%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU247+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:51:07 AM UTC 2026 % Result : Theorem 0.41s 0.84s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU247+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 % 0.17/0.35 % Computer : n017.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % 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 16:46:31 EDT 2026 % 0.17/0.35 % CPUTime : % 0.39/0.56 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.84 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.84 % SZS status Theorem % 0.41/0.84 % SZS output start Proof % 0.41/0.84 ( % 0.41/0.84 (declare-sort $$unsorted 0) % 0.41/0.84 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.well_founded_relation (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.empty_set $$unsorted) % 0.41/0.84 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.well_orders (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.is_antisymmetric_in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.relation_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.function (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.is_well_founded_in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.ordinal_subset (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.is_reflexive_in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.antisymmetric (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.is_connected_in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.reflexive (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.unordered_triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.connected (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.fiber (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.well_ordering (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.is_transitive_in (-> $$unsorted $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.being_limit_ordinal (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.transitive (-> $$unsorted Bool)) % 0.41/0.84 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.84 (declare-const tptp.function_inverse (-> $$unsorted $$unsorted)) % 0.41/0.84 (define @t1 () (@var "A" $$unsorted)) % 0.41/0.84 (define @t2 () (@var "B" $$unsorted)) % 0.41/0.84 (define @t3 () (tptp.in @t2 @t1)) % 0.41/0.84 (define @t4 () (not @t3)) % 0.41/0.84 (define @t5 () (tptp.in @t1 @t2)) % 0.41/0.84 (define @t6 () (@list @t1 @t2)) % 0.41/0.84 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.41/0.84 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.41/0.84 (define @t9 () (tptp.function @t1)) % 0.41/0.84 (define @t10 () (tptp.empty @t1)) % 0.41/0.84 (define @t11 () (@list @t1)) % 0.41/0.84 (define @t12 () (tptp.epsilon_connected @t1)) % 0.41/0.84 (define @t13 () (tptp.epsilon_transitive @t1)) % 0.41/0.84 (define @t14 () (and @t13 @t12)) % 0.41/0.84 (define @t15 () (tptp.ordinal @t1)) % 0.41/0.84 (define @t16 () (tptp.relation @t1)) % 0.41/0.84 (define @t17 () (tptp.one_to_one @t1)) % 0.41/0.84 (define @t18 () (and @t16 @t9 @t17)) % 0.41/0.84 (define @t19 () (and @t16 @t10 @t9)) % 0.41/0.84 (define @t20 () (and @t13 @t12 @t15)) % 0.41/0.84 (define @t21 () (tptp.unordered_pair @t1 @t2)) % 0.41/0.84 (define @t22 () (tptp.set_union2 @t2 @t1)) % 0.41/0.84 (define @t23 () (tptp.set_union2 @t1 @t2)) % 0.41/0.84 (define @t24 () (tptp.set_intersection2 @t1 @t2)) % 0.41/0.84 (define @t25 () (tptp.ordinal_subset @t1 @t2)) % 0.41/0.84 (define @t26 () (tptp.ordinal @t2)) % 0.41/0.84 (define @t27 () (and @t15 @t26)) % 0.41/0.84 (define @t28 () (@var "D" $$unsorted)) % 0.41/0.84 (define @t29 () (@var "C" $$unsorted)) % 0.41/0.84 (define @t30 () (= @t29 @t28)) % 0.41/0.84 (define @t31 () (tptp.in @t29 @t1)) % 0.41/0.84 (define @t32 () (tptp.ordered_pair @t29 @t28)) % 0.41/0.84 (define @t33 () (tptp.in @t32 @t2)) % 0.41/0.84 (define @t34 () (@list @t29 @t28)) % 0.41/0.84 (define @t35 () (tptp.identity_relation @t1)) % 0.41/0.84 (define @t36 () (= @t2 @t35)) % 0.41/0.84 (define @t37 () (tptp.relation @t2)) % 0.41/0.84 (define @t38 () (tptp.subset @t2 @t1)) % 0.41/0.84 (define @t39 () (tptp.subset @t1 @t2)) % 0.41/0.84 (define @t40 () (= @t1 @t2)) % 0.41/0.84 (define @t41 () (@var "E" $$unsorted)) % 0.41/0.84 (define @t42 () (tptp.ordered_pair @t28 @t41)) % 0.41/0.84 (define @t43 () (tptp.in @t42 @t1)) % 0.41/0.84 (define @t44 () (tptp.in @t28 @t2)) % 0.41/0.84 (define @t45 () (tptp.in @t42 @t29)) % 0.41/0.84 (define @t46 () (@list @t28 @t41)) % 0.41/0.84 (define @t47 () (tptp.relation_dom_restriction @t1 @t2)) % 0.41/0.84 (define @t48 () (tptp.relation @t29)) % 0.41/0.84 (define @t49 () (@list @t2 @t29)) % 0.41/0.84 (define @t50 () (tptp.in @t41 @t2)) % 0.41/0.84 (define @t51 () (tptp.relation_dom @t1)) % 0.41/0.84 (define @t52 () (@list @t41)) % 0.41/0.84 (define @t53 () (tptp.in @t28 @t29)) % 0.41/0.84 (define @t54 () (@list @t28)) % 0.41/0.84 (define @t55 () (= @t29 (tptp.relation_image @t1 @t2))) % 0.41/0.84 (define @t56 () (and @t16 @t9)) % 0.41/0.84 (define @t57 () (tptp.in @t41 @t1)) % 0.41/0.84 (define @t58 () (tptp.relation_rng_restriction @t1 @t2)) % 0.41/0.84 (define @t59 () (@list @t29)) % 0.41/0.84 (define @t60 () (tptp.relation_field @t1)) % 0.41/0.84 (define @t61 () (tptp.antisymmetric @t1)) % 0.41/0.84 (define @t62 () (tptp.apply @t1 @t28)) % 0.41/0.84 (define @t63 () (tptp.in @t28 @t51)) % 0.41/0.84 (define @t64 () (= @t29 (tptp.relation_inverse_image @t1 @t2))) % 0.41/0.84 (define @t65 () (tptp.connected @t1)) % 0.41/0.84 (define @t66 () (tptp.transitive @t1)) % 0.41/0.84 (define @t67 () (tptp.in @t41 @t28)) % 0.41/0.84 (define @t68 () (@list @t1 @t2 @t29 @t28)) % 0.41/0.84 (define @t69 () (tptp.singleton @t1)) % 0.41/0.84 (define @t70 () (tptp.succ @t1)) % 0.41/0.84 (define @t71 () (@list @t2)) % 0.41/0.84 (define @t72 () (tptp.in @t29 @t2)) % 0.41/0.84 (define @t73 () (tptp.is_reflexive_in @t1 @t2)) % 0.41/0.84 (define @t74 () (= @t2 tptp.empty_set)) % 0.41/0.84 (define @t75 () (= @t2 (tptp.set_meet @t1))) % 0.41/0.84 (define @t76 () (= @t1 tptp.empty_set)) % 0.41/0.84 (define @t77 () (tptp.in @t29 @t28)) % 0.41/0.84 (define @t78 () (tptp.in @t28 @t1)) % 0.41/0.84 (define @t79 () (not @t76)) % 0.41/0.84 (define @t80 () (tptp.powerset @t1)) % 0.41/0.84 (define @t81 () (tptp.in @t32 @t1)) % 0.41/0.84 (define @t82 () (tptp.empty @t2)) % 0.41/0.84 (define @t83 () (tptp.element @t2 @t1)) % 0.41/0.84 (define @t84 () (not @t10)) % 0.41/0.84 (define @t85 () (@list @t1 @t2 @t29)) % 0.41/0.84 (define @t86 () (not @t74)) % 0.41/0.84 (define @t87 () (tptp.well_founded_relation @t1)) % 0.41/0.84 (define @t88 () (@var "F" $$unsorted)) % 0.41/0.84 (define @t89 () (tptp.cartesian_product2 @t1 @t2)) % 0.41/0.84 (define @t90 () (not @t72)) % 0.41/0.84 (define @t91 () (= @t2 @t29)) % 0.41/0.84 (define @t92 () (not @t91)) % 0.41/0.84 (define @t93 () (tptp.in @t2 @t29)) % 0.41/0.84 (define @t94 () (forall @t59 (=> @t31 @t72))) % 0.41/0.84 (define @t95 () (= @t29 tptp.empty_set)) % 0.41/0.84 (define @t96 () (tptp.subset @t29 @t2)) % 0.41/0.84 (define @t97 () (tptp.is_well_founded_in @t1 @t2)) % 0.41/0.84 (define @t98 () (tptp.apply @t1 @t2)) % 0.41/0.84 (define @t99 () (= @t29 @t98)) % 0.41/0.84 (define @t100 () (tptp.in @t2 @t51)) % 0.41/0.84 (define @t101 () (tptp.in (tptp.ordered_pair @t2 @t29) @t1)) % 0.41/0.84 (define @t102 () (tptp.in (tptp.ordered_pair @t28 @t29) @t1)) % 0.41/0.84 (define @t103 () (tptp.is_antisymmetric_in @t1 @t2)) % 0.41/0.84 (define @t104 () (tptp.cast_to_subset @t1)) % 0.41/0.84 (define @t105 () (tptp.union @t1)) % 0.41/0.84 (define @t106 () (tptp.reflexive @t1)) % 0.41/0.84 (define @t107 () (tptp.well_ordering @t1)) % 0.41/0.84 (define @t108 () (tptp.set_difference @t1 @t2)) % 0.41/0.84 (define @t109 () (and @t63 (= @t29 @t62))) % 0.41/0.84 (define @t110 () (tptp.relation_rng @t1)) % 0.41/0.84 (define @t111 () (= @t2 @t110)) % 0.41/0.84 (define @t112 () (tptp.subset_complement @t1 @t2)) % 0.41/0.84 (define @t113 () (tptp.element @t2 @t80)) % 0.41/0.84 (define @t114 () (tptp.ordered_pair @t1 @t2)) % 0.41/0.84 (define @t115 () (tptp.is_connected_in @t1 @t2)) % 0.41/0.84 (define @t116 () (tptp.is_transitive_in @t1 @t2)) % 0.41/0.84 (define @t117 () (tptp.being_limit_ordinal @t1)) % 0.41/0.84 (define @t118 () (tptp.cartesian_product2 @t2 @t2)) % 0.41/0.84 (define @t119 () (tptp.relation_restriction @t1 @t2)) % 0.41/0.84 (define @t120 () (tptp.relation_inverse @t1)) % 0.41/0.84 (define @t121 () (tptp.disjoint @t1 @t2)) % 0.41/0.84 (define @t122 () (tptp.relation_composition @t1 @t2)) % 0.41/0.84 (define @t123 () (tptp.complements_of_subsets @t1 @t2)) % 0.41/0.84 (define @t124 () (tptp.powerset @t80)) % 0.41/0.84 (define @t125 () (tptp.element @t2 @t124)) % 0.41/0.84 (define @t126 () (not @t40)) % 0.41/0.84 (define @t127 () (tptp.function_inverse @t1)) % 0.41/0.84 (define @t128 () (tptp.relation @t120)) % 0.41/0.84 (define @t129 () (tptp.relation @t122)) % 0.41/0.84 (define @t130 () (and @t16 @t37)) % 0.41/0.84 (define @t131 () (tptp.union_of_subsets @t1 @t2)) % 0.41/0.84 (define @t132 () (tptp.relation @t35)) % 0.41/0.84 (define @t133 () (tptp.meet_of_subsets @t1 @t2)) % 0.41/0.84 (define @t134 () (tptp.subset_difference @t1 @t2 @t29)) % 0.41/0.84 (define @t135 () (tptp.element @t29 @t80)) % 0.41/0.84 (define @t136 () (and @t113 @t135)) % 0.41/0.84 (define @t137 () (tptp.relation @t47)) % 0.41/0.84 (define @t138 () (tptp.relation @t58)) % 0.41/0.84 (define @t139 () (tptp.relation_composition @t2 @t1)) % 0.41/0.84 (define @t140 () (and @t10 @t37)) % 0.41/0.84 (define @t141 () (tptp.relation_empty_yielding tptp.empty_set)) % 0.41/0.84 (define @t142 () (tptp.relation tptp.empty_set)) % 0.41/0.84 (define @t143 () (tptp.empty tptp.empty_set)) % 0.41/0.84 (define @t144 () (tptp.relation_empty_yielding @t1)) % 0.41/0.84 (define @t145 () (and @t16 @t144)) % 0.41/0.84 (define @t146 () (tptp.function @t2)) % 0.41/0.84 (define @t147 () (not (tptp.empty @t70))) % 0.41/0.84 (define @t148 () (not @t82)) % 0.41/0.84 (define @t149 () (and @t37 @t146)) % 0.41/0.84 (define @t150 () (tptp.empty @t51)) % 0.41/0.84 (define @t151 () (and @t84 @t16)) % 0.41/0.84 (define @t152 () (tptp.empty @t110)) % 0.41/0.84 (define @t153 () (tptp.in @t2 @t60)) % 0.41/0.84 (define @t154 () (tptp.disjoint @t69 @t2)) % 0.41/0.84 (define @t155 () (not @t5)) % 0.41/0.84 (define @t156 () (tptp.in (tptp.ordered_pair @t29 @t2) @t1)) % 0.41/0.84 (define @t157 () (not @t101)) % 0.41/0.84 (define @t158 () (tptp.singleton @t2)) % 0.41/0.84 (define @t159 () (tptp.union @t2)) % 0.41/0.84 (define @t160 () (tptp.in @t1 @t29)) % 0.41/0.84 (define @t161 () (tptp.element @t1 (tptp.powerset @t2))) % 0.41/0.84 (define @t162 () (tptp.relation_dom @t29)) % 0.41/0.84 (define @t163 () (tptp.relation_dom_restriction @t29 @t1)) % 0.41/0.84 (define @t164 () (tptp.in @t2 (tptp.relation_dom @t163))) % 0.41/0.84 (define @t165 () (and @t48 (tptp.function @t29))) % 0.41/0.84 (define @t166 () (tptp.set_difference @t2 @t29)) % 0.41/0.84 (define @t167 () (= @t1 @t29)) % 0.41/0.84 (define @t168 () (tptp.relation_rng @t29)) % 0.41/0.84 (define @t169 () (tptp.relation_rng @t58)) % 0.41/0.84 (define @t170 () (tptp.relation_rng @t2)) % 0.41/0.84 (define @t171 () (tptp.cartesian_product2 @t1 @t29)) % 0.41/0.84 (define @t172 () (forall @t59 (not (and @t96 (not (tptp.are_equipotent @t29 @t2)) @t90)))) % 0.41/0.84 (define @t173 () (tptp.powerset @t29)) % 0.41/0.84 (define @t174 () (forall @t34 (=> (and @t72 (tptp.subset @t28 @t29)) @t44))) % 0.41/0.84 (define @t175 () (tptp.relation_dom_restriction @t29 @t2)) % 0.41/0.84 (define @t176 () (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t29) @t2) (tptp.relation_rng_restriction @t1 @t175))) % 0.41/0.84 (define @t177 () (forall @t85 (=> @t48 @t176))) % 0.41/0.84 (define @t178 () (tptp.relation_image @t2 @t1)) % 0.41/0.84 (define @t179 () (tptp.relation_inverse_image @t2 @t1)) % 0.41/0.84 (define @t180 () (tptp.relation_image @t2 @t179)) % 0.41/0.84 (define @t181 () (tptp.relation_dom @t2)) % 0.41/0.84 (define @t182 () (tptp.set_intersection2 @t181 @t1)) % 0.41/0.84 (define @t183 () (tptp.subset @t1 @t170)) % 0.41/0.84 (define @t184 () (tptp.relation_rng @t122)) % 0.41/0.84 (define @t185 () (tptp.relation_inverse_image @t29 @t2)) % 0.41/0.84 (define @t186 () (tptp.relation_restriction @t2 @t1)) % 0.41/0.84 (define @t187 () (= @t186 (tptp.relation_dom_restriction @t58 @t1))) % 0.41/0.84 (define @t188 () (forall @t6 (=> @t37 @t187))) % 0.41/0.84 (define @t189 () (tptp.relation_dom_restriction @t2 @t1)) % 0.41/0.84 (define @t190 () (= @t186 (tptp.relation_rng_restriction @t1 @t189))) % 0.41/0.84 (define @t191 () (forall @t6 (=> @t37 @t190))) % 0.41/0.84 (define @t192 () (not @t191)) % 0.41/0.84 (define @t193 () (tptp.set_intersection2 @t2 @t29)) % 0.41/0.84 (define @t194 () (tptp.subset @t1 @t29)) % 0.41/0.84 (define @t195 () (tptp.element @t1 @t2)) % 0.41/0.84 (define @t196 () (tptp.in @t1 @t162)) % 0.41/0.84 (define @t197 () (tptp.in @t114 @t29)) % 0.41/0.84 (define @t198 () (tptp.apply @t29 @t1)) % 0.41/0.84 (define @t199 () (tptp.relation_composition @t29 @t2)) % 0.41/0.84 (define @t200 () (tptp.in @t1 (tptp.relation_dom @t199))) % 0.41/0.84 (define @t201 () (tptp.relation_field @t29)) % 0.41/0.84 (define @t202 () (tptp.apply @t2 @t29)) % 0.41/0.84 (define @t203 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.41/0.84 (define @t204 () (and @t31 @t72)) % 0.41/0.84 (define @t205 () (not @t121)) % 0.41/0.84 (define @t206 () (tptp.succ @t2)) % 0.41/0.84 (define @t207 () (= @t1 @t206)) % 0.41/0.84 (define @t208 () (tptp.subset_complement @t1 @t29)) % 0.41/0.84 (define @t209 () (tptp.disjoint @t2 @t29)) % 0.41/0.84 (define @t210 () (tptp.relation_dom @t122)) % 0.41/0.84 (define @t211 () (tptp.element @t2 @t173)) % 0.41/0.84 (define @t212 () (tptp.in @t29 @t24)) % 0.41/0.84 (define @t213 () (and (tptp.in @t29 @t110) (= @t28 @t202))) % 0.41/0.84 (define @t214 () (tptp.function_inverse @t2)) % 0.41/0.84 (define @t215 () (= @t110 tptp.empty_set)) % 0.41/0.84 (define @t216 () (= @t51 tptp.empty_set)) % 0.41/0.84 (define @t217 () (= (tptp.apply @t163 @t2) (tptp.apply @t29 @t2))) % 0.41/0.84 (define @t218 () (= @t69 (tptp.unordered_pair @t2 @t29))) % 0.41/0.84 (define @t219 () (forall @t6 (or (not @t37) @t190))) % 0.41/0.84 (define @t220 () (@quantifiers_skolemize @t219 0)) % 0.41/0.84 (define @t221 () (@quantifiers_skolemize @t219 1)) % 0.41/0.84 (define @t222 () (tptp.relation_rng_restriction @t220 (tptp.relation_dom_restriction @t221 @t220))) % 0.41/0.84 (define @t223 () (tptp.relation_restriction @t221 @t220)) % 0.41/0.84 (define @t224 () (= @t223 @t222)) % 0.41/0.84 (define @t225 () (tptp.relation @t221)) % 0.41/0.84 (define @t226 () (not @t225)) % 0.41/0.84 (define @t227 () (or @t226 @t224)) % 0.41/0.84 (define @t228 () (not @t224)) % 0.41/0.84 (define @t229 () (@list true)) % 0.41/0.84 (define @t230 () (@list @t227)) % 0.41/0.84 (define @t231 () (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t220 @t221) @t220)) % 0.41/0.84 (define @t232 () (or @t226 (= @t231 @t222))) % 0.41/0.84 (define @t233 () (forall @t85 (or (not @t48) @t176))) % 0.41/0.84 (define @t234 () (= @t222 @t231)) % 0.41/0.84 (define @t235 () (or @t226 @t234)) % 0.41/0.84 (define @t236 () (@list false false)) % 0.41/0.84 (define @t237 () (= @t223 @t231)) % 0.41/0.84 (define @t238 () (or @t226 @t237)) % 0.41/0.84 (define @t239 () (not @t237)) % 0.41/0.84 (define @t240 () (not @t234)) % 0.41/0.84 (define @t241 () (and @t228 @t234)) % 0.41/0.84 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.41/0.84 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.41/0.84 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.41/0.84 (assume @p4 (forall @t11 (=> @t15 @t14))) % 0.41/0.84 (assume @p5 (forall @t11 (=> @t10 @t16))) % 0.41/0.84 (assume @p6 (forall @t11 (=> @t19 @t18))) % 0.41/0.84 (assume @p7 (forall @t11 (=> @t14 @t15))) % 0.41/0.84 (assume @p8 (forall @t11 (=> @t10 @t20))) % 0.41/0.84 (assume @p9 (forall @t6 (= @t21 (tptp.unordered_pair @t2 @t1)))) % 0.41/0.84 (assume @p10 (forall @t6 (= @t23 @t22))) % 0.41/0.84 (assume @p11 (forall @t6 (= @t24 (tptp.set_intersection2 @t2 @t1)))) % 0.41/0.84 (assume @p12 (forall @t6 (=> @t27 (or @t25 (tptp.ordinal_subset @t2 @t1))))) % 0.41/0.84 (assume @p13 (forall @t6 (=> @t37 (= @t36 (forall @t34 (= @t33 (and @t31 @t30))))))) % 0.41/0.84 (assume @p14 (forall @t6 (= @t40 (and @t39 @t38)))) % 0.41/0.84 (assume @p15 (forall @t11 (=> @t16 (forall @t49 (=> @t48 (= (= @t29 @t47) (forall @t46 (= @t45 (and @t44 @t43))))))))) % 0.41/0.84 (assume @p16 (forall @t11 (=> @t56 (forall @t49 (= @t55 (forall @t54 (= @t53 (exists @t52 (and (tptp.in @t41 @t51) @t50 (= @t28 (tptp.apply @t1 @t41))))))))))) % 0.41/0.84 (assume @p17 (forall @t6 (=> @t37 (forall @t59 (=> @t48 (= (= @t29 @t58) (forall @t46 (= @t45 (and @t57 (tptp.in @t42 @t2)))))))))) % 0.41/0.84 (assume @p18 (forall @t11 (=> @t16 (= @t61 (tptp.is_antisymmetric_in @t1 @t60))))) % 0.41/0.84 (assume @p19 (forall @t11 (=> @t56 (forall @t49 (= @t64 (forall @t54 (= @t53 (and @t63 (tptp.in @t62 @t2))))))))) % 0.41/0.84 (assume @p20 (forall @t11 (=> @t16 (forall @t49 (= @t55 (forall @t54 (= @t53 (exists @t52 (and (tptp.in (tptp.ordered_pair @t41 @t28) @t1) @t50))))))))) % 0.41/0.84 (assume @p21 (forall @t11 (=> @t16 (forall @t49 (= @t64 (forall @t54 (= @t53 (exists @t52 (and @t43 @t50))))))))) % 0.41/0.84 (assume @p22 (forall @t11 (=> @t16 (= @t65 (tptp.is_connected_in @t1 @t60))))) % 0.41/0.84 (assume @p23 (forall @t11 (=> @t16 (= @t66 (tptp.is_transitive_in @t1 @t60))))) % 0.41/0.84 (assume @p24 (forall @t68 (= (= @t28 (tptp.unordered_triple @t1 @t2 @t29)) (forall @t52 (= @t67 (not (and (not (= @t41 @t1)) (not (= @t41 @t2)) (not (= @t41 @t29))))))))) % 0.41/0.84 (assume @p25 (forall @t11 (= @t70 (tptp.set_union2 @t1 @t69)))) % 0.41/0.84 (assume @p26 (forall @t11 (= @t16 (forall @t71 (not (and @t3 (forall @t34 (not (= @t2 @t32))))))))) % 0.41/0.84 (assume @p27 (forall @t11 (=> @t16 (forall @t71 (= @t73 (forall @t59 (=> @t72 (tptp.in (tptp.ordered_pair @t29 @t29) @t1)))))))) % 0.41/0.84 (assume @p28 (forall @t6 (and (=> @t79 (= @t75 (forall @t59 (= @t72 (forall @t54 (=> @t78 @t77)))))) (=> @t76 (= @t75 @t74))))) % 0.41/0.84 (assume @p29 (forall @t6 (= (= @t2 @t69) (forall @t59 (= @t72 (= @t29 @t1)))))) % 0.41/0.84 (assume @p30 (forall @t11 (= @t76 (forall @t71 @t4)))) % 0.41/0.84 (assume @p31 (forall @t6 (= (= @t2 @t80) (forall @t59 (= @t72 (tptp.subset @t29 @t1)))))) % 0.41/0.84 (assume @p32 (forall @t11 (= @t13 (forall @t71 (=> @t3 @t38))))) % 0.41/0.84 (assume @p33 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (= @t40 (forall @t34 (= @t81 @t33)))))))) % 0.41/0.84 (assume @p34 (forall @t6 (and (=> @t84 (= @t83 @t3)) (=> @t10 (= @t83 @t82))))) % 0.41/0.84 (assume @p35 (forall @t85 (= (= @t29 @t21) (forall @t54 (= @t53 (or (= @t28 @t1) (= @t28 @t2))))))) % 0.41/0.84 (assume @p36 (forall @t11 (=> @t16 (= @t87 (forall @t71 (not (and (tptp.subset @t2 @t60) @t86 (forall @t59 (not (and @t72 (tptp.disjoint (tptp.fiber @t1 @t29) @t2))))))))))) % 0.41/0.84 (assume @p37 (forall @t85 (= (= @t29 @t23) (forall @t54 (= @t53 (or @t78 @t44)))))) % 0.41/0.84 (assume @p38 (forall @t85 (= (= @t29 @t89) (forall @t54 (= @t53 (exists (@list @t41 @t88) (and @t57 (tptp.in @t88 @t2) (= @t28 (tptp.ordered_pair @t41 @t88))))))))) % 0.41/0.84 (assume @p39 (forall @t11 (= @t12 (forall @t49 (not (and @t3 @t31 (not @t93) @t92 @t90)))))) % 0.41/0.84 (assume @p40 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (= @t39 (forall @t34 (=> @t81 @t33)))))))) % 0.41/0.84 (assume @p41 (forall @t6 (= @t39 @t94))) % 0.41/0.84 (assume @p42 (forall @t11 (=> @t16 (forall @t71 (= @t97 (forall @t59 (not (and @t96 (not @t95) (forall @t54 (not (and @t53 (tptp.disjoint (tptp.fiber @t1 @t28) @t29)))))))))))) % 0.41/0.84 (assume @p43 (forall @t85 (= (= @t29 @t24) (forall @t54 (= @t53 (and @t78 @t44)))))) % 0.41/0.84 (assume @p44 (forall @t11 (=> @t56 (forall @t49 (and (=> @t100 (= @t99 @t101)) (=> (not @t100) (= @t99 @t95))))))) % 0.41/0.84 (assume @p45 (forall @t11 (= @t15 @t14))) % 0.41/0.84 (assume @p46 (forall @t11 (=> @t16 (forall @t71 (= (= @t2 @t51) (forall @t59 (= @t72 (exists @t54 @t81)))))))) % 0.41/0.84 (assume @p47 (forall @t11 (=> @t16 (forall @t71 (= @t103 (forall @t34 (=> (and @t72 @t44 @t81 @t102) @t30))))))) % 0.41/0.84 (assume @p48 (forall @t11 (= @t104 @t1))) % 0.41/0.84 (assume @p49 (forall @t6 (= (= @t2 @t105) (forall @t59 (= @t72 (exists @t54 (and @t77 @t78))))))) % 0.41/0.84 (assume @p50 (forall @t11 (=> @t16 (= @t107 (and @t106 @t66 @t61 @t65 @t87))))) % 0.41/0.84 (assume @p51 (forall @t85 (= (= @t29 @t108) (forall @t54 (= @t53 (and @t78 (not @t44))))))) % 0.41/0.84 (assume @p52 (forall @t11 (=> @t56 (forall @t71 (= @t111 (forall @t59 (= @t72 (exists @t54 @t109)))))))) % 0.41/0.84 (assume @p53 (forall @t11 (=> @t16 (forall @t71 (= @t111 (forall @t59 (= @t72 (exists @t54 @t102)))))))) % 0.41/0.84 (assume @p54 (forall @t6 (=> @t113 (= @t112 @t108)))) % 0.41/0.84 (assume @p55 (forall @t6 (= @t114 (tptp.unordered_pair @t21 @t69)))) % 0.41/0.84 (assume @p56 (forall @t11 (=> @t16 (forall @t71 (= (tptp.well_orders @t1 @t2) (and @t73 @t116 @t103 @t115 @t97)))))) % 0.41/0.84 (assume @p57 (forall @t11 (= @t117 (= @t1 @t105)))) % 0.41/0.84 (assume @p58 (forall @t11 (=> @t16 (= @t60 (tptp.set_union2 @t51 @t110))))) % 0.41/0.84 (assume @p59 (forall @t11 (=> @t16 (forall @t71 (= @t115 (forall @t34 (not (and @t72 @t44 (not @t30) (not @t81) (not @t102))))))))) % 0.41/0.84 (assume @p60 (forall @t11 (=> @t16 (forall @t71 (= @t119 (tptp.set_intersection2 @t1 @t118)))))) % 0.41/0.84 (assume @p61 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (= (= @t2 @t120) (forall @t34 (= @t33 @t102)))))))) % 0.41/0.84 (assume @p62 (forall @t6 (= @t121 (= @t24 tptp.empty_set)))) % 0.41/0.84 (assume @p63 (forall @t11 (=> @t56 (= @t17 (forall @t49 (=> (and @t100 (tptp.in @t29 @t51) (= @t98 (tptp.apply @t1 @t29))) @t91)))))) % 0.41/0.84 (assume @p64 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (forall @t59 (=> @t48 (= (= @t29 @t122) (forall @t46 (= @t45 (exists (@list @t88) (and (tptp.in (tptp.ordered_pair @t28 @t88) @t1) (tptp.in (tptp.ordered_pair @t88 @t41) @t2))))))))))))) % 0.41/0.84 (assume @p65 (forall @t11 (=> @t16 (forall @t71 (= @t116 (forall (@list @t29 @t28 @t41) (=> (and @t72 @t44 @t50 @t81 @t43) (tptp.in (tptp.ordered_pair @t29 @t41) @t1)))))))) % 0.41/0.84 (assume @p66 (forall @t6 (=> @t125 (forall @t59 (=> (tptp.element @t29 @t124) (= (= @t29 @t123) (forall @t54 (=> (tptp.element @t28 @t80) (= @t53 (tptp.in (tptp.subset_complement @t1 @t28) @t2)))))))))) % 0.41/0.84 (assume @p67 (forall @t6 (= @t8 (and @t39 @t126)))) % 0.41/0.84 (assume @p68 (forall @t11 (=> @t56 (=> @t17 (= @t127 @t120))))) % 0.41/0.84 (assume @p69 (forall @t11 (=> @t16 (= @t106 (tptp.is_reflexive_in @t1 @t60))))) % 0.41/0.84 (assume @p70 true) % 0.41/0.84 (assume @p71 (forall @t11 (=> @t56 (and (tptp.relation @t127) (tptp.function @t127))))) % 0.41/0.84 (assume @p72 (forall @t11 (tptp.element @t104 @t80))) % 0.41/0.84 (assume @p73 (forall @t6 (=> @t16 (tptp.relation @t119)))) % 0.41/0.84 (assume @p74 (forall @t6 (=> @t113 (tptp.element @t112 @t80)))) % 0.41/0.84 (assume @p75 (forall @t11 (=> @t16 @t128))) % 0.41/0.84 (assume @p76 (forall @t6 (=> @t130 @t129))) % 0.41/0.84 (assume @p77 (forall @t6 (=> @t125 (tptp.element @t131 @t80)))) % 0.41/0.84 (assume @p78 (forall @t11 @t132)) % 0.41/0.84 (assume @p79 (forall @t6 (=> @t125 (tptp.element @t133 @t80)))) % 0.41/0.84 (assume @p80 (forall @t85 (=> @t136 (tptp.element @t134 @t80)))) % 0.41/0.84 (assume @p81 (forall @t6 (=> @t16 @t137))) % 0.41/0.84 (assume @p82 (forall @t6 (=> @t125 (tptp.element @t123 @t124)))) % 0.41/0.84 (assume @p83 (forall @t6 (=> @t37 @t138))) % 0.41/0.84 (assume @p84 (forall @t11 (exists @t71 @t83))) % 0.41/0.84 (assume @p85 (forall @t6 (=> @t140 (and (tptp.empty @t139) (tptp.relation @t139))))) % 0.41/0.84 (assume @p86 (forall @t11 (=> @t10 (and (tptp.empty @t120) @t128)))) % 0.41/0.84 (assume @p87 (and @t143 @t142 @t141)) % 0.41/0.84 (assume @p88 (forall @t6 (=> @t145 (and @t137 (tptp.relation_empty_yielding @t47))))) % 0.41/0.84 (assume @p89 (forall @t6 (=> (and @t16 @t9 @t37 @t146) (and @t129 (tptp.function @t122))))) % 0.41/0.84 (assume @p90 (forall @t11 @t147)) % 0.41/0.84 (assume @p91 (forall @t6 (=> @t130 (tptp.relation @t24)))) % 0.41/0.84 (assume @p92 (forall @t11 (not (tptp.empty @t80)))) % 0.41/0.84 (assume @p93 @t143) % 0.41/0.84 (assume @p94 (forall @t6 (not (tptp.empty @t114)))) % 0.41/0.84 (assume @p95 (forall @t11 (and @t132 (tptp.function @t35)))) % 0.41/0.84 (assume @p96 (and @t142 @t141 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t143 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 0.41/0.84 (assume @p97 (forall @t6 (=> @t130 (tptp.relation @t23)))) % 0.41/0.84 (assume @p98 (forall @t11 (not (tptp.empty @t69)))) % 0.41/0.84 (assume @p99 (forall @t6 (=> @t84 (not (tptp.empty @t23))))) % 0.41/0.84 (assume @p100 (forall @t11 (=> @t18 (and @t128 (tptp.function @t120))))) % 0.41/0.84 (assume @p101 (forall @t11 (=> @t15 (and @t147 (tptp.epsilon_transitive @t70) (tptp.epsilon_connected @t70) (tptp.ordinal @t70))))) % 0.41/0.84 (assume @p102 (forall @t6 (=> @t130 (tptp.relation @t108)))) % 0.41/0.84 (assume @p103 (forall @t6 (not (tptp.empty @t21)))) % 0.41/0.84 (assume @p104 (forall @t6 (=> @t84 (not (tptp.empty @t22))))) % 0.41/0.84 (assume @p105 (forall @t6 (=> @t56 (and @t137 (tptp.function @t47))))) % 0.41/0.84 (assume @p106 (forall @t11 (=> @t15 (and (tptp.epsilon_transitive @t105) (tptp.epsilon_connected @t105) (tptp.ordinal @t105))))) % 0.41/0.84 (assume @p107 (and @t143 @t142)) % 0.41/0.84 (assume @p108 (forall @t6 (=> (and @t84 @t148) (not (tptp.empty @t89))))) % 0.41/0.84 (assume @p109 (forall @t6 (=> @t149 (and @t138 (tptp.function @t58))))) % 0.41/0.84 (assume @p110 (forall @t11 (=> @t151 (not @t150)))) % 0.41/0.84 (assume @p111 (forall @t11 (=> @t151 (not @t152)))) % 0.41/0.84 (assume @p112 (forall @t11 (=> @t10 (and @t150 (tptp.relation @t51))))) % 0.41/0.84 (assume @p113 (forall @t11 (=> @t10 (and @t152 (tptp.relation @t110))))) % 0.41/0.84 (assume @p114 (forall @t6 (=> @t140 (and (tptp.empty @t122) @t129)))) % 0.41/0.84 (assume @p115 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.41/0.84 (assume @p116 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.41/0.84 (assume @p117 (forall @t6 (=> @t113 (= (tptp.subset_complement @t1 @t112) @t2)))) % 0.41/0.84 (assume @p118 (forall @t11 (=> @t16 (= (tptp.relation_inverse @t120) @t1)))) % 0.41/0.84 (assume @p119 (forall @t6 (=> @t125 (= (tptp.complements_of_subsets @t1 @t123) @t2)))) % 0.41/0.84 (assume @p120 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.41/0.84 (assume @p121 (forall @t11 (=> @t16 (= @t106 (forall @t71 (=> @t153 (tptp.in (tptp.ordered_pair @t2 @t2) @t1))))))) % 0.41/0.84 (assume @p122 (forall @t11 (not (= @t69 tptp.empty_set)))) % 0.41/0.84 (assume @p123 (forall @t6 (=> @t5 (= (tptp.set_union2 @t69 @t2) @t2)))) % 0.41/0.84 (assume @p124 (forall @t6 (not (and @t154 @t5)))) % 0.41/0.84 (assume @p125 (forall @t6 (=> @t155 @t154))) % 0.41/0.84 (assume @p126 (forall @t11 (=> @t16 (= @t66 (forall (@list @t2 @t29 @t28) (=> (and @t101 @t81) (tptp.in (tptp.ordered_pair @t2 @t28) @t1))))))) % 0.41/0.84 (assume @p127 (forall @t6 (= (tptp.subset @t69 @t2) @t5))) % 0.41/0.84 (assume @p128 (forall @t6 (= (= @t108 tptp.empty_set) @t39))) % 0.41/0.84 (assume @p129 (forall @t6 (=> @t113 (forall @t59 (=> @t72 @t31))))) % 0.41/0.84 (assume @p130 (forall @t11 (=> @t16 (= @t61 (forall @t49 (=> (and @t101 @t156) @t91)))))) % 0.41/0.84 (assume @p131 (forall @t85 (=> @t39 (or @t31 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t29))))))) % 0.41/0.84 (assume @p132 (forall @t11 (=> @t16 (= @t65 (forall @t49 (not (and @t153 (tptp.in @t29 @t60) @t92 @t157 (not @t156)))))))) % 0.41/0.84 (assume @p133 (forall @t6 (= (tptp.subset @t1 @t158) (or @t76 (= @t1 @t158))))) % 0.41/0.84 (assume @p134 (forall @t6 (=> @t5 (tptp.subset @t1 @t159)))) % 0.41/0.84 (assume @p135 (forall @t68 (= (tptp.in @t114 (tptp.cartesian_product2 @t29 @t28)) (and @t160 (tptp.in @t2 @t28))))) % 0.41/0.84 (assume @p136 (forall @t6 (=> @t94 @t161))) % 0.41/0.84 (assume @p137 (forall @t85 (=> @t165 (= @t164 (and (tptp.in @t2 @t162) @t3))))) % 0.41/0.84 (assume @p138 (exists @t11 @t56)) % 0.41/0.84 (assume @p139 (exists @t11 @t20)) % 0.41/0.84 (assume @p140 (exists @t11 (and @t10 @t16))) % 0.41/0.84 (assume @p141 (forall @t11 (=> @t84 (exists @t71 (and @t113 @t148))))) % 0.41/0.84 (assume @p142 (exists @t11 @t10)) % 0.41/0.84 (assume @p143 (exists @t11 @t19)) % 0.41/0.84 (assume @p144 (exists @t11 (and @t16 @t9 @t17 @t10 @t13 @t12 @t15))) % 0.41/0.84 (assume @p145 (exists @t11 @t151)) % 0.41/0.84 (assume @p146 (forall @t11 (exists @t71 (and @t113 @t82)))) % 0.41/0.84 (assume @p147 (exists @t11 @t84)) % 0.41/0.84 (assume @p148 (exists @t11 @t18)) % 0.41/0.84 (assume @p149 (exists @t11 (and @t84 @t13 @t12 @t15))) % 0.41/0.84 (assume @p150 (exists @t11 @t145)) % 0.41/0.84 (assume @p151 (exists @t11 (and @t16 @t144 @t9))) % 0.41/0.84 (assume @p152 (forall @t6 (=> @t125 (= @t131 @t159)))) % 0.41/0.84 (assume @p153 (forall @t6 (=> @t125 (= @t133 (tptp.set_meet @t2))))) % 0.41/0.84 (assume @p154 (forall @t85 (=> @t136 (= @t134 @t166)))) % 0.41/0.84 (assume @p155 (forall @t6 (=> @t27 (= @t25 @t39)))) % 0.41/0.84 (assume @p156 (forall @t6 (=> @t27 (tptp.ordinal_subset @t1 @t1)))) % 0.41/0.84 (assume @p157 (forall @t6 (tptp.subset @t1 @t1))) % 0.41/0.84 (assume @p158 (forall @t6 (=> @t121 (tptp.disjoint @t2 @t1)))) % 0.41/0.84 (assume @p159 (forall @t11 (tptp.in @t1 @t70))) % 0.41/0.84 (assume @p160 (forall @t68 (not (and (= @t21 (tptp.unordered_pair @t29 @t28)) (not @t167) (not (= @t1 @t28)))))) % 0.41/0.84 (assume @p161 (forall @t85 (=> @t48 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t29))) (and @t5 (tptp.in @t1 @t168)))))) % 0.41/0.84 (assume @p162 (forall @t6 (=> @t37 (tptp.subset @t169 @t1)))) % 0.41/0.84 (assume @p163 (forall @t6 (=> @t37 (tptp.subset @t58 @t2)))) % 0.41/0.84 (assume @p164 (forall @t6 (=> @t37 (tptp.subset @t169 @t170)))) % 0.41/0.84 (assume @p165 (forall @t85 (=> @t39 (and (tptp.subset @t171 (tptp.cartesian_product2 @t2 @t29)) (tptp.subset (tptp.cartesian_product2 @t29 @t1) (tptp.cartesian_product2 @t29 @t2)))))) % 0.41/0.84 (assume @p166 (forall @t6 (=> @t37 (= @t169 (tptp.set_intersection2 @t170 @t1))))) % 0.41/0.84 (assume @p167 (forall @t68 (=> (and @t39 (tptp.subset @t29 @t28)) (tptp.subset @t171 (tptp.cartesian_product2 @t2 @t28))))) % 0.41/0.84 (assume @p168 (forall @t6 (=> @t39 (= @t23 @t2)))) % 0.41/0.84 (assume @p169 (forall @t11 (exists @t71 (and @t5 @t174 (forall @t59 (=> @t72 (tptp.in @t173 @t2))) @t172)))) % 0.41/0.84 (assume @p170 @t177) % 0.41/0.84 (assume @p171 (forall @t85 (=> @t48 (= (tptp.in @t1 (tptp.relation_image @t29 @t2)) (exists @t54 (and (tptp.in @t28 @t162) (tptp.in (tptp.ordered_pair @t28 @t1) @t29) @t44)))))) % 0.41/0.84 (assume @p172 (forall @t6 (=> @t37 (tptp.subset @t178 @t170)))) % 0.41/0.84 (assume @p173 (forall @t6 (=> @t149 (tptp.subset @t180 @t1)))) % 0.41/0.84 (assume @p174 (forall @t6 (=> @t37 (= @t178 (tptp.relation_image @t2 @t182))))) % 0.41/0.84 (assume @p175 (forall @t6 (=> @t37 (=> (tptp.subset @t1 @t181) (tptp.subset @t1 (tptp.relation_inverse_image @t2 @t178)))))) % 0.41/0.84 (assume @p176 (forall @t11 (=> @t16 (= (tptp.relation_image @t1 @t51) @t110)))) % 0.41/0.84 (assume @p177 (forall @t6 (=> @t149 (=> @t183 (= @t180 @t1))))) % 0.41/0.84 (assume @p178 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (= @t184 (tptp.relation_image @t2 @t110))))))) % 0.41/0.84 (assume @p179 (forall @t85 (=> @t48 (= (tptp.in @t1 @t185) (exists @t54 (and (tptp.in @t28 @t168) (tptp.in (tptp.ordered_pair @t1 @t28) @t29) @t44)))))) % 0.41/0.84 (assume @p180 (forall @t6 (=> @t37 (tptp.subset @t179 @t181)))) % 0.41/0.84 (assume @p181 (forall @t85 (=> @t48 (= (tptp.in @t1 (tptp.relation_restriction @t29 @t2)) (and @t160 (tptp.in @t1 @t118)))))) % 0.41/0.84 (assume @p182 (forall @t6 (=> @t37 (not (and @t79 @t183 (= @t179 tptp.empty_set)))))) % 0.41/0.84 (assume @p183 (forall @t85 (=> @t48 (=> @t39 (tptp.subset (tptp.relation_inverse_image @t29 @t1) @t185))))) % 0.41/0.84 (assume @p184 @t188) % 0.41/0.84 (assume @p185 (forall @t6 (tptp.subset @t24 @t1))) % 0.41/0.84 (assume @p186 @t192) % 0.41/0.84 (assume @p187 (forall @t85 (=> (and @t39 @t194) (tptp.subset @t1 @t193)))) % 0.41/0.84 (assume @p188 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.41/0.84 (assume @p189 (forall @t6 (=> @t5 @t195))) % 0.41/0.84 (assume @p190 (forall @t85 (=> (and @t39 (tptp.subset @t2 @t29)) @t194))) % 0.41/0.84 (assume @p191 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.41/0.84 (assume @p192 (forall @t85 (=> @t48 (=> @t197 (and @t196 (tptp.in @t2 @t168)))))) % 0.41/0.84 (assume @p193 (forall @t6 (=> @t149 (forall @t59 (=> @t165 (= @t200 (and @t196 (tptp.in @t198 @t181)))))))) % 0.41/0.84 (assume @p194 (forall @t11 (=> @t13 (forall @t71 (=> @t26 (=> @t8 @t5)))))) % 0.41/0.84 (assume @p195 (forall @t11 (=> @t16 (tptp.subset @t1 (tptp.cartesian_product2 @t51 @t110))))) % 0.41/0.84 (assume @p196 (forall @t6 (=> @t149 (forall @t59 (=> @t165 (=> @t200 (= (tptp.apply @t199 @t1) (tptp.apply @t2 @t198)))))))) % 0.41/0.84 (assume @p197 (forall @t6 (=> @t149 (forall @t59 (=> @t165 (=> (tptp.in @t1 @t181) (= (tptp.apply (tptp.relation_composition @t2 @t29) @t1) (tptp.apply @t29 (tptp.apply @t2 @t1))))))))) % 0.41/0.84 (assume @p198 (forall @t6 (=> @t26 (=> @t5 @t15)))) % 0.41/0.84 (assume @p199 (forall @t11 (=> @t15 (forall @t71 (=> @t26 (not (and @t155 @t126 @t4))))))) % 0.41/0.84 (assume @p200 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (=> @t39 (and (tptp.subset @t51 @t181) (tptp.subset @t110 @t170)))))))) % 0.41/0.84 (assume @p201 (forall @t85 (=> @t39 (tptp.subset (tptp.set_intersection2 @t1 @t29) @t193)))) % 0.41/0.84 (assume @p202 (forall @t6 (=> @t39 (= @t24 @t1)))) % 0.41/0.84 (assume @p203 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.41/0.84 (assume @p204 (forall @t6 (=> @t195 (or @t82 @t5)))) % 0.41/0.84 (assume @p205 (forall @t6 (=> (forall @t59 (= @t31 @t72)) @t40))) % 0.41/0.84 (assume @p206 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.41/0.84 (assume @p207 (forall @t85 (=> @t48 (=> @t197 (and (tptp.in @t1 @t201) (tptp.in @t2 @t201)))))) % 0.41/0.84 (assume @p208 (forall @t11 (=> (forall @t71 (=> @t3 (and @t26 @t38))) @t15))) % 0.41/0.84 (assume @p209 (forall @t6 (=> @t26 (not (and @t39 @t79 (forall @t59 (=> (tptp.ordinal @t29) (not (and @t31 (forall @t54 (=> (tptp.ordinal @t28) (=> @t78 (tptp.ordinal_subset @t29 @t28))))))))))))) % 0.41/0.84 (assume @p210 (forall @t11 (=> @t15 (forall @t71 (=> @t26 (= @t5 (tptp.ordinal_subset @t70 @t2))))))) % 0.41/0.84 (assume @p211 (forall @t85 (=> @t39 (tptp.subset (tptp.set_difference @t1 @t29) @t166)))) % 0.41/0.84 (assume @p212 (forall @t68 (=> (= @t114 @t32) (and @t167 (= @t2 @t28))))) % 0.41/0.84 (assume @p213 (forall @t6 (=> @t149 (= @t36 (and (= @t181 @t1) (forall @t59 (=> @t31 (= @t202 @t29)))))))) % 0.41/0.84 (assume @p214 (forall @t6 (=> @t3 (= (tptp.apply @t35 @t2) @t2)))) % 0.41/0.84 (assume @p215 (forall @t6 (tptp.subset @t108 @t1))) % 0.41/0.84 (assume @p216 (forall @t11 (=> @t16 (and (= @t110 (tptp.relation_dom @t120)) (= @t51 (tptp.relation_rng @t120)))))) % 0.41/0.84 (assume @p217 (forall @t85 (= (tptp.subset @t21 @t29) (and @t160 @t93)))) % 0.41/0.84 (assume @p218 (forall @t6 (= @t203 @t23))) % 0.41/0.84 (assume @p219 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.41/0.84 (assume @p220 (forall @t85 (not (and @t5 @t93 @t31)))) % 0.41/0.84 (assume @p221 (forall @t6 (= @t161 @t39))) % 0.41/0.84 (assume @p222 (forall @t6 (and (not (and @t205 (forall @t59 (not @t204)))) (not (and (exists @t59 @t204) @t121))))) % 0.41/0.84 (assume @p223 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t76))) % 0.41/0.84 (assume @p224 (forall @t6 (= (tptp.set_difference @t23 @t2) @t108))) % 0.41/0.84 (assume @p225 (forall @t11 (=> @t15 (= @t117 (forall @t71 (=> @t26 (=> @t3 (tptp.in @t206 @t1)))))))) % 0.41/0.84 (assume @p226 (forall @t11 (=> @t15 (and (not (and (not @t117) (forall @t71 (=> @t26 (not @t207))))) (not (and (exists @t71 (and @t26 @t207)) @t117)))))) % 0.41/0.84 (assume @p227 (forall @t6 (=> @t113 (forall @t59 (=> @t135 (= @t209 (tptp.subset @t2 @t208))))))) % 0.41/0.84 (assume @p228 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (tptp.subset @t210 @t51)))))) % 0.41/0.84 (assume @p229 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (tptp.subset @t184 @t170)))))) % 0.41/0.84 (assume @p230 (forall @t6 (=> @t39 (= @t2 @t203)))) % 0.41/0.84 (assume @p231 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (=> (tptp.subset @t110 @t181) (= @t210 @t51))))))) % 0.41/0.84 (assume @p232 (forall @t6 (=> @t125 (not (and @t86 (= @t123 tptp.empty_set)))))) % 0.41/0.84 (assume @p233 (forall @t11 (=> @t16 (forall @t71 (=> @t37 (=> (tptp.subset @t51 @t170) (= (tptp.relation_rng @t139) @t110))))))) % 0.41/0.84 (assume @p234 (forall @t6 (=> @t125 (=> @t86 (= (tptp.subset_difference @t1 @t104 @t131) (tptp.meet_of_subsets @t1 @t123)))))) % 0.41/0.84 (assume @p235 (forall @t6 (=> @t125 (=> @t86 (= (tptp.union_of_subsets @t1 @t123) (tptp.subset_difference @t1 @t104 @t133)))))) % 0.41/0.84 (assume @p236 (forall @t6 (= (tptp.set_difference @t1 @t108) @t24))) % 0.41/0.84 (assume @p237 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.41/0.84 (assume @p238 (forall @t85 (=> (and @t5 @t211) (tptp.element @t1 @t29)))) % 0.41/0.84 (assume @p239 (forall @t6 (and (not (and @t205 (forall @t59 (not @t212)))) (not (and (exists @t59 @t212) @t121))))) % 0.41/0.84 (assume @p240 (forall @t11 (=> @t79 (forall @t71 (=> @t113 (forall @t59 (=> (tptp.element @t29 @t1) (=> @t90 (tptp.in @t29 @t112))))))))) % 0.41/0.84 (assume @p241 (forall @t11 (=> @t56 (=> @t17 (forall @t71 (=> @t149 (= (= @t2 @t127) (and (= @t181 @t110) (forall @t34 (and (=> @t213 @t109) (=> @t109 @t213))))))))))) % 0.41/0.84 (assume @p242 (forall @t85 (=> @t135 (not (and (tptp.in @t2 @t208) @t93))))) % 0.41/0.84 (assume @p243 (forall @t11 (=> @t56 (=> @t17 (and (= @t110 (tptp.relation_dom @t127)) (= @t51 (tptp.relation_rng @t127))))))) % 0.41/0.84 (assume @p244 (forall @t11 (=> @t16 (=> (forall @t49 @t157) @t76)))) % 0.41/0.84 (assume @p245 (forall @t6 (=> @t149 (=> (and (tptp.one_to_one @t2) (tptp.in @t1 @t170)) (and (= @t1 (tptp.apply @t2 (tptp.apply @t214 @t1))) (= @t1 (tptp.apply (tptp.relation_composition @t214 @t2) @t1))))))) % 0.41/0.84 (assume @p246 (forall @t85 (not (and @t5 @t211 (tptp.empty @t29))))) % 0.41/0.84 (assume @p247 (forall @t11 (=> @t16 (= @t87 (tptp.is_well_founded_in @t1 @t60))))) % 0.41/0.84 (assume @p248 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 0.41/0.84 (assume @p249 (forall @t6 (not (and @t39 @t7)))) % 0.41/0.84 (assume @p250 (forall @t11 (=> @t56 (=> @t17 (tptp.one_to_one @t127))))) % 0.41/0.84 (assume @p251 (forall @t85 (=> (and @t39 @t209) (tptp.disjoint @t1 @t29)))) % 0.41/0.84 (assume @p252 (forall @t11 (=> @t16 (=> (or @t216 @t215) @t76)))) % 0.41/0.84 (assume @p253 (forall @t11 (=> @t16 (= @t216 @t215)))) % 0.41/0.84 (assume @p254 (forall @t6 (= (= (tptp.set_difference @t1 @t158) @t1) @t4))) % 0.41/0.84 (assume @p255 (forall @t6 (=> @t149 (forall @t59 (=> @t165 (= (= @t2 @t163) (and (= @t181 (tptp.set_intersection2 @t162 @t1)) (forall @t54 (=> (tptp.in @t28 @t181) (= (tptp.apply @t2 @t28) (tptp.apply @t29 @t28))))))))))) % 0.41/0.84 (assume @p256 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t69))) % 0.41/0.84 (assume @p257 (forall @t11 (=> @t10 @t76))) % 0.41/0.84 (assume @p258 (forall @t6 (=> (tptp.subset @t69 @t158) @t40))) % 0.41/0.84 (assume @p259 (forall @t85 (=> @t165 (=> @t164 @t217)))) % 0.41/0.84 (assume @p260 (forall @t11 (and (= (tptp.relation_dom @t35) @t1) (= (tptp.relation_rng @t35) @t1)))) % 0.41/0.84 (assume @p261 (forall @t85 (=> @t165 (=> @t3 @t217)))) % 0.41/0.84 (assume @p262 (forall @t68 (=> (tptp.relation @t28) (= (tptp.in @t114 (tptp.relation_composition (tptp.identity_relation @t29) @t28)) (and @t160 (tptp.in @t114 @t28)))))) % 0.41/0.84 (assume @p263 (forall @t6 (not (and @t5 @t82)))) % 0.41/0.84 (assume @p264 (forall @t6 (not (and @t5 (forall @t59 (not (and @t72 (forall @t54 (not (and @t44 @t53)))))))))) % 0.41/0.84 (assume @p265 (forall @t6 (tptp.subset @t1 @t23))) % 0.41/0.84 (assume @p266 (forall @t6 (= @t121 (= @t108 @t1)))) % 0.41/0.84 (assume @p267 (forall @t85 (=> @t48 (= (tptp.in @t1 (tptp.relation_dom @t175)) (and @t5 @t196))))) % 0.41/0.84 (assume @p268 (forall @t6 (=> @t37 (tptp.subset @t189 @t2)))) % 0.41/0.84 (assume @p269 (forall @t6 (not (and @t10 @t126 @t82)))) % 0.41/0.84 (assume @p270 (forall @t85 (=> @t165 (= @t197 (and @t196 (= @t2 @t198)))))) % 0.41/0.84 (assume @p271 (forall @t11 (=> @t16 (= (tptp.well_orders @t1 @t60) @t107)))) % 0.41/0.84 (assume @p272 (forall @t85 (=> (and @t39 @t96) (tptp.subset (tptp.set_union2 @t1 @t29) @t2)))) % 0.41/0.84 (assume @p273 (forall @t85 (=> @t218 @t40))) % 0.41/0.84 (assume @p274 (forall @t6 (=> @t37 (= (tptp.relation_dom @t189) @t182)))) % 0.41/0.84 (assume @p275 (forall @t6 (=> @t37 (= @t189 (tptp.relation_composition @t35 @t2))))) % 0.41/0.84 (assume @p276 (forall @t6 (=> @t37 (tptp.subset (tptp.relation_rng @t189) @t170)))) % 0.41/0.84 (assume @p277 (forall @t11 (= (tptp.union @t80) @t1))) % 0.41/0.84 (assume @p278 (forall @t11 (exists @t71 (and @t5 @t174 (forall @t59 (not (and @t72 (forall @t54 (not (and @t44 (forall @t52 (=> (tptp.subset @t41 @t29) @t67)))))))) @t172)))) % 0.41/0.84 (assume @p279 (forall @t85 (=> @t218 @t91))) % 0.41/0.84 (step @p280 :rule bool-impl-elim :args (@t37 @t190)) % 0.41/0.84 (step @p281 :rule cong :premises (@p280) :args (@t191)) % 0.41/0.84 (step @p282 :rule cong :premises (@p281) :args (@t192)) % 0.41/0.84 (step @p283 :rule eq_resolve :premises (@p186 @p282)) % 0.41/0.84 (step @p284 :rule skolemize :premises (@p283)) % 0.41/0.84 (step @p285 :rule cnf_or_neg :args (@t227 1)) % 0.41/0.84 (step @p286 :rule chain_m_resolution :premises (@p285 @p284) :args (@t228 @t229 @t230)) % 0.41/0.84 (step @p287 :rule bool-impl-elim :args (@t48 @t176)) % 0.41/0.84 (step @p288 :rule cong :premises (@p287) :args (@t177)) % 0.41/0.84 (step @p289 :rule eq_resolve :premises (@p170 @p288)) % 0.41/0.84 (step @p290 :rule eq-symm :args (@t231 @t222)) % 0.41/0.84 (step @p291 :rule refl :args (@t226)) % 0.41/0.84 (step @p292 :rule nary_cong :premises (@p291 @p290) :args (@t232)) % 0.41/0.84 (step @p293 :rule refl :args (@t233)) % 0.41/0.84 (step @p294 :rule cong :premises (@p293 @p292) :args ((=> @t233 @t232))) % 0.41/0.84 (assume-push @p339 @t233) % 0.41/0.84 (step @p296 :rule instantiate :premises (@p289) :args ((@list @t220 @t220 @t221))) % 0.41/0.84 (step-pop @p340 :rule scope :premises (@p296)) % 0.41/0.84 (step @p297 :rule process_scope :premises (@p340) :args (@t232)) % 0.41/0.84 (step @p299 :rule eq_resolve :premises (@p297 @p294)) % 0.41/0.84 (step @p300 :rule implies_elim :premises (@p299)) % 0.41/0.84 (step @p301 :rule chain_m_resolution :premises (@p300 @p289) :args (@t235 (@list false) (@list @t233))) % 0.41/0.84 (step @p302 :rule bool-double-not-elim :args (@t225)) % 0.41/0.84 (step @p303 :rule refl :args (@t227)) % 0.41/0.84 (step @p304 :rule nary_cong :premises (@p303 @p302) :args ((or @t227 (not @t226)))) % 0.41/0.84 (step @p305 :rule cnf_or_neg :args (@t227 0)) % 0.41/0.84 (step @p306 :rule eq_resolve :premises (@p305 @p304)) % 0.41/0.84 (step @p307 :rule reordering :premises (@p306) :args ((or @t225 @t227))) % 0.41/0.84 (step @p308 :rule chain_m_resolution :premises (@p307 @p284) :args (@t225 @t229 @t230)) % 0.41/0.84 (step @p309 :rule cnf_or_pos :args (@t235)) % 0.41/0.84 (step @p310 :rule reordering :premises (@p309) :args ((or @t226 @t234 (not @t235)))) % 0.41/0.84 (step @p311 :rule chain_m_resolution :premises (@p310 @p308 @p301) :args (@t234 @t236 (@list @t225 @t235))) % 0.41/0.84 (step @p312 :rule bool-impl-elim :args (@t37 @t187)) % 0.41/0.84 (step @p313 :rule cong :premises (@p312) :args (@t188)) % 0.41/0.84 (step @p314 :rule eq_resolve :premises (@p184 @p313)) % 0.41/0.84 (step @p315 :rule instantiate :premises (@p314) :args ((@list @t220 @t221))) % 0.41/0.84 (step @p316 :rule cnf_or_pos :args (@t238)) % 0.41/0.84 (step @p317 :rule reordering :premises (@p316) :args ((or @t226 @t237 (not @t238)))) % 0.41/0.84 (step @p318 :rule chain_m_resolution :premises (@p317 @p308 @p315) :args (@t237 @t236 (@list @t225 @t238))) % 0.41/0.84 (step @p319 :rule refl :args (@t239)) % 0.41/0.84 (step @p320 :rule refl :args (@t240)) % 0.41/0.84 (step @p321 :rule bool-double-not-elim :args (@t224)) % 0.41/0.84 (step @p322 :rule nary_cong :premises (@p321 @p320 @p319) :args ((or (not @t228) @t240 @t239))) % 0.41/0.84 (assume-push @p341 @t228) % 0.41/0.84 (assume-push @p342 @t234) % 0.41/0.84 (step @p325 :rule false_intro :premises (@p286)) % 0.41/0.84 (step @p326 :rule symm :premises (@p311)) % 0.41/0.84 (step @p327 :rule refl :args (@t223)) % 0.41/0.84 (step @p328 :rule cong :premises (@p327 @p326) :args (@t237)) % 0.41/0.84 (step @p329 :rule trans :premises (@p328 @p325)) % 0.41/0.84 (step @p330 :rule false_elim :premises (@p329)) % 0.41/0.84 (step-pop @p343 :rule scope :premises (@p330)) % 0.41/0.84 (step-pop @p344 :rule scope :premises (@p343)) % 0.41/0.84 (step @p331 :rule process_scope :premises (@p344) :args (@t239)) % 0.41/0.84 (step @p334 :rule implies_elim :premises (@p331)) % 0.41/0.84 (step @p335 :rule cnf_and_neg :args (@t241)) % 0.41/0.84 (step @p336 :rule resolution :premises (@p335 @p334) :args (true @t241)) % 0.41/0.84 (step @p337 :rule eq_resolve :premises (@p336 @p322)) % 0.41/0.84 (step @p338 false :rule chain_m_resolution :premises (@p337 @p318 @p311 @p286) :args (false (@list false false true) (@list @t237 @t234 @t224))) % 0.41/0.84 ) % 0.41/0.84 % SZS output end Proof % 0.41/0.84 % cvc5 exiting %------------------------------------------------------------------------------