%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU211+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 : n007.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 08:50:57 AM UTC 2026 % Result : Theorem 1.14s 1.34s % Output : Proof 1.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU211+2 : TPTP v9.2.1. Released v3.3.0. % 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.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 16:39:41 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.53 %----Proving TF0_NAR, FOF, or CNF % 1.14/1.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.14/1.34 % SZS status Theorem % 1.14/1.34 % SZS output start Proof % 1.14/1.34 ( % 1.14/1.34 (declare-sort $$unsorted 0) % 1.14/1.34 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_rng_restriction (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_image (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation (-> $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.empty_set $$unsorted) % 1.14/1.34 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 1.14/1.34 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.14/1.34 (define @t1 () (@var "A" $$unsorted)) % 1.14/1.34 (define @t2 () (@var "B" $$unsorted)) % 1.14/1.34 (define @t3 () (tptp.in @t2 @t1)) % 1.14/1.34 (define @t4 () (not @t3)) % 1.14/1.34 (define @t5 () (tptp.in @t1 @t2)) % 1.14/1.34 (define @t6 () (@list @t1 @t2)) % 1.14/1.34 (define @t7 () (tptp.proper_subset @t2 @t1)) % 1.14/1.34 (define @t8 () (tptp.proper_subset @t1 @t2)) % 1.14/1.34 (define @t9 () (tptp.relation @t1)) % 1.14/1.34 (define @t10 () (tptp.empty @t1)) % 1.14/1.34 (define @t11 () (@list @t1)) % 1.14/1.34 (define @t12 () (tptp.unordered_pair @t1 @t2)) % 1.14/1.34 (define @t13 () (tptp.set_union2 @t2 @t1)) % 1.14/1.34 (define @t14 () (tptp.set_union2 @t1 @t2)) % 1.14/1.34 (define @t15 () (tptp.set_intersection2 @t1 @t2)) % 1.14/1.34 (define @t16 () (@var "D" $$unsorted)) % 1.14/1.34 (define @t17 () (@var "C" $$unsorted)) % 1.14/1.34 (define @t18 () (tptp.in @t17 @t1)) % 1.14/1.34 (define @t19 () (tptp.ordered_pair @t17 @t16)) % 1.14/1.34 (define @t20 () (tptp.in @t19 @t2)) % 1.14/1.34 (define @t21 () (@list @t17 @t16)) % 1.14/1.34 (define @t22 () (tptp.identity_relation @t1)) % 1.14/1.34 (define @t23 () (tptp.relation @t2)) % 1.14/1.34 (define @t24 () (tptp.subset @t1 @t2)) % 1.14/1.34 (define @t25 () (= @t1 @t2)) % 1.14/1.34 (define @t26 () (@var "E" $$unsorted)) % 1.14/1.34 (define @t27 () (tptp.ordered_pair @t16 @t26)) % 1.14/1.34 (define @t28 () (tptp.in @t27 @t1)) % 1.14/1.34 (define @t29 () (tptp.in @t16 @t2)) % 1.14/1.34 (define @t30 () (tptp.in @t27 @t17)) % 1.14/1.34 (define @t31 () (@list @t16 @t26)) % 1.14/1.34 (define @t32 () (tptp.relation_dom_restriction @t1 @t2)) % 1.14/1.34 (define @t33 () (tptp.relation @t17)) % 1.14/1.34 (define @t34 () (@list @t2 @t17)) % 1.14/1.34 (define @t35 () (tptp.in @t26 @t1)) % 1.14/1.34 (define @t36 () (tptp.relation_rng_restriction @t1 @t2)) % 1.14/1.34 (define @t37 () (@list @t17)) % 1.14/1.34 (define @t38 () (tptp.in @t26 @t2)) % 1.14/1.34 (define @t39 () (@list @t26)) % 1.14/1.34 (define @t40 () (tptp.in @t16 @t17)) % 1.14/1.34 (define @t41 () (@list @t16)) % 1.14/1.34 (define @t42 () (@list @t2)) % 1.14/1.34 (define @t43 () (= @t2 tptp.empty_set)) % 1.14/1.34 (define @t44 () (= @t2 (tptp.set_meet @t1))) % 1.14/1.34 (define @t45 () (= @t1 tptp.empty_set)) % 1.14/1.34 (define @t46 () (tptp.in @t17 @t16)) % 1.14/1.34 (define @t47 () (tptp.in @t16 @t1)) % 1.14/1.34 (define @t48 () (tptp.in @t17 @t2)) % 1.14/1.34 (define @t49 () (not @t45)) % 1.14/1.34 (define @t50 () (tptp.singleton @t1)) % 1.14/1.34 (define @t51 () (tptp.powerset @t1)) % 1.14/1.34 (define @t52 () (tptp.in @t19 @t1)) % 1.14/1.34 (define @t53 () (tptp.empty @t2)) % 1.14/1.34 (define @t54 () (tptp.element @t2 @t1)) % 1.14/1.34 (define @t55 () (not @t10)) % 1.14/1.34 (define @t56 () (@list @t1 @t2 @t17)) % 1.14/1.34 (define @t57 () (@var "F" $$unsorted)) % 1.14/1.34 (define @t58 () (tptp.cartesian_product2 @t1 @t2)) % 1.14/1.34 (define @t59 () (forall @t37 (=> @t18 @t48))) % 1.14/1.34 (define @t60 () (= @t24 @t59)) % 1.14/1.34 (define @t61 () (forall @t6 @t60)) % 1.14/1.34 (define @t62 () (tptp.relation_dom @t1)) % 1.14/1.34 (define @t63 () (tptp.cast_to_subset @t1)) % 1.14/1.34 (define @t64 () (not @t29)) % 1.14/1.34 (define @t65 () (tptp.set_difference @t1 @t2)) % 1.14/1.34 (define @t66 () (tptp.in (tptp.ordered_pair @t16 @t17) @t1)) % 1.14/1.34 (define @t67 () (tptp.relation_rng @t1)) % 1.14/1.34 (define @t68 () (tptp.subset_complement @t1 @t2)) % 1.14/1.34 (define @t69 () (tptp.element @t2 @t51)) % 1.14/1.34 (define @t70 () (tptp.ordered_pair @t1 @t2)) % 1.14/1.34 (define @t71 () (tptp.relation_inverse @t1)) % 1.14/1.34 (define @t72 () (tptp.disjoint @t1 @t2)) % 1.14/1.34 (define @t73 () (tptp.relation_composition @t1 @t2)) % 1.14/1.34 (define @t74 () (tptp.complements_of_subsets @t1 @t2)) % 1.14/1.34 (define @t75 () (tptp.powerset @t51)) % 1.14/1.34 (define @t76 () (tptp.element @t2 @t75)) % 1.14/1.34 (define @t77 () (not @t25)) % 1.14/1.34 (define @t78 () (tptp.relation @t73)) % 1.14/1.34 (define @t79 () (and @t9 @t23)) % 1.14/1.34 (define @t80 () (tptp.union_of_subsets @t1 @t2)) % 1.14/1.34 (define @t81 () (tptp.meet_of_subsets @t1 @t2)) % 1.14/1.34 (define @t82 () (tptp.subset_difference @t1 @t2 @t17)) % 1.14/1.34 (define @t83 () (tptp.element @t17 @t51)) % 1.14/1.34 (define @t84 () (and @t69 @t83)) % 1.14/1.34 (define @t85 () (tptp.relation_composition @t2 @t1)) % 1.14/1.34 (define @t86 () (and @t10 @t23)) % 1.14/1.34 (define @t87 () (tptp.empty tptp.empty_set)) % 1.14/1.34 (define @t88 () (not @t53)) % 1.14/1.34 (define @t89 () (tptp.empty @t62)) % 1.14/1.34 (define @t90 () (and @t55 @t9)) % 1.14/1.34 (define @t91 () (tptp.empty @t67)) % 1.14/1.34 (define @t92 () (tptp.disjoint @t50 @t2)) % 1.14/1.34 (define @t93 () (forall @t37 (=> @t48 @t18))) % 1.14/1.34 (define @t94 () (=> @t69 @t93)) % 1.14/1.34 (define @t95 () (forall @t6 @t94)) % 1.14/1.34 (define @t96 () (tptp.singleton @t2)) % 1.14/1.34 (define @t97 () (tptp.union @t2)) % 1.14/1.34 (define @t98 () (tptp.in @t1 @t17)) % 1.14/1.34 (define @t99 () (@list @t1 @t2 @t17 @t16)) % 1.14/1.34 (define @t100 () (tptp.element @t1 (tptp.powerset @t2))) % 1.14/1.34 (define @t101 () (tptp.set_difference @t2 @t17)) % 1.14/1.34 (define @t102 () (= @t1 @t17)) % 1.14/1.34 (define @t103 () (tptp.relation_rng @t17)) % 1.14/1.34 (define @t104 () (tptp.relation_rng @t36)) % 1.14/1.34 (define @t105 () (tptp.relation_rng @t2)) % 1.14/1.34 (define @t106 () (tptp.cartesian_product2 @t1 @t17)) % 1.14/1.34 (define @t107 () (not @t48)) % 1.14/1.34 (define @t108 () (tptp.subset @t17 @t2)) % 1.14/1.34 (define @t109 () (forall @t37 (not (and @t108 (not (tptp.are_equipotent @t17 @t2)) @t107)))) % 1.14/1.34 (define @t110 () (tptp.powerset @t17)) % 1.14/1.34 (define @t111 () (forall @t21 (=> (and @t48 (tptp.subset @t16 @t17)) @t29))) % 1.14/1.34 (define @t112 () (tptp.relation_dom_restriction @t17 @t2)) % 1.14/1.34 (define @t113 () (tptp.relation_dom @t17)) % 1.14/1.34 (define @t114 () (tptp.relation_image @t2 @t1)) % 1.14/1.34 (define @t115 () (tptp.relation_dom @t2)) % 1.14/1.34 (define @t116 () (tptp.set_intersection2 @t115 @t1)) % 1.14/1.34 (define @t117 () (tptp.relation_rng @t73)) % 1.14/1.34 (define @t118 () (tptp.in (tptp.ordered_pair @t1 @t16) @t17)) % 1.14/1.34 (define @t119 () (tptp.in @t16 @t103)) % 1.14/1.34 (define @t120 () (and @t119 @t118 @t29)) % 1.14/1.34 (define @t121 () (exists @t41 @t120)) % 1.14/1.34 (define @t122 () (tptp.relation_inverse_image @t17 @t2)) % 1.14/1.34 (define @t123 () (tptp.in @t1 @t122)) % 1.14/1.34 (define @t124 () (= @t123 @t121)) % 1.14/1.34 (define @t125 () (=> @t33 @t124)) % 1.14/1.34 (define @t126 () (forall @t56 @t125)) % 1.14/1.34 (define @t127 () (tptp.relation_inverse_image @t2 @t1)) % 1.14/1.34 (define @t128 () (tptp.subset (tptp.relation_inverse_image @t17 @t1) @t122)) % 1.14/1.34 (define @t129 () (=> @t24 @t128)) % 1.14/1.34 (define @t130 () (forall @t56 (=> @t33 @t129))) % 1.14/1.34 (define @t131 () (not @t130)) % 1.14/1.34 (define @t132 () (tptp.set_intersection2 @t2 @t17)) % 1.14/1.34 (define @t133 () (tptp.subset @t1 @t17)) % 1.14/1.34 (define @t134 () (tptp.element @t1 @t2)) % 1.14/1.34 (define @t135 () (tptp.in @t1 @t113)) % 1.14/1.34 (define @t136 () (tptp.in @t70 @t17)) % 1.14/1.34 (define @t137 () (tptp.relation_field @t17)) % 1.14/1.34 (define @t138 () (tptp.in @t2 @t17)) % 1.14/1.34 (define @t139 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 1.14/1.34 (define @t140 () (forall @t6 (= @t100 @t24))) % 1.14/1.34 (define @t141 () (and @t18 @t48)) % 1.14/1.34 (define @t142 () (not @t72)) % 1.14/1.34 (define @t143 () (tptp.subset_complement @t1 @t17)) % 1.14/1.34 (define @t144 () (tptp.disjoint @t2 @t17)) % 1.14/1.34 (define @t145 () (tptp.relation_dom @t73)) % 1.14/1.34 (define @t146 () (not @t43)) % 1.14/1.34 (define @t147 () (tptp.element @t2 @t110)) % 1.14/1.34 (define @t148 () (tptp.in @t17 @t15)) % 1.14/1.34 (define @t149 () (= @t67 tptp.empty_set)) % 1.14/1.34 (define @t150 () (= @t62 tptp.empty_set)) % 1.14/1.34 (define @t151 () (tptp.relation_dom_restriction @t2 @t1)) % 1.14/1.34 (define @t152 () (= @t50 (tptp.unordered_pair @t2 @t17))) % 1.14/1.34 (define @t153 () (not @t118)) % 1.14/1.34 (define @t154 () (not @t119)) % 1.14/1.34 (define @t155 () (or @t154 @t153 @t64)) % 1.14/1.34 (define @t156 () (= @t123 (not (forall @t41 @t155)))) % 1.14/1.34 (define @t157 () (forall @t41 (not @t120))) % 1.14/1.34 (define @t158 () (not @t157)) % 1.14/1.34 (define @t159 () (not @t24)) % 1.14/1.34 (define @t160 () (not @t33)) % 1.14/1.34 (define @t161 () (or @t160 @t159 @t128)) % 1.14/1.34 (define @t162 () (forall @t56 @t161)) % 1.14/1.34 (define @t163 () (@quantifiers_skolemize @t162 2)) % 1.14/1.34 (define @t164 () (@quantifiers_skolemize @t162 0)) % 1.14/1.34 (define @t165 () (@quantifiers_skolemize @t162 1)) % 1.14/1.34 (define @t166 () (tptp.relation_inverse_image @t163 @t165)) % 1.14/1.34 (define @t167 () (tptp.relation_inverse_image @t163 @t164)) % 1.14/1.34 (define @t168 () (forall @t37 (or (not (tptp.in @t17 @t167)) (tptp.in @t17 @t166)))) % 1.14/1.34 (define @t169 () (@quantifiers_skolemize @t168 0)) % 1.14/1.34 (define @t170 () (tptp.relation @t163)) % 1.14/1.34 (define @t171 () (tptp.subset @t167 @t166)) % 1.14/1.34 (define @t172 () (tptp.subset @t164 @t165)) % 1.14/1.34 (define @t173 () (not @t172)) % 1.14/1.34 (define @t174 () (not @t170)) % 1.14/1.34 (define @t175 () (or @t174 @t173 @t171)) % 1.14/1.34 (define @t176 () (@list true)) % 1.14/1.34 (define @t177 () (@list @t175)) % 1.14/1.34 (define @t178 () (not (tptp.in (tptp.ordered_pair @t169 @t16) @t163))) % 1.14/1.34 (define @t179 () (tptp.relation_rng @t163)) % 1.14/1.34 (define @t180 () (not (tptp.in @t16 @t179))) % 1.14/1.34 (define @t181 () (forall @t41 (or @t180 @t178 (not (tptp.in @t16 @t164))))) % 1.14/1.34 (define @t182 () (not @t181)) % 1.14/1.34 (define @t183 () (tptp.in @t169 @t167)) % 1.14/1.34 (define @t184 () (= @t183 @t182)) % 1.14/1.34 (define @t185 () (or @t174 @t184)) % 1.14/1.34 (define @t186 () (@list false false)) % 1.14/1.34 (define @t187 () (= @t171 @t168)) % 1.14/1.34 (define @t188 () (not @t168)) % 1.14/1.34 (define @t189 () (@list true false)) % 1.14/1.34 (define @t190 () (tptp.in @t169 @t166)) % 1.14/1.34 (define @t191 () (not @t183)) % 1.14/1.34 (define @t192 () (or @t191 @t190)) % 1.14/1.34 (define @t193 () (@list @t192)) % 1.14/1.34 (define @t194 () (@quantifiers_skolemize @t181 0)) % 1.14/1.34 (define @t195 () (tptp.in @t194 @t179)) % 1.14/1.34 (define @t196 () (tptp.in @t194 @t164)) % 1.14/1.34 (define @t197 () (not @t196)) % 1.14/1.34 (define @t198 () (tptp.in (tptp.ordered_pair @t169 @t194) @t163)) % 1.14/1.34 (define @t199 () (not @t198)) % 1.14/1.34 (define @t200 () (not @t195)) % 1.14/1.34 (define @t201 () (or @t200 @t199 @t197)) % 1.14/1.34 (define @t202 () (@list @t201)) % 1.14/1.34 (define @t203 () (forall @t41 (or @t180 @t178 (not (tptp.in @t16 @t165))))) % 1.14/1.34 (define @t204 () (not @t203)) % 1.14/1.34 (define @t205 () (= @t190 @t204)) % 1.14/1.34 (define @t206 () (or @t174 @t205)) % 1.14/1.34 (define @t207 () (not @t205)) % 1.14/1.34 (define @t208 () (@var "BOUND_VARIABLE_9128" $$unsorted)) % 1.14/1.34 (define @t209 () (tptp.in @t208 @t1)) % 1.14/1.34 (define @t210 () (not (tptp.in @t208 @t2))) % 1.14/1.34 (define @t211 () (not @t69)) % 1.14/1.34 (define @t212 () (or @t210 @t209)) % 1.14/1.34 (define @t213 () (or @t211 @t212)) % 1.14/1.34 (define @t214 () (forall (@list @t1 @t2 @t208) @t213)) % 1.14/1.34 (define @t215 () (@list @t208)) % 1.14/1.34 (define @t216 () (forall @t215 @t213)) % 1.14/1.34 (define @t217 () (forall @t215 @t212)) % 1.14/1.34 (define @t218 () (or @t211 @t217)) % 1.14/1.34 (define @t219 () (forall @t37 (or @t107 @t18))) % 1.14/1.34 (define @t220 () (tptp.element @t164 (tptp.powerset @t165))) % 1.14/1.34 (define @t221 () (= @t172 @t220)) % 1.14/1.34 (define @t222 () (tptp.in @t194 @t165)) % 1.14/1.34 (define @t223 () (not @t220)) % 1.14/1.34 (define @t224 () (or @t223 @t197 @t222)) % 1.14/1.34 (define @t225 () (not @t222)) % 1.14/1.34 (define @t226 () (or @t200 @t199 @t225)) % 1.14/1.34 (assume @p1 (forall @t6 (=> @t5 @t4))) % 1.14/1.34 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 1.14/1.34 (assume @p3 (forall @t11 (=> @t10 @t9))) % 1.14/1.34 (assume @p4 (forall @t6 (= @t12 (tptp.unordered_pair @t2 @t1)))) % 1.14/1.34 (assume @p5 (forall @t6 (= @t14 @t13))) % 1.14/1.34 (assume @p6 (forall @t6 (= @t15 (tptp.set_intersection2 @t2 @t1)))) % 1.14/1.34 (assume @p7 (forall @t6 (=> @t23 (= (= @t2 @t22) (forall @t21 (= @t20 (and @t18 (= @t17 @t16)))))))) % 1.14/1.34 (assume @p8 (forall @t6 (= @t25 (and @t24 (tptp.subset @t2 @t1))))) % 1.14/1.34 (assume @p9 (forall @t11 (=> @t9 (forall @t34 (=> @t33 (= (= @t17 @t32) (forall @t31 (= @t30 (and @t29 @t28))))))))) % 1.14/1.34 (assume @p10 (forall @t6 (=> @t23 (forall @t37 (=> @t33 (= (= @t17 @t36) (forall @t31 (= @t30 (and @t35 (tptp.in @t27 @t2)))))))))) % 1.14/1.34 (assume @p11 (forall @t11 (=> @t9 (forall @t34 (= (= @t17 (tptp.relation_image @t1 @t2)) (forall @t41 (= @t40 (exists @t39 (and (tptp.in (tptp.ordered_pair @t26 @t16) @t1) @t38))))))))) % 1.14/1.34 (assume @p12 (forall @t11 (=> @t9 (forall @t34 (= (= @t17 (tptp.relation_inverse_image @t1 @t2)) (forall @t41 (= @t40 (exists @t39 (and @t28 @t38))))))))) % 1.14/1.34 (assume @p13 (forall @t11 (= @t9 (forall @t42 (not (and @t3 (forall @t21 (not (= @t2 @t19))))))))) % 1.14/1.34 (assume @p14 (forall @t6 (and (=> @t49 (= @t44 (forall @t37 (= @t48 (forall @t41 (=> @t47 @t46)))))) (=> @t45 (= @t44 @t43))))) % 1.14/1.34 (assume @p15 (forall @t6 (= (= @t2 @t50) (forall @t37 (= @t48 (= @t17 @t1)))))) % 1.14/1.34 (assume @p16 (forall @t11 (= @t45 (forall @t42 @t4)))) % 1.14/1.34 (assume @p17 (forall @t6 (= (= @t2 @t51) (forall @t37 (= @t48 (tptp.subset @t17 @t1)))))) % 1.14/1.34 (assume @p18 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= @t25 (forall @t21 (= @t52 @t20)))))))) % 1.14/1.34 (assume @p19 (forall @t6 (and (=> @t55 (= @t54 @t3)) (=> @t10 (= @t54 @t53))))) % 1.14/1.34 (assume @p20 (forall @t56 (= (= @t17 @t12) (forall @t41 (= @t40 (or (= @t16 @t1) (= @t16 @t2))))))) % 1.14/1.34 (assume @p21 (forall @t56 (= (= @t17 @t14) (forall @t41 (= @t40 (or @t47 @t29)))))) % 1.14/1.34 (assume @p22 (forall @t56 (= (= @t17 @t58) (forall @t41 (= @t40 (exists (@list @t26 @t57) (and @t35 (tptp.in @t57 @t2) (= @t16 (tptp.ordered_pair @t26 @t57))))))))) % 1.14/1.34 (assume @p23 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= @t24 (forall @t21 (=> @t52 @t20)))))))) % 1.14/1.34 (assume @p24 @t61) % 1.14/1.34 (assume @p25 (forall @t56 (= (= @t17 @t15) (forall @t41 (= @t40 (and @t47 @t29)))))) % 1.14/1.34 (assume @p26 (forall @t11 (=> @t9 (forall @t42 (= (= @t2 @t62) (forall @t37 (= @t48 (exists @t41 @t52)))))))) % 1.14/1.34 (assume @p27 (forall @t11 (= @t63 @t1))) % 1.14/1.34 (assume @p28 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t37 (= @t48 (exists @t41 (and @t46 @t47))))))) % 1.14/1.34 (assume @p29 (forall @t56 (= (= @t17 @t65) (forall @t41 (= @t40 (and @t47 @t64)))))) % 1.14/1.34 (assume @p30 (forall @t11 (=> @t9 (forall @t42 (= (= @t2 @t67) (forall @t37 (= @t48 (exists @t41 @t66)))))))) % 1.14/1.34 (assume @p31 (forall @t6 (=> @t69 (= @t68 @t65)))) % 1.14/1.34 (assume @p32 (forall @t6 (= @t70 (tptp.unordered_pair @t12 @t50)))) % 1.14/1.34 (assume @p33 (forall @t11 (=> @t9 (= (tptp.relation_field @t1) (tptp.set_union2 @t62 @t67))))) % 1.14/1.34 (assume @p34 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= (= @t2 @t71) (forall @t21 (= @t20 @t66)))))))) % 1.14/1.34 (assume @p35 (forall @t6 (= @t72 (= @t15 tptp.empty_set)))) % 1.14/1.34 (assume @p36 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (forall @t37 (=> @t33 (= (= @t17 @t73) (forall @t31 (= @t30 (exists (@list @t57) (and (tptp.in (tptp.ordered_pair @t16 @t57) @t1) (tptp.in (tptp.ordered_pair @t57 @t26) @t2))))))))))))) % 1.14/1.34 (assume @p37 (forall @t6 (=> @t76 (forall @t37 (=> (tptp.element @t17 @t75) (= (= @t17 @t74) (forall @t41 (=> (tptp.element @t16 @t51) (= @t40 (tptp.in (tptp.subset_complement @t1 @t16) @t2)))))))))) % 1.14/1.34 (assume @p38 (forall @t6 (= @t8 (and @t24 @t77)))) % 1.14/1.34 (assume @p39 true) % 1.14/1.34 (assume @p40 (forall @t11 (tptp.element @t63 @t51))) % 1.14/1.34 (assume @p41 (forall @t6 (=> @t69 (tptp.element @t68 @t51)))) % 1.14/1.34 (assume @p42 (forall @t11 (=> @t9 (tptp.relation @t71)))) % 1.14/1.34 (assume @p43 (forall @t6 (=> @t79 @t78))) % 1.14/1.34 (assume @p44 (forall @t6 (=> @t76 (tptp.element @t80 @t51)))) % 1.14/1.34 (assume @p45 (forall @t11 (tptp.relation @t22))) % 1.14/1.34 (assume @p46 (forall @t6 (=> @t76 (tptp.element @t81 @t51)))) % 1.14/1.34 (assume @p47 (forall @t56 (=> @t84 (tptp.element @t82 @t51)))) % 1.14/1.34 (assume @p48 (forall @t6 (=> @t9 (tptp.relation @t32)))) % 1.14/1.34 (assume @p49 (forall @t6 (=> @t76 (tptp.element @t74 @t75)))) % 1.14/1.34 (assume @p50 (forall @t6 (=> @t23 (tptp.relation @t36)))) % 1.14/1.34 (assume @p51 (forall @t11 (exists @t42 @t54))) % 1.14/1.34 (assume @p52 (forall @t6 (=> @t86 (and (tptp.empty @t85) (tptp.relation @t85))))) % 1.14/1.34 (assume @p53 (forall @t6 (=> @t79 (tptp.relation @t15)))) % 1.14/1.34 (assume @p54 (forall @t11 (not (tptp.empty @t51)))) % 1.14/1.34 (assume @p55 @t87) % 1.14/1.34 (assume @p56 (forall @t6 (not (tptp.empty @t70)))) % 1.14/1.34 (assume @p57 (forall @t6 (=> @t79 (tptp.relation @t14)))) % 1.14/1.34 (assume @p58 (forall @t11 (not (tptp.empty @t50)))) % 1.14/1.34 (assume @p59 (forall @t6 (=> @t55 (not (tptp.empty @t14))))) % 1.14/1.34 (assume @p60 (forall @t6 (not (tptp.empty @t12)))) % 1.14/1.34 (assume @p61 (forall @t6 (=> @t55 (not (tptp.empty @t13))))) % 1.14/1.34 (assume @p62 (and @t87 (tptp.relation tptp.empty_set))) % 1.14/1.34 (assume @p63 (forall @t6 (=> (and @t55 @t88) (not (tptp.empty @t58))))) % 1.14/1.34 (assume @p64 (forall @t11 (=> @t90 (not @t89)))) % 1.14/1.34 (assume @p65 (forall @t11 (=> @t90 (not @t91)))) % 1.14/1.34 (assume @p66 (forall @t11 (=> @t10 (and @t89 (tptp.relation @t62))))) % 1.14/1.34 (assume @p67 (forall @t11 (=> @t10 (and @t91 (tptp.relation @t67))))) % 1.14/1.34 (assume @p68 (forall @t6 (=> @t86 (and (tptp.empty @t73) @t78)))) % 1.14/1.34 (assume @p69 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 1.14/1.34 (assume @p70 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 1.14/1.34 (assume @p71 (forall @t6 (=> @t69 (= (tptp.subset_complement @t1 @t68) @t2)))) % 1.14/1.34 (assume @p72 (forall @t11 (=> @t9 (= (tptp.relation_inverse @t71) @t1)))) % 1.14/1.34 (assume @p73 (forall @t6 (=> @t76 (= (tptp.complements_of_subsets @t1 @t74) @t2)))) % 1.14/1.34 (assume @p74 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 1.14/1.34 (assume @p75 (forall @t11 (not (= @t50 tptp.empty_set)))) % 1.14/1.34 (assume @p76 (forall @t6 (=> @t5 (= (tptp.set_union2 @t50 @t2) @t2)))) % 1.14/1.34 (assume @p77 (forall @t6 (not (and @t92 @t5)))) % 1.14/1.34 (assume @p78 (forall @t6 (=> (not @t5) @t92))) % 1.14/1.34 (assume @p79 (forall @t6 (= (tptp.subset @t50 @t2) @t5))) % 1.14/1.34 (assume @p80 (forall @t6 (= (= @t65 tptp.empty_set) @t24))) % 1.14/1.34 (assume @p81 @t95) % 1.14/1.34 (assume @p82 (forall @t56 (=> @t24 (or @t18 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t17))))))) % 1.14/1.34 (assume @p83 (forall @t6 (= (tptp.subset @t1 @t96) (or @t45 (= @t1 @t96))))) % 1.14/1.34 (assume @p84 (forall @t6 (=> @t5 (tptp.subset @t1 @t97)))) % 1.14/1.34 (assume @p85 (forall @t99 (= (tptp.in @t70 (tptp.cartesian_product2 @t17 @t16)) (and @t98 (tptp.in @t2 @t16))))) % 1.14/1.34 (assume @p86 (forall @t6 (=> @t59 @t100))) % 1.14/1.34 (assume @p87 (exists @t11 (and @t10 @t9))) % 1.14/1.34 (assume @p88 (forall @t11 (=> @t55 (exists @t42 (and @t69 @t88))))) % 1.14/1.34 (assume @p89 (exists @t11 @t10)) % 1.14/1.34 (assume @p90 (exists @t11 @t90)) % 1.14/1.34 (assume @p91 (forall @t11 (exists @t42 (and @t69 @t53)))) % 1.14/1.34 (assume @p92 (exists @t11 @t55)) % 1.14/1.34 (assume @p93 (forall @t6 (=> @t76 (= @t80 @t97)))) % 1.14/1.34 (assume @p94 (forall @t6 (=> @t76 (= @t81 (tptp.set_meet @t2))))) % 1.14/1.34 (assume @p95 (forall @t56 (=> @t84 (= @t82 @t101)))) % 1.14/1.34 (assume @p96 (forall @t6 (tptp.subset @t1 @t1))) % 1.14/1.34 (assume @p97 (forall @t6 (=> @t72 (tptp.disjoint @t2 @t1)))) % 1.14/1.34 (assume @p98 (forall @t99 (not (and (= @t12 (tptp.unordered_pair @t17 @t16)) (not @t102) (not (= @t1 @t16)))))) % 1.14/1.34 (assume @p99 (forall @t56 (=> @t33 (= (tptp.in @t1 (tptp.relation_rng (tptp.relation_rng_restriction @t2 @t17))) (and @t5 (tptp.in @t1 @t103)))))) % 1.14/1.34 (assume @p100 (forall @t6 (=> @t23 (tptp.subset @t104 @t1)))) % 1.14/1.34 (assume @p101 (forall @t6 (=> @t23 (tptp.subset @t36 @t2)))) % 1.14/1.34 (assume @p102 (forall @t6 (=> @t23 (tptp.subset @t104 @t105)))) % 1.14/1.34 (assume @p103 (forall @t56 (=> @t24 (and (tptp.subset @t106 (tptp.cartesian_product2 @t2 @t17)) (tptp.subset (tptp.cartesian_product2 @t17 @t1) (tptp.cartesian_product2 @t17 @t2)))))) % 1.14/1.34 (assume @p104 (forall @t6 (=> @t23 (= @t104 (tptp.set_intersection2 @t105 @t1))))) % 1.14/1.34 (assume @p105 (forall @t99 (=> (and @t24 (tptp.subset @t17 @t16)) (tptp.subset @t106 (tptp.cartesian_product2 @t2 @t16))))) % 1.14/1.34 (assume @p106 (forall @t6 (=> @t24 (= @t14 @t2)))) % 1.14/1.34 (assume @p107 (forall @t11 (exists @t42 (and @t5 @t111 (forall @t37 (=> @t48 (tptp.in @t110 @t2))) @t109)))) % 1.14/1.34 (assume @p108 (forall @t56 (=> @t33 (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction @t1 @t17) @t2) (tptp.relation_rng_restriction @t1 @t112))))) % 1.14/1.34 (assume @p109 (forall @t56 (=> @t33 (= (tptp.in @t1 (tptp.relation_image @t17 @t2)) (exists @t41 (and (tptp.in @t16 @t113) (tptp.in (tptp.ordered_pair @t16 @t1) @t17) @t29)))))) % 1.14/1.34 (assume @p110 (forall @t6 (=> @t23 (tptp.subset @t114 @t105)))) % 1.14/1.34 (assume @p111 (forall @t6 (=> @t23 (= @t114 (tptp.relation_image @t2 @t116))))) % 1.14/1.34 (assume @p112 (forall @t11 (=> @t9 (= (tptp.relation_image @t1 @t62) @t67)))) % 1.14/1.34 (assume @p113 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (= @t117 (tptp.relation_image @t2 @t67))))))) % 1.14/1.34 (assume @p114 @t126) % 1.14/1.34 (assume @p115 (forall @t6 (=> @t23 (tptp.subset @t127 @t115)))) % 1.14/1.34 (assume @p116 (forall @t6 (=> @t23 (not (and @t49 (tptp.subset @t1 @t105) (= @t127 tptp.empty_set)))))) % 1.14/1.34 (assume @p117 @t131) % 1.14/1.34 (assume @p118 (forall @t6 (tptp.subset @t15 @t1))) % 1.14/1.34 (assume @p119 (forall @t56 (=> (and @t24 @t133) (tptp.subset @t1 @t132)))) % 1.14/1.34 (assume @p120 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 1.14/1.34 (assume @p121 (forall @t6 (=> @t5 @t134))) % 1.14/1.34 (assume @p122 (forall @t56 (=> (and @t24 (tptp.subset @t2 @t17)) @t133))) % 1.14/1.34 (assume @p123 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 1.14/1.34 (assume @p124 (forall @t56 (=> @t33 (=> @t136 (and @t135 (tptp.in @t2 @t103)))))) % 1.14/1.34 (assume @p125 (forall @t11 (=> @t9 (tptp.subset @t1 (tptp.cartesian_product2 @t62 @t67))))) % 1.14/1.34 (assume @p126 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> @t24 (and (tptp.subset @t62 @t115) (tptp.subset @t67 @t105)))))))) % 1.14/1.34 (assume @p127 (forall @t56 (=> @t24 (tptp.subset (tptp.set_intersection2 @t1 @t17) @t132)))) % 1.14/1.34 (assume @p128 (forall @t6 (=> @t24 (= @t15 @t1)))) % 1.14/1.34 (assume @p129 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.14/1.34 (assume @p130 (forall @t6 (=> @t134 (or @t53 @t5)))) % 1.14/1.34 (assume @p131 (forall @t6 (=> (forall @t37 (= @t18 @t48)) @t25))) % 1.14/1.34 (assume @p132 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 1.14/1.34 (assume @p133 (forall @t56 (=> @t33 (=> @t136 (and (tptp.in @t1 @t137) (tptp.in @t2 @t137)))))) % 1.14/1.34 (assume @p134 (forall @t56 (=> @t24 (tptp.subset (tptp.set_difference @t1 @t17) @t101)))) % 1.14/1.34 (assume @p135 (forall @t99 (=> (= @t70 @t19) (and @t102 (= @t2 @t16))))) % 1.14/1.34 (assume @p136 (forall @t6 (tptp.subset @t65 @t1))) % 1.14/1.34 (assume @p137 (forall @t11 (=> @t9 (and (= @t67 (tptp.relation_dom @t71)) (= @t62 (tptp.relation_rng @t71)))))) % 1.14/1.34 (assume @p138 (forall @t56 (= (tptp.subset @t12 @t17) (and @t98 @t138)))) % 1.14/1.34 (assume @p139 (forall @t6 (= @t139 @t14))) % 1.14/1.34 (assume @p140 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 1.14/1.34 (assume @p141 @t140) % 1.14/1.34 (assume @p142 (forall @t6 (and (not (and @t142 (forall @t37 (not @t141)))) (not (and (exists @t37 @t141) @t72))))) % 1.14/1.34 (assume @p143 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t45))) % 1.14/1.34 (assume @p144 (forall @t6 (= (tptp.set_difference @t14 @t2) @t65))) % 1.14/1.34 (assume @p145 (forall @t6 (=> @t69 (forall @t37 (=> @t83 (= @t144 (tptp.subset @t2 @t143))))))) % 1.14/1.34 (assume @p146 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (tptp.subset @t145 @t62)))))) % 1.14/1.34 (assume @p147 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (tptp.subset @t117 @t105)))))) % 1.14/1.34 (assume @p148 (forall @t6 (=> @t24 (= @t2 @t139)))) % 1.14/1.34 (assume @p149 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> (tptp.subset @t67 @t115) (= @t145 @t62))))))) % 1.14/1.34 (assume @p150 (forall @t6 (=> @t76 (not (and @t146 (= @t74 tptp.empty_set)))))) % 1.14/1.34 (assume @p151 (forall @t11 (=> @t9 (forall @t42 (=> @t23 (=> (tptp.subset @t62 @t105) (= (tptp.relation_rng @t85) @t67))))))) % 1.14/1.34 (assume @p152 (forall @t6 (=> @t76 (=> @t146 (= (tptp.subset_difference @t1 @t63 @t80) (tptp.meet_of_subsets @t1 @t74)))))) % 1.14/1.34 (assume @p153 (forall @t6 (=> @t76 (=> @t146 (= (tptp.union_of_subsets @t1 @t74) (tptp.subset_difference @t1 @t63 @t81)))))) % 1.14/1.34 (assume @p154 (forall @t6 (= (tptp.set_difference @t1 @t65) @t15))) % 1.14/1.34 (assume @p155 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 1.14/1.34 (assume @p156 (forall @t56 (=> (and @t5 @t147) (tptp.element @t1 @t17)))) % 1.14/1.34 (assume @p157 (forall @t6 (and (not (and @t142 (forall @t37 (not @t148)))) (not (and (exists @t37 @t148) @t72))))) % 1.14/1.34 (assume @p158 (forall @t11 (=> @t49 (forall @t42 (=> @t69 (forall @t37 (=> (tptp.element @t17 @t1) (=> @t107 (tptp.in @t17 @t68))))))))) % 1.14/1.34 (assume @p159 (forall @t56 (=> @t83 (not (and (tptp.in @t2 @t143) @t138))))) % 1.14/1.34 (assume @p160 (forall @t11 (=> @t9 (=> (forall @t34 (not (tptp.in (tptp.ordered_pair @t2 @t17) @t1))) @t45)))) % 1.14/1.34 (assume @p161 (forall @t56 (not (and @t5 @t147 (tptp.empty @t17))))) % 1.14/1.34 (assume @p162 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 1.14/1.34 (assume @p163 (forall @t6 (not (and @t24 @t7)))) % 1.14/1.34 (assume @p164 (forall @t56 (=> (and @t24 @t144) (tptp.disjoint @t1 @t17)))) % 1.14/1.34 (assume @p165 (forall @t11 (=> @t9 (=> (or @t150 @t149) @t45)))) % 1.14/1.34 (assume @p166 (forall @t11 (=> @t9 (= @t150 @t149)))) % 1.14/1.34 (assume @p167 (forall @t6 (= (= (tptp.set_difference @t1 @t96) @t1) @t4))) % 1.14/1.34 (assume @p168 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t50))) % 1.14/1.34 (assume @p169 (forall @t11 (=> @t10 @t45))) % 1.14/1.34 (assume @p170 (forall @t6 (=> (tptp.subset @t50 @t96) @t25))) % 1.14/1.34 (assume @p171 (forall @t11 (and (= (tptp.relation_dom @t22) @t1) (= (tptp.relation_rng @t22) @t1)))) % 1.14/1.34 (assume @p172 (forall @t99 (=> (tptp.relation @t16) (= (tptp.in @t70 (tptp.relation_composition (tptp.identity_relation @t17) @t16)) (and @t98 (tptp.in @t70 @t16)))))) % 1.14/1.34 (assume @p173 (forall @t6 (not (and @t5 @t53)))) % 1.14/1.34 (assume @p174 (forall @t6 (tptp.subset @t1 @t14))) % 1.14/1.34 (assume @p175 (forall @t6 (= @t72 (= @t65 @t1)))) % 1.14/1.34 (assume @p176 (forall @t56 (=> @t33 (= (tptp.in @t1 (tptp.relation_dom @t112)) (and @t5 @t135))))) % 1.14/1.34 (assume @p177 (forall @t6 (=> @t23 (tptp.subset @t151 @t2)))) % 1.14/1.34 (assume @p178 (forall @t6 (not (and @t10 @t77 @t53)))) % 1.14/1.34 (assume @p179 (forall @t56 (=> (and @t24 @t108) (tptp.subset (tptp.set_union2 @t1 @t17) @t2)))) % 1.14/1.34 (assume @p180 (forall @t56 (=> @t152 @t25))) % 1.14/1.34 (assume @p181 (forall @t6 (=> @t23 (= (tptp.relation_dom @t151) @t116)))) % 1.14/1.34 (assume @p182 (forall @t6 (=> @t23 (= @t151 (tptp.relation_composition @t22 @t2))))) % 1.14/1.34 (assume @p183 (forall @t6 (=> @t23 (tptp.subset (tptp.relation_rng @t151) @t105)))) % 1.14/1.34 (assume @p184 (forall @t11 (= (tptp.union @t51) @t1))) % 1.14/1.34 (assume @p185 (forall @t11 (exists @t42 (and @t5 @t111 (forall @t37 (not (and @t48 (forall @t41 (not (and @t29 (forall @t39 (=> (tptp.subset @t26 @t17) (tptp.in @t26 @t16))))))))) @t109)))) % 1.14/1.34 (assume @p186 (forall @t56 (=> @t152 (= @t2 @t17)))) % 1.14/1.34 (step @p187 :rule bool-impl-elim :args (@t33 @t156)) % 1.14/1.34 (step @p188 :rule cong :premises (@p187) :args ((forall @t56 (=> @t33 @t156)))) % 1.14/1.34 (step @p189 :rule aci_norm :args ((= (or @t154 (or @t153 @t64)) @t155))) % 1.14/1.34 (step @p190 :rule bool-and-de-morgan :args (@t118 @t29 true)) % 1.14/1.34 (step @p191 :rule refl :args (@t154)) % 1.14/1.34 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t154 (not (and @t118 @t29))))) % 1.14/1.34 (step @p193 :rule bool-and-de-morgan :args (@t119 @t118 (and @t29))) % 1.14/1.34 (step @p194 :rule trans :premises (@p193 @p192)) % 1.14/1.34 (step @p195 :rule trans :premises (@p194 @p189)) % 1.14/1.34 (step @p196 :rule cong :premises (@p195) :args (@t157)) % 1.14/1.34 (step @p197 :rule cong :premises (@p196) :args (@t158)) % 1.14/1.34 (step @p198 :rule exists-elim :args ((= @t121 @t158))) % 1.14/1.34 (step @p199 :rule trans :premises (@p198 @p197)) % 1.14/1.34 (step @p200 :rule refl :args (@t123)) % 1.14/1.34 (step @p201 :rule cong :premises (@p200 @p199) :args (@t124)) % 1.14/1.34 (step @p202 :rule refl :args (@t33)) % 1.14/1.34 (step @p203 :rule cong :premises (@p202 @p201) :args (@t125)) % 1.14/1.34 (step @p204 :rule cong :premises (@p203) :args (@t126)) % 1.14/1.34 (step @p205 :rule trans :premises (@p204 @p188)) % 1.14/1.34 (step @p206 :rule eq_resolve :premises (@p114 @p205)) % 1.14/1.34 (step @p207 :rule instantiate :premises (@p206) :args ((@list @t169 @t164 @t163))) % 1.14/1.34 (step @p208 :rule aci_norm :args ((= (or @t160 (or @t159 @t128)) @t161))) % 1.14/1.34 (step @p209 :rule bool-impl-elim :args (@t24 @t128)) % 1.14/1.34 (step @p210 :rule refl :args (@t160)) % 1.14/1.34 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t160 @t129))) % 1.14/1.34 (step @p212 :rule trans :premises (@p211 @p208)) % 1.14/1.34 (step @p213 :rule bool-impl-elim :args (@t33 @t129)) % 1.14/1.34 (step @p214 :rule trans :premises (@p213 @p212)) % 1.14/1.34 (step @p215 :rule cong :premises (@p214) :args (@t130)) % 1.14/1.34 (step @p216 :rule cong :premises (@p215) :args (@t131)) % 1.14/1.34 (step @p217 :rule eq_resolve :premises (@p117 @p216)) % 1.14/1.34 (step @p218 :rule skolemize :premises (@p217)) % 1.14/1.34 (step @p219 :rule bool-double-not-elim :args (@t170)) % 1.14/1.34 (step @p220 :rule refl :args (@t175)) % 1.14/1.34 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or @t175 (not @t174)))) % 1.14/1.34 (step @p222 :rule cnf_or_neg :args (@t175 0)) % 1.14/1.34 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 1.14/1.34 (step @p224 :rule reordering :premises (@p223) :args ((or @t170 @t175))) % 1.14/1.34 (step @p225 :rule chain_m_resolution :premises (@p224 @p218) :args (@t170 @t176 @t177)) % 1.14/1.34 (step @p226 :rule cnf_or_pos :args (@t185)) % 1.14/1.34 (step @p227 :rule reordering :premises (@p226) :args ((or @t174 @t184 (not @t185)))) % 1.14/1.34 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p207) :args (@t184 @t186 (@list @t170 @t185))) % 1.14/1.34 (step @p229 :rule bool-impl-elim :args (@t18 @t48)) % 1.14/1.34 (step @p230 :rule cong :premises (@p229) :args (@t59)) % 1.14/1.34 (step @p231 :rule refl :args (@t24)) % 1.14/1.34 (step @p232 :rule cong :premises (@p231 @p230) :args (@t60)) % 1.14/1.34 (step @p233 :rule cong :premises (@p232) :args (@t61)) % 1.14/1.34 (step @p234 :rule eq_resolve :premises (@p24 @p233)) % 1.14/1.34 (step @p235 :rule instantiate :premises (@p234) :args ((@list @t167 @t166))) % 1.14/1.34 (step @p236 :rule cnf_or_neg :args (@t175 2)) % 1.14/1.34 (step @p237 :rule chain_m_resolution :premises (@p236 @p218) :args ((not @t171) @t176 @t177)) % 1.14/1.34 (step @p238 :rule cnf_equiv_pos2 :args (@t187)) % 1.14/1.34 (step @p239 :rule reordering :premises (@p238) :args ((or @t171 @t188 (not @t187)))) % 1.14/1.34 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p235) :args (@t188 @t189 (@list @t171 @t187))) % 1.14/1.34 (step @p241 :rule skolemize :premises (@p240)) % 1.14/1.34 (step @p242 :rule bool-double-not-elim :args (@t183)) % 1.14/1.34 (step @p243 :rule refl :args (@t192)) % 1.14/1.34 (step @p244 :rule nary_cong :premises (@p243 @p242) :args ((or @t192 (not @t191)))) % 1.14/1.34 (step @p245 :rule cnf_or_neg :args (@t192 0)) % 1.14/1.34 (step @p246 :rule eq_resolve :premises (@p245 @p244)) % 1.14/1.34 (step @p247 :rule reordering :premises (@p246) :args ((or @t183 @t192))) % 1.14/1.34 (step @p248 :rule chain_m_resolution :premises (@p247 @p241) :args (@t183 @t176 @t193)) % 1.14/1.34 (step @p249 :rule cnf_equiv_pos1 :args (@t184)) % 1.14/1.34 (step @p250 :rule reordering :premises (@p249) :args ((or @t191 @t182 (not @t184)))) % 1.14/1.34 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p228) :args (@t182 @t186 (@list @t183 @t184))) % 1.14/1.34 (step @p252 :rule skolemize :premises (@p251)) % 1.14/1.34 (step @p253 :rule bool-double-not-elim :args (@t195)) % 1.14/1.34 (step @p254 :rule refl :args (@t201)) % 1.14/1.34 (step @p255 :rule nary_cong :premises (@p254 @p253) :args ((or @t201 (not @t200)))) % 1.14/1.34 (step @p256 :rule cnf_or_neg :args (@t201 0)) % 1.14/1.34 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 1.14/1.34 (step @p258 :rule reordering :premises (@p257) :args ((or @t195 @t201))) % 1.14/1.34 (step @p259 :rule chain_m_resolution :premises (@p258 @p252) :args (@t195 @t176 @t202)) % 1.14/1.34 (step @p260 :rule bool-double-not-elim :args (@t198)) % 1.14/1.34 (step @p261 :rule nary_cong :premises (@p254 @p260) :args ((or @t201 (not @t199)))) % 1.14/1.34 (step @p262 :rule cnf_or_neg :args (@t201 1)) % 1.14/1.34 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 1.14/1.34 (step @p264 :rule reordering :premises (@p263) :args ((or @t198 @t201))) % 1.14/1.34 (step @p265 :rule chain_m_resolution :premises (@p264 @p252) :args (@t198 @t176 @t202)) % 1.14/1.34 (step @p266 :rule instantiate :premises (@p206) :args ((@list @t169 @t165 @t163))) % 1.14/1.34 (step @p267 :rule cnf_or_pos :args (@t206)) % 1.14/1.34 (step @p268 :rule reordering :premises (@p267) :args ((or @t174 @t205 (not @t206)))) % 1.14/1.34 (step @p269 :rule chain_m_resolution :premises (@p268 @p225 @p266) :args (@t205 @t186 (@list @t170 @t206))) % 1.14/1.34 (step @p270 :rule cnf_or_neg :args (@t192 1)) % 1.14/1.34 (step @p271 :rule chain_m_resolution :premises (@p270 @p241) :args ((not @t190) @t176 @t193)) % 1.14/1.34 (step @p272 :rule bool-double-not-elim :args (@t203)) % 1.14/1.34 (step @p273 :rule refl :args (@t190)) % 1.14/1.34 (step @p274 :rule refl :args (@t207)) % 1.14/1.34 (step @p275 :rule nary_cong :premises (@p274 @p273 @p272) :args ((or @t207 @t190 (not @t204)))) % 1.14/1.34 (step @p276 :rule cnf_equiv_pos2 :args (@t205)) % 1.14/1.34 (step @p277 :rule eq_resolve :premises (@p276 @p275)) % 1.14/1.34 (step @p278 :rule reordering :premises (@p277) :args ((or @t190 @t203 @t207))) % 1.14/1.34 (step @p279 :rule chain_m_resolution :premises (@p278 @p271 @p269) :args (@t203 @t189 (@list @t190 @t205))) % 1.14/1.34 (step @p280 :rule instantiate :premises (@p279) :args ((@list @t194))) % 1.14/1.34 (step @p281 :rule aci_norm :args ((= @t213 (or @t211 @t210 @t209)))) % 1.14/1.34 (step @p282 :rule cong :premises (@p281) :args (@t214)) % 1.14/1.34 (step @p283 :rule quant-merge-prenex :args ((= (forall @t6 @t216) @t214))) % 1.14/1.34 (step @p284 :rule alpha_equiv :args (@t217 (@list @t208) (@list @t17))) % 1.14/1.34 (step @p285 :rule refl :args (@t211)) % 1.14/1.34 (step @p286 :rule nary_cong :premises (@p285 @p284) :args (@t218)) % 1.14/1.34 (step @p287 :rule quant-miniscope-or :args ((= @t216 @t218))) % 1.14/1.34 (step @p288 :rule trans :premises (@p287 @p286)) % 1.14/1.34 (step @p289 :rule symm :premises (@p288)) % 1.14/1.34 (step @p290 :rule cong :premises (@p289) :args ((forall @t6 (or @t211 @t219)))) % 1.14/1.34 (step @p291 :rule trans :premises (@p290 @p283)) % 1.14/1.34 (step @p292 :rule trans :premises (@p291 @p282)) % 1.14/1.34 (step @p293 :rule bool-impl-elim :args (@t69 @t219)) % 1.14/1.34 (step @p294 :rule cong :premises (@p293) :args ((forall @t6 (=> @t69 @t219)))) % 1.14/1.34 (step @p295 :rule trans :premises (@p294 @p292)) % 1.14/1.34 (step @p296 :rule bool-impl-elim :args (@t48 @t18)) % 1.14/1.34 (step @p297 :rule cong :premises (@p296) :args (@t93)) % 1.14/1.34 (step @p298 :rule refl :args (@t69)) % 1.14/1.34 (step @p299 :rule cong :premises (@p298 @p297) :args (@t94)) % 1.14/1.34 (step @p300 :rule cong :premises (@p299) :args (@t95)) % 1.14/1.34 (step @p301 :rule trans :premises (@p300 @p295)) % 1.14/1.34 (step @p302 :rule eq_resolve :premises (@p81 @p301)) % 1.14/1.34 (step @p303 :rule instantiate :premises (@p302) :args ((@list @t165 @t164 @t194))) % 1.14/1.34 (step @p304 :rule bool-double-not-elim :args (@t196)) % 1.14/1.34 (step @p305 :rule nary_cong :premises (@p254 @p304) :args ((or @t201 (not @t197)))) % 1.14/1.34 (step @p306 :rule cnf_or_neg :args (@t201 2)) % 1.14/1.34 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 1.14/1.34 (step @p308 :rule reordering :premises (@p307) :args ((or @t196 @t201))) % 1.14/1.34 (step @p309 :rule chain_m_resolution :premises (@p308 @p252) :args (@t196 @t176 @t202)) % 1.14/1.34 (step @p310 :rule eq-symm :args (@t100 @t24)) % 1.14/1.34 (step @p311 :rule cong :premises (@p310) :args (@t140)) % 1.14/1.34 (step @p312 :rule eq_resolve :premises (@p141 @p311)) % 1.14/1.34 (step @p313 :rule instantiate :premises (@p312) :args ((@list @t164 @t165))) % 1.14/1.34 (step @p314 :rule bool-double-not-elim :args (@t172)) % 1.14/1.34 (step @p315 :rule nary_cong :premises (@p220 @p314) :args ((or @t175 (not @t173)))) % 1.14/1.34 (step @p316 :rule cnf_or_neg :args (@t175 1)) % 1.14/1.34 (step @p317 :rule eq_resolve :premises (@p316 @p315)) % 1.14/1.34 (step @p318 :rule reordering :premises (@p317) :args ((or @t172 @t175))) % 1.14/1.34 (step @p319 :rule chain_m_resolution :premises (@p318 @p218) :args (@t172 @t176 @t177)) % 1.14/1.34 (step @p320 :rule cnf_equiv_pos1 :args (@t221)) % 1.14/1.34 (step @p321 :rule reordering :premises (@p320) :args ((or @t173 @t220 (not @t221)))) % 1.14/1.34 (step @p322 :rule chain_m_resolution :premises (@p321 @p319 @p313) :args (@t220 @t186 (@list @t172 @t221))) % 1.14/1.34 (step @p323 :rule cnf_or_pos :args (@t224)) % 1.14/1.34 (step @p324 :rule reordering :premises (@p323) :args ((or @t223 @t197 @t222 (not @t224)))) % 1.14/1.34 (step @p325 :rule chain_m_resolution :premises (@p324 @p322 @p309 @p303) :args (@t222 (@list false false false) (@list @t220 @t196 @t224))) % 1.14/1.34 (step @p326 :rule cnf_or_pos :args (@t226)) % 1.14/1.34 (step @p327 :rule reordering :premises (@p326) :args ((or @t200 @t199 @t225 (not @t226)))) % 1.14/1.34 (step @p328 false :rule chain_m_resolution :premises (@p327 @p325 @p280 @p265 @p259) :args (false (@list false false false false) (@list @t222 @t226 @t198 @t195))) % 1.14/1.34 ) % 1.14/1.34 % SZS output end Proof % 1.14/1.34 % cvc5 exiting %------------------------------------------------------------------------------