%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU239+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 : n011.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 08:51:05 AM UTC 2026 % Result : Theorem 1.12s 1.31s % Output : Proof 1.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU239+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 % 0.16/0.34 % Computer : n011.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:46:20 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.55 %----Proving TF0_NAR, FOF, or CNF % 1.12/1.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.12/1.31 % SZS status Theorem % 1.12/1.31 % SZS output start Proof % 1.12/1.31 ( % 1.12/1.31 (declare-sort $$unsorted 0) % 1.12/1.31 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.reflexive (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.function_inverse (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.ordinal_subset (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.empty_set $$unsorted) % 1.12/1.31 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.function (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.is_reflexive_in (-> $$unsorted $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.being_limit_ordinal (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.unordered_triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 1.12/1.31 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.12/1.31 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 1.12/1.31 (define @t1 () (@var "A" $$unsorted)) % 1.12/1.31 (define @t2 () (@var "B" $$unsorted)) % 1.12/1.31 (define @t3 () (tptp.in @t2 @t1)) % 1.12/1.31 (define @t4 () (not @t3)) % 1.12/1.31 (define @t5 () (tptp.in @t1 @t2)) % 1.12/1.31 (define @t6 () (@list @t1 @t2)) % 1.12/1.31 (define @t7 () (tptp.proper_subset @t2 @t1)) % 1.12/1.31 (define @t8 () (tptp.proper_subset @t1 @t2)) % 1.12/1.31 (define @t9 () (tptp.function @t1)) % 1.12/1.31 (define @t10 () (tptp.empty @t1)) % 1.12/1.31 (define @t11 () (@list @t1)) % 1.12/1.31 (define @t12 () (tptp.epsilon_connected @t1)) % 1.12/1.31 (define @t13 () (tptp.epsilon_transitive @t1)) % 1.12/1.31 (define @t14 () (and @t13 @t12)) % 1.12/1.31 (define @t15 () (tptp.ordinal @t1)) % 1.12/1.31 (define @t16 () (tptp.relation @t1)) % 1.12/1.31 (define @t17 () (tptp.one_to_one @t1)) % 1.12/1.31 (define @t18 () (and @t16 @t9 @t17)) % 1.12/1.31 (define @t19 () (and @t16 @t10 @t9)) % 1.12/1.31 (define @t20 () (and @t13 @t12 @t15)) % 1.12/1.31 (define @t21 () (tptp.unordered_pair @t1 @t2)) % 1.12/1.31 (define @t22 () (tptp.set_union2 @t2 @t1)) % 1.12/1.31 (define @t23 () (tptp.set_union2 @t1 @t2)) % 1.12/1.31 (define @t24 () (tptp.set_intersection2 @t1 @t2)) % 1.12/1.31 (define @t25 () (tptp.ordinal_subset @t1 @t2)) % 1.12/1.31 (define @t26 () (tptp.ordinal @t2)) % 1.12/1.31 (define @t27 () (and @t15 @t26)) % 1.12/1.31 (define @t28 () (@var "D" $$unsorted)) % 1.12/1.31 (define @t29 () (@var "C" $$unsorted)) % 1.12/1.31 (define @t30 () (tptp.in @t29 @t1)) % 1.12/1.31 (define @t31 () (tptp.ordered_pair @t29 @t28)) % 1.12/1.31 (define @t32 () (tptp.in @t31 @t2)) % 1.12/1.31 (define @t33 () (@list @t29 @t28)) % 1.12/1.31 (define @t34 () (tptp.identity_relation @t1)) % 1.12/1.31 (define @t35 () (= @t2 @t34)) % 1.12/1.31 (define @t36 () (tptp.relation @t2)) % 1.12/1.31 (define @t37 () (tptp.subset @t2 @t1)) % 1.12/1.31 (define @t38 () (tptp.subset @t1 @t2)) % 1.12/1.31 (define @t39 () (= @t1 @t2)) % 1.12/1.31 (define @t40 () (@var "E" $$unsorted)) % 1.12/1.31 (define @t41 () (tptp.ordered_pair @t28 @t40)) % 1.12/1.31 (define @t42 () (tptp.in @t41 @t1)) % 1.12/1.31 (define @t43 () (tptp.in @t28 @t2)) % 1.12/1.31 (define @t44 () (tptp.in @t41 @t29)) % 1.12/1.31 (define @t45 () (@list @t28 @t40)) % 1.12/1.31 (define @t46 () (tptp.relation_dom_restriction @t1 @t2)) % 1.12/1.31 (define @t47 () (tptp.relation @t29)) % 1.12/1.31 (define @t48 () (@list @t2 @t29)) % 1.12/1.31 (define @t49 () (tptp.in @t40 @t2)) % 1.12/1.31 (define @t50 () (tptp.relation_dom @t1)) % 1.12/1.31 (define @t51 () (@list @t40)) % 1.12/1.31 (define @t52 () (tptp.in @t28 @t29)) % 1.12/1.31 (define @t53 () (@list @t28)) % 1.12/1.31 (define @t54 () (= @t29 (tptp.relation_image @t1 @t2))) % 1.12/1.31 (define @t55 () (and @t16 @t9)) % 1.12/1.31 (define @t56 () (tptp.in @t40 @t1)) % 1.12/1.31 (define @t57 () (tptp.relation_rng_restriction @t1 @t2)) % 1.12/1.31 (define @t58 () (@list @t29)) % 1.12/1.31 (define @t59 () (tptp.apply @t1 @t28)) % 1.12/1.31 (define @t60 () (tptp.in @t28 @t50)) % 1.12/1.31 (define @t61 () (= @t29 (tptp.relation_inverse_image @t1 @t2))) % 1.12/1.31 (define @t62 () (tptp.in @t40 @t28)) % 1.12/1.31 (define @t63 () (@list @t1 @t2 @t29 @t28)) % 1.12/1.31 (define @t64 () (tptp.singleton @t1)) % 1.12/1.31 (define @t65 () (tptp.succ @t1)) % 1.12/1.31 (define @t66 () (@list @t2)) % 1.12/1.31 (define @t67 () (tptp.ordered_pair @t29 @t29)) % 1.12/1.31 (define @t68 () (tptp.in @t67 @t1)) % 1.12/1.31 (define @t69 () (tptp.in @t29 @t2)) % 1.12/1.31 (define @t70 () (forall @t58 (=> @t69 @t68))) % 1.12/1.31 (define @t71 () (tptp.is_reflexive_in @t1 @t2)) % 1.12/1.31 (define @t72 () (= @t71 @t70)) % 1.12/1.31 (define @t73 () (forall @t66 @t72)) % 1.12/1.31 (define @t74 () (=> @t16 @t73)) % 1.12/1.31 (define @t75 () (forall @t11 @t74)) % 1.12/1.31 (define @t76 () (= @t2 tptp.empty_set)) % 1.12/1.31 (define @t77 () (= @t2 (tptp.set_meet @t1))) % 1.12/1.31 (define @t78 () (= @t1 tptp.empty_set)) % 1.12/1.31 (define @t79 () (tptp.in @t29 @t28)) % 1.12/1.31 (define @t80 () (tptp.in @t28 @t1)) % 1.12/1.31 (define @t81 () (not @t78)) % 1.12/1.31 (define @t82 () (tptp.powerset @t1)) % 1.12/1.31 (define @t83 () (tptp.in @t31 @t1)) % 1.12/1.31 (define @t84 () (tptp.empty @t2)) % 1.12/1.31 (define @t85 () (tptp.element @t2 @t1)) % 1.12/1.31 (define @t86 () (not @t10)) % 1.12/1.31 (define @t87 () (@list @t1 @t2 @t29)) % 1.12/1.31 (define @t88 () (@var "F" $$unsorted)) % 1.12/1.31 (define @t89 () (tptp.cartesian_product2 @t1 @t2)) % 1.12/1.31 (define @t90 () (not @t69)) % 1.12/1.31 (define @t91 () (= @t2 @t29)) % 1.12/1.31 (define @t92 () (tptp.in @t2 @t29)) % 1.12/1.31 (define @t93 () (forall @t58 (=> @t30 @t69))) % 1.12/1.31 (define @t94 () (tptp.apply @t1 @t2)) % 1.12/1.31 (define @t95 () (= @t29 @t94)) % 1.12/1.31 (define @t96 () (tptp.in @t2 @t50)) % 1.12/1.31 (define @t97 () (tptp.in (tptp.ordered_pair @t2 @t29) @t1)) % 1.12/1.31 (define @t98 () (tptp.cast_to_subset @t1)) % 1.12/1.31 (define @t99 () (tptp.union @t1)) % 1.12/1.31 (define @t100 () (tptp.set_difference @t1 @t2)) % 1.12/1.31 (define @t101 () (and @t60 (= @t29 @t59))) % 1.12/1.31 (define @t102 () (tptp.relation_rng @t1)) % 1.12/1.31 (define @t103 () (= @t2 @t102)) % 1.12/1.31 (define @t104 () (tptp.in (tptp.ordered_pair @t28 @t29) @t1)) % 1.12/1.31 (define @t105 () (tptp.subset_complement @t1 @t2)) % 1.12/1.31 (define @t106 () (tptp.element @t2 @t82)) % 1.12/1.31 (define @t107 () (tptp.ordered_pair @t1 @t2)) % 1.12/1.31 (define @t108 () (tptp.being_limit_ordinal @t1)) % 1.12/1.31 (define @t109 () (tptp.relation_field @t1)) % 1.12/1.31 (define @t110 () (tptp.relation_inverse @t1)) % 1.12/1.31 (define @t111 () (tptp.disjoint @t1 @t2)) % 1.12/1.31 (define @t112 () (tptp.relation_composition @t1 @t2)) % 1.12/1.31 (define @t113 () (tptp.complements_of_subsets @t1 @t2)) % 1.12/1.31 (define @t114 () (tptp.powerset @t82)) % 1.12/1.31 (define @t115 () (tptp.element @t2 @t114)) % 1.12/1.31 (define @t116 () (not @t39)) % 1.12/1.31 (define @t117 () (tptp.function_inverse @t1)) % 1.12/1.31 (define @t118 () (tptp.reflexive @t1)) % 1.12/1.31 (define @t119 () (= @t118 (tptp.is_reflexive_in @t1 @t109))) % 1.12/1.31 (define @t120 () (forall @t11 (=> @t16 @t119))) % 1.12/1.31 (define @t121 () (tptp.relation @t110)) % 1.12/1.31 (define @t122 () (tptp.relation @t112)) % 1.12/1.31 (define @t123 () (and @t16 @t36)) % 1.12/1.31 (define @t124 () (tptp.union_of_subsets @t1 @t2)) % 1.12/1.31 (define @t125 () (tptp.relation @t34)) % 1.12/1.31 (define @t126 () (tptp.meet_of_subsets @t1 @t2)) % 1.12/1.31 (define @t127 () (tptp.subset_difference @t1 @t2 @t29)) % 1.12/1.31 (define @t128 () (tptp.element @t29 @t82)) % 1.12/1.31 (define @t129 () (and @t106 @t128)) % 1.12/1.31 (define @t130 () (tptp.relation @t46)) % 1.12/1.31 (define @t131 () (tptp.relation_composition @t2 @t1)) % 1.12/1.31 (define @t132 () (and @t10 @t36)) % 1.12/1.31 (define @t133 () (tptp.relation_empty_yielding tptp.empty_set)) % 1.12/1.31 (define @t134 () (tptp.relation tptp.empty_set)) % 1.12/1.31 (define @t135 () (tptp.empty tptp.empty_set)) % 1.12/1.31 (define @t136 () (tptp.relation_empty_yielding @t1)) % 1.12/1.31 (define @t137 () (and @t16 @t136)) % 1.12/1.31 (define @t138 () (tptp.function @t2)) % 1.12/1.31 (define @t139 () (not (tptp.empty @t65))) % 1.12/1.31 (define @t140 () (not @t84)) % 1.12/1.31 (define @t141 () (tptp.empty @t50)) % 1.12/1.31 (define @t142 () (and @t86 @t16)) % 1.12/1.31 (define @t143 () (tptp.empty @t102)) % 1.12/1.31 (define @t144 () (tptp.ordered_pair @t2 @t2)) % 1.12/1.31 (define @t145 () (tptp.in @t144 @t1)) % 1.12/1.31 (define @t146 () (tptp.in @t2 @t109)) % 1.12/1.31 (define @t147 () (forall @t66 (=> @t146 @t145))) % 1.12/1.31 (define @t148 () (= @t118 @t147)) % 1.12/1.31 (define @t149 () (=> @t16 @t148)) % 1.12/1.31 (define @t150 () (forall @t11 @t149)) % 1.12/1.31 (define @t151 () (not @t150)) % 1.12/1.31 (define @t152 () (tptp.disjoint @t64 @t2)) % 1.12/1.31 (define @t153 () (not @t5)) % 1.12/1.31 (define @t154 () (tptp.singleton @t2)) % 1.12/1.31 (define @t155 () (tptp.union @t2)) % 1.12/1.31 (define @t156 () (tptp.in @t1 @t29)) % 1.12/1.31 (define @t157 () (tptp.element @t1 (tptp.powerset @t2))) % 1.12/1.31 (define @t158 () (tptp.relation_dom @t29)) % 1.12/1.31 (define @t159 () (tptp.relation_dom_restriction @t29 @t1)) % 1.12/1.31 (define @t160 () (tptp.in @t2 (tptp.relation_dom @t159))) % 1.12/1.31 (define @t161 () (and @t47 (tptp.function @t29))) % 1.12/1.31 (define @t162 () (tptp.set_difference @t2 @t29)) % 1.12/1.31 (define @t163 () (= @t1 @t29)) % 1.12/1.31 (define @t164 () (tptp.relation_rng @t29)) % 1.12/1.31 (define @t165 () (tptp.relation_rng @t57)) % 1.12/1.31 (define @t166 () (tptp.relation_rng @t2)) % 1.12/1.31 (define @t167 () (tptp.cartesian_product2 @t1 @t29)) % 1.12/1.31 (define @t168 () (tptp.subset @t29 @t2)) % 1.12/1.31 (define @t169 () (forall @t58 (not (and @t168 (not (tptp.are_equipotent @t29 @t2)) @t90)))) % 1.12/1.31 (define @t170 () (tptp.powerset @t29)) % 1.12/1.31 (define @t171 () (forall @t33 (=> (and @t69 (tptp.subset @t28 @t29)) @t43))) % 1.12/1.31 (define @t172 () (tptp.relation_dom_restriction @t29 @t2)) % 1.12/1.31 (define @t173 () (tptp.relation_image @t2 @t1)) % 1.12/1.31 (define @t174 () (tptp.relation_inverse_image @t2 @t1)) % 1.12/1.31 (define @t175 () (tptp.relation_image @t2 @t174)) % 1.12/1.31 (define @t176 () (and @t36 @t138)) % 1.12/1.31 (define @t177 () (tptp.relation_dom @t2)) % 1.12/1.31 (define @t178 () (tptp.set_intersection2 @t177 @t1)) % 1.12/1.31 (define @t179 () (tptp.subset @t1 @t166)) % 1.12/1.31 (define @t180 () (tptp.relation_rng @t112)) % 1.12/1.31 (define @t181 () (tptp.relation_inverse_image @t29 @t2)) % 1.12/1.31 (define @t182 () (tptp.set_intersection2 @t2 @t29)) % 1.12/1.31 (define @t183 () (tptp.subset @t1 @t29)) % 1.12/1.31 (define @t184 () (tptp.element @t1 @t2)) % 1.12/1.31 (define @t185 () (tptp.in @t1 @t158)) % 1.12/1.31 (define @t186 () (tptp.in @t107 @t29)) % 1.12/1.31 (define @t187 () (tptp.apply @t29 @t1)) % 1.12/1.31 (define @t188 () (tptp.relation_composition @t29 @t2)) % 1.12/1.31 (define @t189 () (tptp.in @t1 (tptp.relation_dom @t188))) % 1.12/1.31 (define @t190 () (tptp.relation_field @t29)) % 1.12/1.31 (define @t191 () (tptp.apply @t2 @t29)) % 1.12/1.31 (define @t192 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 1.12/1.31 (define @t193 () (and @t30 @t69)) % 1.12/1.31 (define @t194 () (not @t111)) % 1.12/1.31 (define @t195 () (tptp.succ @t2)) % 1.12/1.31 (define @t196 () (= @t1 @t195)) % 1.12/1.31 (define @t197 () (tptp.subset_complement @t1 @t29)) % 1.12/1.31 (define @t198 () (tptp.disjoint @t2 @t29)) % 1.12/1.31 (define @t199 () (tptp.relation_dom @t112)) % 1.12/1.31 (define @t200 () (not @t76)) % 1.12/1.31 (define @t201 () (tptp.element @t2 @t170)) % 1.12/1.31 (define @t202 () (tptp.in @t29 @t24)) % 1.12/1.31 (define @t203 () (and (tptp.in @t29 @t102) (= @t28 @t191))) % 1.12/1.31 (define @t204 () (tptp.function_inverse @t2)) % 1.12/1.31 (define @t205 () (= @t102 tptp.empty_set)) % 1.12/1.31 (define @t206 () (= @t50 tptp.empty_set)) % 1.12/1.31 (define @t207 () (= (tptp.apply @t159 @t2) (tptp.apply @t29 @t2))) % 1.12/1.31 (define @t208 () (tptp.relation_dom_restriction @t2 @t1)) % 1.12/1.31 (define @t209 () (= @t64 (tptp.unordered_pair @t2 @t29))) % 1.12/1.31 (define @t210 () (@var "BOUND_VARIABLE_9131" $$unsorted)) % 1.12/1.31 (define @t211 () (= (tptp.is_reflexive_in @t1 @t210) (forall @t58 (or (not (tptp.in @t29 @t210)) @t68)))) % 1.12/1.31 (define @t212 () (not @t16)) % 1.12/1.31 (define @t213 () (or @t212 @t211)) % 1.12/1.31 (define @t214 () (@list @t210)) % 1.12/1.31 (define @t215 () (forall @t214 @t213)) % 1.12/1.31 (define @t216 () (forall @t214 @t211)) % 1.12/1.31 (define @t217 () (@list @t2)) % 1.12/1.31 (define @t218 () (or @t212 @t216)) % 1.12/1.31 (define @t219 () (forall @t66 (= @t71 (forall @t58 (or @t90 @t68))))) % 1.12/1.31 (define @t220 () (= @t118 (forall @t66 (or (not @t146) @t145)))) % 1.12/1.31 (define @t221 () (@quantifiers_skolemize (forall @t11 (or @t212 @t220)) 0)) % 1.12/1.31 (define @t222 () (tptp.relation_field @t221)) % 1.12/1.31 (define @t223 () (tptp.relation @t221)) % 1.12/1.31 (define @t224 () (forall @t66 (or (not (tptp.in @t2 @t222)) (tptp.in @t144 @t221)))) % 1.12/1.31 (define @t225 () (tptp.reflexive @t221)) % 1.12/1.31 (define @t226 () (= @t225 @t224)) % 1.12/1.31 (define @t227 () (not @t223)) % 1.12/1.31 (define @t228 () (or @t227 @t226)) % 1.12/1.31 (define @t229 () (@list true)) % 1.12/1.31 (define @t230 () (@list @t228)) % 1.12/1.31 (define @t231 () (forall @t58 (or (not (tptp.in @t29 @t222)) (tptp.in @t67 @t221)))) % 1.12/1.31 (define @t232 () (tptp.is_reflexive_in @t221 @t222)) % 1.12/1.31 (define @t233 () (= @t232 @t231)) % 1.12/1.31 (define @t234 () (or @t227 @t233)) % 1.12/1.31 (define @t235 () (@list false false)) % 1.12/1.31 (define @t236 () (= @t225 @t232)) % 1.12/1.31 (define @t237 () (or @t227 @t236)) % 1.12/1.31 (define @t238 () (not @t236)) % 1.12/1.31 (define @t239 () (not @t225)) % 1.12/1.31 (define @t240 () (not @t233)) % 1.12/1.31 (define @t241 () (not @t232)) % 1.12/1.31 (assume @p1 (forall @t6 (=> @t5 @t4))) % 1.12/1.31 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 1.12/1.31 (assume @p3 (forall @t11 (=> @t10 @t9))) % 1.12/1.31 (assume @p4 (forall @t11 (=> @t15 @t14))) % 1.12/1.31 (assume @p5 (forall @t11 (=> @t10 @t16))) % 1.12/1.31 (assume @p6 (forall @t11 (=> @t19 @t18))) % 1.12/1.31 (assume @p7 (forall @t11 (=> @t14 @t15))) % 1.12/1.31 (assume @p8 (forall @t11 (=> @t10 @t20))) % 1.12/1.31 (assume @p9 (forall @t6 (= @t21 (tptp.unordered_pair @t2 @t1)))) % 1.12/1.31 (assume @p10 (forall @t6 (= @t23 @t22))) % 1.12/1.31 (assume @p11 (forall @t6 (= @t24 (tptp.set_intersection2 @t2 @t1)))) % 1.12/1.31 (assume @p12 (forall @t6 (=> @t27 (or @t25 (tptp.ordinal_subset @t2 @t1))))) % 1.12/1.31 (assume @p13 (forall @t6 (=> @t36 (= @t35 (forall @t33 (= @t32 (and @t30 (= @t29 @t28)))))))) % 1.12/1.31 (assume @p14 (forall @t6 (= @t39 (and @t38 @t37)))) % 1.12/1.31 (assume @p15 (forall @t11 (=> @t16 (forall @t48 (=> @t47 (= (= @t29 @t46) (forall @t45 (= @t44 (and @t43 @t42))))))))) % 1.12/1.31 (assume @p16 (forall @t11 (=> @t55 (forall @t48 (= @t54 (forall @t53 (= @t52 (exists @t51 (and (tptp.in @t40 @t50) @t49 (= @t28 (tptp.apply @t1 @t40))))))))))) % 1.12/1.31 (assume @p17 (forall @t6 (=> @t36 (forall @t58 (=> @t47 (= (= @t29 @t57) (forall @t45 (= @t44 (and @t56 (tptp.in @t41 @t2)))))))))) % 1.12/1.31 (assume @p18 (forall @t11 (=> @t55 (forall @t48 (= @t61 (forall @t53 (= @t52 (and @t60 (tptp.in @t59 @t2))))))))) % 1.12/1.31 (assume @p19 (forall @t11 (=> @t16 (forall @t48 (= @t54 (forall @t53 (= @t52 (exists @t51 (and (tptp.in (tptp.ordered_pair @t40 @t28) @t1) @t49))))))))) % 1.12/1.31 (assume @p20 (forall @t11 (=> @t16 (forall @t48 (= @t61 (forall @t53 (= @t52 (exists @t51 (and @t42 @t49))))))))) % 1.12/1.31 (assume @p21 (forall @t63 (= (= @t28 (tptp.unordered_triple @t1 @t2 @t29)) (forall @t51 (= @t62 (not (and (not (= @t40 @t1)) (not (= @t40 @t2)) (not (= @t40 @t29))))))))) % 1.12/1.31 (assume @p22 (forall @t11 (= @t65 (tptp.set_union2 @t1 @t64)))) % 1.12/1.31 (assume @p23 (forall @t11 (= @t16 (forall @t66 (not (and @t3 (forall @t33 (not (= @t2 @t31))))))))) % 1.12/1.31 (assume @p24 @t75) % 1.12/1.31 (assume @p25 (forall @t6 (and (=> @t81 (= @t77 (forall @t58 (= @t69 (forall @t53 (=> @t80 @t79)))))) (=> @t78 (= @t77 @t76))))) % 1.12/1.31 (assume @p26 (forall @t6 (= (= @t2 @t64) (forall @t58 (= @t69 (= @t29 @t1)))))) % 1.12/1.31 (assume @p27 (forall @t11 (= @t78 (forall @t66 @t4)))) % 1.12/1.31 (assume @p28 (forall @t6 (= (= @t2 @t82) (forall @t58 (= @t69 (tptp.subset @t29 @t1)))))) % 1.12/1.31 (assume @p29 (forall @t11 (= @t13 (forall @t66 (=> @t3 @t37))))) % 1.12/1.31 (assume @p30 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (= @t39 (forall @t33 (= @t83 @t32)))))))) % 1.12/1.31 (assume @p31 (forall @t6 (and (=> @t86 (= @t85 @t3)) (=> @t10 (= @t85 @t84))))) % 1.12/1.31 (assume @p32 (forall @t87 (= (= @t29 @t21) (forall @t53 (= @t52 (or (= @t28 @t1) (= @t28 @t2))))))) % 1.12/1.31 (assume @p33 (forall @t87 (= (= @t29 @t23) (forall @t53 (= @t52 (or @t80 @t43)))))) % 1.12/1.31 (assume @p34 (forall @t87 (= (= @t29 @t89) (forall @t53 (= @t52 (exists (@list @t40 @t88) (and @t56 (tptp.in @t88 @t2) (= @t28 (tptp.ordered_pair @t40 @t88))))))))) % 1.12/1.31 (assume @p35 (forall @t11 (= @t12 (forall @t48 (not (and @t3 @t30 (not @t92) (not @t91) @t90)))))) % 1.12/1.31 (assume @p36 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (= @t38 (forall @t33 (=> @t83 @t32)))))))) % 1.12/1.31 (assume @p37 (forall @t6 (= @t38 @t93))) % 1.12/1.31 (assume @p38 (forall @t87 (= (= @t29 @t24) (forall @t53 (= @t52 (and @t80 @t43)))))) % 1.12/1.31 (assume @p39 (forall @t11 (=> @t55 (forall @t48 (and (=> @t96 (= @t95 @t97)) (=> (not @t96) (= @t95 (= @t29 tptp.empty_set)))))))) % 1.12/1.31 (assume @p40 (forall @t11 (= @t15 @t14))) % 1.12/1.31 (assume @p41 (forall @t11 (=> @t16 (forall @t66 (= (= @t2 @t50) (forall @t58 (= @t69 (exists @t53 @t83)))))))) % 1.12/1.31 (assume @p42 (forall @t11 (= @t98 @t1))) % 1.12/1.31 (assume @p43 (forall @t6 (= (= @t2 @t99) (forall @t58 (= @t69 (exists @t53 (and @t79 @t80))))))) % 1.12/1.31 (assume @p44 (forall @t87 (= (= @t29 @t100) (forall @t53 (= @t52 (and @t80 (not @t43))))))) % 1.12/1.31 (assume @p45 (forall @t11 (=> @t55 (forall @t66 (= @t103 (forall @t58 (= @t69 (exists @t53 @t101)))))))) % 1.12/1.31 (assume @p46 (forall @t11 (=> @t16 (forall @t66 (= @t103 (forall @t58 (= @t69 (exists @t53 @t104)))))))) % 1.12/1.31 (assume @p47 (forall @t6 (=> @t106 (= @t105 @t100)))) % 1.12/1.31 (assume @p48 (forall @t6 (= @t107 (tptp.unordered_pair @t21 @t64)))) % 1.12/1.31 (assume @p49 (forall @t11 (= @t108 (= @t1 @t99)))) % 1.12/1.31 (assume @p50 (forall @t11 (=> @t16 (= @t109 (tptp.set_union2 @t50 @t102))))) % 1.12/1.31 (assume @p51 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (= (= @t2 @t110) (forall @t33 (= @t32 @t104)))))))) % 1.12/1.31 (assume @p52 (forall @t6 (= @t111 (= @t24 tptp.empty_set)))) % 1.12/1.31 (assume @p53 (forall @t11 (=> @t55 (= @t17 (forall @t48 (=> (and @t96 (tptp.in @t29 @t50) (= @t94 (tptp.apply @t1 @t29))) @t91)))))) % 1.12/1.31 (assume @p54 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (forall @t58 (=> @t47 (= (= @t29 @t112) (forall @t45 (= @t44 (exists (@list @t88) (and (tptp.in (tptp.ordered_pair @t28 @t88) @t1) (tptp.in (tptp.ordered_pair @t88 @t40) @t2))))))))))))) % 1.12/1.31 (assume @p55 (forall @t6 (=> @t115 (forall @t58 (=> (tptp.element @t29 @t114) (= (= @t29 @t113) (forall @t53 (=> (tptp.element @t28 @t82) (= @t52 (tptp.in (tptp.subset_complement @t1 @t28) @t2)))))))))) % 1.12/1.31 (assume @p56 (forall @t6 (= @t8 (and @t38 @t116)))) % 1.12/1.31 (assume @p57 (forall @t11 (=> @t55 (=> @t17 (= @t117 @t110))))) % 1.12/1.31 (assume @p58 @t120) % 1.12/1.31 (assume @p59 true) % 1.12/1.31 (assume @p60 (forall @t11 (=> @t55 (and (tptp.relation @t117) (tptp.function @t117))))) % 1.12/1.31 (assume @p61 (forall @t11 (tptp.element @t98 @t82))) % 1.12/1.31 (assume @p62 (forall @t6 (=> @t106 (tptp.element @t105 @t82)))) % 1.12/1.31 (assume @p63 (forall @t11 (=> @t16 @t121))) % 1.12/1.31 (assume @p64 (forall @t6 (=> @t123 @t122))) % 1.12/1.31 (assume @p65 (forall @t6 (=> @t115 (tptp.element @t124 @t82)))) % 1.12/1.31 (assume @p66 (forall @t11 @t125)) % 1.12/1.31 (assume @p67 (forall @t6 (=> @t115 (tptp.element @t126 @t82)))) % 1.12/1.31 (assume @p68 (forall @t87 (=> @t129 (tptp.element @t127 @t82)))) % 1.12/1.31 (assume @p69 (forall @t6 (=> @t16 @t130))) % 1.12/1.31 (assume @p70 (forall @t6 (=> @t115 (tptp.element @t113 @t114)))) % 1.12/1.31 (assume @p71 (forall @t6 (=> @t36 (tptp.relation @t57)))) % 1.12/1.31 (assume @p72 (forall @t11 (exists @t66 @t85))) % 1.12/1.31 (assume @p73 (forall @t6 (=> @t132 (and (tptp.empty @t131) (tptp.relation @t131))))) % 1.12/1.31 (assume @p74 (forall @t11 (=> @t10 (and (tptp.empty @t110) @t121)))) % 1.12/1.31 (assume @p75 (and @t135 @t134 @t133)) % 1.12/1.31 (assume @p76 (forall @t6 (=> @t137 (and @t130 (tptp.relation_empty_yielding @t46))))) % 1.12/1.31 (assume @p77 (forall @t6 (=> (and @t16 @t9 @t36 @t138) (and @t122 (tptp.function @t112))))) % 1.12/1.31 (assume @p78 (forall @t11 @t139)) % 1.12/1.31 (assume @p79 (forall @t6 (=> @t123 (tptp.relation @t24)))) % 1.12/1.31 (assume @p80 (forall @t11 (not (tptp.empty @t82)))) % 1.12/1.31 (assume @p81 @t135) % 1.12/1.31 (assume @p82 (forall @t6 (not (tptp.empty @t107)))) % 1.12/1.31 (assume @p83 (forall @t11 (and @t125 (tptp.function @t34)))) % 1.12/1.31 (assume @p84 (and @t134 @t133 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t135 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 1.12/1.31 (assume @p85 (forall @t6 (=> @t123 (tptp.relation @t23)))) % 1.12/1.31 (assume @p86 (forall @t11 (not (tptp.empty @t64)))) % 1.12/1.31 (assume @p87 (forall @t6 (=> @t86 (not (tptp.empty @t23))))) % 1.12/1.31 (assume @p88 (forall @t11 (=> @t18 (and @t121 (tptp.function @t110))))) % 1.12/1.31 (assume @p89 (forall @t11 (=> @t15 (and @t139 (tptp.epsilon_transitive @t65) (tptp.epsilon_connected @t65) (tptp.ordinal @t65))))) % 1.12/1.31 (assume @p90 (forall @t6 (=> @t123 (tptp.relation @t100)))) % 1.12/1.31 (assume @p91 (forall @t6 (not (tptp.empty @t21)))) % 1.12/1.31 (assume @p92 (forall @t6 (=> @t86 (not (tptp.empty @t22))))) % 1.12/1.31 (assume @p93 (forall @t6 (=> @t55 (and @t130 (tptp.function @t46))))) % 1.12/1.31 (assume @p94 (forall @t11 (=> @t15 (and (tptp.epsilon_transitive @t99) (tptp.epsilon_connected @t99) (tptp.ordinal @t99))))) % 1.12/1.31 (assume @p95 (and @t135 @t134)) % 1.12/1.31 (assume @p96 (forall @t6 (=> (and @t86 @t140) (not (tptp.empty @t89))))) % 1.12/1.31 (assume @p97 (forall @t11 (=> @t142 (not @t141)))) % 1.12/1.31 (assume @p98 (forall @t11 (=> @t142 (not @t143)))) % 1.12/1.31 (assume @p99 (forall @t11 (=> @t10 (and @t141 (tptp.relation @t50))))) % 1.12/1.31 (assume @p100 (forall @t11 (=> @t10 (and @t143 (tptp.relation @t102))))) % 1.12/1.31 (assume @p101 (forall @t6 (=> @t132 (and (tptp.empty @t112) @t122)))) % 1.12/1.31 (assume @p102 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 1.12/1.31 (assume @p103 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 1.12/1.31 (assume @p104 (forall @t6 (=> @t106 (= (tptp.subset_complement @t1 @t105) @t2)))) % 1.12/1.31 (assume @p105 (forall @t11 (=> @t16 (= (tptp.relation_inverse @t110) @t1)))) % 1.12/1.31 (assume @p106 (forall @t6 (=> @t115 (= (tptp.complements_of_subsets @t1 @t113) @t2)))) % 1.12/1.31 (assume @p107 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 1.12/1.31 (assume @p108 @t151) % 1.12/1.31 (assume @p109 (forall @t11 (not (= @t64 tptp.empty_set)))) % 1.12/1.31 (assume @p110 (forall @t6 (=> @t5 (= (tptp.set_union2 @t64 @t2) @t2)))) % 1.12/1.31 (assume @p111 (forall @t6 (not (and @t152 @t5)))) % 1.12/1.31 (assume @p112 (forall @t6 (=> @t153 @t152))) % 1.12/1.31 (assume @p113 (forall @t6 (= (tptp.subset @t64 @t2) @t5))) % 1.12/1.31 (assume @p114 (forall @t6 (= (= @t100 tptp.empty_set) @t38))) % 1.12/1.31 (assume @p115 (forall @t6 (=> @t106 (forall @t58 (=> @t69 @t30))))) % 1.12/1.31 (assume @p116 (forall @t87 (=> @t38 (or @t30 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t29))))))) % 1.12/1.31 (assume @p117 (forall @t6 (= (tptp.subset @t1 @t154) (or @t78 (= @t1 @t154))))) % 1.12/1.31 (assume @p118 (forall @t6 (=> @t5 (tptp.subset @t1 @t155)))) % 1.12/1.31 (assume @p119 (forall @t63 (= (tptp.in @t107 (tptp.cartesian_product2 @t29 @t28)) (and @t156 (tptp.in @t2 @t28))))) % 1.12/1.31 (assume @p120 (forall @t6 (=> @t93 @t157))) % 1.12/1.31 (assume @p121 (forall @t87 (=> @t161 (= @t160 (and (tptp.in @t2 @t158) @t3))))) % 1.12/1.31 (assume @p122 (exists @t11 @t55)) % 1.12/1.31 (assume @p123 (exists @t11 @t20)) % 1.12/1.31 (assume @p124 (exists @t11 (and @t10 @t16))) % 1.12/1.31 (assume @p125 (forall @t11 (=> @t86 (exists @t66 (and @t106 @t140))))) % 1.12/1.31 (assume @p126 (exists @t11 @t10)) % 1.12/1.31 (assume @p127 (exists @t11 @t19)) % 1.12/1.31 (assume @p128 (exists @t11 (and @t16 @t9 @t17 @t10 @t13 @t12 @t15))) % 1.12/1.31 (assume @p129 (exists @t11 @t142)) % 1.12/1.31 (assume @p130 (forall @t11 (exists @t66 (and @t106 @t84)))) % 1.12/1.31 (assume @p131 (exists @t11 @t86)) % 1.12/1.31 (assume @p132 (exists @t11 @t18)) % 1.12/1.31 (assume @p133 (exists @t11 (and @t86 @t13 @t12 @t15))) % 1.12/1.31 (assume @p134 (exists @t11 @t137)) % 1.12/1.31 (assume @p135 (exists @t11 (and @t16 @t136 @t9))) % 1.12/1.31 (assume @p136 (forall @t6 (=> @t115 (= @t124 @t155)))) % 1.12/1.31 (assume @p137 (forall @t6 (=> @t115 (= @t126 (tptp.set_meet @t2))))) % 1.12/1.31 (assume @p138 (forall @t87 (=> @t129 (= @t127 @t162)))) % 1.12/1.31 (assume @p139 (forall @t6 (=> @t27 (= @t25 @t38)))) % 1.12/1.31 (assume @p140 (forall @t6 (=> @t27 (tptp.ordinal_subset @t1 @t1)))) % 1.12/1.31 (assume @p141 (forall @t6 (tptp.subset @t1 @t1))) % 1.12/1.31 (assume @p142 (forall @t6 (=> @t111 (tptp.disjoint @t2 @t1)))) % 1.12/1.31 (assume @p143 (forall @t11 (tptp.in @t1 @t65))) % 1.12/1.31 (assume @p144 (forall @t63 (not (and (= @t21 (tptp.unordered_pair @t29 @t28)) (not @t163) (not (= @t1 @t28)))))) % 1.12/1.31 (assume @p145 (forall @t87 (=> @t47 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t29))) (and @t5 (tptp.in @t1 @t164)))))) % 1.12/1.31 (assume @p146 (forall @t6 (=> @t36 (tptp.subset @t165 @t1)))) % 1.12/1.31 (assume @p147 (forall @t6 (=> @t36 (tptp.subset @t57 @t2)))) % 1.12/1.31 (assume @p148 (forall @t6 (=> @t36 (tptp.subset @t165 @t166)))) % 1.12/1.31 (assume @p149 (forall @t87 (=> @t38 (and (tptp.subset @t167 (tptp.cartesian_product2 @t2 @t29)) (tptp.subset (tptp.cartesian_product2 @t29 @t1) (tptp.cartesian_product2 @t29 @t2)))))) % 1.12/1.31 (assume @p150 (forall @t6 (=> @t36 (= @t165 (tptp.set_intersection2 @t166 @t1))))) % 1.12/1.31 (assume @p151 (forall @t63 (=> (and @t38 (tptp.subset @t29 @t28)) (tptp.subset @t167 (tptp.cartesian_product2 @t2 @t28))))) % 1.12/1.31 (assume @p152 (forall @t6 (=> @t38 (= @t23 @t2)))) % 1.12/1.31 (assume @p153 (forall @t11 (exists @t66 (and @t5 @t171 (forall @t58 (=> @t69 (tptp.in @t170 @t2))) @t169)))) % 1.12/1.31 (assume @p154 (forall @t87 (=> @t47 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t29) @t2) (tptp.relation_rng_restriction @t1 @t172))))) % 1.12/1.31 (assume @p155 (forall @t87 (=> @t47 (= (tptp.in @t1 (tptp.relation_image @t29 @t2)) (exists @t53 (and (tptp.in @t28 @t158) (tptp.in (tptp.ordered_pair @t28 @t1) @t29) @t43)))))) % 1.12/1.31 (assume @p156 (forall @t6 (=> @t36 (tptp.subset @t173 @t166)))) % 1.12/1.31 (assume @p157 (forall @t6 (=> @t176 (tptp.subset @t175 @t1)))) % 1.12/1.31 (assume @p158 (forall @t6 (=> @t36 (= @t173 (tptp.relation_image @t2 @t178))))) % 1.12/1.31 (assume @p159 (forall @t6 (=> @t36 (=> (tptp.subset @t1 @t177) (tptp.subset @t1 (tptp.relation_inverse_image @t2 @t173)))))) % 1.12/1.31 (assume @p160 (forall @t11 (=> @t16 (= (tptp.relation_image @t1 @t50) @t102)))) % 1.12/1.31 (assume @p161 (forall @t6 (=> @t176 (=> @t179 (= @t175 @t1))))) % 1.12/1.31 (assume @p162 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (= @t180 (tptp.relation_image @t2 @t102))))))) % 1.12/1.31 (assume @p163 (forall @t87 (=> @t47 (= (tptp.in @t1 @t181) (exists @t53 (and (tptp.in @t28 @t164) (tptp.in (tptp.ordered_pair @t1 @t28) @t29) @t43)))))) % 1.12/1.31 (assume @p164 (forall @t6 (=> @t36 (tptp.subset @t174 @t177)))) % 1.12/1.31 (assume @p165 (forall @t6 (=> @t36 (not (and @t81 @t179 (= @t174 tptp.empty_set)))))) % 1.12/1.31 (assume @p166 (forall @t87 (=> @t47 (=> @t38 (tptp.subset (tptp.relation_inverse_image @t29 @t1) @t181))))) % 1.12/1.31 (assume @p167 (forall @t6 (tptp.subset @t24 @t1))) % 1.12/1.31 (assume @p168 (forall @t87 (=> (and @t38 @t183) (tptp.subset @t1 @t182)))) % 1.12/1.31 (assume @p169 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 1.12/1.31 (assume @p170 (forall @t6 (=> @t5 @t184))) % 1.12/1.31 (assume @p171 (forall @t87 (=> (and @t38 (tptp.subset @t2 @t29)) @t183))) % 1.12/1.31 (assume @p172 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 1.12/1.31 (assume @p173 (forall @t87 (=> @t47 (=> @t186 (and @t185 (tptp.in @t2 @t164)))))) % 1.12/1.31 (assume @p174 (forall @t6 (=> @t176 (forall @t58 (=> @t161 (= @t189 (and @t185 (tptp.in @t187 @t177)))))))) % 1.12/1.31 (assume @p175 (forall @t11 (=> @t13 (forall @t66 (=> @t26 (=> @t8 @t5)))))) % 1.12/1.31 (assume @p176 (forall @t11 (=> @t16 (tptp.subset @t1 (tptp.cartesian_product2 @t50 @t102))))) % 1.12/1.31 (assume @p177 (forall @t6 (=> @t176 (forall @t58 (=> @t161 (=> @t189 (= (tptp.apply @t188 @t1) (tptp.apply @t2 @t187)))))))) % 1.12/1.31 (assume @p178 (forall @t6 (=> @t176 (forall @t58 (=> @t161 (=> (tptp.in @t1 @t177) (= (tptp.apply (tptp.relation_composition @t2 @t29) @t1) (tptp.apply @t29 (tptp.apply @t2 @t1))))))))) % 1.12/1.31 (assume @p179 (forall @t6 (=> @t26 (=> @t5 @t15)))) % 1.12/1.31 (assume @p180 (forall @t11 (=> @t15 (forall @t66 (=> @t26 (not (and @t153 @t116 @t4))))))) % 1.12/1.31 (assume @p181 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (=> @t38 (and (tptp.subset @t50 @t177) (tptp.subset @t102 @t166)))))))) % 1.12/1.31 (assume @p182 (forall @t87 (=> @t38 (tptp.subset (tptp.set_intersection2 @t1 @t29) @t182)))) % 1.12/1.31 (assume @p183 (forall @t6 (=> @t38 (= @t24 @t1)))) % 1.12/1.31 (assume @p184 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.12/1.31 (assume @p185 (forall @t6 (=> @t184 (or @t84 @t5)))) % 1.12/1.31 (assume @p186 (forall @t6 (=> (forall @t58 (= @t30 @t69)) @t39))) % 1.12/1.31 (assume @p187 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 1.12/1.31 (assume @p188 (forall @t87 (=> @t47 (=> @t186 (and (tptp.in @t1 @t190) (tptp.in @t2 @t190)))))) % 1.12/1.31 (assume @p189 (forall @t11 (=> (forall @t66 (=> @t3 (and @t26 @t37))) @t15))) % 1.12/1.31 (assume @p190 (forall @t6 (=> @t26 (not (and @t38 @t81 (forall @t58 (=> (tptp.ordinal @t29) (not (and @t30 (forall @t53 (=> (tptp.ordinal @t28) (=> @t80 (tptp.ordinal_subset @t29 @t28))))))))))))) % 1.12/1.31 (assume @p191 (forall @t11 (=> @t15 (forall @t66 (=> @t26 (= @t5 (tptp.ordinal_subset @t65 @t2))))))) % 1.12/1.31 (assume @p192 (forall @t87 (=> @t38 (tptp.subset (tptp.set_difference @t1 @t29) @t162)))) % 1.12/1.31 (assume @p193 (forall @t63 (=> (= @t107 @t31) (and @t163 (= @t2 @t28))))) % 1.12/1.31 (assume @p194 (forall @t6 (=> @t176 (= @t35 (and (= @t177 @t1) (forall @t58 (=> @t30 (= @t191 @t29)))))))) % 1.12/1.31 (assume @p195 (forall @t6 (=> @t3 (= (tptp.apply @t34 @t2) @t2)))) % 1.12/1.31 (assume @p196 (forall @t6 (tptp.subset @t100 @t1))) % 1.12/1.31 (assume @p197 (forall @t11 (=> @t16 (and (= @t102 (tptp.relation_dom @t110)) (= @t50 (tptp.relation_rng @t110)))))) % 1.12/1.31 (assume @p198 (forall @t87 (= (tptp.subset @t21 @t29) (and @t156 @t92)))) % 1.12/1.31 (assume @p199 (forall @t6 (= @t192 @t23))) % 1.12/1.31 (assume @p200 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 1.12/1.31 (assume @p201 (forall @t87 (not (and @t5 @t92 @t30)))) % 1.12/1.31 (assume @p202 (forall @t6 (= @t157 @t38))) % 1.12/1.31 (assume @p203 (forall @t6 (and (not (and @t194 (forall @t58 (not @t193)))) (not (and (exists @t58 @t193) @t111))))) % 1.12/1.31 (assume @p204 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t78))) % 1.12/1.31 (assume @p205 (forall @t6 (= (tptp.set_difference @t23 @t2) @t100))) % 1.12/1.31 (assume @p206 (forall @t11 (=> @t15 (= @t108 (forall @t66 (=> @t26 (=> @t3 (tptp.in @t195 @t1)))))))) % 1.12/1.31 (assume @p207 (forall @t11 (=> @t15 (and (not (and (not @t108) (forall @t66 (=> @t26 (not @t196))))) (not (and (exists @t66 (and @t26 @t196)) @t108)))))) % 1.12/1.31 (assume @p208 (forall @t6 (=> @t106 (forall @t58 (=> @t128 (= @t198 (tptp.subset @t2 @t197))))))) % 1.12/1.31 (assume @p209 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (tptp.subset @t199 @t50)))))) % 1.12/1.31 (assume @p210 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (tptp.subset @t180 @t166)))))) % 1.12/1.31 (assume @p211 (forall @t6 (=> @t38 (= @t2 @t192)))) % 1.12/1.31 (assume @p212 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (=> (tptp.subset @t102 @t177) (= @t199 @t50))))))) % 1.12/1.31 (assume @p213 (forall @t6 (=> @t115 (not (and @t200 (= @t113 tptp.empty_set)))))) % 1.12/1.31 (assume @p214 (forall @t11 (=> @t16 (forall @t66 (=> @t36 (=> (tptp.subset @t50 @t166) (= (tptp.relation_rng @t131) @t102))))))) % 1.12/1.31 (assume @p215 (forall @t6 (=> @t115 (=> @t200 (= (tptp.subset_difference @t1 @t98 @t124) (tptp.meet_of_subsets @t1 @t113)))))) % 1.12/1.31 (assume @p216 (forall @t6 (=> @t115 (=> @t200 (= (tptp.union_of_subsets @t1 @t113) (tptp.subset_difference @t1 @t98 @t126)))))) % 1.12/1.31 (assume @p217 (forall @t6 (= (tptp.set_difference @t1 @t100) @t24))) % 1.12/1.31 (assume @p218 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 1.12/1.31 (assume @p219 (forall @t87 (=> (and @t5 @t201) (tptp.element @t1 @t29)))) % 1.12/1.31 (assume @p220 (forall @t6 (and (not (and @t194 (forall @t58 (not @t202)))) (not (and (exists @t58 @t202) @t111))))) % 1.12/1.31 (assume @p221 (forall @t11 (=> @t81 (forall @t66 (=> @t106 (forall @t58 (=> (tptp.element @t29 @t1) (=> @t90 (tptp.in @t29 @t105))))))))) % 1.12/1.31 (assume @p222 (forall @t11 (=> @t55 (=> @t17 (forall @t66 (=> @t176 (= (= @t2 @t117) (and (= @t177 @t102) (forall @t33 (and (=> @t203 @t101) (=> @t101 @t203))))))))))) % 1.12/1.31 (assume @p223 (forall @t87 (=> @t128 (not (and (tptp.in @t2 @t197) @t92))))) % 1.12/1.31 (assume @p224 (forall @t11 (=> @t55 (=> @t17 (and (= @t102 (tptp.relation_dom @t117)) (= @t50 (tptp.relation_rng @t117))))))) % 1.12/1.31 (assume @p225 (forall @t11 (=> @t16 (=> (forall @t48 (not @t97)) @t78)))) % 1.12/1.31 (assume @p226 (forall @t6 (=> @t176 (=> (and (tptp.one_to_one @t2) (tptp.in @t1 @t166)) (and (= @t1 (tptp.apply @t2 (tptp.apply @t204 @t1))) (= @t1 (tptp.apply (tptp.relation_composition @t204 @t2) @t1))))))) % 1.12/1.31 (assume @p227 (forall @t87 (not (and @t5 @t201 (tptp.empty @t29))))) % 1.12/1.31 (assume @p228 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 1.12/1.31 (assume @p229 (forall @t6 (not (and @t38 @t7)))) % 1.12/1.31 (assume @p230 (forall @t11 (=> @t55 (=> @t17 (tptp.one_to_one @t117))))) % 1.12/1.31 (assume @p231 (forall @t87 (=> (and @t38 @t198) (tptp.disjoint @t1 @t29)))) % 1.12/1.31 (assume @p232 (forall @t11 (=> @t16 (=> (or @t206 @t205) @t78)))) % 1.12/1.31 (assume @p233 (forall @t11 (=> @t16 (= @t206 @t205)))) % 1.12/1.31 (assume @p234 (forall @t6 (= (= (tptp.set_difference @t1 @t154) @t1) @t4))) % 1.12/1.31 (assume @p235 (forall @t6 (=> @t176 (forall @t58 (=> @t161 (= (= @t2 @t159) (and (= @t177 (tptp.set_intersection2 @t158 @t1)) (forall @t53 (=> (tptp.in @t28 @t177) (= (tptp.apply @t2 @t28) (tptp.apply @t29 @t28))))))))))) % 1.12/1.31 (assume @p236 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t64))) % 1.12/1.31 (assume @p237 (forall @t11 (=> @t10 @t78))) % 1.12/1.31 (assume @p238 (forall @t6 (=> (tptp.subset @t64 @t154) @t39))) % 1.12/1.31 (assume @p239 (forall @t87 (=> @t161 (=> @t160 @t207)))) % 1.12/1.31 (assume @p240 (forall @t11 (and (= (tptp.relation_dom @t34) @t1) (= (tptp.relation_rng @t34) @t1)))) % 1.12/1.31 (assume @p241 (forall @t87 (=> @t161 (=> @t3 @t207)))) % 1.12/1.31 (assume @p242 (forall @t63 (=> (tptp.relation @t28) (= (tptp.in @t107 (tptp.relation_composition (tptp.identity_relation @t29) @t28)) (and @t156 (tptp.in @t107 @t28)))))) % 1.12/1.31 (assume @p243 (forall @t6 (not (and @t5 @t84)))) % 1.12/1.31 (assume @p244 (forall @t6 (not (and @t5 (forall @t58 (not (and @t69 (forall @t53 (not (and @t43 @t52)))))))))) % 1.12/1.31 (assume @p245 (forall @t6 (tptp.subset @t1 @t23))) % 1.12/1.31 (assume @p246 (forall @t6 (= @t111 (= @t100 @t1)))) % 1.12/1.31 (assume @p247 (forall @t87 (=> @t47 (= (tptp.in @t1 (tptp.relation_dom @t172)) (and @t5 @t185))))) % 1.12/1.31 (assume @p248 (forall @t6 (=> @t36 (tptp.subset @t208 @t2)))) % 1.12/1.31 (assume @p249 (forall @t6 (not (and @t10 @t116 @t84)))) % 1.12/1.31 (assume @p250 (forall @t87 (=> @t161 (= @t186 (and @t185 (= @t2 @t187)))))) % 1.12/1.31 (assume @p251 (forall @t87 (=> (and @t38 @t168) (tptp.subset (tptp.set_union2 @t1 @t29) @t2)))) % 1.12/1.31 (assume @p252 (forall @t87 (=> @t209 @t39))) % 1.12/1.31 (assume @p253 (forall @t6 (=> @t36 (= (tptp.relation_dom @t208) @t178)))) % 1.12/1.31 (assume @p254 (forall @t6 (=> @t36 (= @t208 (tptp.relation_composition @t34 @t2))))) % 1.12/1.31 (assume @p255 (forall @t6 (=> @t36 (tptp.subset (tptp.relation_rng @t208) @t166)))) % 1.12/1.31 (assume @p256 (forall @t11 (= (tptp.union @t82) @t1))) % 1.12/1.31 (assume @p257 (forall @t11 (exists @t66 (and @t5 @t171 (forall @t58 (not (and @t69 (forall @t53 (not (and @t43 (forall @t51 (=> (tptp.subset @t40 @t29) @t62)))))))) @t169)))) % 1.12/1.31 (assume @p258 (forall @t87 (=> @t209 @t91))) % 1.12/1.31 (step @p259 :rule quant-merge-prenex :args ((= (forall @t11 @t215) (forall (@list @t1 @t210) @t213)))) % 1.12/1.31 (step @p260 :rule alpha_equiv :args (@t216 (@list @t210) @t217)) % 1.12/1.31 (step @p261 :rule refl :args (@t212)) % 1.12/1.31 (step @p262 :rule nary_cong :premises (@p261 @p260) :args (@t218)) % 1.12/1.31 (step @p263 :rule quant-miniscope-or :args ((= @t215 @t218))) % 1.12/1.31 (step @p264 :rule trans :premises (@p263 @p262)) % 1.12/1.31 (step @p265 :rule symm :premises (@p264)) % 1.12/1.31 (step @p266 :rule cong :premises (@p265) :args ((forall @t11 (or @t212 @t219)))) % 1.12/1.31 (step @p267 :rule trans :premises (@p266 @p259)) % 1.12/1.31 (step @p268 :rule bool-impl-elim :args (@t16 @t219)) % 1.12/1.31 (step @p269 :rule cong :premises (@p268) :args ((forall @t11 (=> @t16 @t219)))) % 1.12/1.31 (step @p270 :rule trans :premises (@p269 @p267)) % 1.12/1.31 (step @p271 :rule bool-impl-elim :args (@t69 @t68)) % 1.12/1.31 (step @p272 :rule cong :premises (@p271) :args (@t70)) % 1.12/1.31 (step @p273 :rule refl :args (@t71)) % 1.12/1.31 (step @p274 :rule cong :premises (@p273 @p272) :args (@t72)) % 1.12/1.31 (step @p275 :rule cong :premises (@p274) :args (@t73)) % 1.12/1.31 (step @p276 :rule refl :args (@t16)) % 1.12/1.31 (step @p277 :rule cong :premises (@p276 @p275) :args (@t74)) % 1.12/1.31 (step @p278 :rule cong :premises (@p277) :args (@t75)) % 1.12/1.31 (step @p279 :rule trans :premises (@p278 @p270)) % 1.12/1.31 (step @p280 :rule eq_resolve :premises (@p24 @p279)) % 1.12/1.31 (step @p281 :rule instantiate :premises (@p280) :args ((@list @t221 @t222))) % 1.12/1.31 (step @p282 :rule bool-impl-elim :args (@t16 @t220)) % 1.12/1.31 (step @p283 :rule cong :premises (@p282) :args ((forall @t11 (=> @t16 @t220)))) % 1.12/1.31 (step @p284 :rule bool-impl-elim :args (@t146 @t145)) % 1.12/1.31 (step @p285 :rule cong :premises (@p284) :args (@t147)) % 1.12/1.31 (step @p286 :rule refl :args (@t118)) % 1.12/1.31 (step @p287 :rule cong :premises (@p286 @p285) :args (@t148)) % 1.12/1.31 (step @p288 :rule cong :premises (@p276 @p287) :args (@t149)) % 1.12/1.31 (step @p289 :rule cong :premises (@p288) :args (@t150)) % 1.12/1.31 (step @p290 :rule trans :premises (@p289 @p283)) % 1.12/1.31 (step @p291 :rule cong :premises (@p290) :args (@t151)) % 1.12/1.31 (step @p292 :rule eq_resolve :premises (@p108 @p291)) % 1.12/1.31 (step @p293 :rule skolemize :premises (@p292)) % 1.12/1.31 (step @p294 :rule bool-double-not-elim :args (@t223)) % 1.12/1.31 (step @p295 :rule refl :args (@t228)) % 1.12/1.31 (step @p296 :rule nary_cong :premises (@p295 @p294) :args ((or @t228 (not @t227)))) % 1.12/1.31 (step @p297 :rule cnf_or_neg :args (@t228 0)) % 1.12/1.31 (step @p298 :rule eq_resolve :premises (@p297 @p296)) % 1.12/1.31 (step @p299 :rule reordering :premises (@p298) :args ((or @t223 @t228))) % 1.12/1.31 (step @p300 :rule chain_m_resolution :premises (@p299 @p293) :args (@t223 @t229 @t230)) % 1.12/1.31 (step @p301 :rule cnf_or_pos :args (@t234)) % 1.12/1.31 (step @p302 :rule reordering :premises (@p301) :args ((or @t227 @t233 (not @t234)))) % 1.12/1.32 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p281) :args (@t233 @t235 (@list @t223 @t234))) % 1.12/1.32 (step @p304 :rule bool-impl-elim :args (@t16 @t119)) % 1.12/1.32 (step @p305 :rule cong :premises (@p304) :args (@t120)) % 1.12/1.32 (step @p306 :rule eq_resolve :premises (@p58 @p305)) % 1.12/1.32 (step @p307 :rule instantiate :premises (@p306) :args ((@list @t221))) % 1.12/1.32 (step @p308 :rule cnf_or_pos :args (@t237)) % 1.12/1.32 (step @p309 :rule reordering :premises (@p308) :args ((or @t227 @t236 (not @t237)))) % 1.12/1.32 (step @p310 :rule chain_m_resolution :premises (@p309 @p300 @p307) :args (@t236 @t235 (@list @t223 @t237))) % 1.12/1.32 (step @p311 :rule cnf_or_neg :args (@t228 1)) % 1.12/1.32 (step @p312 :rule chain_m_resolution :premises (@p311 @p293) :args ((not @t226) @t229 @t230)) % 1.12/1.32 (step @p313 :rule cnf_equiv_neg2 :args (@t226)) % 1.12/1.32 (step @p314 :rule cnf_equiv_pos1 :args (@t236)) % 1.12/1.32 (step @p315 :rule reordering :premises (@p314) :args ((or @t239 @t232 @t238))) % 1.12/1.32 (step @p316 :rule alpha_equiv :args (@t224 @t217 (@list @t29))) % 1.12/1.32 (step @p317 :rule equiv_elim2 :premises (@p316)) % 1.12/1.32 (step @p318 :rule cnf_equiv_pos1 :args (@t233)) % 1.12/1.32 (step @p319 :rule reordering :premises (@p318) :args ((or @t241 @t231 @t240))) % 1.12/1.32 (step @p320 :rule chain_m_resolution :premises (@p319 @p303 @p317 @p315 @p310 @p313 @p312) :args (@t239 (@list false true false false true true) (@list @t233 @t231 @t232 @t236 @t224 @t226))) % 1.12/1.32 (step @p321 :rule cnf_equiv_pos2 :args (@t236)) % 1.12/1.32 (step @p322 :rule reordering :premises (@p321) :args ((or @t225 @t241 @t238))) % 1.12/1.32 (step @p323 :rule chain_m_resolution :premises (@p322 @p320 @p310) :args (@t241 (@list true false) (@list @t225 @t236))) % 1.12/1.32 (step @p324 :rule cnf_equiv_neg1 :args (@t226)) % 1.12/1.32 (step @p325 :rule reordering :premises (@p324) :args ((or @t225 @t224 @t226))) % 1.12/1.32 (step @p326 :rule chain_m_resolution :premises (@p325 @p320 @p312) :args (@t224 (@list true true) (@list @t225 @t226))) % 1.12/1.32 (step @p327 :rule equiv_elim1 :premises (@p316)) % 1.12/1.32 (step @p328 :rule chain_m_resolution :premises (@p327 @p326) :args (@t231 (@list false) (@list @t224))) % 1.12/1.32 (step @p329 :rule cnf_equiv_pos2 :args (@t233)) % 1.12/1.32 (step @p330 :rule reordering :premises (@p329) :args ((or @t232 (not @t231) @t240))) % 1.12/1.32 (step @p331 false :rule chain_m_resolution :premises (@p330 @p328 @p323 @p303) :args (false (@list false true false) (@list @t231 @t232 @t233))) % 1.12/1.32 ) % 1.12/1.32 % SZS output end Proof % 1.12/1.32 % cvc5 exiting %------------------------------------------------------------------------------