%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU225+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 : n010.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 08:51:02 AM UTC 2026 % Result : Theorem 0.85s 1.04s % Output : Proof 0.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU225+2 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:42:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.54 %----Proving TF0_NAR, FOF, or CNF % 0.85/1.04 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.85/1.04 % SZS status Theorem % 0.85/1.04 % SZS output start Proof % 0.85/1.04 ( % 0.85/1.04 (declare-sort $$unsorted 0) % 0.85/1.04 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.function_inverse (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.function (-> $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.empty_set $$unsorted) % 0.85/1.04 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.85/1.04 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.85/1.04 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.85/1.04 (define @t1 () (@var "A" $$unsorted)) % 0.85/1.04 (define @t2 () (@var "B" $$unsorted)) % 0.85/1.04 (define @t3 () (tptp.in @t2 @t1)) % 0.85/1.04 (define @t4 () (not @t3)) % 0.85/1.04 (define @t5 () (tptp.in @t1 @t2)) % 0.85/1.04 (define @t6 () (@list @t1 @t2)) % 0.85/1.04 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.85/1.04 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.85/1.04 (define @t9 () (tptp.function @t1)) % 0.85/1.04 (define @t10 () (tptp.empty @t1)) % 0.85/1.04 (define @t11 () (@list @t1)) % 0.85/1.04 (define @t12 () (tptp.relation @t1)) % 0.85/1.04 (define @t13 () (tptp.one_to_one @t1)) % 0.85/1.04 (define @t14 () (and @t12 @t9 @t13)) % 0.85/1.04 (define @t15 () (and @t12 @t10 @t9)) % 0.85/1.04 (define @t16 () (tptp.unordered_pair @t1 @t2)) % 0.85/1.04 (define @t17 () (tptp.set_union2 @t2 @t1)) % 0.85/1.04 (define @t18 () (tptp.set_union2 @t1 @t2)) % 0.85/1.04 (define @t19 () (tptp.set_intersection2 @t1 @t2)) % 0.85/1.04 (define @t20 () (@var "D" $$unsorted)) % 0.85/1.04 (define @t21 () (@var "C" $$unsorted)) % 0.85/1.04 (define @t22 () (tptp.in @t21 @t1)) % 0.85/1.04 (define @t23 () (tptp.ordered_pair @t21 @t20)) % 0.85/1.04 (define @t24 () (tptp.in @t23 @t2)) % 0.85/1.04 (define @t25 () (@list @t21 @t20)) % 0.85/1.04 (define @t26 () (tptp.identity_relation @t1)) % 0.85/1.04 (define @t27 () (= @t2 @t26)) % 0.85/1.04 (define @t28 () (tptp.relation @t2)) % 0.85/1.04 (define @t29 () (tptp.subset @t1 @t2)) % 0.85/1.04 (define @t30 () (= @t1 @t2)) % 0.85/1.04 (define @t31 () (@var "E" $$unsorted)) % 0.85/1.04 (define @t32 () (tptp.ordered_pair @t20 @t31)) % 0.85/1.04 (define @t33 () (tptp.in @t32 @t1)) % 0.85/1.04 (define @t34 () (tptp.in @t20 @t2)) % 0.85/1.04 (define @t35 () (tptp.in @t32 @t21)) % 0.85/1.04 (define @t36 () (@list @t20 @t31)) % 0.85/1.04 (define @t37 () (tptp.relation_dom_restriction @t1 @t2)) % 0.85/1.04 (define @t38 () (tptp.relation @t21)) % 0.85/1.04 (define @t39 () (@list @t2 @t21)) % 0.85/1.04 (define @t40 () (tptp.in @t31 @t1)) % 0.85/1.04 (define @t41 () (tptp.relation_rng_restriction @t1 @t2)) % 0.85/1.04 (define @t42 () (@list @t21)) % 0.85/1.04 (define @t43 () (tptp.in @t31 @t2)) % 0.85/1.04 (define @t44 () (@list @t31)) % 0.85/1.04 (define @t45 () (tptp.in @t20 @t21)) % 0.85/1.04 (define @t46 () (@list @t20)) % 0.85/1.04 (define @t47 () (@list @t2)) % 0.85/1.04 (define @t48 () (= @t2 tptp.empty_set)) % 0.85/1.04 (define @t49 () (= @t2 (tptp.set_meet @t1))) % 0.85/1.04 (define @t50 () (= @t1 tptp.empty_set)) % 0.85/1.04 (define @t51 () (tptp.in @t21 @t20)) % 0.85/1.04 (define @t52 () (tptp.in @t20 @t1)) % 0.85/1.04 (define @t53 () (tptp.in @t21 @t2)) % 0.85/1.04 (define @t54 () (not @t50)) % 0.85/1.04 (define @t55 () (tptp.singleton @t1)) % 0.85/1.04 (define @t56 () (tptp.powerset @t1)) % 0.85/1.04 (define @t57 () (tptp.in @t23 @t1)) % 0.85/1.04 (define @t58 () (tptp.empty @t2)) % 0.85/1.04 (define @t59 () (tptp.element @t2 @t1)) % 0.85/1.04 (define @t60 () (not @t10)) % 0.85/1.04 (define @t61 () (@list @t1 @t2 @t21)) % 0.85/1.04 (define @t62 () (@var "F" $$unsorted)) % 0.85/1.04 (define @t63 () (tptp.cartesian_product2 @t1 @t2)) % 0.85/1.04 (define @t64 () (forall @t42 (=> @t22 @t53))) % 0.85/1.04 (define @t65 () (tptp.apply @t1 @t2)) % 0.85/1.04 (define @t66 () (= @t21 @t65)) % 0.85/1.04 (define @t67 () (tptp.relation_dom @t1)) % 0.85/1.04 (define @t68 () (tptp.in @t2 @t67)) % 0.85/1.04 (define @t69 () (tptp.in (tptp.ordered_pair @t2 @t21) @t1)) % 0.85/1.04 (define @t70 () (and @t12 @t9)) % 0.85/1.04 (define @t71 () (tptp.cast_to_subset @t1)) % 0.85/1.04 (define @t72 () (tptp.set_difference @t1 @t2)) % 0.85/1.04 (define @t73 () (tptp.in (tptp.ordered_pair @t20 @t21) @t1)) % 0.85/1.04 (define @t74 () (tptp.relation_rng @t1)) % 0.85/1.04 (define @t75 () (tptp.subset_complement @t1 @t2)) % 0.85/1.04 (define @t76 () (tptp.element @t2 @t56)) % 0.85/1.04 (define @t77 () (tptp.ordered_pair @t1 @t2)) % 0.85/1.04 (define @t78 () (tptp.relation_inverse @t1)) % 0.85/1.04 (define @t79 () (tptp.disjoint @t1 @t2)) % 0.85/1.04 (define @t80 () (= @t2 @t21)) % 0.85/1.04 (define @t81 () (tptp.relation_composition @t1 @t2)) % 0.85/1.04 (define @t82 () (tptp.complements_of_subsets @t1 @t2)) % 0.85/1.04 (define @t83 () (tptp.powerset @t56)) % 0.85/1.04 (define @t84 () (tptp.element @t2 @t83)) % 0.85/1.04 (define @t85 () (not @t30)) % 0.85/1.04 (define @t86 () (tptp.function_inverse @t1)) % 0.85/1.04 (define @t87 () (tptp.relation @t78)) % 0.85/1.04 (define @t88 () (tptp.relation @t81)) % 0.85/1.04 (define @t89 () (and @t12 @t28)) % 0.85/1.04 (define @t90 () (tptp.union_of_subsets @t1 @t2)) % 0.85/1.04 (define @t91 () (tptp.relation @t26)) % 0.85/1.04 (define @t92 () (forall @t11 @t91)) % 0.85/1.04 (define @t93 () (tptp.meet_of_subsets @t1 @t2)) % 0.85/1.04 (define @t94 () (tptp.subset_difference @t1 @t2 @t21)) % 0.85/1.04 (define @t95 () (tptp.element @t21 @t56)) % 0.85/1.04 (define @t96 () (and @t76 @t95)) % 0.85/1.04 (define @t97 () (tptp.relation @t37)) % 0.85/1.04 (define @t98 () (tptp.relation_composition @t2 @t1)) % 0.85/1.04 (define @t99 () (and @t10 @t28)) % 0.85/1.04 (define @t100 () (tptp.relation tptp.empty_set)) % 0.85/1.04 (define @t101 () (tptp.empty tptp.empty_set)) % 0.85/1.04 (define @t102 () (and @t12 (tptp.relation_empty_yielding @t1))) % 0.85/1.04 (define @t103 () (tptp.function @t2)) % 0.85/1.04 (define @t104 () (tptp.function @t26)) % 0.85/1.04 (define @t105 () (forall @t11 (and @t91 @t104))) % 0.85/1.04 (define @t106 () (not @t58)) % 0.85/1.04 (define @t107 () (tptp.empty @t67)) % 0.85/1.04 (define @t108 () (and @t60 @t12)) % 0.85/1.04 (define @t109 () (tptp.empty @t74)) % 0.85/1.04 (define @t110 () (tptp.disjoint @t55 @t2)) % 0.85/1.04 (define @t111 () (tptp.singleton @t2)) % 0.85/1.04 (define @t112 () (tptp.union @t2)) % 0.85/1.04 (define @t113 () (tptp.in @t1 @t21)) % 0.85/1.04 (define @t114 () (@list @t1 @t2 @t21 @t20)) % 0.85/1.04 (define @t115 () (tptp.element @t1 (tptp.powerset @t2))) % 0.85/1.04 (define @t116 () (tptp.relation_dom @t21)) % 0.85/1.04 (define @t117 () (tptp.relation_dom_restriction @t21 @t1)) % 0.85/1.04 (define @t118 () (tptp.in @t2 (tptp.relation_dom @t117))) % 0.85/1.04 (define @t119 () (tptp.function @t21)) % 0.85/1.04 (define @t120 () (and @t38 @t119)) % 0.85/1.04 (define @t121 () (tptp.set_difference @t2 @t21)) % 0.85/1.04 (define @t122 () (= @t1 @t21)) % 0.85/1.04 (define @t123 () (tptp.relation_rng @t21)) % 0.85/1.04 (define @t124 () (tptp.relation_rng @t41)) % 0.85/1.04 (define @t125 () (tptp.relation_rng @t2)) % 0.85/1.04 (define @t126 () (tptp.cartesian_product2 @t1 @t21)) % 0.85/1.04 (define @t127 () (not @t53)) % 0.85/1.04 (define @t128 () (tptp.subset @t21 @t2)) % 0.85/1.04 (define @t129 () (forall @t42 (not (and @t128 (not (tptp.are_equipotent @t21 @t2)) @t127)))) % 0.85/1.04 (define @t130 () (tptp.powerset @t21)) % 0.85/1.04 (define @t131 () (forall @t25 (=> (and @t53 (tptp.subset @t20 @t21)) @t34))) % 0.85/1.04 (define @t132 () (tptp.relation_dom_restriction @t21 @t2)) % 0.85/1.04 (define @t133 () (tptp.relation_image @t2 @t1)) % 0.85/1.04 (define @t134 () (tptp.relation_dom @t2)) % 0.85/1.04 (define @t135 () (tptp.set_intersection2 @t134 @t1)) % 0.85/1.04 (define @t136 () (tptp.relation_rng @t81)) % 0.85/1.04 (define @t137 () (tptp.relation_inverse_image @t21 @t2)) % 0.85/1.04 (define @t138 () (tptp.relation_inverse_image @t2 @t1)) % 0.85/1.04 (define @t139 () (tptp.set_intersection2 @t2 @t21)) % 0.85/1.04 (define @t140 () (tptp.subset @t1 @t21)) % 0.85/1.04 (define @t141 () (tptp.element @t1 @t2)) % 0.85/1.04 (define @t142 () (tptp.in @t1 @t116)) % 0.85/1.04 (define @t143 () (tptp.in @t77 @t21)) % 0.85/1.04 (define @t144 () (tptp.apply @t21 @t1)) % 0.85/1.04 (define @t145 () (tptp.relation_composition @t21 @t2)) % 0.85/1.04 (define @t146 () (tptp.in @t1 (tptp.relation_dom @t145))) % 0.85/1.04 (define @t147 () (and @t28 @t103)) % 0.85/1.04 (define @t148 () (tptp.apply @t2 @t1)) % 0.85/1.04 (define @t149 () (= (tptp.apply (tptp.relation_composition @t2 @t21) @t1) (tptp.apply @t21 @t148))) % 0.85/1.04 (define @t150 () (tptp.in @t1 @t134)) % 0.85/1.04 (define @t151 () (=> @t150 @t149)) % 0.85/1.04 (define @t152 () (forall @t42 (=> @t120 @t151))) % 0.85/1.04 (define @t153 () (=> @t147 @t152)) % 0.85/1.04 (define @t154 () (forall @t6 @t153)) % 0.85/1.04 (define @t155 () (tptp.relation_field @t21)) % 0.85/1.04 (define @t156 () (tptp.apply @t2 @t21)) % 0.85/1.04 (define @t157 () (tptp.apply @t26 @t2)) % 0.85/1.04 (define @t158 () (=> @t3 (= @t157 @t2))) % 0.85/1.04 (define @t159 () (forall @t6 @t158)) % 0.85/1.04 (define @t160 () (tptp.in @t2 @t21)) % 0.85/1.04 (define @t161 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.85/1.04 (define @t162 () (and @t22 @t53)) % 0.85/1.04 (define @t163 () (not @t79)) % 0.85/1.04 (define @t164 () (tptp.subset_complement @t1 @t21)) % 0.85/1.04 (define @t165 () (tptp.disjoint @t2 @t21)) % 0.85/1.04 (define @t166 () (tptp.relation_dom @t81)) % 0.85/1.04 (define @t167 () (not @t48)) % 0.85/1.04 (define @t168 () (tptp.element @t2 @t130)) % 0.85/1.04 (define @t169 () (tptp.in @t21 @t19)) % 0.85/1.04 (define @t170 () (and (tptp.in @t21 @t74) (= @t20 @t156))) % 0.85/1.04 (define @t171 () (and (tptp.in @t20 @t67) (= @t21 (tptp.apply @t1 @t20)))) % 0.85/1.04 (define @t172 () (tptp.function_inverse @t2)) % 0.85/1.04 (define @t173 () (= @t74 tptp.empty_set)) % 0.85/1.04 (define @t174 () (= @t67 tptp.empty_set)) % 0.85/1.04 (define @t175 () (= (tptp.apply @t117 @t2) (tptp.apply @t21 @t2))) % 0.85/1.04 (define @t176 () (tptp.relation_rng @t26)) % 0.85/1.04 (define @t177 () (tptp.relation_dom @t26)) % 0.85/1.04 (define @t178 () (and (= @t177 @t1) (= @t176 @t1))) % 0.85/1.04 (define @t179 () (forall @t11 @t178)) % 0.85/1.04 (define @t180 () (=> @t3 @t175)) % 0.85/1.04 (define @t181 () (forall @t61 (=> @t120 @t180))) % 0.85/1.04 (define @t182 () (not @t181)) % 0.85/1.04 (define @t183 () (tptp.relation_dom_restriction @t2 @t1)) % 0.85/1.04 (define @t184 () (= @t55 (tptp.unordered_pair @t2 @t21))) % 0.85/1.04 (define @t185 () (= @t183 (tptp.relation_composition @t26 @t2))) % 0.85/1.04 (define @t186 () (forall @t6 (=> @t28 @t185))) % 0.85/1.04 (define @t187 () (not @t119)) % 0.85/1.04 (define @t188 () (not @t38)) % 0.85/1.04 (define @t189 () (or @t188 @t187 @t4 @t175)) % 0.85/1.04 (define @t190 () (or @t188 @t187)) % 0.85/1.04 (define @t191 () (not @t120)) % 0.85/1.04 (define @t192 () (forall @t61 @t189)) % 0.85/1.04 (define @t193 () (@quantifiers_skolemize @t192 2)) % 0.85/1.04 (define @t194 () (tptp.relation @t193)) % 0.85/1.04 (define @t195 () (@quantifiers_skolemize @t192 1)) % 0.85/1.04 (define @t196 () (@quantifiers_skolemize @t192 0)) % 0.85/1.04 (define @t197 () (tptp.relation_dom_restriction @t193 @t196)) % 0.85/1.04 (define @t198 () (= (tptp.apply @t197 @t195) (tptp.apply @t193 @t195))) % 0.85/1.04 (define @t199 () (tptp.in @t195 @t196)) % 0.85/1.04 (define @t200 () (not @t199)) % 0.85/1.04 (define @t201 () (tptp.function @t193)) % 0.85/1.04 (define @t202 () (not @t201)) % 0.85/1.04 (define @t203 () (not @t194)) % 0.85/1.04 (define @t204 () (or @t203 @t202 @t200 @t198)) % 0.85/1.04 (define @t205 () (@list true)) % 0.85/1.04 (define @t206 () (@list @t204)) % 0.85/1.04 (define @t207 () (forall @t11 @t104)) % 0.85/1.04 (define @t208 () (@list @t1)) % 0.85/1.04 (define @t209 () (and @t92 @t207)) % 0.85/1.04 (define @t210 () (@list @t196)) % 0.85/1.04 (define @t211 () (@var "BOUND_VARIABLE_9815" $$unsorted)) % 0.85/1.04 (define @t212 () (= (tptp.apply (tptp.relation_composition @t2 @t211) @t1) (tptp.apply @t211 @t148))) % 0.85/1.04 (define @t213 () (not (tptp.function @t211))) % 0.85/1.04 (define @t214 () (not (tptp.relation @t211))) % 0.85/1.04 (define @t215 () (not @t150)) % 0.85/1.04 (define @t216 () (not @t103)) % 0.85/1.04 (define @t217 () (not @t28)) % 0.85/1.04 (define @t218 () (or @t214 @t213 @t212)) % 0.85/1.04 (define @t219 () (or @t217 @t216 @t215 @t218)) % 0.85/1.04 (define @t220 () (forall (@list @t1 @t2 @t211) @t219)) % 0.85/1.04 (define @t221 () (@list @t211)) % 0.85/1.04 (define @t222 () (forall @t221 @t219)) % 0.85/1.04 (define @t223 () (forall @t221 @t218)) % 0.85/1.04 (define @t224 () (or @t217 @t216 @t215 @t223)) % 0.85/1.04 (define @t225 () (or @t188 @t187 @t149)) % 0.85/1.04 (define @t226 () (forall @t42 @t225)) % 0.85/1.04 (define @t227 () (or @t217 @t216 @t215 @t226)) % 0.85/1.04 (define @t228 () (or @t215 @t226)) % 0.85/1.04 (define @t229 () (or @t215 @t225)) % 0.85/1.04 (define @t230 () (or @t188 @t187 @t215 @t149)) % 0.85/1.04 (define @t231 () (tptp.identity_relation @t196)) % 0.85/1.04 (define @t232 () (= @t2 @t157)) % 0.85/1.04 (define @t233 () (tptp.apply @t231 @t195)) % 0.85/1.04 (define @t234 () (= @t195 @t233)) % 0.85/1.04 (define @t235 () (or @t200 @t234)) % 0.85/1.04 (define @t236 () (@list false false)) % 0.85/1.04 (define @t237 () (tptp.apply @t193 @t233)) % 0.85/1.04 (define @t238 () (tptp.relation_composition @t231 @t193)) % 0.85/1.04 (define @t239 () (= @t197 @t238)) % 0.85/1.04 (define @t240 () (or @t203 @t239)) % 0.85/1.04 (define @t241 () (tptp.apply @t238 @t195)) % 0.85/1.04 (define @t242 () (= @t241 @t237)) % 0.85/1.04 (define @t243 () (= @t1 @t176)) % 0.85/1.04 (define @t244 () (forall @t11 @t243)) % 0.85/1.04 (define @t245 () (= @t1 @t177)) % 0.85/1.04 (define @t246 () (forall @t11 @t245)) % 0.85/1.04 (define @t247 () (and @t246 @t244)) % 0.85/1.04 (define @t248 () (tptp.in @t195 (tptp.relation_dom @t231))) % 0.85/1.04 (define @t249 () (not @t248)) % 0.85/1.04 (define @t250 () (tptp.function @t231)) % 0.85/1.04 (define @t251 () (not @t250)) % 0.85/1.04 (define @t252 () (tptp.relation @t231)) % 0.85/1.04 (define @t253 () (not @t252)) % 0.85/1.04 (define @t254 () (or @t253 @t251 @t249 @t203 @t202 @t242)) % 0.85/1.04 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.85/1.04 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.85/1.04 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.85/1.04 (assume @p4 (forall @t11 (=> @t10 @t12))) % 0.85/1.04 (assume @p5 (forall @t11 (=> @t15 @t14))) % 0.85/1.04 (assume @p6 (forall @t6 (= @t16 (tptp.unordered_pair @t2 @t1)))) % 0.85/1.04 (assume @p7 (forall @t6 (= @t18 @t17))) % 0.85/1.04 (assume @p8 (forall @t6 (= @t19 (tptp.set_intersection2 @t2 @t1)))) % 0.85/1.04 (assume @p9 (forall @t6 (=> @t28 (= @t27 (forall @t25 (= @t24 (and @t22 (= @t21 @t20)))))))) % 0.85/1.04 (assume @p10 (forall @t6 (= @t30 (and @t29 (tptp.subset @t2 @t1))))) % 0.85/1.04 (assume @p11 (forall @t11 (=> @t12 (forall @t39 (=> @t38 (= (= @t21 @t37) (forall @t36 (= @t35 (and @t34 @t33))))))))) % 0.85/1.04 (assume @p12 (forall @t6 (=> @t28 (forall @t42 (=> @t38 (= (= @t21 @t41) (forall @t36 (= @t35 (and @t40 (tptp.in @t32 @t2)))))))))) % 0.85/1.04 (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))))))))) % 0.85/1.04 (assume @p14 (forall @t11 (=> @t12 (forall @t39 (= (= @t21 (tptp.relation_inverse_image @t1 @t2)) (forall @t46 (= @t45 (exists @t44 (and @t33 @t43))))))))) % 0.85/1.04 (assume @p15 (forall @t11 (= @t12 (forall @t47 (not (and @t3 (forall @t25 (not (= @t2 @t23))))))))) % 0.85/1.04 (assume @p16 (forall @t6 (and (=> @t54 (= @t49 (forall @t42 (= @t53 (forall @t46 (=> @t52 @t51)))))) (=> @t50 (= @t49 @t48))))) % 0.85/1.04 (assume @p17 (forall @t6 (= (= @t2 @t55) (forall @t42 (= @t53 (= @t21 @t1)))))) % 0.85/1.04 (assume @p18 (forall @t11 (= @t50 (forall @t47 @t4)))) % 0.85/1.04 (assume @p19 (forall @t6 (= (= @t2 @t56) (forall @t42 (= @t53 (tptp.subset @t21 @t1)))))) % 0.85/1.04 (assume @p20 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t30 (forall @t25 (= @t57 @t24)))))))) % 0.85/1.04 (assume @p21 (forall @t6 (and (=> @t60 (= @t59 @t3)) (=> @t10 (= @t59 @t58))))) % 0.85/1.04 (assume @p22 (forall @t61 (= (= @t21 @t16) (forall @t46 (= @t45 (or (= @t20 @t1) (= @t20 @t2))))))) % 0.85/1.04 (assume @p23 (forall @t61 (= (= @t21 @t18) (forall @t46 (= @t45 (or @t52 @t34)))))) % 0.85/1.04 (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))))))))) % 0.85/1.04 (assume @p25 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t29 (forall @t25 (=> @t57 @t24)))))))) % 0.85/1.04 (assume @p26 (forall @t6 (= @t29 @t64))) % 0.85/1.04 (assume @p27 (forall @t61 (= (= @t21 @t19) (forall @t46 (= @t45 (and @t52 @t34)))))) % 0.85/1.04 (assume @p28 (forall @t11 (=> @t70 (forall @t39 (and (=> @t68 (= @t66 @t69)) (=> (not @t68) (= @t66 (= @t21 tptp.empty_set)))))))) % 0.85/1.04 (assume @p29 (forall @t11 (=> @t12 (forall @t47 (= (= @t2 @t67) (forall @t42 (= @t53 (exists @t46 @t57)))))))) % 0.85/1.04 (assume @p30 (forall @t11 (= @t71 @t1))) % 0.85/1.04 (assume @p31 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t42 (= @t53 (exists @t46 (and @t51 @t52))))))) % 0.85/1.04 (assume @p32 (forall @t61 (= (= @t21 @t72) (forall @t46 (= @t45 (and @t52 (not @t34))))))) % 0.85/1.04 (assume @p33 (forall @t11 (=> @t12 (forall @t47 (= (= @t2 @t74) (forall @t42 (= @t53 (exists @t46 @t73)))))))) % 0.85/1.04 (assume @p34 (forall @t6 (=> @t76 (= @t75 @t72)))) % 0.85/1.04 (assume @p35 (forall @t6 (= @t77 (tptp.unordered_pair @t16 @t55)))) % 0.85/1.04 (assume @p36 (forall @t11 (=> @t12 (= (tptp.relation_field @t1) (tptp.set_union2 @t67 @t74))))) % 0.85/1.04 (assume @p37 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= (= @t2 @t78) (forall @t25 (= @t24 @t73)))))))) % 0.85/1.04 (assume @p38 (forall @t6 (= @t79 (= @t19 tptp.empty_set)))) % 0.85/1.04 (assume @p39 (forall @t11 (=> @t70 (= @t13 (forall @t39 (=> (and @t68 (tptp.in @t21 @t67) (= @t65 (tptp.apply @t1 @t21))) @t80)))))) % 0.85/1.04 (assume @p40 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (forall @t42 (=> @t38 (= (= @t21 @t81) (forall @t36 (= @t35 (exists (@list @t62) (and (tptp.in (tptp.ordered_pair @t20 @t62) @t1) (tptp.in (tptp.ordered_pair @t62 @t31) @t2))))))))))))) % 0.85/1.04 (assume @p41 (forall @t6 (=> @t84 (forall @t42 (=> (tptp.element @t21 @t83) (= (= @t21 @t82) (forall @t46 (=> (tptp.element @t20 @t56) (= @t45 (tptp.in (tptp.subset_complement @t1 @t20) @t2)))))))))) % 0.85/1.04 (assume @p42 (forall @t6 (= @t8 (and @t29 @t85)))) % 0.85/1.04 (assume @p43 (forall @t11 (=> @t70 (=> @t13 (= @t86 @t78))))) % 0.85/1.04 (assume @p44 true) % 0.85/1.04 (assume @p45 (forall @t11 (=> @t70 (and (tptp.relation @t86) (tptp.function @t86))))) % 0.85/1.04 (assume @p46 (forall @t11 (tptp.element @t71 @t56))) % 0.85/1.04 (assume @p47 (forall @t6 (=> @t76 (tptp.element @t75 @t56)))) % 0.85/1.04 (assume @p48 (forall @t11 (=> @t12 @t87))) % 0.85/1.04 (assume @p49 (forall @t6 (=> @t89 @t88))) % 0.85/1.04 (assume @p50 (forall @t6 (=> @t84 (tptp.element @t90 @t56)))) % 0.85/1.04 (assume @p51 @t92) % 0.85/1.04 (assume @p52 (forall @t6 (=> @t84 (tptp.element @t93 @t56)))) % 0.85/1.04 (assume @p53 (forall @t61 (=> @t96 (tptp.element @t94 @t56)))) % 0.85/1.04 (assume @p54 (forall @t6 (=> @t12 @t97))) % 0.85/1.04 (assume @p55 (forall @t6 (=> @t84 (tptp.element @t82 @t83)))) % 0.85/1.04 (assume @p56 (forall @t6 (=> @t28 (tptp.relation @t41)))) % 0.85/1.04 (assume @p57 (forall @t11 (exists @t47 @t59))) % 0.85/1.04 (assume @p58 (forall @t6 (=> @t99 (and (tptp.empty @t98) (tptp.relation @t98))))) % 0.85/1.04 (assume @p59 (forall @t11 (=> @t10 (and (tptp.empty @t78) @t87)))) % 0.85/1.04 (assume @p60 (and @t101 @t100 (tptp.relation_empty_yielding tptp.empty_set))) % 0.85/1.04 (assume @p61 (forall @t6 (=> @t102 (and @t97 (tptp.relation_empty_yielding @t37))))) % 0.85/1.04 (assume @p62 (forall @t6 (=> (and @t12 @t9 @t28 @t103) (and @t88 (tptp.function @t81))))) % 0.85/1.04 (assume @p63 (forall @t6 (=> @t89 (tptp.relation @t19)))) % 0.85/1.04 (assume @p64 (forall @t11 (not (tptp.empty @t56)))) % 0.85/1.04 (assume @p65 @t101) % 0.85/1.04 (assume @p66 (forall @t6 (not (tptp.empty @t77)))) % 0.85/1.04 (assume @p67 @t105) % 0.85/1.04 (assume @p68 (forall @t6 (=> @t89 (tptp.relation @t18)))) % 0.85/1.04 (assume @p69 (forall @t11 (not (tptp.empty @t55)))) % 0.85/1.04 (assume @p70 (forall @t6 (=> @t60 (not (tptp.empty @t18))))) % 0.85/1.04 (assume @p71 (forall @t11 (=> @t14 (and @t87 (tptp.function @t78))))) % 0.85/1.04 (assume @p72 (forall @t6 (not (tptp.empty @t16)))) % 0.85/1.04 (assume @p73 (forall @t6 (=> @t60 (not (tptp.empty @t17))))) % 0.85/1.04 (assume @p74 (forall @t6 (=> @t70 (and @t97 (tptp.function @t37))))) % 0.85/1.04 (assume @p75 (and @t101 @t100)) % 0.85/1.04 (assume @p76 (forall @t6 (=> (and @t60 @t106) (not (tptp.empty @t63))))) % 0.85/1.04 (assume @p77 (forall @t11 (=> @t108 (not @t107)))) % 0.85/1.04 (assume @p78 (forall @t11 (=> @t108 (not @t109)))) % 0.85/1.04 (assume @p79 (forall @t11 (=> @t10 (and @t107 (tptp.relation @t67))))) % 0.85/1.04 (assume @p80 (forall @t11 (=> @t10 (and @t109 (tptp.relation @t74))))) % 0.85/1.04 (assume @p81 (forall @t6 (=> @t99 (and (tptp.empty @t81) @t88)))) % 0.85/1.04 (assume @p82 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.85/1.04 (assume @p83 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.85/1.04 (assume @p84 (forall @t6 (=> @t76 (= (tptp.subset_complement @t1 @t75) @t2)))) % 0.85/1.04 (assume @p85 (forall @t11 (=> @t12 (= (tptp.relation_inverse @t78) @t1)))) % 0.85/1.04 (assume @p86 (forall @t6 (=> @t84 (= (tptp.complements_of_subsets @t1 @t82) @t2)))) % 0.85/1.04 (assume @p87 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.85/1.04 (assume @p88 (forall @t11 (not (= @t55 tptp.empty_set)))) % 0.85/1.04 (assume @p89 (forall @t6 (=> @t5 (= (tptp.set_union2 @t55 @t2) @t2)))) % 0.85/1.04 (assume @p90 (forall @t6 (not (and @t110 @t5)))) % 0.85/1.04 (assume @p91 (forall @t6 (=> (not @t5) @t110))) % 0.85/1.04 (assume @p92 (forall @t6 (= (tptp.subset @t55 @t2) @t5))) % 0.85/1.04 (assume @p93 (forall @t6 (= (= @t72 tptp.empty_set) @t29))) % 0.85/1.04 (assume @p94 (forall @t6 (=> @t76 (forall @t42 (=> @t53 @t22))))) % 0.85/1.04 (assume @p95 (forall @t61 (=> @t29 (or @t22 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t21))))))) % 0.85/1.04 (assume @p96 (forall @t6 (= (tptp.subset @t1 @t111) (or @t50 (= @t1 @t111))))) % 0.85/1.04 (assume @p97 (forall @t6 (=> @t5 (tptp.subset @t1 @t112)))) % 0.85/1.04 (assume @p98 (forall @t114 (= (tptp.in @t77 (tptp.cartesian_product2 @t21 @t20)) (and @t113 (tptp.in @t2 @t20))))) % 0.85/1.04 (assume @p99 (forall @t6 (=> @t64 @t115))) % 0.85/1.04 (assume @p100 (forall @t61 (=> @t120 (= @t118 (and (tptp.in @t2 @t116) @t3))))) % 0.85/1.04 (assume @p101 (exists @t11 @t70)) % 0.85/1.04 (assume @p102 (exists @t11 (and @t10 @t12))) % 0.85/1.04 (assume @p103 (forall @t11 (=> @t60 (exists @t47 (and @t76 @t106))))) % 0.85/1.04 (assume @p104 (exists @t11 @t10)) % 0.85/1.04 (assume @p105 (exists @t11 @t15)) % 0.85/1.04 (assume @p106 (exists @t11 @t108)) % 0.85/1.04 (assume @p107 (forall @t11 (exists @t47 (and @t76 @t58)))) % 0.85/1.04 (assume @p108 (exists @t11 @t60)) % 0.85/1.04 (assume @p109 (exists @t11 @t14)) % 0.85/1.04 (assume @p110 (exists @t11 @t102)) % 0.85/1.04 (assume @p111 (forall @t6 (=> @t84 (= @t90 @t112)))) % 0.85/1.04 (assume @p112 (forall @t6 (=> @t84 (= @t93 (tptp.set_meet @t2))))) % 0.85/1.04 (assume @p113 (forall @t61 (=> @t96 (= @t94 @t121)))) % 0.85/1.04 (assume @p114 (forall @t6 (tptp.subset @t1 @t1))) % 0.85/1.04 (assume @p115 (forall @t6 (=> @t79 (tptp.disjoint @t2 @t1)))) % 0.85/1.04 (assume @p116 (forall @t114 (not (and (= @t16 (tptp.unordered_pair @t21 @t20)) (not @t122) (not (= @t1 @t20)))))) % 0.85/1.04 (assume @p117 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t21))) (and @t5 (tptp.in @t1 @t123)))))) % 0.85/1.04 (assume @p118 (forall @t6 (=> @t28 (tptp.subset @t124 @t1)))) % 0.85/1.04 (assume @p119 (forall @t6 (=> @t28 (tptp.subset @t41 @t2)))) % 0.85/1.04 (assume @p120 (forall @t6 (=> @t28 (tptp.subset @t124 @t125)))) % 0.85/1.04 (assume @p121 (forall @t61 (=> @t29 (and (tptp.subset @t126 (tptp.cartesian_product2 @t2 @t21)) (tptp.subset (tptp.cartesian_product2 @t21 @t1) (tptp.cartesian_product2 @t21 @t2)))))) % 0.85/1.04 (assume @p122 (forall @t6 (=> @t28 (= @t124 (tptp.set_intersection2 @t125 @t1))))) % 0.85/1.04 (assume @p123 (forall @t114 (=> (and @t29 (tptp.subset @t21 @t20)) (tptp.subset @t126 (tptp.cartesian_product2 @t2 @t20))))) % 0.85/1.04 (assume @p124 (forall @t6 (=> @t29 (= @t18 @t2)))) % 0.85/1.04 (assume @p125 (forall @t11 (exists @t47 (and @t5 @t131 (forall @t42 (=> @t53 (tptp.in @t130 @t2))) @t129)))) % 0.85/1.04 (assume @p126 (forall @t61 (=> @t38 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t21) @t2) (tptp.relation_rng_restriction @t1 @t132))))) % 0.85/1.04 (assume @p127 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_image @t21 @t2)) (exists @t46 (and (tptp.in @t20 @t116) (tptp.in (tptp.ordered_pair @t20 @t1) @t21) @t34)))))) % 0.85/1.04 (assume @p128 (forall @t6 (=> @t28 (tptp.subset @t133 @t125)))) % 0.85/1.04 (assume @p129 (forall @t6 (=> @t28 (= @t133 (tptp.relation_image @t2 @t135))))) % 0.85/1.04 (assume @p130 (forall @t11 (=> @t12 (= (tptp.relation_image @t1 @t67) @t74)))) % 0.85/1.04 (assume @p131 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (= @t136 (tptp.relation_image @t2 @t74))))))) % 0.85/1.04 (assume @p132 (forall @t61 (=> @t38 (= (tptp.in @t1 @t137) (exists @t46 (and (tptp.in @t20 @t123) (tptp.in (tptp.ordered_pair @t1 @t20) @t21) @t34)))))) % 0.85/1.04 (assume @p133 (forall @t6 (=> @t28 (tptp.subset @t138 @t134)))) % 0.85/1.04 (assume @p134 (forall @t6 (=> @t28 (not (and @t54 (tptp.subset @t1 @t125) (= @t138 tptp.empty_set)))))) % 0.85/1.04 (assume @p135 (forall @t61 (=> @t38 (=> @t29 (tptp.subset (tptp.relation_inverse_image @t21 @t1) @t137))))) % 0.85/1.04 (assume @p136 (forall @t6 (tptp.subset @t19 @t1))) % 0.85/1.04 (assume @p137 (forall @t61 (=> (and @t29 @t140) (tptp.subset @t1 @t139)))) % 0.85/1.04 (assume @p138 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.85/1.04 (assume @p139 (forall @t6 (=> @t5 @t141))) % 0.85/1.04 (assume @p140 (forall @t61 (=> (and @t29 (tptp.subset @t2 @t21)) @t140))) % 0.85/1.04 (assume @p141 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.85/1.04 (assume @p142 (forall @t61 (=> @t38 (=> @t143 (and @t142 (tptp.in @t2 @t123)))))) % 0.85/1.04 (assume @p143 (forall @t6 (=> @t147 (forall @t42 (=> @t120 (= @t146 (and @t142 (tptp.in @t144 @t134)))))))) % 0.85/1.04 (assume @p144 (forall @t11 (=> @t12 (tptp.subset @t1 (tptp.cartesian_product2 @t67 @t74))))) % 0.85/1.04 (assume @p145 (forall @t6 (=> @t147 (forall @t42 (=> @t120 (=> @t146 (= (tptp.apply @t145 @t1) (tptp.apply @t2 @t144)))))))) % 0.85/1.04 (assume @p146 @t154) % 0.85/1.04 (assume @p147 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> @t29 (and (tptp.subset @t67 @t134) (tptp.subset @t74 @t125)))))))) % 0.85/1.04 (assume @p148 (forall @t61 (=> @t29 (tptp.subset (tptp.set_intersection2 @t1 @t21) @t139)))) % 0.85/1.04 (assume @p149 (forall @t6 (=> @t29 (= @t19 @t1)))) % 0.85/1.04 (assume @p150 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.85/1.04 (assume @p151 (forall @t6 (=> @t141 (or @t58 @t5)))) % 0.85/1.04 (assume @p152 (forall @t6 (=> (forall @t42 (= @t22 @t53)) @t30))) % 0.85/1.04 (assume @p153 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.85/1.04 (assume @p154 (forall @t61 (=> @t38 (=> @t143 (and (tptp.in @t1 @t155) (tptp.in @t2 @t155)))))) % 0.85/1.04 (assume @p155 (forall @t61 (=> @t29 (tptp.subset (tptp.set_difference @t1 @t21) @t121)))) % 0.85/1.04 (assume @p156 (forall @t114 (=> (= @t77 @t23) (and @t122 (= @t2 @t20))))) % 0.85/1.04 (assume @p157 (forall @t6 (=> @t147 (= @t27 (and (= @t134 @t1) (forall @t42 (=> @t22 (= @t156 @t21)))))))) % 0.85/1.04 (assume @p158 @t159) % 0.85/1.04 (assume @p159 (forall @t6 (tptp.subset @t72 @t1))) % 0.85/1.04 (assume @p160 (forall @t11 (=> @t12 (and (= @t74 (tptp.relation_dom @t78)) (= @t67 (tptp.relation_rng @t78)))))) % 0.85/1.04 (assume @p161 (forall @t61 (= (tptp.subset @t16 @t21) (and @t113 @t160)))) % 0.85/1.04 (assume @p162 (forall @t6 (= @t161 @t18))) % 0.85/1.04 (assume @p163 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.85/1.04 (assume @p164 (forall @t6 (= @t115 @t29))) % 0.85/1.04 (assume @p165 (forall @t6 (and (not (and @t163 (forall @t42 (not @t162)))) (not (and (exists @t42 @t162) @t79))))) % 0.85/1.04 (assume @p166 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t50))) % 0.85/1.04 (assume @p167 (forall @t6 (= (tptp.set_difference @t18 @t2) @t72))) % 0.85/1.04 (assume @p168 (forall @t6 (=> @t76 (forall @t42 (=> @t95 (= @t165 (tptp.subset @t2 @t164))))))) % 0.85/1.04 (assume @p169 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (tptp.subset @t166 @t67)))))) % 0.85/1.04 (assume @p170 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (tptp.subset @t136 @t125)))))) % 0.85/1.04 (assume @p171 (forall @t6 (=> @t29 (= @t2 @t161)))) % 0.85/1.04 (assume @p172 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> (tptp.subset @t74 @t134) (= @t166 @t67))))))) % 0.85/1.04 (assume @p173 (forall @t6 (=> @t84 (not (and @t167 (= @t82 tptp.empty_set)))))) % 0.85/1.04 (assume @p174 (forall @t11 (=> @t12 (forall @t47 (=> @t28 (=> (tptp.subset @t67 @t125) (= (tptp.relation_rng @t98) @t74))))))) % 0.85/1.04 (assume @p175 (forall @t6 (=> @t84 (=> @t167 (= (tptp.subset_difference @t1 @t71 @t90) (tptp.meet_of_subsets @t1 @t82)))))) % 0.85/1.04 (assume @p176 (forall @t6 (=> @t84 (=> @t167 (= (tptp.union_of_subsets @t1 @t82) (tptp.subset_difference @t1 @t71 @t93)))))) % 0.85/1.04 (assume @p177 (forall @t6 (= (tptp.set_difference @t1 @t72) @t19))) % 0.85/1.04 (assume @p178 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.85/1.04 (assume @p179 (forall @t61 (=> (and @t5 @t168) (tptp.element @t1 @t21)))) % 0.85/1.04 (assume @p180 (forall @t6 (and (not (and @t163 (forall @t42 (not @t169)))) (not (and (exists @t42 @t169) @t79))))) % 0.85/1.04 (assume @p181 (forall @t11 (=> @t54 (forall @t47 (=> @t76 (forall @t42 (=> (tptp.element @t21 @t1) (=> @t127 (tptp.in @t21 @t75))))))))) % 0.85/1.04 (assume @p182 (forall @t11 (=> @t70 (=> @t13 (forall @t47 (=> @t147 (= (= @t2 @t86) (and (= @t134 @t74) (forall @t25 (and (=> @t170 @t171) (=> @t171 @t170))))))))))) % 0.85/1.04 (assume @p183 (forall @t61 (=> @t95 (not (and (tptp.in @t2 @t164) @t160))))) % 0.85/1.04 (assume @p184 (forall @t11 (=> @t70 (=> @t13 (and (= @t74 (tptp.relation_dom @t86)) (= @t67 (tptp.relation_rng @t86))))))) % 0.85/1.04 (assume @p185 (forall @t11 (=> @t12 (=> (forall @t39 (not @t69)) @t50)))) % 0.85/1.04 (assume @p186 (forall @t6 (=> @t147 (=> (and (tptp.one_to_one @t2) (tptp.in @t1 @t125)) (and (= @t1 (tptp.apply @t2 (tptp.apply @t172 @t1))) (= @t1 (tptp.apply (tptp.relation_composition @t172 @t2) @t1))))))) % 0.85/1.04 (assume @p187 (forall @t61 (not (and @t5 @t168 (tptp.empty @t21))))) % 0.85/1.04 (assume @p188 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 0.85/1.04 (assume @p189 (forall @t6 (not (and @t29 @t7)))) % 0.85/1.04 (assume @p190 (forall @t11 (=> @t70 (=> @t13 (tptp.one_to_one @t86))))) % 0.85/1.04 (assume @p191 (forall @t61 (=> (and @t29 @t165) (tptp.disjoint @t1 @t21)))) % 0.85/1.04 (assume @p192 (forall @t11 (=> @t12 (=> (or @t174 @t173) @t50)))) % 0.85/1.04 (assume @p193 (forall @t11 (=> @t12 (= @t174 @t173)))) % 0.85/1.04 (assume @p194 (forall @t6 (= (= (tptp.set_difference @t1 @t111) @t1) @t4))) % 0.85/1.04 (assume @p195 (forall @t6 (=> @t147 (forall @t42 (=> @t120 (= (= @t2 @t117) (and (= @t134 (tptp.set_intersection2 @t116 @t1)) (forall @t46 (=> (tptp.in @t20 @t134) (= (tptp.apply @t2 @t20) (tptp.apply @t21 @t20))))))))))) % 0.85/1.04 (assume @p196 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t55))) % 0.85/1.04 (assume @p197 (forall @t11 (=> @t10 @t50))) % 0.85/1.04 (assume @p198 (forall @t6 (=> (tptp.subset @t55 @t111) @t30))) % 0.85/1.04 (assume @p199 (forall @t61 (=> @t120 (=> @t118 @t175)))) % 0.85/1.04 (assume @p200 @t179) % 0.85/1.04 (assume @p201 @t182) % 0.85/1.04 (assume @p202 (forall @t114 (=> (tptp.relation @t20) (= (tptp.in @t77 (tptp.relation_composition (tptp.identity_relation @t21) @t20)) (and @t113 (tptp.in @t77 @t20)))))) % 0.85/1.04 (assume @p203 (forall @t6 (not (and @t5 @t58)))) % 0.85/1.04 (assume @p204 (forall @t6 (tptp.subset @t1 @t18))) % 0.85/1.04 (assume @p205 (forall @t6 (= @t79 (= @t72 @t1)))) % 0.85/1.04 (assume @p206 (forall @t61 (=> @t38 (= (tptp.in @t1 (tptp.relation_dom @t132)) (and @t5 @t142))))) % 0.85/1.04 (assume @p207 (forall @t6 (=> @t28 (tptp.subset @t183 @t2)))) % 0.85/1.04 (assume @p208 (forall @t6 (not (and @t10 @t85 @t58)))) % 0.85/1.04 (assume @p209 (forall @t61 (=> @t120 (= @t143 (and @t142 (= @t2 @t144)))))) % 0.85/1.04 (assume @p210 (forall @t61 (=> (and @t29 @t128) (tptp.subset (tptp.set_union2 @t1 @t21) @t2)))) % 0.85/1.04 (assume @p211 (forall @t61 (=> @t184 @t30))) % 0.85/1.04 (assume @p212 (forall @t6 (=> @t28 (= (tptp.relation_dom @t183) @t135)))) % 0.85/1.04 (assume @p213 @t186) % 0.85/1.04 (assume @p214 (forall @t6 (=> @t28 (tptp.subset (tptp.relation_rng @t183) @t125)))) % 0.85/1.04 (assume @p215 (forall @t11 (= (tptp.union @t56) @t1))) % 0.85/1.04 (assume @p216 (forall @t11 (exists @t47 (and @t5 @t131 (forall @t42 (not (and @t53 (forall @t46 (not (and @t34 (forall @t44 (=> (tptp.subset @t31 @t21) (tptp.in @t31 @t20))))))))) @t129)))) % 0.85/1.04 (assume @p217 (forall @t61 (=> @t184 @t80))) % 0.85/1.04 (step @p218 :rule aci_norm :args ((= (or @t190 (or @t4 @t175)) @t189))) % 0.85/1.04 (step @p219 :rule bool-impl-elim :args (@t3 @t175)) % 0.85/1.04 (step @p220 :rule bool-and-de-morgan :args (@t38 @t119 true)) % 0.85/1.04 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or @t191 @t180))) % 0.85/1.04 (step @p222 :rule trans :premises (@p221 @p218)) % 0.85/1.04 (step @p223 :rule bool-impl-elim :args (@t120 @t180)) % 0.85/1.04 (step @p224 :rule trans :premises (@p223 @p222)) % 0.85/1.04 (step @p225 :rule cong :premises (@p224) :args (@t181)) % 0.85/1.04 (step @p226 :rule cong :premises (@p225) :args (@t182)) % 0.85/1.04 (step @p227 :rule eq_resolve :premises (@p201 @p226)) % 0.85/1.04 (step @p228 :rule skolemize :premises (@p227)) % 0.85/1.04 (step @p229 :rule bool-double-not-elim :args (@t194)) % 0.85/1.04 (step @p230 :rule refl :args (@t204)) % 0.85/1.04 (step @p231 :rule nary_cong :premises (@p230 @p229) :args ((or @t204 (not @t203)))) % 0.85/1.04 (step @p232 :rule cnf_or_neg :args (@t204 0)) % 0.85/1.04 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.85/1.04 (step @p234 :rule reordering :premises (@p233) :args ((or @t194 @t204))) % 0.85/1.04 (step @p235 :rule chain_m_resolution :premises (@p234 @p228) :args (@t194 @t205 @t206)) % 0.85/1.04 (step @p236 :rule bool-double-not-elim :args (@t201)) % 0.85/1.04 (step @p237 :rule nary_cong :premises (@p230 @p236) :args ((or @t204 (not @t202)))) % 0.85/1.04 (step @p238 :rule cnf_or_neg :args (@t204 1)) % 0.85/1.04 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.85/1.04 (step @p240 :rule reordering :premises (@p239) :args ((or @t201 @t204))) % 0.85/1.04 (step @p241 :rule chain_m_resolution :premises (@p240 @p228) :args (@t201 @t205 @t206)) % 0.85/1.04 (step @p242 :rule alpha_equiv :args (@t207 @t208 (@list (@var "BOUND_VARIABLE_9369" $$unsorted)))) % 0.85/1.04 (step @p243 :rule alpha_equiv :args (@t92 @t208 (@list (@var "BOUND_VARIABLE_9363" $$unsorted)))) % 0.85/1.04 (step @p244 :rule nary_cong :premises (@p243 @p242) :args (@t209)) % 0.85/1.04 (step @p245 :rule quant-miniscope-and :args ((= @t105 @t209))) % 0.85/1.04 (step @p246 :rule trans :premises (@p245 @p244)) % 0.85/1.04 (step @p247 :rule eq_resolve :premises (@p67 @p246)) % 0.85/1.04 (step @p248 :rule and_elim :premises (@p247) :args (1)) % 0.85/1.04 (step @p249 :rule instantiate :premises (@p248) :args (@t210)) % 0.85/1.04 (step @p250 :rule aci_norm :args ((= @t219 (or @t217 @t216 @t215 @t214 @t213 @t212)))) % 0.85/1.04 (step @p251 :rule cong :premises (@p250) :args (@t220)) % 0.85/1.04 (step @p252 :rule quant-merge-prenex :args ((= (forall @t6 @t222) @t220))) % 0.85/1.04 (step @p253 :rule alpha_equiv :args (@t223 (@list @t211) (@list @t21))) % 0.85/1.04 (step @p254 :rule refl :args (@t215)) % 0.85/1.04 (step @p255 :rule refl :args (@t216)) % 0.85/1.04 (step @p256 :rule refl :args (@t217)) % 0.85/1.04 (step @p257 :rule nary_cong :premises (@p256 @p255 @p254 @p253) :args (@t224)) % 0.85/1.04 (step @p258 :rule quant-miniscope-or :args ((= @t222 @t224))) % 0.85/1.04 (step @p259 :rule trans :premises (@p258 @p257)) % 0.85/1.04 (step @p260 :rule symm :premises (@p259)) % 0.85/1.04 (step @p261 :rule cong :premises (@p260) :args ((forall @t6 @t227))) % 0.85/1.04 (step @p262 :rule trans :premises (@p261 @p252)) % 0.85/1.04 (step @p263 :rule trans :premises (@p262 @p251)) % 0.85/1.04 (step @p264 :rule aci_norm :args ((= (or (or @t217 @t216) @t228) @t227))) % 0.85/1.04 (step @p265 :rule refl :args (@t228)) % 0.85/1.04 (step @p266 :rule bool-and-de-morgan :args (@t28 @t103 true)) % 0.85/1.04 (step @p267 :rule nary_cong :premises (@p266 @p265) :args ((or (not @t147) @t228))) % 0.85/1.04 (step @p268 :rule trans :premises (@p267 @p264)) % 0.85/1.04 (step @p269 :rule bool-impl-elim :args (@t147 @t228)) % 0.85/1.04 (step @p270 :rule trans :premises (@p269 @p268)) % 0.85/1.04 (step @p271 :rule cong :premises (@p270) :args ((forall @t6 (=> @t147 @t228)))) % 0.85/1.04 (step @p272 :rule trans :premises (@p271 @p263)) % 0.85/1.04 (step @p273 :rule quant-miniscope-or :args ((= (forall @t42 @t229) @t228))) % 0.85/1.04 (step @p274 :rule aci_norm :args ((= @t230 @t229))) % 0.85/1.04 (step @p275 :rule cong :premises (@p274) :args ((forall @t42 @t230))) % 0.85/1.04 (step @p276 :rule trans :premises (@p275 @p273)) % 0.85/1.04 (step @p277 :rule aci_norm :args ((= (or @t190 (or @t215 @t149)) @t230))) % 0.85/1.04 (step @p278 :rule bool-impl-elim :args (@t150 @t149)) % 0.85/1.04 (step @p279 :rule nary_cong :premises (@p220 @p278) :args ((or @t191 @t151))) % 0.85/1.04 (step @p280 :rule trans :premises (@p279 @p277)) % 0.85/1.04 (step @p281 :rule bool-impl-elim :args (@t120 @t151)) % 0.85/1.04 (step @p282 :rule trans :premises (@p281 @p280)) % 0.85/1.04 (step @p283 :rule cong :premises (@p282) :args (@t152)) % 0.85/1.04 (step @p284 :rule trans :premises (@p283 @p276)) % 0.85/1.04 (step @p285 :rule refl :args (@t147)) % 0.85/1.04 (step @p286 :rule cong :premises (@p285 @p284) :args (@t153)) % 0.85/1.04 (step @p287 :rule cong :premises (@p286) :args (@t154)) % 0.85/1.04 (step @p288 :rule trans :premises (@p287 @p272)) % 0.85/1.04 (step @p289 :rule eq_resolve :premises (@p146 @p288)) % 0.85/1.04 (step @p290 :rule instantiate :premises (@p289) :args ((@list @t195 @t231 @t193))) % 0.85/1.04 (step @p291 :rule instantiate :premises (@p51) :args (@t210)) % 0.85/1.04 (step @p292 :rule cnf_or_neg :args (@t204 3)) % 0.85/1.04 (step @p293 :rule chain_m_resolution :premises (@p292 @p228) :args ((not @t198) @t205 @t206)) % 0.85/1.04 (step @p294 :rule false_intro :premises (@p293)) % 0.85/1.04 (step @p295 :rule bool-impl-elim :args (@t3 @t232)) % 0.85/1.04 (step @p296 :rule cong :premises (@p295) :args ((forall @t6 (=> @t3 @t232)))) % 0.85/1.04 (step @p297 :rule eq-symm :args (@t157 @t2)) % 0.85/1.04 (step @p298 :rule refl :args (@t3)) % 0.85/1.04 (step @p299 :rule cong :premises (@p298 @p297) :args (@t158)) % 0.85/1.04 (step @p300 :rule cong :premises (@p299) :args (@t159)) % 0.85/1.04 (step @p301 :rule trans :premises (@p300 @p296)) % 0.85/1.04 (step @p302 :rule eq_resolve :premises (@p158 @p301)) % 0.85/1.04 (step @p303 :rule instantiate :premises (@p302) :args ((@list @t196 @t195))) % 0.85/1.04 (step @p304 :rule bool-double-not-elim :args (@t199)) % 0.85/1.04 (step @p305 :rule nary_cong :premises (@p230 @p304) :args ((or @t204 (not @t200)))) % 0.85/1.04 (step @p306 :rule cnf_or_neg :args (@t204 2)) % 0.85/1.04 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 0.85/1.04 (step @p308 :rule reordering :premises (@p307) :args ((or @t199 @t204))) % 0.85/1.04 (step @p309 :rule chain_m_resolution :premises (@p308 @p228) :args (@t199 @t205 @t206)) % 0.85/1.04 (step @p310 :rule cnf_or_pos :args (@t235)) % 0.85/1.04 (step @p311 :rule reordering :premises (@p310) :args ((or @t200 @t234 (not @t235)))) % 0.85/1.04 (step @p312 :rule chain_m_resolution :premises (@p311 @p309 @p303) :args (@t234 @t236 (@list @t199 @t235))) % 0.85/1.04 (step @p313 :rule symm :premises (@p312)) % 0.85/1.04 (step @p314 :rule refl :args (@t193)) % 0.85/1.04 (step @p315 :rule cong :premises (@p314 @p313) :args (@t237)) % 0.85/1.04 (step @p316 :rule refl :args (@t195)) % 0.85/1.04 (step @p317 :rule bool-impl-elim :args (@t28 @t185)) % 0.85/1.04 (step @p318 :rule cong :premises (@p317) :args (@t186)) % 0.85/1.04 (step @p319 :rule eq_resolve :premises (@p213 @p318)) % 0.85/1.04 (step @p320 :rule instantiate :premises (@p319) :args ((@list @t196 @t193))) % 0.85/1.04 (step @p321 :rule cnf_or_pos :args (@t240)) % 0.85/1.04 (step @p322 :rule reordering :premises (@p321) :args ((or @t203 @t239 (not @t240)))) % 0.85/1.04 (step @p323 :rule chain_m_resolution :premises (@p322 @p235 @p320) :args (@t239 @t236 (@list @t194 @t240))) % 0.85/1.04 (step @p324 :rule symm :premises (@p323)) % 0.85/1.04 (step @p325 :rule cong :premises (@p324 @p316) :args (@t241)) % 0.85/1.04 (step @p326 :rule cong :premises (@p325 @p315) :args (@t242)) % 0.85/1.04 (step @p327 :rule trans :premises (@p326 @p294)) % 0.85/1.04 (step @p328 :rule false_elim :premises (@p327)) % 0.85/1.04 (step @p329 :rule true_intro :premises (@p309)) % 0.85/1.04 (step @p330 :rule alpha_equiv :args (@t244 @t208 (@list (@var "BOUND_VARIABLE_10476" $$unsorted)))) % 0.85/1.04 (step @p331 :rule alpha_equiv :args (@t246 @t208 (@list (@var "BOUND_VARIABLE_10469" $$unsorted)))) % 0.85/1.04 (step @p332 :rule nary_cong :premises (@p331 @p330) :args (@t247)) % 0.85/1.04 (step @p333 :rule quant-miniscope-and :args ((= (forall @t11 (and @t245 @t243)) @t247))) % 0.85/1.04 (step @p334 :rule trans :premises (@p333 @p332)) % 0.85/1.04 (step @p335 :rule eq-symm :args (@t176 @t1)) % 0.85/1.04 (step @p336 :rule eq-symm :args (@t177 @t1)) % 0.85/1.04 (step @p337 :rule nary_cong :premises (@p336 @p335) :args (@t178)) % 0.85/1.04 (step @p338 :rule cong :premises (@p337) :args (@t179)) % 0.85/1.04 (step @p339 :rule trans :premises (@p338 @p334)) % 0.85/1.04 (step @p340 :rule eq_resolve :premises (@p200 @p339)) % 0.85/1.04 (step @p341 :rule and_elim :premises (@p340) :args (0)) % 0.85/1.04 (step @p342 :rule instantiate :premises (@p341) :args (@t210)) % 0.85/1.04 (step @p343 :rule symm :premises (@p342)) % 0.85/1.04 (step @p344 :rule cong :premises (@p316 @p343) :args (@t248)) % 0.85/1.04 (step @p345 :rule trans :premises (@p344 @p329)) % 0.85/1.04 (step @p346 :rule true_elim :premises (@p345)) % 0.85/1.04 (step @p347 :rule cnf_or_pos :args (@t254)) % 0.85/1.04 (step @p348 :rule reordering :premises (@p347) :args ((or @t203 @t202 @t253 @t251 @t249 @t242 (not @t254)))) % 0.85/1.04 (step @p349 false :rule chain_m_resolution :premises (@p348 @p346 @p328 @p291 @p290 @p249 @p241 @p235) :args (false (@list false true false false false false false) (@list @t248 @t242 @t252 @t254 @t250 @t201 @t194))) % 0.85/1.04 ) % 0.85/1.04 % SZS output end Proof % 0.85/1.04 % cvc5 exiting %------------------------------------------------------------------------------