args (@t180)) % 0.37/0.74 (step @p259 :rule nary_cong :premises (@p252 @p258) :args ((or @t184 (not @t181)))) % 0.37/0.74 (step @p260 :rule cnf_or_neg :args (@t184 1)) % 0.37/0.74 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.37/0.74 (step @p262 :rule reordering :premises (@p261) :args ((or @t180 @t184))) % 0.37/0.74 (step @p263 :rule chain_m_resolution :premises (@p262 @p219) :args (@t180 @t185 @t186)) % 0.37/0.74 (step @p264 :rule bool-double-not-elim :args (@t182)) % 0.37/0.74 (step @p265 :rule nary_cong :premises (@p252 @p264) :args ((or @t184 (not @t183)))) % 0.37/0.74 (step @p266 :rule cnf_or_neg :args (@t184 0)) % 0.37/0.74 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.37/0.74 (step @p268 :rule reordering :premises (@p267) :args ((or @t182 @t184))) % 0.37/0.74 (step @p269 :rule chain_m_resolution :premises (@p268 @p219) :args (@t182 @t185 @t186)) % 0.37/0.74 (step @p270 :rule cnf_or_pos :args (@t195)) % 0.37/0.74 (step @p271 :rule reordering :premises (@p270) :args ((or @t183 @t181 @t179 @t194 (not @t195)))) % 0.37/0.74 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p263 @p257 @p250) :args (@t194 (@list false false false false) (@list @t182 @t180 @t178 @t195))) % 0.37/0.74 (step @p273 :rule symm :premises (@p272)) % 0.37/0.74 (step @p274 :rule cong :premises (@p273) :args (@t197)) % 0.37/0.74 (step @p275 :rule bool-impl-elim :args (@t12 @t143)) % 0.37/0.74 (step @p276 :rule cong :premises (@p275) :args (@t144)) % 0.37/0.74 (step @p277 :rule eq_resolve :premises (@p156 @p276)) % 0.37/0.74 (step @p278 :rule instantiate :premises (@p277) :args (@t193)) % 0.37/0.74 (step @p279 :rule cnf_or_pos :args (@t202)) % 0.37/0.74 (step @p280 :rule reordering :premises (@p279) :args ((or @t183 @t201 (not @t202)))) % 0.37/0.74 (step @p281 :rule chain_m_resolution :premises (@p280 @p269 @p278) :args (@t201 (@list false false) (@list @t182 @t202))) % 0.37/0.74 (step @p282 :rule cnf_and_pos :args (@t201 0)) % 0.37/0.74 (step @p283 :rule reordering :premises (@p282) :args ((or @t200 @t203))) % 0.37/0.74 (step @p284 :rule chain_m_resolution :premises (@p283 @p281) :args (@t200 @t196 @t204)) % 0.37/0.74 (step @p285 :rule trans :premises (@p284 @p274)) % 0.37/0.74 (step @p286 :rule cong :premises (@p273) :args (@t198)) % 0.37/0.74 (step @p287 :rule cnf_and_pos :args (@t201 1)) % 0.37/0.74 (step @p288 :rule reordering :premises (@p287) :args ((or @t199 @t203))) % 0.37/0.74 (step @p289 :rule chain_m_resolution :premises (@p288 @p281) :args (@t199 @t196 @t204)) % 0.37/0.74 (step @p290 :rule trans :premises (@p289 @p286)) % 0.37/0.74 (step @p291 :rule cnf_and_neg :args (@t177)) % 0.37/0.74 (step @p292 false :rule chain_m_resolution :premises (@p291 @p290 @p285 @p221) :args (false (@list false false true) (@list @t174 @t176 @t177))) % 0.37/0.74 ) % 0.37/0.74 % SZS output end Proof % 0.37/0.74 % cvc5 exiting %------------------------------------------------------------------------------