%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU215+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:58 AM UTC 2026 % Result : Theorem 28.13s 28.34s % Output : Proof 28.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU215+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n018.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 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:40:35 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 28.13/28.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 28.13/28.34 --- Run --no-e-matching --full-saturate-quant at 6... % 28.13/28.34 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 28.13/28.34 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 28.13/28.34 % SZS status Theorem % 28.13/28.34 % SZS output start Proof % 28.13/28.34 ( % 28.13/28.34 (declare-sort $$unsorted 0) % 28.13/28.34 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.empty (-> $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation (-> $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.empty_set $$unsorted) % 28.13/28.34 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.function (-> $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 28.13/28.34 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 28.13/28.34 (define @t1 () (@var "A" $$unsorted)) % 28.13/28.34 (define @t2 () (@var "B" $$unsorted)) % 28.13/28.34 (define @t3 () (tptp.in @t2 @t1)) % 28.13/28.34 (define @t4 () (not @t3)) % 28.13/28.34 (define @t5 () (tptp.in @t1 @t2)) % 28.13/28.34 (define @t6 () (@list @t1 @t2)) % 28.13/28.34 (define @t7 () (tptp.proper_subset @t2 @t1)) % 28.13/28.34 (define @t8 () (tptp.proper_subset @t1 @t2)) % 28.13/28.34 (define @t9 () (tptp.function @t1)) % 28.13/28.34 (define @t10 () (tptp.empty @t1)) % 28.13/28.34 (define @t11 () (@list @t1)) % 28.13/28.34 (define @t12 () (tptp.relation @t1)) % 28.13/28.34 (define @t13 () (tptp.unordered_pair @t1 @t2)) % 28.13/28.34 (define @t14 () (tptp.set_union2 @t2 @t1)) % 28.13/28.34 (define @t15 () (tptp.set_union2 @t1 @t2)) % 28.13/28.34 (define @t16 () (tptp.set_intersection2 @t1 @t2)) % 28.13/28.34 (define @t17 () (@var "D" $$unsorted)) % 28.13/28.34 (define @t18 () (@var "C" $$unsorted)) % 28.13/28.34 (define @t19 () (tptp.in @t18 @t1)) % 28.13/28.34 (define @t20 () (tptp.ordered_pair @t18 @t17)) % 28.13/28.34 (define @t21 () (tptp.in @t20 @t2)) % 28.13/28.34 (define @t22 () (@list @t18 @t17)) % 28.13/28.34 (define @t23 () (tptp.identity_relation @t1)) % 28.13/28.34 (define @t24 () (tptp.relation @t2)) % 28.13/28.34 (define @t25 () (tptp.subset @t1 @t2)) % 28.13/28.34 (define @t26 () (= @t1 @t2)) % 28.13/28.34 (define @t27 () (@var "E" $$unsorted)) % 28.13/28.34 (define @t28 () (tptp.ordered_pair @t17 @t27)) % 28.13/28.34 (define @t29 () (tptp.in @t28 @t1)) % 28.13/28.34 (define @t30 () (tptp.in @t17 @t2)) % 28.13/28.34 (define @t31 () (tptp.in @t28 @t18)) % 28.13/28.34 (define @t32 () (@list @t17 @t27)) % 28.13/28.34 (define @t33 () (tptp.relation_dom_restriction @t1 @t2)) % 28.13/28.34 (define @t34 () (tptp.relation @t18)) % 28.13/28.34 (define @t35 () (@list @t2 @t18)) % 28.13/28.34 (define @t36 () (tptp.in @t27 @t1)) % 28.13/28.34 (define @t37 () (tptp.relation_rng_restriction @t1 @t2)) % 28.13/28.34 (define @t38 () (@list @t18)) % 28.13/28.34 (define @t39 () (tptp.in @t27 @t2)) % 28.13/28.34 (define @t40 () (@list @t27)) % 28.13/28.34 (define @t41 () (tptp.in @t17 @t18)) % 28.13/28.34 (define @t42 () (@list @t17)) % 28.13/28.34 (define @t43 () (@list @t2)) % 28.13/28.34 (define @t44 () (= @t2 tptp.empty_set)) % 28.13/28.34 (define @t45 () (= @t2 (tptp.set_meet @t1))) % 28.13/28.34 (define @t46 () (= @t1 tptp.empty_set)) % 28.13/28.34 (define @t47 () (tptp.in @t18 @t17)) % 28.13/28.34 (define @t48 () (tptp.in @t17 @t1)) % 28.13/28.34 (define @t49 () (tptp.in @t18 @t2)) % 28.13/28.34 (define @t50 () (not @t46)) % 28.13/28.34 (define @t51 () (tptp.singleton @t1)) % 28.13/28.34 (define @t52 () (tptp.powerset @t1)) % 28.13/28.34 (define @t53 () (tptp.in @t20 @t1)) % 28.13/28.34 (define @t54 () (tptp.empty @t2)) % 28.13/28.34 (define @t55 () (tptp.element @t2 @t1)) % 28.13/28.34 (define @t56 () (not @t10)) % 28.13/28.34 (define @t57 () (@list @t1 @t2 @t18)) % 28.13/28.34 (define @t58 () (@var "F" $$unsorted)) % 28.13/28.34 (define @t59 () (tptp.cartesian_product2 @t1 @t2)) % 28.13/28.34 (define @t60 () (forall @t38 (=> @t19 @t49))) % 28.13/28.34 (define @t61 () (= @t18 (tptp.apply @t1 @t2))) % 28.13/28.34 (define @t62 () (= @t61 (= @t18 tptp.empty_set))) % 28.13/28.34 (define @t63 () (tptp.relation_dom @t1)) % 28.13/28.34 (define @t64 () (tptp.in @t2 @t63)) % 28.13/28.34 (define @t65 () (not @t64)) % 28.13/28.34 (define @t66 () (tptp.in (tptp.ordered_pair @t2 @t18) @t1)) % 28.13/28.34 (define @t67 () (= @t61 @t66)) % 28.13/28.34 (define @t68 () (and (=> @t64 @t67) (=> @t65 @t62))) % 28.13/28.34 (define @t69 () (forall @t35 @t68)) % 28.13/28.34 (define @t70 () (and @t12 @t9)) % 28.13/28.34 (define @t71 () (=> @t70 @t69)) % 28.13/28.34 (define @t72 () (forall @t11 @t71)) % 28.13/28.34 (define @t73 () (tptp.cast_to_subset @t1)) % 28.13/28.34 (define @t74 () (tptp.set_difference @t1 @t2)) % 28.13/28.34 (define @t75 () (tptp.in (tptp.ordered_pair @t17 @t18) @t1)) % 28.13/28.34 (define @t76 () (tptp.relation_rng @t1)) % 28.13/28.34 (define @t77 () (tptp.subset_complement @t1 @t2)) % 28.13/28.34 (define @t78 () (tptp.element @t2 @t52)) % 28.13/28.34 (define @t79 () (tptp.ordered_pair @t1 @t2)) % 28.13/28.34 (define @t80 () (tptp.relation_inverse @t1)) % 28.13/28.34 (define @t81 () (tptp.disjoint @t1 @t2)) % 28.13/28.34 (define @t82 () (tptp.relation_composition @t1 @t2)) % 28.13/28.34 (define @t83 () (tptp.complements_of_subsets @t1 @t2)) % 28.13/28.34 (define @t84 () (tptp.powerset @t52)) % 28.13/28.34 (define @t85 () (tptp.element @t2 @t84)) % 28.13/28.34 (define @t86 () (not @t26)) % 28.13/28.34 (define @t87 () (tptp.relation @t82)) % 28.13/28.34 (define @t88 () (and @t12 @t24)) % 28.13/28.34 (define @t89 () (tptp.union_of_subsets @t1 @t2)) % 28.13/28.34 (define @t90 () (tptp.meet_of_subsets @t1 @t2)) % 28.13/28.34 (define @t91 () (tptp.subset_difference @t1 @t2 @t18)) % 28.13/28.34 (define @t92 () (tptp.element @t18 @t52)) % 28.13/28.34 (define @t93 () (and @t78 @t92)) % 28.13/28.34 (define @t94 () (tptp.relation_composition @t2 @t1)) % 28.13/28.34 (define @t95 () (and @t10 @t24)) % 28.13/28.34 (define @t96 () (tptp.relation tptp.empty_set)) % 28.13/28.34 (define @t97 () (tptp.empty tptp.empty_set)) % 28.13/28.34 (define @t98 () (and @t87 (tptp.function @t82))) % 28.13/28.34 (define @t99 () (tptp.function @t2)) % 28.13/28.34 (define @t100 () (and @t12 @t9 @t24 @t99)) % 28.13/28.34 (define @t101 () (forall @t6 (=> @t100 @t98))) % 28.13/28.34 (define @t102 () (not @t54)) % 28.13/28.34 (define @t103 () (tptp.empty @t63)) % 28.13/28.34 (define @t104 () (and @t56 @t12)) % 28.13/28.34 (define @t105 () (tptp.empty @t76)) % 28.13/28.34 (define @t106 () (tptp.disjoint @t51 @t2)) % 28.13/28.34 (define @t107 () (tptp.singleton @t2)) % 28.13/28.34 (define @t108 () (tptp.union @t2)) % 28.13/28.34 (define @t109 () (tptp.in @t1 @t18)) % 28.13/28.34 (define @t110 () (@list @t1 @t2 @t18 @t17)) % 28.13/28.34 (define @t111 () (tptp.element @t1 (tptp.powerset @t2))) % 28.13/28.34 (define @t112 () (tptp.set_difference @t2 @t18)) % 28.13/28.34 (define @t113 () (= @t1 @t18)) % 28.13/28.34 (define @t114 () (tptp.relation_rng @t18)) % 28.13/28.34 (define @t115 () (tptp.relation_rng @t37)) % 28.13/28.34 (define @t116 () (tptp.relation_rng @t2)) % 28.13/28.34 (define @t117 () (tptp.cartesian_product2 @t1 @t18)) % 28.13/28.34 (define @t118 () (not @t49)) % 28.13/28.34 (define @t119 () (tptp.subset @t18 @t2)) % 28.13/28.34 (define @t120 () (forall @t38 (not (and @t119 (not (tptp.are_equipotent @t18 @t2)) @t118)))) % 28.13/28.34 (define @t121 () (tptp.powerset @t18)) % 28.13/28.34 (define @t122 () (forall @t22 (=> (and @t49 (tptp.subset @t17 @t18)) @t30))) % 28.13/28.34 (define @t123 () (tptp.relation_dom_restriction @t18 @t2)) % 28.13/28.34 (define @t124 () (tptp.relation_dom @t18)) % 28.13/28.34 (define @t125 () (tptp.relation_image @t2 @t1)) % 28.13/28.34 (define @t126 () (tptp.relation_dom @t2)) % 28.13/28.34 (define @t127 () (tptp.set_intersection2 @t126 @t1)) % 28.13/28.34 (define @t128 () (tptp.relation_rng @t82)) % 28.13/28.34 (define @t129 () (tptp.relation_inverse_image @t18 @t2)) % 28.13/28.34 (define @t130 () (tptp.relation_inverse_image @t2 @t1)) % 28.13/28.34 (define @t131 () (tptp.set_intersection2 @t2 @t18)) % 28.13/28.34 (define @t132 () (tptp.subset @t1 @t18)) % 28.13/28.34 (define @t133 () (tptp.element @t1 @t2)) % 28.13/28.34 (define @t134 () (tptp.in @t1 @t124)) % 28.13/28.34 (define @t135 () (tptp.in @t79 @t18)) % 28.13/28.34 (define @t136 () (tptp.apply @t18 @t1)) % 28.13/28.34 (define @t137 () (tptp.relation_composition @t18 @t2)) % 28.13/28.34 (define @t138 () (tptp.in @t1 (tptp.relation_dom @t137))) % 28.13/28.34 (define @t139 () (= @t138 (and @t134 (tptp.in @t136 @t126)))) % 28.13/28.34 (define @t140 () (tptp.function @t18)) % 28.13/28.34 (define @t141 () (and @t34 @t140)) % 28.13/28.34 (define @t142 () (forall @t38 (=> @t141 @t139))) % 28.13/28.34 (define @t143 () (and @t24 @t99)) % 28.13/28.34 (define @t144 () (=> @t143 @t142)) % 28.13/28.34 (define @t145 () (forall @t6 @t144)) % 28.13/28.34 (define @t146 () (= (tptp.apply @t137 @t1) (tptp.apply @t2 @t136))) % 28.13/28.34 (define @t147 () (=> @t138 @t146)) % 28.13/28.34 (define @t148 () (forall @t38 (=> @t141 @t147))) % 28.13/28.34 (define @t149 () (=> @t143 @t148)) % 28.13/28.34 (define @t150 () (forall @t6 @t149)) % 28.13/28.34 (define @t151 () (tptp.apply @t2 @t1)) % 28.13/28.34 (define @t152 () (= (tptp.apply (tptp.relation_composition @t2 @t18) @t1) (tptp.apply @t18 @t151))) % 28.13/28.34 (define @t153 () (tptp.in @t1 @t126)) % 28.13/28.34 (define @t154 () (=> @t153 @t152)) % 28.13/28.34 (define @t155 () (forall @t38 (=> @t141 @t154))) % 28.13/28.34 (define @t156 () (=> @t143 @t155)) % 28.13/28.34 (define @t157 () (forall @t6 @t156)) % 28.13/28.34 (define @t158 () (not @t157)) % 28.13/28.34 (define @t159 () (tptp.relation_field @t18)) % 28.13/28.34 (define @t160 () (tptp.in @t2 @t18)) % 28.13/28.34 (define @t161 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 28.13/28.34 (define @t162 () (and @t19 @t49)) % 28.13/28.34 (define @t163 () (not @t81)) % 28.13/28.34 (define @t164 () (tptp.subset_complement @t1 @t18)) % 28.13/28.34 (define @t165 () (tptp.disjoint @t2 @t18)) % 28.13/28.34 (define @t166 () (tptp.relation_dom @t82)) % 28.13/28.34 (define @t167 () (not @t44)) % 28.13/28.34 (define @t168 () (tptp.element @t2 @t121)) % 28.13/28.34 (define @t169 () (tptp.in @t18 @t16)) % 28.13/28.34 (define @t170 () (= @t76 tptp.empty_set)) % 28.13/28.34 (define @t171 () (= @t63 tptp.empty_set)) % 28.13/28.34 (define @t172 () (tptp.relation_dom_restriction @t2 @t1)) % 28.13/28.34 (define @t173 () (= @t51 (tptp.unordered_pair @t2 @t18))) % 28.13/28.34 (define @t174 () (@var "BOUND_VARIABLE_8906" $$unsorted)) % 28.13/28.34 (define @t175 () (@var "BOUND_VARIABLE_8904" $$unsorted)) % 28.13/28.34 (define @t176 () (or (tptp.in @t175 @t63) (= (= @t174 (tptp.apply @t1 @t175)) (= tptp.empty_set @t174)))) % 28.13/28.34 (define @t177 () (@var "BOUND_VARIABLE_8894" $$unsorted)) % 28.13/28.34 (define @t178 () (@var "BOUND_VARIABLE_8892" $$unsorted)) % 28.13/28.34 (define @t179 () (or (not (tptp.in @t178 @t63)) (= (= @t177 (tptp.apply @t1 @t178)) (tptp.in (tptp.ordered_pair @t178 @t177) @t1)))) % 28.13/28.34 (define @t180 () (and @t179 @t176)) % 28.13/28.34 (define @t181 () (not @t9)) % 28.13/28.34 (define @t182 () (not @t12)) % 28.13/28.34 (define @t183 () (or @t182 @t181 @t180)) % 28.13/28.34 (define @t184 () (forall (@list @t1 @t178 @t177 @t175 @t174) @t183)) % 28.13/28.34 (define @t185 () (@list @t178 @t177 @t175 @t174)) % 28.13/28.34 (define @t186 () (forall @t185 @t183)) % 28.13/28.34 (define @t187 () (forall (@list @t175 @t174) @t176)) % 28.13/28.34 (define @t188 () (@var "BOUND_VARIABLE_8869" $$unsorted)) % 28.13/28.34 (define @t189 () (@var "BOUND_VARIABLE_8867" $$unsorted)) % 28.13/28.34 (define @t190 () (@list @t189 @t188)) % 28.13/28.34 (define @t191 () (forall @t185 @t176)) % 28.13/28.34 (define @t192 () (forall (@list @t178 @t177) @t179)) % 28.13/28.34 (define @t193 () (@var "BOUND_VARIABLE_8855" $$unsorted)) % 28.13/28.34 (define @t194 () (@var "BOUND_VARIABLE_8853" $$unsorted)) % 28.13/28.34 (define @t195 () (@list @t194 @t193)) % 28.13/28.34 (define @t196 () (forall @t185 @t179)) % 28.13/28.34 (define @t197 () (and @t196 @t191)) % 28.13/28.34 (define @t198 () (forall @t185 @t180)) % 28.13/28.34 (define @t199 () (or @t182 @t181 @t198)) % 28.13/28.34 (define @t200 () (= @t188 (tptp.apply @t1 @t189))) % 28.13/28.34 (define @t201 () (tptp.in @t189 @t63)) % 28.13/28.34 (define @t202 () (@list @t189 @t188)) % 28.13/28.34 (define @t203 () (forall (@list @t194 @t193) (or (not (tptp.in @t194 @t63)) (= (= @t193 (tptp.apply @t1 @t194)) (tptp.in (tptp.ordered_pair @t194 @t193) @t1))))) % 28.13/28.34 (define @t204 () (and @t203 (forall @t202 (or @t201 (= @t200 (= tptp.empty_set @t188)))))) % 28.13/28.34 (define @t205 () (or @t182 @t181 @t204)) % 28.13/28.34 (define @t206 () (= @t200 (= @t188 tptp.empty_set))) % 28.13/28.34 (define @t207 () (or @t201 @t206)) % 28.13/28.34 (define @t208 () (forall @t202 @t207)) % 28.13/28.34 (define @t209 () (or @t64 @t62)) % 28.13/28.34 (define @t210 () (forall @t35 @t209)) % 28.13/28.34 (define @t211 () (@list @t2 @t18)) % 28.13/28.34 (define @t212 () (or @t65 @t67)) % 28.13/28.34 (define @t213 () (forall @t35 @t212)) % 28.13/28.34 (define @t214 () (and @t213 @t210)) % 28.13/28.34 (define @t215 () (@var "BOUND_VARIABLE_9607" $$unsorted)) % 28.13/28.34 (define @t216 () (= (tptp.apply (tptp.relation_composition @t2 @t215) @t1) (tptp.apply @t215 @t151))) % 28.13/28.34 (define @t217 () (not (tptp.function @t215))) % 28.13/28.34 (define @t218 () (not (tptp.relation @t215))) % 28.13/28.34 (define @t219 () (not @t153)) % 28.13/28.34 (define @t220 () (not @t99)) % 28.13/28.34 (define @t221 () (not @t24)) % 28.13/28.34 (define @t222 () (or @t221 @t220 @t219 @t218 @t217 @t216)) % 28.13/28.34 (define @t223 () (@list @t1 @t2 @t215)) % 28.13/28.34 (define @t224 () (forall @t223 @t222)) % 28.13/28.34 (define @t225 () (@quantifiers_skolemize @t224 0)) % 28.13/28.34 (define @t226 () (@quantifiers_skolemize @t224 1)) % 28.13/28.34 (define @t227 () (tptp.apply @t226 @t225)) % 28.13/28.34 (define @t228 () (@quantifiers_skolemize @t224 2)) % 28.13/28.34 (define @t229 () (tptp.apply @t228 @t227)) % 28.13/28.34 (define @t230 () (= tptp.empty_set @t229)) % 28.13/28.34 (define @t231 () (= @t229 @t229)) % 28.13/28.34 (define @t232 () (tptp.relation_dom @t228)) % 28.13/28.34 (define @t233 () (tptp.in @t227 @t232)) % 28.13/28.34 (define @t234 () (or @t233 (= @t231 @t230))) % 28.13/28.34 (define @t235 () (tptp.ordered_pair tptp.empty_set tptp.empty_set)) % 28.13/28.34 (define @t236 () (or (not (tptp.in tptp.empty_set @t232)) (= (= tptp.empty_set (tptp.apply @t228 tptp.empty_set)) (tptp.in @t235 @t228)))) % 28.13/28.34 (define @t237 () (and @t236 @t234)) % 28.13/28.34 (define @t238 () (tptp.function @t228)) % 28.13/28.34 (define @t239 () (not @t238)) % 28.13/28.34 (define @t240 () (tptp.relation @t228)) % 28.13/28.34 (define @t241 () (not @t240)) % 28.13/28.34 (define @t242 () (or @t241 @t239 @t237)) % 28.13/28.34 (define @t243 () (or @t233 @t230)) % 28.13/28.34 (define @t244 () (and @t236 @t243)) % 28.13/28.34 (define @t245 () (or @t241 @t239 @t244)) % 28.13/28.34 (define @t246 () (@list false)) % 28.13/28.34 (define @t247 () (@list @t184)) % 28.13/28.34 (define @t248 () (or @t218 @t217 @t216)) % 28.13/28.34 (define @t249 () (or @t221 @t220 @t219 @t248)) % 28.13/28.34 (define @t250 () (forall @t223 @t249)) % 28.13/28.34 (define @t251 () (@list @t215)) % 28.13/28.34 (define @t252 () (forall @t251 @t249)) % 28.13/28.34 (define @t253 () (forall @t251 @t248)) % 28.13/28.34 (define @t254 () (@list @t18)) % 28.13/28.34 (define @t255 () (or @t221 @t220 @t219 @t253)) % 28.13/28.34 (define @t256 () (not @t140)) % 28.13/28.34 (define @t257 () (not @t34)) % 28.13/28.34 (define @t258 () (or @t257 @t256 @t152)) % 28.13/28.34 (define @t259 () (forall @t38 @t258)) % 28.13/28.34 (define @t260 () (or @t221 @t220 @t219 @t259)) % 28.13/28.34 (define @t261 () (or @t219 @t259)) % 28.13/28.34 (define @t262 () (or @t221 @t220)) % 28.13/28.34 (define @t263 () (not @t143)) % 28.13/28.34 (define @t264 () (or @t219 @t258)) % 28.13/28.34 (define @t265 () (or @t257 @t256 @t219 @t152)) % 28.13/28.34 (define @t266 () (or @t257 @t256)) % 28.13/28.34 (define @t267 () (not @t141)) % 28.13/28.34 (define @t268 () (tptp.relation_composition @t226 @t228)) % 28.13/28.34 (define @t269 () (tptp.apply @t268 @t225)) % 28.13/28.34 (define @t270 () (= @t269 @t229)) % 28.13/28.34 (define @t271 () (tptp.in @t225 (tptp.relation_dom @t226))) % 28.13/28.34 (define @t272 () (not @t271)) % 28.13/28.34 (define @t273 () (tptp.function @t226)) % 28.13/28.34 (define @t274 () (not @t273)) % 28.13/28.34 (define @t275 () (tptp.relation @t226)) % 28.13/28.34 (define @t276 () (not @t275)) % 28.13/28.34 (define @t277 () (or @t276 @t274 @t272 @t241 @t239 @t270)) % 28.13/28.34 (define @t278 () (@list true)) % 28.13/28.34 (define @t279 () (@list @t277)) % 28.13/28.34 (define @t280 () (@list false false false)) % 28.13/28.34 (define @t281 () (@var "BOUND_VARIABLE_9542" $$unsorted)) % 28.13/28.34 (define @t282 () (= (tptp.in @t1 (tptp.relation_dom (tptp.relation_composition @t281 @t2))) (and (tptp.in @t1 (tptp.relation_dom @t281)) (tptp.in (tptp.apply @t281 @t1) @t126)))) % 28.13/28.34 (define @t283 () (not (tptp.function @t281))) % 28.13/28.34 (define @t284 () (not (tptp.relation @t281))) % 28.13/28.34 (define @t285 () (or @t284 @t283 @t282)) % 28.13/28.34 (define @t286 () (or @t221 @t220 @t285)) % 28.13/28.34 (define @t287 () (forall (@list @t1 @t2 @t281) @t286)) % 28.13/28.34 (define @t288 () (@list @t281)) % 28.13/28.34 (define @t289 () (forall @t288 @t286)) % 28.13/28.34 (define @t290 () (forall @t288 @t285)) % 28.13/28.34 (define @t291 () (or @t221 @t220 @t290)) % 28.13/28.34 (define @t292 () (or @t257 @t256 @t139)) % 28.13/28.34 (define @t293 () (forall @t38 @t292)) % 28.13/28.34 (define @t294 () (or @t221 @t220 @t293)) % 28.13/28.34 (define @t295 () (@list @t225 @t228 @t226)) % 28.13/28.34 (define @t296 () (and @t271 @t233)) % 28.13/28.34 (define @t297 () (tptp.relation_dom @t268)) % 28.13/28.34 (define @t298 () (tptp.in @t225 @t297)) % 28.13/28.34 (define @t299 () (= @t298 @t296)) % 28.13/28.34 (define @t300 () (or @t241 @t239 @t276 @t274 @t299)) % 28.13/28.34 (define @t301 () (@list false false false false false)) % 28.13/28.34 (define @t302 () (@var "BOUND_VARIABLE_9575" $$unsorted)) % 28.13/28.34 (define @t303 () (tptp.relation_composition @t302 @t2)) % 28.13/28.34 (define @t304 () (= (tptp.apply @t303 @t1) (tptp.apply @t2 (tptp.apply @t302 @t1)))) % 28.13/28.34 (define @t305 () (not (tptp.in @t1 (tptp.relation_dom @t303)))) % 28.13/28.34 (define @t306 () (not (tptp.function @t302))) % 28.13/28.34 (define @t307 () (not (tptp.relation @t302))) % 28.13/28.34 (define @t308 () (or @t307 @t306 @t305 @t304)) % 28.13/28.34 (define @t309 () (or @t221 @t220 @t308)) % 28.13/28.34 (define @t310 () (forall (@list @t1 @t2 @t302) @t309)) % 28.13/28.34 (define @t311 () (@list @t302)) % 28.13/28.34 (define @t312 () (forall @t311 @t309)) % 28.13/28.34 (define @t313 () (forall @t311 @t308)) % 28.13/28.34 (define @t314 () (or @t221 @t220 @t313)) % 28.13/28.34 (define @t315 () (not @t138)) % 28.13/28.34 (define @t316 () (or @t257 @t256 @t315 @t146)) % 28.13/28.34 (define @t317 () (forall @t38 @t316)) % 28.13/28.34 (define @t318 () (or @t221 @t220 @t317)) % 28.13/28.34 (define @t319 () (not @t298)) % 28.13/28.34 (define @t320 () (or @t241 @t239 @t276 @t274 @t319 @t270)) % 28.13/28.34 (define @t321 () (not @t296)) % 28.13/28.34 (define @t322 () (@list true false)) % 28.13/28.34 (define @t323 () (not @t233)) % 28.13/28.34 (define @t324 () (= tptp.empty_set @t269)) % 28.13/28.34 (define @t325 () (= @t269 @t269)) % 28.13/28.34 (define @t326 () (or @t298 (= @t325 @t324))) % 28.13/28.34 (define @t327 () (or (not (tptp.in tptp.empty_set @t297)) (= (= tptp.empty_set (tptp.apply @t268 tptp.empty_set)) (tptp.in @t235 @t268)))) % 28.13/28.34 (define @t328 () (and @t327 @t326)) % 28.13/28.34 (define @t329 () (tptp.function @t268)) % 28.13/28.34 (define @t330 () (not @t329)) % 28.13/28.34 (define @t331 () (tptp.relation @t268)) % 28.13/28.34 (define @t332 () (not @t331)) % 28.13/28.34 (define @t333 () (or @t332 @t330 @t328)) % 28.13/28.34 (define @t334 () (or @t298 @t324)) % 28.13/28.34 (define @t335 () (and @t327 @t334)) % 28.13/28.34 (define @t336 () (or @t332 @t330 @t335)) % 28.13/28.34 (define @t337 () (or @t182 @t181 @t221 @t220)) % 28.13/28.34 (define @t338 () (and @t331 @t329)) % 28.13/28.34 (define @t339 () (or @t276 @t274 @t241 @t239 @t338)) % 28.13/28.34 (define @t340 () (not @t338)) % 28.13/28.34 (define @t341 () (@list @t338)) % 28.13/28.34 (assume @p1 (forall @t6 (=> @t5 @t4))) % 28.13/28.34 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 28.13/28.34 (assume @p3 (forall @t11 (=> @t10 @t9))) % 28.13/28.34 (assume @p4 (forall @t11 (=> @t10 @t12))) % 28.13/28.34 (assume @p5 (forall @t6 (= @t13 (tptp.unordered_pair @t2 @t1)))) % 28.13/28.34 (assume @p6 (forall @t6 (= @t15 @t14))) % 28.13/28.34 (assume @p7 (forall @t6 (= @t16 (tptp.set_intersection2 @t2 @t1)))) % 28.13/28.34 (assume @p8 (forall @t6 (=> @t24 (= (= @t2 @t23) (forall @t22 (= @t21 (and @t19 (= @t18 @t17)))))))) % 28.13/28.34 (assume @p9 (forall @t6 (= @t26 (and @t25 (tptp.subset @t2 @t1))))) % 28.13/28.34 (assume @p10 (forall @t11 (=> @t12 (forall @t35 (=> @t34 (= (= @t18 @t33) (forall @t32 (= @t31 (and @t30 @t29))))))))) % 28.13/28.34 (assume @p11 (forall @t6 (=> @t24 (forall @t38 (=> @t34 (= (= @t18 @t37) (forall @t32 (= @t31 (and @t36 (tptp.in @t28 @t2)))))))))) % 28.13/28.34 (assume @p12 (forall @t11 (=> @t12 (forall @t35 (= (= @t18 (tptp.relation_image @t1 @t2)) (forall @t42 (= @t41 (exists @t40 (and (tptp.in (tptp.ordered_pair @t27 @t17) @t1) @t39))))))))) % 28.13/28.34 (assume @p13 (forall @t11 (=> @t12 (forall @t35 (= (= @t18 (tptp.relation_inverse_image @t1 @t2)) (forall @t42 (= @t41 (exists @t40 (and @t29 @t39))))))))) % 28.13/28.34 (assume @p14 (forall @t11 (= @t12 (forall @t43 (not (and @t3 (forall @t22 (not (= @t2 @t20))))))))) % 28.13/28.34 (assume @p15 (forall @t6 (and (=> @t50 (= @t45 (forall @t38 (= @t49 (forall @t42 (=> @t48 @t47)))))) (=> @t46 (= @t45 @t44))))) % 28.13/28.34 (assume @p16 (forall @t6 (= (= @t2 @t51) (forall @t38 (= @t49 (= @t18 @t1)))))) % 28.13/28.34 (assume @p17 (forall @t11 (= @t46 (forall @t43 @t4)))) % 28.13/28.34 (assume @p18 (forall @t6 (= (= @t2 @t52) (forall @t38 (= @t49 (tptp.subset @t18 @t1)))))) % 28.13/28.34 (assume @p19 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (= @t26 (forall @t22 (= @t53 @t21)))))))) % 28.13/28.34 (assume @p20 (forall @t6 (and (=> @t56 (= @t55 @t3)) (=> @t10 (= @t55 @t54))))) % 28.13/28.34 (assume @p21 (forall @t57 (= (= @t18 @t13) (forall @t42 (= @t41 (or (= @t17 @t1) (= @t17 @t2))))))) % 28.13/28.34 (assume @p22 (forall @t57 (= (= @t18 @t15) (forall @t42 (= @t41 (or @t48 @t30)))))) % 28.13/28.34 (assume @p23 (forall @t57 (= (= @t18 @t59) (forall @t42 (= @t41 (exists (@list @t27 @t58) (and @t36 (tptp.in @t58 @t2) (= @t17 (tptp.ordered_pair @t27 @t58))))))))) % 28.13/28.34 (assume @p24 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (= @t25 (forall @t22 (=> @t53 @t21)))))))) % 28.13/28.34 (assume @p25 (forall @t6 (= @t25 @t60))) % 28.13/28.34 (assume @p26 (forall @t57 (= (= @t18 @t16) (forall @t42 (= @t41 (and @t48 @t30)))))) % 28.13/28.34 (assume @p27 @t72) % 28.13/28.34 (assume @p28 (forall @t11 (=> @t12 (forall @t43 (= (= @t2 @t63) (forall @t38 (= @t49 (exists @t42 @t53)))))))) % 28.13/28.34 (assume @p29 (forall @t11 (= @t73 @t1))) % 28.13/28.34 (assume @p30 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t38 (= @t49 (exists @t42 (and @t47 @t48))))))) % 28.13/28.34 (assume @p31 (forall @t57 (= (= @t18 @t74) (forall @t42 (= @t41 (and @t48 (not @t30))))))) % 28.13/28.34 (assume @p32 (forall @t11 (=> @t12 (forall @t43 (= (= @t2 @t76) (forall @t38 (= @t49 (exists @t42 @t75)))))))) % 28.13/28.34 (assume @p33 (forall @t6 (=> @t78 (= @t77 @t74)))) % 28.13/28.34 (assume @p34 (forall @t6 (= @t79 (tptp.unordered_pair @t13 @t51)))) % 28.13/28.34 (assume @p35 (forall @t11 (=> @t12 (= (tptp.relation_field @t1) (tptp.set_union2 @t63 @t76))))) % 28.13/28.34 (assume @p36 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (= (= @t2 @t80) (forall @t22 (= @t21 @t75)))))))) % 28.13/28.34 (assume @p37 (forall @t6 (= @t81 (= @t16 tptp.empty_set)))) % 28.13/28.34 (assume @p38 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (forall @t38 (=> @t34 (= (= @t18 @t82) (forall @t32 (= @t31 (exists (@list @t58) (and (tptp.in (tptp.ordered_pair @t17 @t58) @t1) (tptp.in (tptp.ordered_pair @t58 @t27) @t2))))))))))))) % 28.13/28.34 (assume @p39 (forall @t6 (=> @t85 (forall @t38 (=> (tptp.element @t18 @t84) (= (= @t18 @t83) (forall @t42 (=> (tptp.element @t17 @t52) (= @t41 (tptp.in (tptp.subset_complement @t1 @t17) @t2)))))))))) % 28.13/28.34 (assume @p40 (forall @t6 (= @t8 (and @t25 @t86)))) % 28.13/28.34 (assume @p41 true) % 28.13/28.34 (assume @p42 (forall @t11 (tptp.element @t73 @t52))) % 28.13/28.34 (assume @p43 (forall @t6 (=> @t78 (tptp.element @t77 @t52)))) % 28.13/28.34 (assume @p44 (forall @t11 (=> @t12 (tptp.relation @t80)))) % 28.13/28.34 (assume @p45 (forall @t6 (=> @t88 @t87))) % 28.13/28.34 (assume @p46 (forall @t6 (=> @t85 (tptp.element @t89 @t52)))) % 28.13/28.34 (assume @p47 (forall @t11 (tptp.relation @t23))) % 28.13/28.34 (assume @p48 (forall @t6 (=> @t85 (tptp.element @t90 @t52)))) % 28.13/28.34 (assume @p49 (forall @t57 (=> @t93 (tptp.element @t91 @t52)))) % 28.13/28.34 (assume @p50 (forall @t6 (=> @t12 (tptp.relation @t33)))) % 28.13/28.34 (assume @p51 (forall @t6 (=> @t85 (tptp.element @t83 @t84)))) % 28.13/28.34 (assume @p52 (forall @t6 (=> @t24 (tptp.relation @t37)))) % 28.13/28.34 (assume @p53 (forall @t11 (exists @t43 @t55))) % 28.13/28.34 (assume @p54 (forall @t6 (=> @t95 (and (tptp.empty @t94) (tptp.relation @t94))))) % 28.13/28.34 (assume @p55 (and @t97 @t96 (tptp.relation_empty_yielding tptp.empty_set))) % 28.13/28.34 (assume @p56 @t101) % 28.13/28.34 (assume @p57 (forall @t6 (=> @t88 (tptp.relation @t16)))) % 28.13/28.34 (assume @p58 (forall @t11 (not (tptp.empty @t52)))) % 28.13/28.34 (assume @p59 @t97) % 28.13/28.34 (assume @p60 (forall @t6 (not (tptp.empty @t79)))) % 28.13/28.34 (assume @p61 (forall @t6 (=> @t88 (tptp.relation @t15)))) % 28.13/28.34 (assume @p62 (forall @t11 (not (tptp.empty @t51)))) % 28.13/28.34 (assume @p63 (forall @t6 (=> @t56 (not (tptp.empty @t15))))) % 28.13/28.34 (assume @p64 (forall @t6 (not (tptp.empty @t13)))) % 28.13/28.34 (assume @p65 (forall @t6 (=> @t56 (not (tptp.empty @t14))))) % 28.13/28.34 (assume @p66 (and @t97 @t96)) % 28.13/28.34 (assume @p67 (forall @t6 (=> (and @t56 @t102) (not (tptp.empty @t59))))) % 28.13/28.34 (assume @p68 (forall @t11 (=> @t104 (not @t103)))) % 28.13/28.34 (assume @p69 (forall @t11 (=> @t104 (not @t105)))) % 28.13/28.34 (assume @p70 (forall @t11 (=> @t10 (and @t103 (tptp.relation @t63))))) % 28.13/28.34 (assume @p71 (forall @t11 (=> @t10 (and @t105 (tptp.relation @t76))))) % 28.13/28.34 (assume @p72 (forall @t6 (=> @t95 (and (tptp.empty @t82) @t87)))) % 28.13/28.34 (assume @p73 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 28.13/28.34 (assume @p74 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 28.13/28.34 (assume @p75 (forall @t6 (=> @t78 (= (tptp.subset_complement @t1 @t77) @t2)))) % 28.13/28.34 (assume @p76 (forall @t11 (=> @t12 (= (tptp.relation_inverse @t80) @t1)))) % 28.13/28.34 (assume @p77 (forall @t6 (=> @t85 (= (tptp.complements_of_subsets @t1 @t83) @t2)))) % 28.13/28.34 (assume @p78 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 28.13/28.34 (assume @p79 (forall @t11 (not (= @t51 tptp.empty_set)))) % 28.13/28.34 (assume @p80 (forall @t6 (=> @t5 (= (tptp.set_union2 @t51 @t2) @t2)))) % 28.13/28.34 (assume @p81 (forall @t6 (not (and @t106 @t5)))) % 28.13/28.34 (assume @p82 (forall @t6 (=> (not @t5) @t106))) % 28.13/28.34 (assume @p83 (forall @t6 (= (tptp.subset @t51 @t2) @t5))) % 28.13/28.34 (assume @p84 (forall @t6 (= (= @t74 tptp.empty_set) @t25))) % 28.13/28.34 (assume @p85 (forall @t6 (=> @t78 (forall @t38 (=> @t49 @t19))))) % 28.13/28.34 (assume @p86 (forall @t57 (=> @t25 (or @t19 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t18))))))) % 28.13/28.34 (assume @p87 (forall @t6 (= (tptp.subset @t1 @t107) (or @t46 (= @t1 @t107))))) % 28.13/28.34 (assume @p88 (forall @t6 (=> @t5 (tptp.subset @t1 @t108)))) % 28.13/28.34 (assume @p89 (forall @t110 (= (tptp.in @t79 (tptp.cartesian_product2 @t18 @t17)) (and @t109 (tptp.in @t2 @t17))))) % 28.13/28.34 (assume @p90 (forall @t6 (=> @t60 @t111))) % 28.13/28.34 (assume @p91 (exists @t11 @t70)) % 28.13/28.34 (assume @p92 (exists @t11 (and @t10 @t12))) % 28.13/28.34 (assume @p93 (forall @t11 (=> @t56 (exists @t43 (and @t78 @t102))))) % 28.13/28.34 (assume @p94 (exists @t11 @t10)) % 28.13/28.34 (assume @p95 (exists @t11 @t104)) % 28.13/28.34 (assume @p96 (forall @t11 (exists @t43 (and @t78 @t54)))) % 28.13/28.34 (assume @p97 (exists @t11 @t56)) % 28.13/28.34 (assume @p98 (exists @t11 (and @t12 (tptp.relation_empty_yielding @t1)))) % 28.13/28.34 (assume @p99 (forall @t6 (=> @t85 (= @t89 @t108)))) % 28.13/28.34 (assume @p100 (forall @t6 (=> @t85 (= @t90 (tptp.set_meet @t2))))) % 28.13/28.34 (assume @p101 (forall @t57 (=> @t93 (= @t91 @t112)))) % 28.13/28.34 (assume @p102 (forall @t6 (tptp.subset @t1 @t1))) % 28.13/28.34 (assume @p103 (forall @t6 (=> @t81 (tptp.disjoint @t2 @t1)))) % 28.13/28.34 (assume @p104 (forall @t110 (not (and (= @t13 (tptp.unordered_pair @t18 @t17)) (not @t113) (not (= @t1 @t17)))))) % 28.13/28.34 (assume @p105 (forall @t57 (=> @t34 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t18))) (and @t5 (tptp.in @t1 @t114)))))) % 28.13/28.34 (assume @p106 (forall @t6 (=> @t24 (tptp.subset @t115 @t1)))) % 28.13/28.34 (assume @p107 (forall @t6 (=> @t24 (tptp.subset @t37 @t2)))) % 28.13/28.34 (assume @p108 (forall @t6 (=> @t24 (tptp.subset @t115 @t116)))) % 28.13/28.34 (assume @p109 (forall @t57 (=> @t25 (and (tptp.subset @t117 (tptp.cartesian_product2 @t2 @t18)) (tptp.subset (tptp.cartesian_product2 @t18 @t1) (tptp.cartesian_product2 @t18 @t2)))))) % 28.13/28.34 (assume @p110 (forall @t6 (=> @t24 (= @t115 (tptp.set_intersection2 @t116 @t1))))) % 28.13/28.34 (assume @p111 (forall @t110 (=> (and @t25 (tptp.subset @t18 @t17)) (tptp.subset @t117 (tptp.cartesian_product2 @t2 @t17))))) % 28.13/28.34 (assume @p112 (forall @t6 (=> @t25 (= @t15 @t2)))) % 28.13/28.34 (assume @p113 (forall @t11 (exists @t43 (and @t5 @t122 (forall @t38 (=> @t49 (tptp.in @t121 @t2))) @t120)))) % 28.13/28.34 (assume @p114 (forall @t57 (=> @t34 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t18) @t2) (tptp.relation_rng_restriction @t1 @t123))))) % 28.13/28.34 (assume @p115 (forall @t57 (=> @t34 (= (tptp.in @t1 (tptp.relation_image @t18 @t2)) (exists @t42 (and (tptp.in @t17 @t124) (tptp.in (tptp.ordered_pair @t17 @t1) @t18) @t30)))))) % 28.13/28.34 (assume @p116 (forall @t6 (=> @t24 (tptp.subset @t125 @t116)))) % 28.13/28.34 (assume @p117 (forall @t6 (=> @t24 (= @t125 (tptp.relation_image @t2 @t127))))) % 28.13/28.34 (assume @p118 (forall @t11 (=> @t12 (= (tptp.relation_image @t1 @t63) @t76)))) % 28.13/28.34 (assume @p119 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (= @t128 (tptp.relation_image @t2 @t76))))))) % 28.13/28.34 (assume @p120 (forall @t57 (=> @t34 (= (tptp.in @t1 @t129) (exists @t42 (and (tptp.in @t17 @t114) (tptp.in (tptp.ordered_pair @t1 @t17) @t18) @t30)))))) % 28.13/28.34 (assume @p121 (forall @t6 (=> @t24 (tptp.subset @t130 @t126)))) % 28.13/28.34 (assume @p122 (forall @t6 (=> @t24 (not (and @t50 (tptp.subset @t1 @t116) (= @t130 tptp.empty_set)))))) % 28.13/28.34 (assume @p123 (forall @t57 (=> @t34 (=> @t25 (tptp.subset (tptp.relation_inverse_image @t18 @t1) @t129))))) % 28.13/28.34 (assume @p124 (forall @t6 (tptp.subset @t16 @t1))) % 28.13/28.34 (assume @p125 (forall @t57 (=> (and @t25 @t132) (tptp.subset @t1 @t131)))) % 28.13/28.34 (assume @p126 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 28.13/28.34 (assume @p127 (forall @t6 (=> @t5 @t133))) % 28.13/28.34 (assume @p128 (forall @t57 (=> (and @t25 (tptp.subset @t2 @t18)) @t132))) % 28.13/28.34 (assume @p129 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 28.13/28.34 (assume @p130 (forall @t57 (=> @t34 (=> @t135 (and @t134 (tptp.in @t2 @t114)))))) % 28.13/28.34 (assume @p131 @t145) % 28.13/28.34 (assume @p132 (forall @t11 (=> @t12 (tptp.subset @t1 (tptp.cartesian_product2 @t63 @t76))))) % 28.13/28.34 (assume @p133 @t150) % 28.13/28.34 (assume @p134 @t158) % 28.13/28.34 (assume @p135 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (=> @t25 (and (tptp.subset @t63 @t126) (tptp.subset @t76 @t116)))))))) % 28.13/28.34 (assume @p136 (forall @t57 (=> @t25 (tptp.subset (tptp.set_intersection2 @t1 @t18) @t131)))) % 28.13/28.34 (assume @p137 (forall @t6 (=> @t25 (= @t16 @t1)))) % 28.13/28.34 (assume @p138 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 28.13/28.34 (assume @p139 (forall @t6 (=> @t133 (or @t54 @t5)))) % 28.13/28.34 (assume @p140 (forall @t6 (=> (forall @t38 (= @t19 @t49)) @t26))) % 28.13/28.34 (assume @p141 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 28.13/28.34 (assume @p142 (forall @t57 (=> @t34 (=> @t135 (and (tptp.in @t1 @t159) (tptp.in @t2 @t159)))))) % 28.13/28.34 (assume @p143 (forall @t57 (=> @t25 (tptp.subset (tptp.set_difference @t1 @t18) @t112)))) % 28.13/28.34 (assume @p144 (forall @t110 (=> (= @t79 @t20) (and @t113 (= @t2 @t17))))) % 28.13/28.34 (assume @p145 (forall @t6 (tptp.subset @t74 @t1))) % 28.13/28.34 (assume @p146 (forall @t11 (=> @t12 (and (= @t76 (tptp.relation_dom @t80)) (= @t63 (tptp.relation_rng @t80)))))) % 28.13/28.34 (assume @p147 (forall @t57 (= (tptp.subset @t13 @t18) (and @t109 @t160)))) % 28.13/28.34 (assume @p148 (forall @t6 (= @t161 @t15))) % 28.13/28.34 (assume @p149 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 28.13/28.34 (assume @p150 (forall @t6 (= @t111 @t25))) % 28.13/28.34 (assume @p151 (forall @t6 (and (not (and @t163 (forall @t38 (not @t162)))) (not (and (exists @t38 @t162) @t81))))) % 28.13/28.34 (assume @p152 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t46))) % 28.13/28.34 (assume @p153 (forall @t6 (= (tptp.set_difference @t15 @t2) @t74))) % 28.13/28.34 (assume @p154 (forall @t6 (=> @t78 (forall @t38 (=> @t92 (= @t165 (tptp.subset @t2 @t164))))))) % 28.13/28.34 (assume @p155 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (tptp.subset @t166 @t63)))))) % 28.13/28.34 (assume @p156 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (tptp.subset @t128 @t116)))))) % 28.13/28.34 (assume @p157 (forall @t6 (=> @t25 (= @t2 @t161)))) % 28.13/28.34 (assume @p158 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (=> (tptp.subset @t76 @t126) (= @t166 @t63))))))) % 28.13/28.34 (assume @p159 (forall @t6 (=> @t85 (not (and @t167 (= @t83 tptp.empty_set)))))) % 28.13/28.34 (assume @p160 (forall @t11 (=> @t12 (forall @t43 (=> @t24 (=> (tptp.subset @t63 @t116) (= (tptp.relation_rng @t94) @t76))))))) % 28.13/28.34 (assume @p161 (forall @t6 (=> @t85 (=> @t167 (= (tptp.subset_difference @t1 @t73 @t89) (tptp.meet_of_subsets @t1 @t83)))))) % 28.13/28.34 (assume @p162 (forall @t6 (=> @t85 (=> @t167 (= (tptp.union_of_subsets @t1 @t83) (tptp.subset_difference @t1 @t73 @t90)))))) % 28.13/28.34 (assume @p163 (forall @t6 (= (tptp.set_difference @t1 @t74) @t16))) % 28.13/28.34 (assume @p164 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 28.13/28.34 (assume @p165 (forall @t57 (=> (and @t5 @t168) (tptp.element @t1 @t18)))) % 28.13/28.34 (assume @p166 (forall @t6 (and (not (and @t163 (forall @t38 (not @t169)))) (not (and (exists @t38 @t169) @t81))))) % 28.13/28.34 (assume @p167 (forall @t11 (=> @t50 (forall @t43 (=> @t78 (forall @t38 (=> (tptp.element @t18 @t1) (=> @t118 (tptp.in @t18 @t77))))))))) % 28.13/28.34 (assume @p168 (forall @t57 (=> @t92 (not (and (tptp.in @t2 @t164) @t160))))) % 28.13/28.34 (assume @p169 (forall @t11 (=> @t12 (=> (forall @t35 (not @t66)) @t46)))) % 28.13/28.34 (assume @p170 (forall @t57 (not (and @t5 @t168 (tptp.empty @t18))))) % 28.13/28.34 (assume @p171 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 28.13/28.34 (assume @p172 (forall @t6 (not (and @t25 @t7)))) % 28.13/28.34 (assume @p173 (forall @t57 (=> (and @t25 @t165) (tptp.disjoint @t1 @t18)))) % 28.13/28.34 (assume @p174 (forall @t11 (=> @t12 (=> (or @t171 @t170) @t46)))) % 28.13/28.34 (assume @p175 (forall @t11 (=> @t12 (= @t171 @t170)))) % 28.13/28.34 (assume @p176 (forall @t6 (= (= (tptp.set_difference @t1 @t107) @t1) @t4))) % 28.13/28.34 (assume @p177 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t51))) % 28.13/28.34 (assume @p178 (forall @t11 (=> @t10 @t46))) % 28.13/28.34 (assume @p179 (forall @t6 (=> (tptp.subset @t51 @t107) @t26))) % 28.13/28.34 (assume @p180 (forall @t11 (and (= (tptp.relation_dom @t23) @t1) (= (tptp.relation_rng @t23) @t1)))) % 28.13/28.34 (assume @p181 (forall @t110 (=> (tptp.relation @t17) (= (tptp.in @t79 (tptp.relation_composition (tptp.identity_relation @t18) @t17)) (and @t109 (tptp.in @t79 @t17)))))) % 28.13/28.34 (assume @p182 (forall @t6 (not (and @t5 @t54)))) % 28.13/28.34 (assume @p183 (forall @t6 (tptp.subset @t1 @t15))) % 28.13/28.34 (assume @p184 (forall @t6 (= @t81 (= @t74 @t1)))) % 28.13/28.34 (assume @p185 (forall @t57 (=> @t34 (= (tptp.in @t1 (tptp.relation_dom @t123)) (and @t5 @t134))))) % 28.13/28.34 (assume @p186 (forall @t6 (=> @t24 (tptp.subset @t172 @t2)))) % 28.13/28.34 (assume @p187 (forall @t6 (not (and @t10 @t86 @t54)))) % 28.13/28.34 (assume @p188 (forall @t57 (=> @t141 (= @t135 (and @t134 (= @t2 @t136)))))) % 28.13/28.34 (assume @p189 (forall @t57 (=> (and @t25 @t119) (tptp.subset (tptp.set_union2 @t1 @t18) @t2)))) % 28.13/28.34 (assume @p190 (forall @t57 (=> @t173 @t26))) % 28.13/28.34 (assume @p191 (forall @t6 (=> @t24 (= (tptp.relation_dom @t172) @t127)))) % 28.13/28.34 (assume @p192 (forall @t6 (=> @t24 (= @t172 (tptp.relation_composition @t23 @t2))))) % 28.13/28.34 (assume @p193 (forall @t6 (=> @t24 (tptp.subset (tptp.relation_rng @t172) @t116)))) % 28.13/28.34 (assume @p194 (forall @t11 (= (tptp.union @t52) @t1))) % 28.13/28.34 (assume @p195 (forall @t11 (exists @t43 (and @t5 @t122 (forall @t38 (not (and @t49 (forall @t42 (not (and @t30 (forall @t40 (=> (tptp.subset @t27 @t18) (tptp.in @t27 @t17))))))))) @t120)))) % 28.13/28.34 (assume @p196 (forall @t57 (=> @t173 (= @t2 @t18)))) % 28.13/28.34 (step @p197 :rule evaluate :args ((= false true))) % 28.13/28.34 (step @p198 :rule and_elim :premises (@p171) :args (0)) % 28.13/28.34 (step @p199 :rule symm :premises (@p198)) % 28.13/28.34 (step @p200 :rule quant-merge-prenex :args ((= (forall @t11 @t186) @t184))) % 28.13/28.34 (step @p201 :rule alpha_equiv :args (@t187 (@list @t175 @t174) @t190)) % 28.13/28.34 (step @p202 :rule quant-unused-vars :args ((= @t191 @t187))) % 28.13/28.34 (step @p203 :rule trans :premises (@p202 @p201)) % 28.13/28.34 (step @p204 :rule alpha_equiv :args (@t192 (@list @t178 @t177) @t195)) % 28.13/28.34 (step @p205 :rule quant-unused-vars :args ((= @t196 @t192))) % 28.13/28.34 (step @p206 :rule trans :premises (@p205 @p204)) % 28.13/28.34 (step @p207 :rule nary_cong :premises (@p206 @p203) :args (@t197)) % 28.13/28.34 (step @p208 :rule quant-miniscope-and :args ((= @t198 @t197))) % 28.13/28.34 (step @p209 :rule trans :premises (@p208 @p207)) % 28.13/28.34 (step @p210 :rule refl :args (@t181)) % 28.13/28.34 (step @p211 :rule refl :args (@t182)) % 28.13/28.34 (step @p212 :rule nary_cong :premises (@p211 @p210 @p209) :args (@t199)) % 28.13/28.34 (step @p213 :rule quant-miniscope-or :args ((= @t186 @t199))) % 28.13/28.34 (step @p214 :rule trans :premises (@p213 @p212)) % 28.13/28.34 (step @p215 :rule symm :premises (@p214)) % 28.13/28.34 (step @p216 :rule cong :premises (@p215) :args ((forall @t11 @t205))) % 28.13/28.34 (step @p217 :rule trans :premises (@p216 @p200)) % 28.13/28.34 (step @p218 :rule aci_norm :args ((= (or (or @t182 @t181) @t204) @t205))) % 28.13/28.34 (step @p219 :rule refl :args (@t204)) % 28.13/28.34 (step @p220 :rule bool-and-de-morgan :args (@t12 @t9 true)) % 28.13/28.34 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or (not @t70) @t204))) % 28.13/28.34 (step @p222 :rule trans :premises (@p221 @p218)) % 28.13/28.34 (step @p223 :rule bool-impl-elim :args (@t70 @t204)) % 28.13/28.34 (step @p224 :rule trans :premises (@p223 @p222)) % 28.13/28.34 (step @p225 :rule cong :premises (@p224) :args ((forall @t11 (=> @t70 @t204)))) % 28.13/28.34 (step @p226 :rule trans :premises (@p225 @p217)) % 28.13/28.34 (step @p227 :rule eq-symm :args (@t188 tptp.empty_set)) % 28.13/28.34 (step @p228 :rule refl :args (@t200)) % 28.13/28.34 (step @p229 :rule cong :premises (@p228 @p227) :args (@t206)) % 28.13/28.34 (step @p230 :rule refl :args (@t201)) % 28.13/28.34 (step @p231 :rule nary_cong :premises (@p230 @p229) :args (@t207)) % 28.13/28.34 (step @p232 :rule cong :premises (@p231) :args (@t208)) % 28.13/28.34 (step @p233 :rule refl :args (@t203)) % 28.13/28.34 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((and @t203 @t208))) % 28.13/28.34 (step @p235 :rule alpha_equiv :args (@t210 @t211 @t190)) % 28.13/28.34 (step @p236 :rule alpha_equiv :args (@t213 @t211 @t195)) % 28.13/28.34 (step @p237 :rule nary_cong :premises (@p236 @p235) :args (@t214)) % 28.13/28.34 (step @p238 :rule quant-miniscope-and :args ((= (forall @t35 (and @t212 @t209)) @t214))) % 28.13/28.34 (step @p239 :rule trans :premises (@p238 @p237)) % 28.13/28.34 (step @p240 :rule trans :premises (@p239 @p234)) % 28.13/28.34 (step @p241 :rule refl :args (@t62)) % 28.13/28.34 (step @p242 :rule bool-double-not-elim :args (@t64)) % 28.13/28.34 (step @p243 :rule nary_cong :premises (@p242 @p241) :args ((or (not @t65) @t62))) % 28.13/28.34 (step @p244 :rule bool-impl-elim :args (@t65 @t62)) % 28.13/28.34 (step @p245 :rule trans :premises (@p244 @p243)) % 28.13/28.34 (step @p246 :rule bool-impl-elim :args (@t64 @t67)) % 28.13/28.34 (step @p247 :rule nary_cong :premises (@p246 @p245) :args (@t68)) % 28.13/28.34 (step @p248 :rule cong :premises (@p247) :args (@t69)) % 28.13/28.34 (step @p249 :rule trans :premises (@p248 @p240)) % 28.13/28.34 (step @p250 :rule refl :args (@t70)) % 28.13/28.34 (step @p251 :rule cong :premises (@p250 @p249) :args (@t71)) % 28.13/28.34 (step @p252 :rule cong :premises (@p251) :args (@t72)) % 28.13/28.34 (step @p253 :rule trans :premises (@p252 @p226)) % 28.13/28.34 (step @p254 :rule eq_resolve :premises (@p27 @p253)) % 28.13/28.34 (step @p255 :rule bool-eq-true :args (@t230)) % 28.13/28.34 (step @p256 :rule eq-refl :args (@t229)) % 28.13/28.34 (step @p257 :rule refl :args (@t230)) % 28.13/28.34 (step @p258 :rule cong :premises (@p257 @p256) :args ((= @t230 @t231))) % 28.13/28.34 (step @p259 :rule trans :premises (@p258 @p255)) % 28.13/28.34 (step @p260 :rule eq-symm :args (@t231 @t230)) % 28.13/28.34 (step @p261 :rule trans :premises (@p260 @p259)) % 28.13/28.34 (step @p262 :rule refl :args (@t233)) % 28.13/28.34 (step @p263 :rule nary_cong :premises (@p262 @p261) :args (@t234)) % 28.13/28.34 (step @p264 :rule refl :args (@t236)) % 28.13/28.34 (step @p265 :rule nary_cong :premises (@p264 @p263) :args (@t237)) % 28.13/28.34 (step @p266 :rule refl :args (@t239)) % 28.13/28.34 (step @p267 :rule refl :args (@t241)) % 28.13/28.34 (step @p268 :rule nary_cong :premises (@p267 @p266 @p265) :args (@t242)) % 28.13/28.34 (step @p269 :rule refl :args (@t184)) % 28.13/28.34 (step @p270 :rule cong :premises (@p269 @p268) :args ((=> @t184 @t242))) % 28.13/28.34 (assume-push @p504 @t184) % 28.13/28.34 (step @p272 :rule instantiate :premises (@p254) :args ((@list @t228 tptp.empty_set tptp.empty_set @t227 @t229))) % 28.13/28.34 (step-pop @p505 :rule scope :premises (@p272)) % 28.13/28.34 (step @p273 :rule process_scope :premises (@p505) :args (@t242)) % 28.13/28.34 (step @p275 :rule eq_resolve :premises (@p273 @p270)) % 28.13/28.34 (step @p276 :rule implies_elim :premises (@p275)) % 28.13/28.34 (step @p277 :rule chain_m_resolution :premises (@p276 @p254) :args (@t245 @t246 @t247)) % 28.13/28.34 (step @p278 :rule aci_norm :args ((= @t249 @t222))) % 28.13/28.34 (step @p279 :rule cong :premises (@p278) :args (@t250)) % 28.13/28.34 (step @p280 :rule quant-merge-prenex :args ((= (forall @t6 @t252) @t250))) % 28.13/28.34 (step @p281 :rule alpha_equiv :args (@t253 (@list @t215) @t254)) % 28.13/28.34 (step @p282 :rule refl :args (@t219)) % 28.13/28.34 (step @p283 :rule refl :args (@t220)) % 28.13/28.34 (step @p284 :rule refl :args (@t221)) % 28.13/28.34 (step @p285 :rule nary_cong :premises (@p284 @p283 @p282 @p281) :args (@t255)) % 28.13/28.34 (step @p286 :rule quant-miniscope-or :args ((= @t252 @t255))) % 28.13/28.34 (step @p287 :rule trans :premises (@p286 @p285)) % 28.13/28.34 (step @p288 :rule symm :premises (@p287)) % 28.13/28.34 (step @p289 :rule cong :premises (@p288) :args ((forall @t6 @t260))) % 28.13/28.34 (step @p290 :rule trans :premises (@p289 @p280)) % 28.13/28.34 (step @p291 :rule trans :premises (@p290 @p279)) % 28.13/28.34 (step @p292 :rule aci_norm :args ((= (or @t262 @t261) @t260))) % 28.13/28.34 (step @p293 :rule refl :args (@t261)) % 28.13/28.34 (step @p294 :rule bool-and-de-morgan :args (@t24 @t99 true)) % 28.13/28.34 (step @p295 :rule nary_cong :premises (@p294 @p293) :args ((or @t263 @t261))) % 28.13/28.34 (step @p296 :rule trans :premises (@p295 @p292)) % 28.13/28.34 (step @p297 :rule bool-impl-elim :args (@t143 @t261)) % 28.13/28.34 (step @p298 :rule trans :premises (@p297 @p296)) % 28.13/28.34 (step @p299 :rule cong :premises (@p298) :args ((forall @t6 (=> @t143 @t261)))) % 28.13/28.34 (step @p300 :rule trans :premises (@p299 @p291)) % 28.13/28.34 (step @p301 :rule quant-miniscope-or :args ((= (forall @t38 @t264) @t261))) % 28.13/28.34 (step @p302 :rule aci_norm :args ((= @t265 @t264))) % 28.13/28.34 (step @p303 :rule cong :premises (@p302) :args ((forall @t38 @t265))) % 28.13/28.34 (step @p304 :rule trans :premises (@p303 @p301)) % 28.13/28.34 (step @p305 :rule aci_norm :args ((= (or @t266 (or @t219 @t152)) @t265))) % 28.13/28.34 (step @p306 :rule bool-impl-elim :args (@t153 @t152)) % 28.13/28.34 (step @p307 :rule bool-and-de-morgan :args (@t34 @t140 true)) % 28.13/28.34 (step @p308 :rule nary_cong :premises (@p307 @p306) :args ((or @t267 @t154))) % 28.13/28.34 (step @p309 :rule trans :premises (@p308 @p305)) % 28.13/28.34 (step @p310 :rule bool-impl-elim :args (@t141 @t154)) % 28.13/28.34 (step @p311 :rule trans :premises (@p310 @p309)) % 28.13/28.34 (step @p312 :rule cong :premises (@p311) :args (@t155)) % 28.13/28.34 (step @p313 :rule trans :premises (@p312 @p304)) % 28.13/28.34 (step @p314 :rule refl :args (@t143)) % 28.13/28.34 (step @p315 :rule cong :premises (@p314 @p313) :args (@t156)) % 28.13/28.34 (step @p316 :rule cong :premises (@p315) :args (@t157)) % 28.13/28.34 (step @p317 :rule trans :premises (@p316 @p300)) % 28.13/28.34 (step @p318 :rule cong :premises (@p317) :args (@t158)) % 28.13/28.34 (step @p319 :rule eq_resolve :premises (@p134 @p318)) % 28.13/28.34 (step @p320 :rule skolemize :premises (@p319)) % 28.13/28.34 (step @p321 :rule bool-double-not-elim :args (@t238)) % 28.13/28.34 (step @p322 :rule refl :args (@t277)) % 28.13/28.34 (step @p323 :rule nary_cong :premises (@p322 @p321) :args ((or @t277 (not @t239)))) % 28.13/28.34 (step @p324 :rule cnf_or_neg :args (@t277 4)) % 28.13/28.34 (step @p325 :rule eq_resolve :premises (@p324 @p323)) % 28.13/28.34 (step @p326 :rule reordering :premises (@p325) :args ((or @t238 @t277))) % 28.13/28.34 (step @p327 :rule chain_m_resolution :premises (@p326 @p320) :args (@t238 @t278 @t279)) % 28.13/28.34 (step @p328 :rule bool-double-not-elim :args (@t240)) % 28.13/28.34 (step @p329 :rule nary_cong :premises (@p322 @p328) :args ((or @t277 (not @t241)))) % 28.13/28.34 (step @p330 :rule cnf_or_neg :args (@t277 3)) % 28.13/28.34 (step @p331 :rule eq_resolve :premises (@p330 @p329)) % 28.13/28.34 (step @p332 :rule reordering :premises (@p331) :args ((or @t240 @t277))) % 28.13/28.34 (step @p333 :rule chain_m_resolution :premises (@p332 @p320) :args (@t240 @t278 @t279)) % 28.13/28.34 (step @p334 :rule cnf_or_pos :args (@t245)) % 28.13/28.34 (step @p335 :rule reordering :premises (@p334) :args ((or @t241 @t239 @t244 (not @t245)))) % 28.13/28.34 (step @p336 :rule chain_m_resolution :premises (@p335 @p333 @p327 @p277) :args (@t244 @t280 (@list @t240 @t238 @t245))) % 28.13/28.34 (step @p337 :rule cnf_and_pos :args (@t244 1)) % 28.13/28.34 (step @p338 :rule reordering :premises (@p337) :args ((or @t243 (not @t244)))) % 28.13/28.34 (step @p339 :rule chain_m_resolution :premises (@p338 @p336) :args (@t243 @t246 (@list @t244))) % 28.13/28.34 (step @p340 :rule aci_norm :args ((= @t286 (or @t221 @t220 @t284 @t283 @t282)))) % 28.13/28.34 (step @p341 :rule cong :premises (@p340) :args (@t287)) % 28.13/28.34 (step @p342 :rule quant-merge-prenex :args ((= (forall @t6 @t289) @t287))) % 28.13/28.34 (step @p343 :rule alpha_equiv :args (@t290 (@list @t281) @t254)) % 28.13/28.34 (step @p344 :rule nary_cong :premises (@p284 @p283 @p343) :args (@t291)) % 28.13/28.34 (step @p345 :rule quant-miniscope-or :args ((= @t289 @t291))) % 28.13/28.34 (step @p346 :rule trans :premises (@p345 @p344)) % 28.13/28.34 (step @p347 :rule symm :premises (@p346)) % 28.13/28.34 (step @p348 :rule cong :premises (@p347) :args ((forall @t6 @t294))) % 28.13/28.34 (step @p349 :rule trans :premises (@p348 @p342)) % 28.13/28.34 (step @p350 :rule trans :premises (@p349 @p341)) % 28.13/28.34 (step @p351 :rule aci_norm :args ((= (or @t262 @t293) @t294))) % 28.13/28.34 (step @p352 :rule refl :args (@t293)) % 28.13/28.34 (step @p353 :rule nary_cong :premises (@p294 @p352) :args ((or @t263 @t293))) % 28.13/28.34 (step @p354 :rule trans :premises (@p353 @p351)) % 28.13/28.34 (step @p355 :rule bool-impl-elim :args (@t143 @t293)) % 28.13/28.34 (step @p356 :rule trans :premises (@p355 @p354)) % 28.13/28.34 (step @p357 :rule cong :premises (@p356) :args ((forall @t6 (=> @t143 @t293)))) % 28.13/28.34 (step @p358 :rule trans :premises (@p357 @p350)) % 28.13/28.34 (step @p359 :rule aci_norm :args ((= (or @t266 @t139) @t292))) % 28.13/28.34 (step @p360 :rule refl :args (@t139)) % 28.13/28.34 (step @p361 :rule nary_cong :premises (@p307 @p360) :args ((or @t267 @t139))) % 28.13/28.34 (step @p362 :rule trans :premises (@p361 @p359)) % 28.13/28.34 (step @p363 :rule bool-impl-elim :args (@t141 @t139)) % 28.13/28.34 (step @p364 :rule trans :premises (@p363 @p362)) % 28.13/28.34 (step @p365 :rule cong :premises (@p364) :args (@t142)) % 28.13/28.34 (step @p366 :rule cong :premises (@p314 @p365) :args (@t144)) % 28.13/28.34 (step @p367 :rule cong :premises (@p366) :args (@t145)) % 28.13/28.34 (step @p368 :rule trans :premises (@p367 @p358)) % 28.13/28.34 (step @p369 :rule eq_resolve :premises (@p131 @p368)) % 28.13/28.34 (step @p370 :rule instantiate :premises (@p369) :args (@t295)) % 28.13/28.34 (step @p371 :rule bool-double-not-elim :args (@t273)) % 28.13/28.34 (step @p372 :rule nary_cong :premises (@p322 @p371) :args ((or @t277 (not @t274)))) % 28.13/28.34 (step @p373 :rule cnf_or_neg :args (@t277 1)) % 28.13/28.34 (step @p374 :rule eq_resolve :premises (@p373 @p372)) % 28.13/28.34 (step @p375 :rule reordering :premises (@p374) :args ((or @t273 @t277))) % 28.13/28.34 (step @p376 :rule chain_m_resolution :premises (@p375 @p320) :args (@t273 @t278 @t279)) % 28.13/28.34 (step @p377 :rule bool-double-not-elim :args (@t275)) % 28.13/28.34 (step @p378 :rule nary_cong :premises (@p322 @p377) :args ((or @t277 (not @t276)))) % 28.13/28.34 (step @p379 :rule cnf_or_neg :args (@t277 0)) % 28.13/28.34 (step @p380 :rule eq_resolve :premises (@p379 @p378)) % 28.13/28.34 (step @p381 :rule reordering :premises (@p380) :args ((or @t275 @t277))) % 28.13/28.34 (step @p382 :rule chain_m_resolution :premises (@p381 @p320) :args (@t275 @t278 @t279)) % 28.13/28.34 (step @p383 :rule cnf_or_pos :args (@t300)) % 28.13/28.34 (step @p384 :rule reordering :premises (@p383) :args ((or @t276 @t274 @t241 @t239 @t299 (not @t300)))) % 28.13/28.34 (step @p385 :rule chain_m_resolution :premises (@p384 @p382 @p376 @p333 @p327 @p370) :args (@t299 @t301 (@list @t275 @t273 @t240 @t238 @t300))) % 28.13/28.34 (step @p386 :rule aci_norm :args ((= @t309 (or @t221 @t220 @t307 @t306 @t305 @t304)))) % 28.13/28.34 (step @p387 :rule cong :premises (@p386) :args (@t310)) % 28.13/28.34 (step @p388 :rule quant-merge-prenex :args ((= (forall @t6 @t312) @t310))) % 28.13/28.34 (step @p389 :rule alpha_equiv :args (@t313 (@list @t302) @t254)) % 28.13/28.34 (step @p390 :rule nary_cong :premises (@p284 @p283 @p389) :args (@t314)) % 28.13/28.34 (step @p391 :rule quant-miniscope-or :args ((= @t312 @t314))) % 28.13/28.34 (step @p392 :rule trans :premises (@p391 @p390)) % 28.13/28.34 (step @p393 :rule symm :premises (@p392)) % 28.13/28.34 (step @p394 :rule cong :premises (@p393) :args ((forall @t6 @t318))) % 28.13/28.34 (step @p395 :rule trans :premises (@p394 @p388)) % 28.13/28.34 (step @p396 :rule trans :premises (@p395 @p387)) % 28.13/28.34 (step @p397 :rule aci_norm :args ((= (or @t262 @t317) @t318))) % 28.13/28.34 (step @p398 :rule refl :args (@t317)) % 28.13/28.34 (step @p399 :rule nary_cong :premises (@p294 @p398) :args ((or @t263 @t317))) % 28.13/28.34 (step @p400 :rule trans :premises (@p399 @p397)) % 28.13/28.34 (step @p401 :rule bool-impl-elim :args (@t143 @t317)) % 28.13/28.34 (step @p402 :rule trans :premises (@p401 @p400)) % 28.13/28.34 (step @p403 :rule cong :premises (@p402) :args ((forall @t6 (=> @t143 @t317)))) % 28.13/28.34 (step @p404 :rule trans :premises (@p403 @p396)) % 28.13/28.34 (step @p405 :rule aci_norm :args ((= (or @t266 (or @t315 @t146)) @t316))) % 28.13/28.34 (step @p406 :rule bool-impl-elim :args (@t138 @t146)) % 28.13/28.34 (step @p407 :rule nary_cong :premises (@p307 @p406) :args ((or @t267 @t147))) % 28.13/28.34 (step @p408 :rule trans :premises (@p407 @p405)) % 28.13/28.34 (step @p409 :rule bool-impl-elim :args (@t141 @t147)) % 28.13/28.34 (step @p410 :rule trans :premises (@p409 @p408)) % 28.13/28.34 (step @p411 :rule cong :premises (@p410) :args (@t148)) % 28.13/28.34 (step @p412 :rule cong :premises (@p314 @p411) :args (@t149)) % 28.13/28.34 (step @p413 :rule cong :premises (@p412) :args (@t150)) % 28.13/28.34 (step @p414 :rule trans :premises (@p413 @p404)) % 28.13/28.34 (step @p415 :rule eq_resolve :premises (@p133 @p414)) % 28.13/28.34 (step @p416 :rule instantiate :premises (@p415) :args (@t295)) % 28.13/28.34 (step @p417 :rule cnf_or_neg :args (@t277 5)) % 28.13/28.34 (step @p418 :rule chain_m_resolution :premises (@p417 @p320) :args ((not @t270) @t278 @t279)) % 28.13/28.34 (step @p419 :rule cnf_or_pos :args (@t320)) % 28.13/28.34 (step @p420 :rule reordering :premises (@p419) :args ((or @t276 @t274 @t241 @t239 @t270 @t319 (not @t320)))) % 28.13/28.34 (step @p421 :rule chain_m_resolution :premises (@p420 @p382 @p376 @p333 @p327 @p418 @p416) :args (@t319 (@list false false false false true false) (@list @t275 @t273 @t240 @t238 @t270 @t320))) % 28.13/28.34 (step @p422 :rule cnf_equiv_pos2 :args (@t299)) % 28.13/28.34 (step @p423 :rule reordering :premises (@p422) :args ((or @t298 @t321 (not @t299)))) % 28.13/28.34 (step @p424 :rule chain_m_resolution :premises (@p423 @p421 @p385) :args (@t321 @t322 (@list @t298 @t299))) % 28.13/28.34 (step @p425 :rule bool-double-not-elim :args (@t271)) % 28.13/28.34 (step @p426 :rule nary_cong :premises (@p322 @p425) :args ((or @t277 (not @t272)))) % 28.13/28.34 (step @p427 :rule cnf_or_neg :args (@t277 2)) % 28.13/28.34 (step @p428 :rule eq_resolve :premises (@p427 @p426)) % 28.13/28.34 (step @p429 :rule reordering :premises (@p428) :args ((or @t271 @t277))) % 28.13/28.34 (step @p430 :rule chain_m_resolution :premises (@p429 @p320) :args (@t271 @t278 @t279)) % 28.13/28.34 (step @p431 :rule cnf_and_neg :args (@t296)) % 28.13/28.34 (step @p432 :rule reordering :premises (@p431) :args ((or @t272 @t296 @t323))) % 28.13/28.34 (step @p433 :rule chain_m_resolution :premises (@p432 @p430 @p424) :args (@t323 (@list false true) (@list @t271 @t296))) % 28.13/28.34 (step @p434 :rule cnf_or_pos :args (@t243)) % 28.13/28.34 (step @p435 :rule reordering :premises (@p434) :args ((or @t230 @t233 (not @t243)))) % 28.13/28.34 (step @p436 :rule chain_m_resolution :premises (@p435 @p433 @p339) :args (@t230 @t322 (@list @t233 @t243))) % 28.13/28.34 (step @p437 :rule symm :premises (@p436)) % 28.13/28.34 (step @p438 :rule trans :premises (@p437 @p199)) % 28.13/28.34 (step @p439 :rule symm :premises (@p438)) % 28.13/28.34 (step @p440 :rule bool-eq-true :args (@t324)) % 28.13/28.34 (step @p441 :rule eq-refl :args (@t269)) % 28.13/28.34 (step @p442 :rule refl :args (@t324)) % 28.13/28.34 (step @p443 :rule cong :premises (@p442 @p441) :args ((= @t324 @t325))) % 28.13/28.34 (step @p444 :rule trans :premises (@p443 @p440)) % 28.13/28.34 (step @p445 :rule eq-symm :args (@t325 @t324)) % 28.13/28.34 (step @p446 :rule trans :premises (@p445 @p444)) % 28.13/28.34 (step @p447 :rule refl :args (@t298)) % 28.13/28.34 (step @p448 :rule nary_cong :premises (@p447 @p446) :args (@t326)) % 28.13/28.34 (step @p449 :rule refl :args (@t327)) % 28.13/28.34 (step @p450 :rule nary_cong :premises (@p449 @p448) :args (@t328)) % 28.13/28.34 (step @p451 :rule refl :args (@t330)) % 28.13/28.34 (step @p452 :rule refl :args (@t332)) % 28.13/28.34 (step @p453 :rule nary_cong :premises (@p452 @p451 @p450) :args (@t333)) % 28.13/28.34 (step @p454 :rule cong :premises (@p269 @p453) :args ((=> @t184 @t333))) % 28.13/28.34 (assume-push @p506 @t184) % 28.13/28.34 (step @p456 :rule instantiate :premises (@p254) :args ((@list @t268 tptp.empty_set tptp.empty_set @t225 @t269))) % 28.13/28.34 (step-pop @p507 :rule scope :premises (@p456)) % 28.13/28.34 (step @p457 :rule process_scope :premises (@p507) :args (@t333)) % 28.13/28.34 (step @p459 :rule eq_resolve :premises (@p457 @p454)) % 28.13/28.34 (step @p460 :rule implies_elim :premises (@p459)) % 28.13/28.34 (step @p461 :rule chain_m_resolution :premises (@p460 @p254) :args (@t336 @t246 @t247)) % 28.13/28.34 (step @p462 :rule aci_norm :args ((= (or @t337 @t98) (or @t182 @t181 @t221 @t220 @t98)))) % 28.13/28.34 (step @p463 :rule refl :args (@t98)) % 28.13/28.34 (step @p464 :rule aci_norm :args ((= (or @t182 (or @t181 @t262)) @t337))) % 28.13/28.34 (step @p465 :rule nary_cong :premises (@p210 @p294) :args ((or @t181 @t263))) % 28.13/28.34 (step @p466 :rule bool-and-de-morgan :args (@t9 @t24 (and @t99))) % 28.13/28.34 (step @p467 :rule trans :premises (@p466 @p465)) % 28.13/28.34 (step @p468 :rule nary_cong :premises (@p211 @p467) :args ((or @t182 (not (and @t9 @t24 @t99))))) % 28.13/28.34 (step @p469 :rule bool-and-de-morgan :args (@t12 @t9 (and @t24 @t99))) % 28.13/28.34 (step @p470 :rule trans :premises (@p469 @p468)) % 28.13/28.34 (step @p471 :rule trans :premises (@p470 @p464)) % 28.13/28.34 (step @p472 :rule nary_cong :premises (@p471 @p463) :args ((or (not @t100) @t98))) % 28.13/28.34 (step @p473 :rule trans :premises (@p472 @p462)) % 28.13/28.34 (step @p474 :rule bool-impl-elim :args (@t100 @t98)) % 28.13/28.34 (step @p475 :rule trans :premises (@p474 @p473)) % 28.13/28.34 (step @p476 :rule cong :premises (@p475) :args (@t101)) % 28.13/28.34 (step @p477 :rule eq_resolve :premises (@p56 @p476)) % 28.13/28.34 (step @p478 :rule instantiate :premises (@p477) :args ((@list @t226 @t228))) % 28.13/28.34 (step @p479 :rule cnf_or_pos :args (@t339)) % 28.13/28.34 (step @p480 :rule reordering :premises (@p479) :args ((or @t276 @t274 @t241 @t239 @t338 (not @t339)))) % 28.13/28.34 (step @p481 :rule chain_m_resolution :premises (@p480 @p382 @p376 @p333 @p327 @p478) :args (@t338 @t301 (@list @t275 @t273 @t240 @t238 @t339))) % 28.13/28.34 (step @p482 :rule cnf_and_pos :args (@t338 1)) % 28.13/28.34 (step @p483 :rule reordering :premises (@p482) :args ((or @t329 @t340))) % 28.13/28.34 (step @p484 :rule chain_m_resolution :premises (@p483 @p481) :args (@t329 @t246 @t341)) % 28.13/28.34 (step @p485 :rule cnf_and_pos :args (@t338 0)) % 28.13/28.34 (step @p486 :rule reordering :premises (@p485) :args ((or @t331 @t340))) % 28.13/28.34 (step @p487 :rule chain_m_resolution :premises (@p486 @p481) :args (@t331 @t246 @t341)) % 28.13/28.34 (step @p488 :rule cnf_or_pos :args (@t336)) % 28.13/28.34 (step @p489 :rule reordering :premises (@p488) :args ((or @t332 @t330 @t335 (not @t336)))) % 28.13/28.34 (step @p490 :rule chain_m_resolution :premises (@p489 @p487 @p484 @p461) :args (@t335 @t280 (@list @t331 @t329 @t336))) % 28.13/28.34 (step @p491 :rule cnf_and_pos :args (@t335 1)) % 28.13/28.34 (step @p492 :rule reordering :premises (@p491) :args ((or @t334 (not @t335)))) % 28.13/28.35 (step @p493 :rule chain_m_resolution :premises (@p492 @p490) :args (@t334 @t246 (@list @t335))) % 28.13/28.35 (step @p494 :rule cnf_or_pos :args (@t334)) % 28.13/28.35 (step @p495 :rule reordering :premises (@p494) :args ((or @t324 @t298 (not @t334)))) % 28.13/28.35 (step @p496 :rule chain_m_resolution :premises (@p495 @p421 @p493) :args (@t324 @t322 (@list @t298 @t334))) % 28.13/28.35 (step @p497 :rule symm :premises (@p496)) % 28.13/28.35 (step @p498 :rule trans :premises (@p497 @p199 @p439)) % 28.13/28.35 (step @p499 :rule true_intro :premises (@p498)) % 28.13/28.35 (step @p500 :rule false_intro :premises (@p418)) % 28.13/28.35 (step @p501 :rule symm :premises (@p500)) % 28.13/28.35 (step @p502 :rule trans :premises (@p501 @p499)) % 28.13/28.35 (step @p503 false :rule eq_resolve :premises (@p502 @p197)) % 28.13/28.35 ) % 28.13/28.35 % SZS output end Proof % 28.13/28.35 % cvc5 exiting %------------------------------------------------------------------------------