%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU217+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 : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:59 AM UTC 2026 % Result : Theorem 18.22s 18.45s % Output : Proof 18.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU217+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 % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:41:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 18.22/18.45 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 18.22/18.45 --- Run --no-e-matching --full-saturate-quant at 6... % 18.22/18.45 % SZS status Theorem % 18.22/18.45 % SZS output start Proof % 18.22/18.45 ( % 18.22/18.45 (declare-sort $$unsorted 0) % 18.22/18.45 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.empty (-> $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation (-> $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.empty_set $$unsorted) % 18.22/18.45 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.function (-> $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 18.22/18.45 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 18.22/18.45 (define @t1 () (@var "A" $$unsorted)) % 18.22/18.45 (define @t2 () (@var "B" $$unsorted)) % 18.22/18.45 (define @t3 () (tptp.in @t2 @t1)) % 18.22/18.45 (define @t4 () (not @t3)) % 18.22/18.45 (define @t5 () (tptp.in @t1 @t2)) % 18.22/18.45 (define @t6 () (@list @t1 @t2)) % 18.22/18.45 (define @t7 () (tptp.proper_subset @t2 @t1)) % 18.22/18.45 (define @t8 () (tptp.proper_subset @t1 @t2)) % 18.22/18.45 (define @t9 () (tptp.function @t1)) % 18.22/18.45 (define @t10 () (tptp.empty @t1)) % 18.22/18.45 (define @t11 () (@list @t1)) % 18.22/18.45 (define @t12 () (tptp.relation @t1)) % 18.22/18.45 (define @t13 () (tptp.unordered_pair @t1 @t2)) % 18.22/18.45 (define @t14 () (tptp.set_union2 @t2 @t1)) % 18.22/18.45 (define @t15 () (tptp.set_union2 @t1 @t2)) % 18.22/18.45 (define @t16 () (tptp.set_intersection2 @t1 @t2)) % 18.22/18.45 (define @t17 () (@var "D" $$unsorted)) % 18.22/18.45 (define @t18 () (@var "C" $$unsorted)) % 18.22/18.45 (define @t19 () (tptp.in @t18 @t1)) % 18.22/18.45 (define @t20 () (tptp.ordered_pair @t18 @t17)) % 18.22/18.45 (define @t21 () (tptp.in @t20 @t2)) % 18.22/18.45 (define @t22 () (@list @t18 @t17)) % 18.22/18.45 (define @t23 () (tptp.identity_relation @t1)) % 18.22/18.45 (define @t24 () (= @t2 @t23)) % 18.22/18.45 (define @t25 () (tptp.relation @t2)) % 18.22/18.45 (define @t26 () (tptp.subset @t1 @t2)) % 18.22/18.45 (define @t27 () (= @t1 @t2)) % 18.22/18.45 (define @t28 () (@var "E" $$unsorted)) % 18.22/18.45 (define @t29 () (tptp.ordered_pair @t17 @t28)) % 18.22/18.45 (define @t30 () (tptp.in @t29 @t1)) % 18.22/18.45 (define @t31 () (tptp.in @t17 @t2)) % 18.22/18.45 (define @t32 () (tptp.in @t29 @t18)) % 18.22/18.45 (define @t33 () (@list @t17 @t28)) % 18.22/18.45 (define @t34 () (tptp.relation_dom_restriction @t1 @t2)) % 18.22/18.45 (define @t35 () (tptp.relation @t18)) % 18.22/18.45 (define @t36 () (@list @t2 @t18)) % 18.22/18.45 (define @t37 () (tptp.in @t28 @t1)) % 18.22/18.45 (define @t38 () (tptp.relation_rng_restriction @t1 @t2)) % 18.22/18.45 (define @t39 () (@list @t18)) % 18.22/18.45 (define @t40 () (tptp.in @t28 @t2)) % 18.22/18.45 (define @t41 () (@list @t28)) % 18.22/18.45 (define @t42 () (tptp.in @t17 @t18)) % 18.22/18.45 (define @t43 () (@list @t17)) % 18.22/18.45 (define @t44 () (@list @t2)) % 18.22/18.45 (define @t45 () (= @t2 tptp.empty_set)) % 18.22/18.45 (define @t46 () (= @t2 (tptp.set_meet @t1))) % 18.22/18.45 (define @t47 () (= @t1 tptp.empty_set)) % 18.22/18.45 (define @t48 () (tptp.in @t18 @t17)) % 18.22/18.45 (define @t49 () (tptp.in @t17 @t1)) % 18.22/18.45 (define @t50 () (tptp.in @t18 @t2)) % 18.22/18.45 (define @t51 () (not @t47)) % 18.22/18.45 (define @t52 () (tptp.singleton @t1)) % 18.22/18.45 (define @t53 () (tptp.powerset @t1)) % 18.22/18.45 (define @t54 () (tptp.in @t20 @t1)) % 18.22/18.45 (define @t55 () (tptp.empty @t2)) % 18.22/18.45 (define @t56 () (tptp.element @t2 @t1)) % 18.22/18.45 (define @t57 () (not @t10)) % 18.22/18.45 (define @t58 () (@list @t1 @t2 @t18)) % 18.22/18.45 (define @t59 () (@var "F" $$unsorted)) % 18.22/18.45 (define @t60 () (tptp.cartesian_product2 @t1 @t2)) % 18.22/18.45 (define @t61 () (forall @t39 (=> @t19 @t50))) % 18.22/18.45 (define @t62 () (= @t18 (tptp.apply @t1 @t2))) % 18.22/18.45 (define @t63 () (tptp.relation_dom @t1)) % 18.22/18.45 (define @t64 () (tptp.in @t2 @t63)) % 18.22/18.45 (define @t65 () (tptp.in (tptp.ordered_pair @t2 @t18) @t1)) % 18.22/18.45 (define @t66 () (and @t12 @t9)) % 18.22/18.45 (define @t67 () (tptp.cast_to_subset @t1)) % 18.22/18.45 (define @t68 () (tptp.set_difference @t1 @t2)) % 18.22/18.45 (define @t69 () (tptp.in (tptp.ordered_pair @t17 @t18) @t1)) % 18.22/18.45 (define @t70 () (tptp.relation_rng @t1)) % 18.22/18.45 (define @t71 () (tptp.subset_complement @t1 @t2)) % 18.22/18.45 (define @t72 () (tptp.element @t2 @t53)) % 18.22/18.45 (define @t73 () (tptp.ordered_pair @t1 @t2)) % 18.22/18.45 (define @t74 () (tptp.relation_inverse @t1)) % 18.22/18.45 (define @t75 () (tptp.disjoint @t1 @t2)) % 18.22/18.45 (define @t76 () (tptp.relation_composition @t1 @t2)) % 18.22/18.45 (define @t77 () (tptp.complements_of_subsets @t1 @t2)) % 18.22/18.45 (define @t78 () (tptp.powerset @t53)) % 18.22/18.45 (define @t79 () (tptp.element @t2 @t78)) % 18.22/18.45 (define @t80 () (not @t27)) % 18.22/18.45 (define @t81 () (tptp.relation @t76)) % 18.22/18.45 (define @t82 () (and @t12 @t25)) % 18.22/18.45 (define @t83 () (tptp.union_of_subsets @t1 @t2)) % 18.22/18.45 (define @t84 () (tptp.relation @t23)) % 18.22/18.45 (define @t85 () (forall @t11 @t84)) % 18.22/18.45 (define @t86 () (tptp.meet_of_subsets @t1 @t2)) % 18.22/18.45 (define @t87 () (tptp.subset_difference @t1 @t2 @t18)) % 18.22/18.45 (define @t88 () (tptp.element @t18 @t53)) % 18.22/18.45 (define @t89 () (and @t72 @t88)) % 18.22/18.45 (define @t90 () (tptp.relation_composition @t2 @t1)) % 18.22/18.45 (define @t91 () (and @t10 @t25)) % 18.22/18.45 (define @t92 () (tptp.relation tptp.empty_set)) % 18.22/18.45 (define @t93 () (tptp.empty tptp.empty_set)) % 18.22/18.45 (define @t94 () (tptp.function @t2)) % 18.22/18.45 (define @t95 () (tptp.function @t23)) % 18.22/18.45 (define @t96 () (forall @t11 (and @t84 @t95))) % 18.22/18.45 (define @t97 () (not @t55)) % 18.22/18.45 (define @t98 () (tptp.empty @t63)) % 18.22/18.45 (define @t99 () (and @t57 @t12)) % 18.22/18.45 (define @t100 () (tptp.empty @t70)) % 18.22/18.45 (define @t101 () (tptp.disjoint @t52 @t2)) % 18.22/18.45 (define @t102 () (tptp.singleton @t2)) % 18.22/18.45 (define @t103 () (tptp.union @t2)) % 18.22/18.45 (define @t104 () (tptp.in @t1 @t18)) % 18.22/18.45 (define @t105 () (@list @t1 @t2 @t18 @t17)) % 18.22/18.45 (define @t106 () (tptp.element @t1 (tptp.powerset @t2))) % 18.22/18.45 (define @t107 () (tptp.set_difference @t2 @t18)) % 18.22/18.45 (define @t108 () (= @t1 @t18)) % 18.22/18.45 (define @t109 () (tptp.relation_rng @t18)) % 18.22/18.45 (define @t110 () (tptp.relation_rng @t38)) % 18.22/18.45 (define @t111 () (tptp.relation_rng @t2)) % 18.22/18.45 (define @t112 () (tptp.cartesian_product2 @t1 @t18)) % 18.22/18.45 (define @t113 () (not @t50)) % 18.22/18.45 (define @t114 () (tptp.subset @t18 @t2)) % 18.22/18.45 (define @t115 () (forall @t39 (not (and @t114 (not (tptp.are_equipotent @t18 @t2)) @t113)))) % 18.22/18.45 (define @t116 () (tptp.powerset @t18)) % 18.22/18.45 (define @t117 () (forall @t22 (=> (and @t50 (tptp.subset @t17 @t18)) @t31))) % 18.22/18.45 (define @t118 () (tptp.relation_dom_restriction @t18 @t2)) % 18.22/18.45 (define @t119 () (tptp.relation_dom @t18)) % 18.22/18.45 (define @t120 () (tptp.relation_image @t2 @t1)) % 18.22/18.45 (define @t121 () (tptp.relation_dom @t2)) % 18.22/18.45 (define @t122 () (tptp.set_intersection2 @t121 @t1)) % 18.22/18.45 (define @t123 () (tptp.relation_rng @t76)) % 18.22/18.45 (define @t124 () (tptp.relation_inverse_image @t18 @t2)) % 18.22/18.45 (define @t125 () (tptp.relation_inverse_image @t2 @t1)) % 18.22/18.45 (define @t126 () (tptp.set_intersection2 @t2 @t18)) % 18.22/18.45 (define @t127 () (tptp.subset @t1 @t18)) % 18.22/18.45 (define @t128 () (tptp.element @t1 @t2)) % 18.22/18.45 (define @t129 () (tptp.in @t1 @t119)) % 18.22/18.45 (define @t130 () (tptp.in @t73 @t18)) % 18.22/18.45 (define @t131 () (tptp.apply @t18 @t1)) % 18.22/18.45 (define @t132 () (tptp.relation_composition @t18 @t2)) % 18.22/18.45 (define @t133 () (tptp.in @t1 (tptp.relation_dom @t132))) % 18.22/18.45 (define @t134 () (and @t35 (tptp.function @t18))) % 18.22/18.45 (define @t135 () (and @t25 @t94)) % 18.22/18.45 (define @t136 () (tptp.relation_field @t18)) % 18.22/18.45 (define @t137 () (tptp.apply @t2 @t18)) % 18.22/18.45 (define @t138 () (=> @t19 (= @t137 @t18))) % 18.22/18.45 (define @t139 () (forall @t39 @t138)) % 18.22/18.45 (define @t140 () (and (= @t121 @t1) @t139)) % 18.22/18.45 (define @t141 () (= @t24 @t140)) % 18.22/18.45 (define @t142 () (=> @t135 @t141)) % 18.22/18.45 (define @t143 () (forall @t6 @t142)) % 18.22/18.45 (define @t144 () (tptp.apply @t23 @t2)) % 18.22/18.45 (define @t145 () (=> @t3 (= @t144 @t2))) % 18.22/18.45 (define @t146 () (forall @t6 @t145)) % 18.22/18.45 (define @t147 () (not @t146)) % 18.22/18.45 (define @t148 () (tptp.in @t2 @t18)) % 18.22/18.45 (define @t149 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 18.22/18.45 (define @t150 () (and @t19 @t50)) % 18.22/18.45 (define @t151 () (not @t75)) % 18.22/18.45 (define @t152 () (tptp.subset_complement @t1 @t18)) % 18.22/18.45 (define @t153 () (tptp.disjoint @t2 @t18)) % 18.22/18.45 (define @t154 () (tptp.relation_dom @t76)) % 18.22/18.45 (define @t155 () (not @t45)) % 18.22/18.45 (define @t156 () (tptp.element @t2 @t116)) % 18.22/18.45 (define @t157 () (tptp.in @t18 @t16)) % 18.22/18.45 (define @t158 () (= @t70 tptp.empty_set)) % 18.22/18.45 (define @t159 () (= @t63 tptp.empty_set)) % 18.22/18.45 (define @t160 () (tptp.relation_dom_restriction @t2 @t1)) % 18.22/18.45 (define @t161 () (= @t52 (tptp.unordered_pair @t2 @t18))) % 18.22/18.45 (define @t162 () (= @t2 @t144)) % 18.22/18.45 (define @t163 () (= @t18 @t137)) % 18.22/18.45 (define @t164 () (= @t24 (and (= @t1 @t121) (forall @t39 (or (not @t19) @t163))))) % 18.22/18.45 (define @t165 () (not @t94)) % 18.22/18.45 (define @t166 () (not @t25)) % 18.22/18.45 (define @t167 () (or @t166 @t165 @t164)) % 18.22/18.45 (define @t168 () (forall @t6 (or @t4 @t162))) % 18.22/18.45 (define @t169 () (@quantifiers_skolemize @t168 0)) % 18.22/18.45 (define @t170 () (tptp.identity_relation @t169)) % 18.22/18.45 (define @t171 () (forall @t39 (or (not (tptp.in @t18 @t169)) (= @t18 (tptp.apply @t170 @t18))))) % 18.22/18.45 (define @t172 () (and (= @t169 (tptp.relation_dom @t170)) @t171)) % 18.22/18.45 (define @t173 () (= (= @t170 @t170) @t172)) % 18.22/18.45 (define @t174 () (tptp.function @t170)) % 18.22/18.45 (define @t175 () (not @t174)) % 18.22/18.45 (define @t176 () (tptp.relation @t170)) % 18.22/18.45 (define @t177 () (not @t176)) % 18.22/18.45 (define @t178 () (or @t177 @t175 @t173)) % 18.22/18.45 (define @t179 () (forall @t6 @t167)) % 18.22/18.45 (define @t180 () (or @t177 @t175 @t172)) % 18.22/18.45 (define @t181 () (@list false)) % 18.22/18.45 (define @t182 () (@list @t169)) % 18.22/18.45 (define @t183 () (forall @t11 @t95)) % 18.22/18.45 (define @t184 () (@list @t1)) % 18.22/18.45 (define @t185 () (and @t85 @t183)) % 18.22/18.45 (define @t186 () (@quantifiers_skolemize @t168 1)) % 18.22/18.45 (define @t187 () (or (not (tptp.in @t186 @t169)) (= @t186 (tptp.apply @t170 @t186)))) % 18.22/18.45 (assume @p1 (forall @t6 (=> @t5 @t4))) % 18.22/18.45 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 18.22/18.45 (assume @p3 (forall @t11 (=> @t10 @t9))) % 18.22/18.45 (assume @p4 (forall @t11 (=> @t10 @t12))) % 18.22/18.45 (assume @p5 (forall @t6 (= @t13 (tptp.unordered_pair @t2 @t1)))) % 18.22/18.45 (assume @p6 (forall @t6 (= @t15 @t14))) % 18.22/18.45 (assume @p7 (forall @t6 (= @t16 (tptp.set_intersection2 @t2 @t1)))) % 18.22/18.45 (assume @p8 (forall @t6 (=> @t25 (= @t24 (forall @t22 (= @t21 (and @t19 (= @t18 @t17)))))))) % 18.22/18.45 (assume @p9 (forall @t6 (= @t27 (and @t26 (tptp.subset @t2 @t1))))) % 18.22/18.45 (assume @p10 (forall @t11 (=> @t12 (forall @t36 (=> @t35 (= (= @t18 @t34) (forall @t33 (= @t32 (and @t31 @t30))))))))) % 18.22/18.45 (assume @p11 (forall @t6 (=> @t25 (forall @t39 (=> @t35 (= (= @t18 @t38) (forall @t33 (= @t32 (and @t37 (tptp.in @t29 @t2)))))))))) % 18.22/18.45 (assume @p12 (forall @t11 (=> @t12 (forall @t36 (= (= @t18 (tptp.relation_image @t1 @t2)) (forall @t43 (= @t42 (exists @t41 (and (tptp.in (tptp.ordered_pair @t28 @t17) @t1) @t40))))))))) % 18.22/18.45 (assume @p13 (forall @t11 (=> @t12 (forall @t36 (= (= @t18 (tptp.relation_inverse_image @t1 @t2)) (forall @t43 (= @t42 (exists @t41 (and @t30 @t40))))))))) % 18.22/18.45 (assume @p14 (forall @t11 (= @t12 (forall @t44 (not (and @t3 (forall @t22 (not (= @t2 @t20))))))))) % 18.22/18.45 (assume @p15 (forall @t6 (and (=> @t51 (= @t46 (forall @t39 (= @t50 (forall @t43 (=> @t49 @t48)))))) (=> @t47 (= @t46 @t45))))) % 18.22/18.45 (assume @p16 (forall @t6 (= (= @t2 @t52) (forall @t39 (= @t50 (= @t18 @t1)))))) % 18.22/18.45 (assume @p17 (forall @t11 (= @t47 (forall @t44 @t4)))) % 18.22/18.45 (assume @p18 (forall @t6 (= (= @t2 @t53) (forall @t39 (= @t50 (tptp.subset @t18 @t1)))))) % 18.22/18.45 (assume @p19 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (= @t27 (forall @t22 (= @t54 @t21)))))))) % 18.22/18.45 (assume @p20 (forall @t6 (and (=> @t57 (= @t56 @t3)) (=> @t10 (= @t56 @t55))))) % 18.22/18.45 (assume @p21 (forall @t58 (= (= @t18 @t13) (forall @t43 (= @t42 (or (= @t17 @t1) (= @t17 @t2))))))) % 18.22/18.45 (assume @p22 (forall @t58 (= (= @t18 @t15) (forall @t43 (= @t42 (or @t49 @t31)))))) % 18.22/18.45 (assume @p23 (forall @t58 (= (= @t18 @t60) (forall @t43 (= @t42 (exists (@list @t28 @t59) (and @t37 (tptp.in @t59 @t2) (= @t17 (tptp.ordered_pair @t28 @t59))))))))) % 18.22/18.45 (assume @p24 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (= @t26 (forall @t22 (=> @t54 @t21)))))))) % 18.22/18.45 (assume @p25 (forall @t6 (= @t26 @t61))) % 18.22/18.45 (assume @p26 (forall @t58 (= (= @t18 @t16) (forall @t43 (= @t42 (and @t49 @t31)))))) % 18.22/18.45 (assume @p27 (forall @t11 (=> @t66 (forall @t36 (and (=> @t64 (= @t62 @t65)) (=> (not @t64) (= @t62 (= @t18 tptp.empty_set)))))))) % 18.22/18.45 (assume @p28 (forall @t11 (=> @t12 (forall @t44 (= (= @t2 @t63) (forall @t39 (= @t50 (exists @t43 @t54)))))))) % 18.22/18.45 (assume @p29 (forall @t11 (= @t67 @t1))) % 18.22/18.45 (assume @p30 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t39 (= @t50 (exists @t43 (and @t48 @t49))))))) % 18.22/18.45 (assume @p31 (forall @t58 (= (= @t18 @t68) (forall @t43 (= @t42 (and @t49 (not @t31))))))) % 18.22/18.45 (assume @p32 (forall @t11 (=> @t12 (forall @t44 (= (= @t2 @t70) (forall @t39 (= @t50 (exists @t43 @t69)))))))) % 18.22/18.45 (assume @p33 (forall @t6 (=> @t72 (= @t71 @t68)))) % 18.22/18.45 (assume @p34 (forall @t6 (= @t73 (tptp.unordered_pair @t13 @t52)))) % 18.22/18.45 (assume @p35 (forall @t11 (=> @t12 (= (tptp.relation_field @t1) (tptp.set_union2 @t63 @t70))))) % 18.22/18.45 (assume @p36 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (= (= @t2 @t74) (forall @t22 (= @t21 @t69)))))))) % 18.22/18.45 (assume @p37 (forall @t6 (= @t75 (= @t16 tptp.empty_set)))) % 18.22/18.45 (assume @p38 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (forall @t39 (=> @t35 (= (= @t18 @t76) (forall @t33 (= @t32 (exists (@list @t59) (and (tptp.in (tptp.ordered_pair @t17 @t59) @t1) (tptp.in (tptp.ordered_pair @t59 @t28) @t2))))))))))))) % 18.22/18.45 (assume @p39 (forall @t6 (=> @t79 (forall @t39 (=> (tptp.element @t18 @t78) (= (= @t18 @t77) (forall @t43 (=> (tptp.element @t17 @t53) (= @t42 (tptp.in (tptp.subset_complement @t1 @t17) @t2)))))))))) % 18.22/18.45 (assume @p40 (forall @t6 (= @t8 (and @t26 @t80)))) % 18.22/18.45 (assume @p41 true) % 18.22/18.45 (assume @p42 (forall @t11 (tptp.element @t67 @t53))) % 18.22/18.45 (assume @p43 (forall @t6 (=> @t72 (tptp.element @t71 @t53)))) % 18.22/18.45 (assume @p44 (forall @t11 (=> @t12 (tptp.relation @t74)))) % 18.22/18.45 (assume @p45 (forall @t6 (=> @t82 @t81))) % 18.22/18.45 (assume @p46 (forall @t6 (=> @t79 (tptp.element @t83 @t53)))) % 18.22/18.45 (assume @p47 @t85) % 18.22/18.45 (assume @p48 (forall @t6 (=> @t79 (tptp.element @t86 @t53)))) % 18.22/18.45 (assume @p49 (forall @t58 (=> @t89 (tptp.element @t87 @t53)))) % 18.22/18.45 (assume @p50 (forall @t6 (=> @t12 (tptp.relation @t34)))) % 18.22/18.45 (assume @p51 (forall @t6 (=> @t79 (tptp.element @t77 @t78)))) % 18.22/18.45 (assume @p52 (forall @t6 (=> @t25 (tptp.relation @t38)))) % 18.22/18.45 (assume @p53 (forall @t11 (exists @t44 @t56))) % 18.22/18.45 (assume @p54 (forall @t6 (=> @t91 (and (tptp.empty @t90) (tptp.relation @t90))))) % 18.22/18.45 (assume @p55 (and @t93 @t92 (tptp.relation_empty_yielding tptp.empty_set))) % 18.22/18.45 (assume @p56 (forall @t6 (=> (and @t12 @t9 @t25 @t94) (and @t81 (tptp.function @t76))))) % 18.22/18.45 (assume @p57 (forall @t6 (=> @t82 (tptp.relation @t16)))) % 18.22/18.45 (assume @p58 (forall @t11 (not (tptp.empty @t53)))) % 18.22/18.45 (assume @p59 @t93) % 18.22/18.45 (assume @p60 (forall @t6 (not (tptp.empty @t73)))) % 18.22/18.45 (assume @p61 @t96) % 18.22/18.45 (assume @p62 (forall @t6 (=> @t82 (tptp.relation @t15)))) % 18.22/18.45 (assume @p63 (forall @t11 (not (tptp.empty @t52)))) % 18.22/18.45 (assume @p64 (forall @t6 (=> @t57 (not (tptp.empty @t15))))) % 18.22/18.45 (assume @p65 (forall @t6 (not (tptp.empty @t13)))) % 18.22/18.45 (assume @p66 (forall @t6 (=> @t57 (not (tptp.empty @t14))))) % 18.22/18.45 (assume @p67 (and @t93 @t92)) % 18.22/18.45 (assume @p68 (forall @t6 (=> (and @t57 @t97) (not (tptp.empty @t60))))) % 18.22/18.45 (assume @p69 (forall @t11 (=> @t99 (not @t98)))) % 18.22/18.45 (assume @p70 (forall @t11 (=> @t99 (not @t100)))) % 18.22/18.45 (assume @p71 (forall @t11 (=> @t10 (and @t98 (tptp.relation @t63))))) % 18.22/18.45 (assume @p72 (forall @t11 (=> @t10 (and @t100 (tptp.relation @t70))))) % 18.22/18.45 (assume @p73 (forall @t6 (=> @t91 (and (tptp.empty @t76) @t81)))) % 18.22/18.45 (assume @p74 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 18.22/18.45 (assume @p75 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 18.22/18.45 (assume @p76 (forall @t6 (=> @t72 (= (tptp.subset_complement @t1 @t71) @t2)))) % 18.22/18.45 (assume @p77 (forall @t11 (=> @t12 (= (tptp.relation_inverse @t74) @t1)))) % 18.22/18.45 (assume @p78 (forall @t6 (=> @t79 (= (tptp.complements_of_subsets @t1 @t77) @t2)))) % 18.22/18.45 (assume @p79 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 18.22/18.45 (assume @p80 (forall @t11 (not (= @t52 tptp.empty_set)))) % 18.22/18.45 (assume @p81 (forall @t6 (=> @t5 (= (tptp.set_union2 @t52 @t2) @t2)))) % 18.22/18.45 (assume @p82 (forall @t6 (not (and @t101 @t5)))) % 18.22/18.45 (assume @p83 (forall @t6 (=> (not @t5) @t101))) % 18.22/18.45 (assume @p84 (forall @t6 (= (tptp.subset @t52 @t2) @t5))) % 18.22/18.45 (assume @p85 (forall @t6 (= (= @t68 tptp.empty_set) @t26))) % 18.22/18.45 (assume @p86 (forall @t6 (=> @t72 (forall @t39 (=> @t50 @t19))))) % 18.22/18.45 (assume @p87 (forall @t58 (=> @t26 (or @t19 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t18))))))) % 18.22/18.45 (assume @p88 (forall @t6 (= (tptp.subset @t1 @t102) (or @t47 (= @t1 @t102))))) % 18.22/18.45 (assume @p89 (forall @t6 (=> @t5 (tptp.subset @t1 @t103)))) % 18.22/18.45 (assume @p90 (forall @t105 (= (tptp.in @t73 (tptp.cartesian_product2 @t18 @t17)) (and @t104 (tptp.in @t2 @t17))))) % 18.22/18.45 (assume @p91 (forall @t6 (=> @t61 @t106))) % 18.22/18.45 (assume @p92 (exists @t11 @t66)) % 18.22/18.45 (assume @p93 (exists @t11 (and @t10 @t12))) % 18.22/18.45 (assume @p94 (forall @t11 (=> @t57 (exists @t44 (and @t72 @t97))))) % 18.22/18.45 (assume @p95 (exists @t11 @t10)) % 18.22/18.45 (assume @p96 (exists @t11 @t99)) % 18.22/18.45 (assume @p97 (forall @t11 (exists @t44 (and @t72 @t55)))) % 18.22/18.45 (assume @p98 (exists @t11 @t57)) % 18.22/18.45 (assume @p99 (exists @t11 (and @t12 (tptp.relation_empty_yielding @t1)))) % 18.22/18.45 (assume @p100 (forall @t6 (=> @t79 (= @t83 @t103)))) % 18.22/18.45 (assume @p101 (forall @t6 (=> @t79 (= @t86 (tptp.set_meet @t2))))) % 18.22/18.45 (assume @p102 (forall @t58 (=> @t89 (= @t87 @t107)))) % 18.22/18.45 (assume @p103 (forall @t6 (tptp.subset @t1 @t1))) % 18.22/18.45 (assume @p104 (forall @t6 (=> @t75 (tptp.disjoint @t2 @t1)))) % 18.22/18.45 (assume @p105 (forall @t105 (not (and (= @t13 (tptp.unordered_pair @t18 @t17)) (not @t108) (not (= @t1 @t17)))))) % 18.22/18.45 (assume @p106 (forall @t58 (=> @t35 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t18))) (and @t5 (tptp.in @t1 @t109)))))) % 18.22/18.45 (assume @p107 (forall @t6 (=> @t25 (tptp.subset @t110 @t1)))) % 18.22/18.45 (assume @p108 (forall @t6 (=> @t25 (tptp.subset @t38 @t2)))) % 18.22/18.45 (assume @p109 (forall @t6 (=> @t25 (tptp.subset @t110 @t111)))) % 18.22/18.45 (assume @p110 (forall @t58 (=> @t26 (and (tptp.subset @t112 (tptp.cartesian_product2 @t2 @t18)) (tptp.subset (tptp.cartesian_product2 @t18 @t1) (tptp.cartesian_product2 @t18 @t2)))))) % 18.22/18.45 (assume @p111 (forall @t6 (=> @t25 (= @t110 (tptp.set_intersection2 @t111 @t1))))) % 18.22/18.45 (assume @p112 (forall @t105 (=> (and @t26 (tptp.subset @t18 @t17)) (tptp.subset @t112 (tptp.cartesian_product2 @t2 @t17))))) % 18.22/18.45 (assume @p113 (forall @t6 (=> @t26 (= @t15 @t2)))) % 18.22/18.45 (assume @p114 (forall @t11 (exists @t44 (and @t5 @t117 (forall @t39 (=> @t50 (tptp.in @t116 @t2))) @t115)))) % 18.22/18.45 (assume @p115 (forall @t58 (=> @t35 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t18) @t2) (tptp.relation_rng_restriction @t1 @t118))))) % 18.22/18.45 (assume @p116 (forall @t58 (=> @t35 (= (tptp.in @t1 (tptp.relation_image @t18 @t2)) (exists @t43 (and (tptp.in @t17 @t119) (tptp.in (tptp.ordered_pair @t17 @t1) @t18) @t31)))))) % 18.22/18.45 (assume @p117 (forall @t6 (=> @t25 (tptp.subset @t120 @t111)))) % 18.22/18.45 (assume @p118 (forall @t6 (=> @t25 (= @t120 (tptp.relation_image @t2 @t122))))) % 18.22/18.45 (assume @p119 (forall @t11 (=> @t12 (= (tptp.relation_image @t1 @t63) @t70)))) % 18.22/18.45 (assume @p120 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (= @t123 (tptp.relation_image @t2 @t70))))))) % 18.22/18.45 (assume @p121 (forall @t58 (=> @t35 (= (tptp.in @t1 @t124) (exists @t43 (and (tptp.in @t17 @t109) (tptp.in (tptp.ordered_pair @t1 @t17) @t18) @t31)))))) % 18.22/18.45 (assume @p122 (forall @t6 (=> @t25 (tptp.subset @t125 @t121)))) % 18.22/18.45 (assume @p123 (forall @t6 (=> @t25 (not (and @t51 (tptp.subset @t1 @t111) (= @t125 tptp.empty_set)))))) % 18.22/18.45 (assume @p124 (forall @t58 (=> @t35 (=> @t26 (tptp.subset (tptp.relation_inverse_image @t18 @t1) @t124))))) % 18.22/18.45 (assume @p125 (forall @t6 (tptp.subset @t16 @t1))) % 18.22/18.45 (assume @p126 (forall @t58 (=> (and @t26 @t127) (tptp.subset @t1 @t126)))) % 18.22/18.45 (assume @p127 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 18.22/18.45 (assume @p128 (forall @t6 (=> @t5 @t128))) % 18.22/18.45 (assume @p129 (forall @t58 (=> (and @t26 (tptp.subset @t2 @t18)) @t127))) % 18.22/18.45 (assume @p130 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 18.22/18.45 (assume @p131 (forall @t58 (=> @t35 (=> @t130 (and @t129 (tptp.in @t2 @t109)))))) % 18.22/18.45 (assume @p132 (forall @t6 (=> @t135 (forall @t39 (=> @t134 (= @t133 (and @t129 (tptp.in @t131 @t121)))))))) % 18.22/18.45 (assume @p133 (forall @t11 (=> @t12 (tptp.subset @t1 (tptp.cartesian_product2 @t63 @t70))))) % 18.22/18.45 (assume @p134 (forall @t6 (=> @t135 (forall @t39 (=> @t134 (=> @t133 (= (tptp.apply @t132 @t1) (tptp.apply @t2 @t131)))))))) % 18.22/18.45 (assume @p135 (forall @t6 (=> @t135 (forall @t39 (=> @t134 (=> (tptp.in @t1 @t121) (= (tptp.apply (tptp.relation_composition @t2 @t18) @t1) (tptp.apply @t18 (tptp.apply @t2 @t1))))))))) % 18.22/18.45 (assume @p136 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (=> @t26 (and (tptp.subset @t63 @t121) (tptp.subset @t70 @t111)))))))) % 18.22/18.45 (assume @p137 (forall @t58 (=> @t26 (tptp.subset (tptp.set_intersection2 @t1 @t18) @t126)))) % 18.22/18.45 (assume @p138 (forall @t6 (=> @t26 (= @t16 @t1)))) % 18.22/18.45 (assume @p139 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 18.22/18.45 (assume @p140 (forall @t6 (=> @t128 (or @t55 @t5)))) % 18.22/18.45 (assume @p141 (forall @t6 (=> (forall @t39 (= @t19 @t50)) @t27))) % 18.22/18.45 (assume @p142 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 18.22/18.45 (assume @p143 (forall @t58 (=> @t35 (=> @t130 (and (tptp.in @t1 @t136) (tptp.in @t2 @t136)))))) % 18.22/18.45 (assume @p144 (forall @t58 (=> @t26 (tptp.subset (tptp.set_difference @t1 @t18) @t107)))) % 18.22/18.45 (assume @p145 (forall @t105 (=> (= @t73 @t20) (and @t108 (= @t2 @t17))))) % 18.22/18.45 (assume @p146 @t143) % 18.22/18.45 (assume @p147 @t147) % 18.22/18.45 (assume @p148 (forall @t6 (tptp.subset @t68 @t1))) % 18.22/18.45 (assume @p149 (forall @t11 (=> @t12 (and (= @t70 (tptp.relation_dom @t74)) (= @t63 (tptp.relation_rng @t74)))))) % 18.22/18.45 (assume @p150 (forall @t58 (= (tptp.subset @t13 @t18) (and @t104 @t148)))) % 18.22/18.45 (assume @p151 (forall @t6 (= @t149 @t15))) % 18.22/18.45 (assume @p152 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 18.22/18.45 (assume @p153 (forall @t6 (= @t106 @t26))) % 18.22/18.45 (assume @p154 (forall @t6 (and (not (and @t151 (forall @t39 (not @t150)))) (not (and (exists @t39 @t150) @t75))))) % 18.22/18.45 (assume @p155 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t47))) % 18.22/18.45 (assume @p156 (forall @t6 (= (tptp.set_difference @t15 @t2) @t68))) % 18.22/18.45 (assume @p157 (forall @t6 (=> @t72 (forall @t39 (=> @t88 (= @t153 (tptp.subset @t2 @t152))))))) % 18.22/18.45 (assume @p158 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (tptp.subset @t154 @t63)))))) % 18.22/18.45 (assume @p159 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (tptp.subset @t123 @t111)))))) % 18.22/18.45 (assume @p160 (forall @t6 (=> @t26 (= @t2 @t149)))) % 18.22/18.45 (assume @p161 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (=> (tptp.subset @t70 @t121) (= @t154 @t63))))))) % 18.22/18.45 (assume @p162 (forall @t6 (=> @t79 (not (and @t155 (= @t77 tptp.empty_set)))))) % 18.22/18.45 (assume @p163 (forall @t11 (=> @t12 (forall @t44 (=> @t25 (=> (tptp.subset @t63 @t111) (= (tptp.relation_rng @t90) @t70))))))) % 18.22/18.45 (assume @p164 (forall @t6 (=> @t79 (=> @t155 (= (tptp.subset_difference @t1 @t67 @t83) (tptp.meet_of_subsets @t1 @t77)))))) % 18.22/18.45 (assume @p165 (forall @t6 (=> @t79 (=> @t155 (= (tptp.union_of_subsets @t1 @t77) (tptp.subset_difference @t1 @t67 @t86)))))) % 18.22/18.45 (assume @p166 (forall @t6 (= (tptp.set_difference @t1 @t68) @t16))) % 18.22/18.45 (assume @p167 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 18.22/18.45 (assume @p168 (forall @t58 (=> (and @t5 @t156) (tptp.element @t1 @t18)))) % 18.22/18.45 (assume @p169 (forall @t6 (and (not (and @t151 (forall @t39 (not @t157)))) (not (and (exists @t39 @t157) @t75))))) % 18.22/18.45 (assume @p170 (forall @t11 (=> @t51 (forall @t44 (=> @t72 (forall @t39 (=> (tptp.element @t18 @t1) (=> @t113 (tptp.in @t18 @t71))))))))) % 18.22/18.45 (assume @p171 (forall @t58 (=> @t88 (not (and (tptp.in @t2 @t152) @t148))))) % 18.22/18.45 (assume @p172 (forall @t11 (=> @t12 (=> (forall @t36 (not @t65)) @t47)))) % 18.22/18.45 (assume @p173 (forall @t58 (not (and @t5 @t156 (tptp.empty @t18))))) % 18.22/18.45 (assume @p174 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 18.22/18.45 (assume @p175 (forall @t6 (not (and @t26 @t7)))) % 18.22/18.45 (assume @p176 (forall @t58 (=> (and @t26 @t153) (tptp.disjoint @t1 @t18)))) % 18.22/18.45 (assume @p177 (forall @t11 (=> @t12 (=> (or @t159 @t158) @t47)))) % 18.22/18.45 (assume @p178 (forall @t11 (=> @t12 (= @t159 @t158)))) % 18.22/18.45 (assume @p179 (forall @t6 (= (= (tptp.set_difference @t1 @t102) @t1) @t4))) % 18.22/18.45 (assume @p180 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t52))) % 18.22/18.45 (assume @p181 (forall @t11 (=> @t10 @t47))) % 18.22/18.45 (assume @p182 (forall @t6 (=> (tptp.subset @t52 @t102) @t27))) % 18.22/18.45 (assume @p183 (forall @t11 (and (= (tptp.relation_dom @t23) @t1) (= (tptp.relation_rng @t23) @t1)))) % 18.22/18.45 (assume @p184 (forall @t105 (=> (tptp.relation @t17) (= (tptp.in @t73 (tptp.relation_composition (tptp.identity_relation @t18) @t17)) (and @t104 (tptp.in @t73 @t17)))))) % 18.22/18.45 (assume @p185 (forall @t6 (not (and @t5 @t55)))) % 18.22/18.45 (assume @p186 (forall @t6 (tptp.subset @t1 @t15))) % 18.22/18.45 (assume @p187 (forall @t6 (= @t75 (= @t68 @t1)))) % 18.22/18.45 (assume @p188 (forall @t58 (=> @t35 (= (tptp.in @t1 (tptp.relation_dom @t118)) (and @t5 @t129))))) % 18.22/18.45 (assume @p189 (forall @t6 (=> @t25 (tptp.subset @t160 @t2)))) % 18.22/18.45 (assume @p190 (forall @t6 (not (and @t10 @t80 @t55)))) % 18.22/18.45 (assume @p191 (forall @t58 (=> @t134 (= @t130 (and @t129 (= @t2 @t131)))))) % 18.22/18.45 (assume @p192 (forall @t58 (=> (and @t26 @t114) (tptp.subset (tptp.set_union2 @t1 @t18) @t2)))) % 18.22/18.45 (assume @p193 (forall @t58 (=> @t161 @t27))) % 18.22/18.45 (assume @p194 (forall @t6 (=> @t25 (= (tptp.relation_dom @t160) @t122)))) % 18.22/18.45 (assume @p195 (forall @t6 (=> @t25 (= @t160 (tptp.relation_composition @t23 @t2))))) % 18.22/18.45 (assume @p196 (forall @t6 (=> @t25 (tptp.subset (tptp.relation_rng @t160) @t111)))) % 18.22/18.45 (assume @p197 (forall @t11 (= (tptp.union @t53) @t1))) % 18.22/18.45 (assume @p198 (forall @t11 (exists @t44 (and @t5 @t117 (forall @t39 (not (and @t50 (forall @t43 (not (and @t31 (forall @t41 (=> (tptp.subset @t28 @t18) (tptp.in @t28 @t17))))))))) @t115)))) % 18.22/18.45 (assume @p199 (forall @t58 (=> @t161 (= @t2 @t18)))) % 18.22/18.45 (step @p200 :rule bool-impl-elim :args (@t3 @t162)) % 18.22/18.45 (step @p201 :rule cong :premises (@p200) :args ((forall @t6 (=> @t3 @t162)))) % 18.22/18.45 (step @p202 :rule eq-symm :args (@t144 @t2)) % 18.22/18.45 (step @p203 :rule refl :args (@t3)) % 18.22/18.45 (step @p204 :rule cong :premises (@p203 @p202) :args (@t145)) % 18.22/18.45 (step @p205 :rule cong :premises (@p204) :args (@t146)) % 18.22/18.45 (step @p206 :rule trans :premises (@p205 @p201)) % 18.22/18.45 (step @p207 :rule cong :premises (@p206) :args (@t147)) % 18.22/18.45 (step @p208 :rule eq_resolve :premises (@p147 @p207)) % 18.22/18.45 (step @p209 :rule skolemize :premises (@p208)) % 18.22/18.45 (step @p210 :rule aci_norm :args ((= (or (or @t166 @t165) @t164) @t167))) % 18.22/18.45 (step @p211 :rule refl :args (@t164)) % 18.22/18.45 (step @p212 :rule bool-and-de-morgan :args (@t25 @t94 true)) % 18.22/18.45 (step @p213 :rule nary_cong :premises (@p212 @p211) :args ((or (not @t135) @t164))) % 18.22/18.45 (step @p214 :rule trans :premises (@p213 @p210)) % 18.22/18.45 (step @p215 :rule bool-impl-elim :args (@t135 @t164)) % 18.22/18.45 (step @p216 :rule trans :premises (@p215 @p214)) % 18.22/18.45 (step @p217 :rule cong :premises (@p216) :args ((forall @t6 (=> @t135 @t164)))) % 18.22/18.45 (step @p218 :rule bool-impl-elim :args (@t19 @t163)) % 18.22/18.45 (step @p219 :rule cong :premises (@p218) :args ((forall @t39 (=> @t19 @t163)))) % 18.22/18.45 (step @p220 :rule eq-symm :args (@t137 @t18)) % 18.22/18.45 (step @p221 :rule refl :args (@t19)) % 18.22/18.45 (step @p222 :rule cong :premises (@p221 @p220) :args (@t138)) % 18.22/18.45 (step @p223 :rule cong :premises (@p222) :args (@t139)) % 18.22/18.45 (step @p224 :rule trans :premises (@p223 @p219)) % 18.22/18.45 (step @p225 :rule eq-symm :args (@t121 @t1)) % 18.22/18.45 (step @p226 :rule nary_cong :premises (@p225 @p224) :args (@t140)) % 18.22/18.45 (step @p227 :rule refl :args (@t24)) % 18.22/18.45 (step @p228 :rule cong :premises (@p227 @p226) :args (@t141)) % 18.22/18.45 (step @p229 :rule refl :args (@t135)) % 18.22/18.45 (step @p230 :rule cong :premises (@p229 @p228) :args (@t142)) % 18.22/18.45 (step @p231 :rule cong :premises (@p230) :args (@t143)) % 18.22/18.45 (step @p232 :rule trans :premises (@p231 @p217)) % 18.22/18.45 (step @p233 :rule eq_resolve :premises (@p146 @p232)) % 18.22/18.45 (step @p234 :rule bool-eq-true :args (@t172)) % 18.22/18.45 (step @p235 :rule eq-symm :args (true @t172)) % 18.22/18.45 (step @p236 :rule trans :premises (@p235 @p234)) % 18.22/18.45 (step @p237 :rule refl :args (@t172)) % 18.22/18.45 (step @p238 :rule eq-refl :args (@t170)) % 18.22/18.45 (step @p239 :rule cong :premises (@p238 @p237) :args (@t173)) % 18.22/18.45 (step @p240 :rule trans :premises (@p239 @p236)) % 18.22/18.45 (step @p241 :rule refl :args (@t175)) % 18.22/18.45 (step @p242 :rule refl :args (@t177)) % 18.22/18.45 (step @p243 :rule nary_cong :premises (@p242 @p241 @p240) :args (@t178)) % 18.22/18.46 (step @p244 :rule refl :args (@t179)) % 18.22/18.46 (step @p245 :rule cong :premises (@p244 @p243) :args ((=> @t179 @t178))) % 18.22/18.46 (assume-push @p275 @t179) % 18.22/18.46 (step @p247 :rule instantiate :premises (@p233) :args ((@list @t169 @t170))) % 18.22/18.46 (step-pop @p276 :rule scope :premises (@p247)) % 18.22/18.46 (step @p248 :rule process_scope :premises (@p276) :args (@t178)) % 18.22/18.46 (step @p250 :rule eq_resolve :premises (@p248 @p245)) % 18.22/18.46 (step @p251 :rule implies_elim :premises (@p250)) % 18.22/18.46 (step @p252 :rule chain_m_resolution :premises (@p251 @p233) :args (@t180 @t181 (@list @t179))) % 18.22/18.46 (step @p253 :rule instantiate :premises (@p47) :args (@t182)) % 18.22/18.46 (step @p254 :rule alpha_equiv :args (@t183 @t184 (@list (@var "BOUND_VARIABLE_9209" $$unsorted)))) % 18.22/18.46 (step @p255 :rule alpha_equiv :args (@t85 @t184 (@list (@var "BOUND_VARIABLE_9203" $$unsorted)))) % 18.22/18.46 (step @p256 :rule nary_cong :premises (@p255 @p254) :args (@t185)) % 18.22/18.46 (step @p257 :rule quant-miniscope-and :args ((= @t96 @t185))) % 18.22/18.46 (step @p258 :rule trans :premises (@p257 @p256)) % 18.22/18.46 (step @p259 :rule eq_resolve :premises (@p61 @p258)) % 18.22/18.46 (step @p260 :rule and_elim :premises (@p259) :args (1)) % 18.22/18.46 (step @p261 :rule instantiate :premises (@p260) :args (@t182)) % 18.22/18.46 (step @p262 :rule cnf_or_pos :args (@t180)) % 18.22/18.46 (step @p263 :rule reordering :premises (@p262) :args ((or @t175 @t177 @t172 (not @t180)))) % 18.22/18.46 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p253 @p252) :args (@t172 (@list false false false) (@list @t174 @t176 @t180))) % 18.22/18.46 (step @p265 :rule cnf_and_pos :args (@t172 1)) % 18.22/18.46 (step @p266 :rule reordering :premises (@p265) :args ((or @t171 (not @t172)))) % 18.22/18.46 (step @p267 :rule chain_m_resolution :premises (@p266 @p264) :args (@t171 @t181 (@list @t172))) % 18.22/18.46 (assume-push @p277 @t171) % 18.22/18.46 (step @p269 :rule instantiate :premises (@p267) :args ((@list @t186))) % 18.22/18.46 (step-pop @p278 :rule scope :premises (@p269)) % 18.22/18.46 (step @p270 :rule process_scope :premises (@p278) :args (@t187)) % 18.22/18.46 (step @p272 :rule implies_elim :premises (@p270)) % 18.22/18.46 (step @p273 :rule reordering :premises (@p272) :args ((or @t187 (not @t171)))) % 18.22/18.46 (step @p274 false :rule chain_m_resolution :premises (@p273 @p267 @p209) :args (false (@list false true) (@list @t171 @t187))) % 18.22/18.46 ) % 18.22/18.46 % SZS output end Proof % 18.22/18.46 % cvc5 exiting %------------------------------------------------------------------------------