%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU340+1 : 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 : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:51:26 AM UTC 2026 % Result : Theorem 0.72s 0.99s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU340+1 : 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 : n006.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:59:19 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.72/0.99 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.72/0.99 % SZS status Theorem % 0.72/0.99 % SZS output start Proof % 0.72/0.99 ( % 0.72/0.99 (declare-sort $$unsorted 0) % 0.72/0.99 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.empty_set $$unsorted) % 0.72/0.99 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.the_InternalRel (-> $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.related (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.relation_of2 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.relation_of2_as_subset (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.is_transitive_in (-> $$unsorted $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.transitive_relstr (-> $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.72/0.99 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 0.72/0.99 (declare-const tptp.rel_str (-> $$unsorted Bool)) % 0.72/0.99 (define @t1 () (@var "A" $$unsorted)) % 0.72/0.99 (define @t2 () (@var "B" $$unsorted)) % 0.72/0.99 (define @t3 () (tptp.in @t1 @t2)) % 0.72/0.99 (define @t4 () (@list @t1 @t2)) % 0.72/0.99 (define @t5 () (@var "C" $$unsorted)) % 0.72/0.99 (define @t6 () (tptp.relation @t5)) % 0.72/0.99 (define @t7 () (tptp.cartesian_product2 @t1 @t2)) % 0.72/0.99 (define @t8 () (tptp.element @t5 (tptp.powerset @t7))) % 0.72/0.99 (define @t9 () (@list @t1 @t2 @t5)) % 0.72/0.99 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.72/0.99 (define @t11 () (tptp.unordered_pair @t1 @t2)) % 0.72/0.99 (define @t12 () (tptp.the_carrier @t1)) % 0.72/0.99 (define @t13 () (tptp.the_InternalRel @t1)) % 0.72/0.99 (define @t14 () (tptp.transitive_relstr @t1)) % 0.72/0.99 (define @t15 () (= @t14 (tptp.is_transitive_in @t13 @t12))) % 0.72/0.99 (define @t16 () (tptp.rel_str @t1)) % 0.72/0.99 (define @t17 () (@list @t1)) % 0.72/0.99 (define @t18 () (forall @t17 (=> @t16 @t15))) % 0.72/0.99 (define @t19 () (tptp.singleton @t1)) % 0.72/0.99 (define @t20 () (tptp.ordered_pair @t1 @t2)) % 0.72/0.99 (define @t21 () (@var "E" $$unsorted)) % 0.72/0.99 (define @t22 () (tptp.ordered_pair @t5 @t21)) % 0.72/0.99 (define @t23 () (tptp.in @t22 @t1)) % 0.72/0.99 (define @t24 () (@var "D" $$unsorted)) % 0.72/0.99 (define @t25 () (tptp.ordered_pair @t24 @t21)) % 0.72/0.99 (define @t26 () (tptp.in @t25 @t1)) % 0.72/0.99 (define @t27 () (tptp.ordered_pair @t5 @t24)) % 0.72/0.99 (define @t28 () (tptp.in @t27 @t1)) % 0.72/0.99 (define @t29 () (tptp.in @t21 @t2)) % 0.72/0.99 (define @t30 () (tptp.in @t24 @t2)) % 0.72/0.99 (define @t31 () (tptp.in @t5 @t2)) % 0.72/0.99 (define @t32 () (and @t31 @t30 @t29 @t28 @t26)) % 0.72/0.99 (define @t33 () (@list @t5 @t24 @t21)) % 0.72/0.99 (define @t34 () (forall @t33 (=> @t32 @t23))) % 0.72/0.99 (define @t35 () (tptp.is_transitive_in @t1 @t2)) % 0.72/0.99 (define @t36 () (= @t35 @t34)) % 0.72/0.99 (define @t37 () (@list @t2)) % 0.72/0.99 (define @t38 () (forall @t37 @t36)) % 0.72/0.99 (define @t39 () (tptp.relation @t1)) % 0.72/0.99 (define @t40 () (=> @t39 @t38)) % 0.72/0.99 (define @t41 () (forall @t17 @t40)) % 0.72/0.99 (define @t42 () (tptp.related @t1 @t2 @t5)) % 0.72/0.99 (define @t43 () (= @t42 (tptp.in (tptp.ordered_pair @t2 @t5) @t13))) % 0.72/0.99 (define @t44 () (tptp.element @t5 @t12)) % 0.72/0.99 (define @t45 () (@list @t5)) % 0.72/0.99 (define @t46 () (forall @t45 (=> @t44 @t43))) % 0.72/0.99 (define @t47 () (tptp.element @t2 @t12)) % 0.72/0.99 (define @t48 () (=> @t47 @t46)) % 0.72/0.99 (define @t49 () (forall @t37 @t48)) % 0.72/0.99 (define @t50 () (=> @t16 @t49)) % 0.72/0.99 (define @t51 () (forall @t17 @t50)) % 0.72/0.99 (define @t52 () (tptp.one_sorted_str @t1)) % 0.72/0.99 (define @t53 () (tptp.relation_of2_as_subset @t5 @t1 @t2)) % 0.72/0.99 (define @t54 () (forall @t9 (=> @t53 @t8))) % 0.72/0.99 (define @t55 () (tptp.relation_of2_as_subset @t13 @t12 @t12)) % 0.72/0.99 (define @t56 () (forall @t17 (=> @t16 @t55))) % 0.72/0.99 (define @t57 () (tptp.relation_of2 @t5 @t1 @t2)) % 0.72/0.99 (define @t58 () (tptp.powerset @t1)) % 0.72/0.99 (define @t59 () (tptp.empty @t2)) % 0.72/0.99 (define @t60 () (not @t59)) % 0.72/0.99 (define @t61 () (tptp.empty @t1)) % 0.72/0.99 (define @t62 () (not @t61)) % 0.72/0.99 (define @t63 () (tptp.element @t2 @t58)) % 0.72/0.99 (define @t64 () (tptp.element @t1 @t2)) % 0.72/0.99 (define @t65 () (tptp.related @t1 @t2 @t24)) % 0.72/0.99 (define @t66 () (tptp.related @t1 @t5 @t24)) % 0.72/0.99 (define @t67 () (and @t42 @t66)) % 0.72/0.99 (define @t68 () (=> @t67 @t65)) % 0.72/0.99 (define @t69 () (tptp.element @t24 @t12)) % 0.72/0.99 (define @t70 () (@list @t24)) % 0.72/0.99 (define @t71 () (forall @t70 (=> @t69 @t68))) % 0.72/0.99 (define @t72 () (=> @t44 @t71)) % 0.72/0.99 (define @t73 () (forall @t45 @t72)) % 0.72/0.99 (define @t74 () (=> @t47 @t73)) % 0.72/0.99 (define @t75 () (forall @t37 @t74)) % 0.72/0.99 (define @t76 () (and @t14 @t16)) % 0.72/0.99 (define @t77 () (=> @t76 @t75)) % 0.72/0.99 (define @t78 () (forall @t17 @t77)) % 0.72/0.99 (define @t79 () (not @t78)) % 0.72/0.99 (define @t80 () (or @t59 @t3)) % 0.72/0.99 (define @t81 () (forall @t4 (=> @t64 @t80))) % 0.72/0.99 (define @t82 () (tptp.element @t1 @t5)) % 0.72/0.99 (define @t83 () (tptp.element @t2 (tptp.powerset @t5))) % 0.72/0.99 (define @t84 () (and @t3 @t83)) % 0.72/0.99 (define @t85 () (forall @t9 (=> @t84 @t82))) % 0.72/0.99 (define @t86 () (tptp.empty @t5)) % 0.72/0.99 (define @t87 () (forall @t9 (not (and @t3 @t83 @t86)))) % 0.72/0.99 (define @t88 () (not @t26)) % 0.72/0.99 (define @t89 () (not @t28)) % 0.72/0.99 (define @t90 () (@var "BOUND_VARIABLE_7638" $$unsorted)) % 0.72/0.99 (define @t91 () (= (tptp.is_transitive_in @t1 @t90) (forall @t33 (or (not (tptp.in @t5 @t90)) (not (tptp.in @t24 @t90)) (not (tptp.in @t21 @t90)) @t89 @t88 @t23)))) % 0.72/0.99 (define @t92 () (not @t39)) % 0.72/0.99 (define @t93 () (or @t92 @t91)) % 0.72/0.99 (define @t94 () (@list @t90)) % 0.72/0.99 (define @t95 () (forall @t94 @t93)) % 0.72/0.99 (define @t96 () (forall @t94 @t91)) % 0.72/0.99 (define @t97 () (or @t92 @t96)) % 0.72/0.99 (define @t98 () (not @t29)) % 0.72/0.99 (define @t99 () (not @t30)) % 0.72/0.99 (define @t100 () (not @t31)) % 0.72/0.99 (define @t101 () (or @t100 @t99 @t98 @t89 @t88 @t23)) % 0.72/0.99 (define @t102 () (forall @t37 (= @t35 (forall @t33 @t101)))) % 0.72/0.99 (define @t103 () (or @t100 @t99 @t98 @t89 @t88)) % 0.72/0.99 (define @t104 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 0.72/0.99 (define @t105 () (@var "BOUND_VARIABLE_7827" $$unsorted)) % 0.72/0.99 (define @t106 () (tptp.related @t1 @t105 @t104)) % 0.72/0.99 (define @t107 () (@var "BOUND_VARIABLE_7829" $$unsorted)) % 0.72/0.99 (define @t108 () (not (tptp.related @t1 @t107 @t104))) % 0.72/0.99 (define @t109 () (not (tptp.element @t104 @t12))) % 0.72/0.99 (define @t110 () (not (tptp.related @t1 @t105 @t107))) % 0.72/0.99 (define @t111 () (not (tptp.element @t107 @t12))) % 0.72/0.99 (define @t112 () (not (tptp.element @t105 @t12))) % 0.72/0.99 (define @t113 () (not @t16)) % 0.72/0.99 (define @t114 () (not @t14)) % 0.72/0.99 (define @t115 () (or @t114 @t113 @t112 @t111 @t110 @t109 @t108 @t106)) % 0.72/0.99 (define @t116 () (@list @t1 @t105 @t107 @t104)) % 0.72/0.99 (define @t117 () (forall @t116 @t115)) % 0.72/0.99 (define @t118 () (@quantifiers_skolemize @t117 0)) % 0.72/0.99 (define @t119 () (tptp.the_carrier @t118)) % 0.72/0.99 (define @t120 () (tptp.the_InternalRel @t118)) % 0.72/0.99 (define @t121 () (@list @t119 @t119 @t120)) % 0.72/0.99 (define @t122 () (@list @t118)) % 0.72/0.99 (define @t123 () (or @t112 @t111 @t110 @t109 @t108 @t106)) % 0.72/0.99 (define @t124 () (or @t114 @t113 @t123)) % 0.72/0.99 (define @t125 () (forall @t116 @t124)) % 0.72/0.99 (define @t126 () (@list @t105 @t107 @t104)) % 0.72/0.99 (define @t127 () (forall @t126 @t124)) % 0.72/0.99 (define @t128 () (forall @t126 @t123)) % 0.72/0.99 (define @t129 () (@var "BOUND_VARIABLE_7803" $$unsorted)) % 0.72/0.99 (define @t130 () (@var "BOUND_VARIABLE_7801" $$unsorted)) % 0.72/0.99 (define @t131 () (or @t114 @t113 @t128)) % 0.72/0.99 (define @t132 () (tptp.related @t1 @t2 @t129)) % 0.72/0.99 (define @t133 () (not (tptp.related @t1 @t130 @t129))) % 0.72/0.99 (define @t134 () (not (tptp.element @t129 @t12))) % 0.72/0.99 (define @t135 () (not (tptp.related @t1 @t2 @t130))) % 0.72/0.99 (define @t136 () (not (tptp.element @t130 @t12))) % 0.72/0.99 (define @t137 () (not @t47)) % 0.72/0.99 (define @t138 () (or @t137 @t136 @t135 @t134 @t133 @t132)) % 0.72/0.99 (define @t139 () (@list @t2 @t130 @t129)) % 0.72/0.99 (define @t140 () (forall @t139 @t138)) % 0.72/0.99 (define @t141 () (or @t114 @t113 @t140)) % 0.72/0.99 (define @t142 () (or @t136 @t135 @t134 @t133 @t132)) % 0.72/0.99 (define @t143 () (or @t137 @t142)) % 0.72/0.99 (define @t144 () (forall @t139 @t143)) % 0.72/0.99 (define @t145 () (@list @t130 @t129)) % 0.72/0.99 (define @t146 () (forall @t145 @t143)) % 0.72/0.99 (define @t147 () (forall @t145 @t142)) % 0.72/0.99 (define @t148 () (@var "BOUND_VARIABLE_7784" $$unsorted)) % 0.72/0.99 (define @t149 () (or @t137 @t147)) % 0.72/0.99 (define @t150 () (tptp.related @t1 @t2 @t148)) % 0.72/0.99 (define @t151 () (not (tptp.related @t1 @t5 @t148))) % 0.72/0.99 (define @t152 () (not (tptp.element @t148 @t12))) % 0.72/0.99 (define @t153 () (not @t42)) % 0.72/0.99 (define @t154 () (not @t44)) % 0.72/0.99 (define @t155 () (or @t154 @t153 @t152 @t151 @t150)) % 0.72/0.99 (define @t156 () (@list @t5 @t148)) % 0.72/0.99 (define @t157 () (forall @t156 @t155)) % 0.72/0.99 (define @t158 () (or @t152 @t151 @t150)) % 0.72/0.99 (define @t159 () (or @t154 @t153 @t158)) % 0.72/0.99 (define @t160 () (forall @t156 @t159)) % 0.72/0.99 (define @t161 () (@list @t148)) % 0.72/0.99 (define @t162 () (forall @t161 @t159)) % 0.72/0.99 (define @t163 () (forall @t161 @t158)) % 0.72/0.99 (define @t164 () (or @t154 @t153 @t163)) % 0.72/0.99 (define @t165 () (not @t66)) % 0.72/0.99 (define @t166 () (not @t69)) % 0.72/0.99 (define @t167 () (or @t166 @t165 @t65)) % 0.72/0.99 (define @t168 () (forall @t70 @t167)) % 0.72/0.99 (define @t169 () (or @t154 @t153 @t168)) % 0.72/0.99 (define @t170 () (or @t153 @t168)) % 0.72/0.99 (define @t171 () (or @t153 @t167)) % 0.72/0.99 (define @t172 () (or @t166 @t153 @t165 @t65)) % 0.72/0.99 (define @t173 () (or @t153 @t165 @t65)) % 0.72/0.99 (define @t174 () (tptp.rel_str @t118)) % 0.72/0.99 (define @t175 () (@quantifiers_skolemize @t117 3)) % 0.72/0.99 (define @t176 () (@quantifiers_skolemize @t117 1)) % 0.72/0.99 (define @t177 () (tptp.related @t118 @t176 @t175)) % 0.72/0.99 (define @t178 () (@quantifiers_skolemize @t117 2)) % 0.72/0.99 (define @t179 () (tptp.related @t118 @t178 @t175)) % 0.72/0.99 (define @t180 () (not @t179)) % 0.72/0.99 (define @t181 () (tptp.element @t175 @t119)) % 0.72/0.99 (define @t182 () (not @t181)) % 0.72/0.99 (define @t183 () (tptp.related @t118 @t176 @t178)) % 0.72/0.99 (define @t184 () (not @t183)) % 0.72/0.99 (define @t185 () (tptp.element @t178 @t119)) % 0.72/0.99 (define @t186 () (not @t185)) % 0.72/0.99 (define @t187 () (tptp.element @t176 @t119)) % 0.72/0.99 (define @t188 () (not @t187)) % 0.72/0.99 (define @t189 () (not @t174)) % 0.72/0.99 (define @t190 () (tptp.transitive_relstr @t118)) % 0.72/0.99 (define @t191 () (not @t190)) % 0.72/0.99 (define @t192 () (or @t191 @t189 @t188 @t186 @t184 @t182 @t180 @t177)) % 0.72/0.99 (define @t193 () (@list true)) % 0.72/0.99 (define @t194 () (@list @t192)) % 0.72/0.99 (define @t195 () (tptp.relation_of2_as_subset @t120 @t119 @t119)) % 0.72/0.99 (define @t196 () (or @t189 @t195)) % 0.72/0.99 (define @t197 () (@list false false)) % 0.72/0.99 (define @t198 () (tptp.cartesian_product2 @t119 @t119)) % 0.72/0.99 (define @t199 () (tptp.element @t120 (tptp.powerset @t198))) % 0.72/0.99 (define @t200 () (not @t195)) % 0.72/0.99 (define @t201 () (or @t200 @t199)) % 0.72/0.99 (define @t202 () (tptp.relation @t120)) % 0.72/0.99 (define @t203 () (not @t199)) % 0.72/0.99 (define @t204 () (or @t203 @t202)) % 0.72/0.99 (define @t205 () (forall @t33 (or (not (tptp.in @t5 @t119)) (not (tptp.in @t24 @t119)) (not (tptp.in @t21 @t119)) (not (tptp.in @t27 @t120)) (not (tptp.in @t25 @t120)) (tptp.in @t22 @t120)))) % 0.72/0.99 (define @t206 () (tptp.is_transitive_in @t120 @t119)) % 0.72/0.99 (define @t207 () (= @t206 @t205)) % 0.72/0.99 (define @t208 () (not @t202)) % 0.72/0.99 (define @t209 () (or @t208 @t207)) % 0.72/0.99 (define @t210 () (= @t190 @t206)) % 0.72/0.99 (define @t211 () (or @t189 @t210)) % 0.72/0.99 (define @t212 () (not @t64)) % 0.72/0.99 (define @t213 () (tptp.ordered_pair @t178 @t175)) % 0.72/0.99 (define @t214 () (not @t83)) % 0.72/0.99 (define @t215 () (not @t3)) % 0.72/0.99 (define @t216 () (@var "BOUND_VARIABLE_7682" $$unsorted)) % 0.72/0.99 (define @t217 () (@var "BOUND_VARIABLE_7680" $$unsorted)) % 0.72/0.99 (define @t218 () (= (tptp.related @t1 @t217 @t216) (tptp.in (tptp.ordered_pair @t217 @t216) @t13))) % 0.72/0.99 (define @t219 () (not (tptp.element @t216 @t12))) % 0.72/0.99 (define @t220 () (not (tptp.element @t217 @t12))) % 0.72/0.99 (define @t221 () (or @t220 @t219 @t218)) % 0.72/0.99 (define @t222 () (or @t113 @t221)) % 0.72/0.99 (define @t223 () (forall (@list @t1 @t217 @t216) @t222)) % 0.72/0.99 (define @t224 () (@list @t217 @t216)) % 0.72/0.99 (define @t225 () (forall @t224 @t222)) % 0.72/0.99 (define @t226 () (forall @t224 @t221)) % 0.72/0.99 (define @t227 () (@var "BOUND_VARIABLE_7662" $$unsorted)) % 0.72/0.99 (define @t228 () (or @t113 @t226)) % 0.72/0.99 (define @t229 () (= (tptp.related @t1 @t2 @t227) (tptp.in (tptp.ordered_pair @t2 @t227) @t13))) % 0.72/0.99 (define @t230 () (not (tptp.element @t227 @t12))) % 0.72/0.99 (define @t231 () (or @t137 @t230 @t229)) % 0.72/0.99 (define @t232 () (@list @t2 @t227)) % 0.72/0.99 (define @t233 () (forall @t232 @t231)) % 0.72/0.99 (define @t234 () (or @t230 @t229)) % 0.72/0.99 (define @t235 () (or @t137 @t234)) % 0.72/0.99 (define @t236 () (forall @t232 @t235)) % 0.72/0.99 (define @t237 () (@list @t227)) % 0.72/0.99 (define @t238 () (forall @t237 @t235)) % 0.72/0.99 (define @t239 () (forall @t237 @t234)) % 0.72/0.99 (define @t240 () (or @t137 @t239)) % 0.72/0.99 (define @t241 () (forall @t45 (or @t154 @t43))) % 0.72/0.99 (define @t242 () (tptp.in @t213 @t120)) % 0.72/0.99 (define @t243 () (= @t179 @t242)) % 0.72/0.99 (define @t244 () (or @t189 @t186 @t182 @t243)) % 0.72/0.99 (define @t245 () (@list false false false false)) % 0.72/0.99 (define @t246 () (tptp.element @t213 @t198)) % 0.72/0.99 (define @t247 () (not @t242)) % 0.72/0.99 (define @t248 () (or @t247 @t203 @t246)) % 0.72/0.99 (define @t249 () (@list false false false)) % 0.72/0.99 (define @t250 () (not @t86)) % 0.72/0.99 (define @t251 () (tptp.ordered_pair @t176 @t178)) % 0.72/0.99 (define @t252 () (@list @t251 @t120 @t198)) % 0.72/0.99 (define @t253 () (tptp.in @t251 @t120)) % 0.72/0.99 (define @t254 () (= @t183 @t253)) % 0.72/0.99 (define @t255 () (or @t189 @t188 @t186 @t254)) % 0.72/0.99 (define @t256 () (tptp.empty @t198)) % 0.72/0.99 (define @t257 () (not @t256)) % 0.72/0.99 (define @t258 () (not @t253)) % 0.72/0.99 (define @t259 () (or @t258 @t203 @t257)) % 0.72/0.99 (define @t260 () (tptp.in @t213 @t198)) % 0.72/0.99 (define @t261 () (not @t246)) % 0.72/0.99 (define @t262 () (or @t261 @t256 @t260)) % 0.72/0.99 (define @t263 () (@list true false false)) % 0.72/0.99 (define @t264 () (tptp.in @t175 @t119)) % 0.72/0.99 (define @t265 () (tptp.in @t178 @t119)) % 0.72/0.99 (define @t266 () (and @t265 @t264)) % 0.72/0.99 (define @t267 () (= @t260 @t266)) % 0.72/0.99 (define @t268 () (@list false)) % 0.72/0.99 (define @t269 () (tptp.element @t251 @t198)) % 0.72/0.99 (define @t270 () (or @t258 @t203 @t269)) % 0.72/0.99 (define @t271 () (tptp.in @t251 @t198)) % 0.72/0.99 (define @t272 () (not @t269)) % 0.72/0.99 (define @t273 () (or @t272 @t256 @t271)) % 0.72/0.99 (define @t274 () (tptp.in @t176 @t119)) % 0.72/0.99 (define @t275 () (and @t274 @t265)) % 0.72/0.99 (define @t276 () (= @t271 @t275)) % 0.72/0.99 (define @t277 () (not @t275)) % 0.72/0.99 (define @t278 () (@list @t275)) % 0.72/0.99 (define @t279 () (tptp.in (tptp.ordered_pair @t176 @t175) @t120)) % 0.72/0.99 (define @t280 () (= @t177 @t279)) % 0.72/0.99 (define @t281 () (or @t189 @t188 @t182 @t280)) % 0.72/0.99 (define @t282 () (not @t279)) % 0.72/0.99 (define @t283 () (@list true false)) % 0.72/0.99 (define @t284 () (not @t264)) % 0.72/0.99 (define @t285 () (not @t265)) % 0.72/0.99 (define @t286 () (not @t274)) % 0.72/0.99 (define @t287 () (or @t286 @t285 @t284 @t258 @t247 @t279)) % 0.72/0.99 (define @t288 () (not @t287)) % 0.72/0.99 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.72/0.99 (assume @p2 @t10) % 0.72/0.99 (assume @p3 (forall @t4 (= @t11 (tptp.unordered_pair @t2 @t1)))) % 0.72/0.99 (assume @p4 @t18) % 0.72/0.99 (assume @p5 (forall @t4 (= @t20 (tptp.unordered_pair @t11 @t19)))) % 0.72/0.99 (assume @p6 @t41) % 0.72/0.99 (assume @p7 @t51) % 0.72/0.99 (assume @p8 true) % 0.72/0.99 (assume @p9 (forall @t17 (=> @t16 @t52))) % 0.72/0.99 (assume @p10 @t54) % 0.72/0.99 (assume @p11 @t56) % 0.72/0.99 (assume @p12 (exists @t17 @t16)) % 0.72/0.99 (assume @p13 (exists @t17 @t52)) % 0.72/0.99 (assume @p14 (forall @t4 (exists @t45 @t57))) % 0.72/0.99 (assume @p15 (forall @t17 (exists @t37 (tptp.element @t2 @t1)))) % 0.72/0.99 (assume @p16 (forall @t4 (exists @t45 @t53))) % 0.72/0.99 (assume @p17 (forall @t17 (not (tptp.empty @t58)))) % 0.72/0.99 (assume @p18 (tptp.empty tptp.empty_set)) % 0.72/0.99 (assume @p19 (forall @t17 (not (tptp.empty @t19)))) % 0.72/0.99 (assume @p20 (forall @t4 (not (tptp.empty @t11)))) % 0.72/0.99 (assume @p21 (forall @t4 (=> (and @t62 @t60) (not (tptp.empty @t7))))) % 0.72/0.99 (assume @p22 (forall @t17 (=> @t62 (exists @t37 (and @t63 @t60))))) % 0.72/0.99 (assume @p23 (exists @t17 @t61)) % 0.72/0.99 (assume @p24 (forall @t17 (exists @t37 (and @t63 @t59)))) % 0.72/0.99 (assume @p25 (exists @t17 @t62)) % 0.72/0.99 (assume @p26 (forall @t9 (= @t53 @t57))) % 0.72/0.99 (assume @p27 (forall @t4 (tptp.subset @t1 @t1))) % 0.72/0.99 (assume @p28 (forall (@list @t1 @t2 @t5 @t24) (= (tptp.in @t20 (tptp.cartesian_product2 @t5 @t24)) (and (tptp.in @t1 @t5) (tptp.in @t2 @t24))))) % 0.72/0.99 (assume @p29 (forall @t4 (=> @t3 @t64))) % 0.72/0.99 (assume @p30 @t79) % 0.72/0.99 (assume @p31 @t81) % 0.72/0.99 (assume @p32 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 0.72/0.99 (assume @p33 @t85) % 0.72/0.99 (assume @p34 @t87) % 0.72/0.99 (assume @p35 (forall @t17 (=> @t61 (= @t1 tptp.empty_set)))) % 0.72/0.99 (assume @p36 (forall @t4 (not (and @t3 @t59)))) % 0.72/0.99 (assume @p37 (forall @t4 (not (and @t61 (not (= @t1 @t2)) @t59)))) % 0.72/0.99 (step @p38 :rule quant-merge-prenex :args ((= (forall @t17 @t95) (forall (@list @t1 @t90) @t93)))) % 0.72/0.99 (step @p39 :rule alpha_equiv :args (@t96 (@list @t90) (@list @t2))) % 0.72/0.99 (step @p40 :rule refl :args (@t92)) % 0.72/0.99 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t97)) % 0.72/0.99 (step @p42 :rule quant-miniscope-or :args ((= @t95 @t97))) % 0.72/0.99 (step @p43 :rule trans :premises (@p42 @p41)) % 0.72/0.99 (step @p44 :rule symm :premises (@p43)) % 0.72/0.99 (step @p45 :rule cong :premises (@p44) :args ((forall @t17 (or @t92 @t102)))) % 0.72/0.99 (step @p46 :rule trans :premises (@p45 @p38)) % 0.72/0.99 (step @p47 :rule bool-impl-elim :args (@t39 @t102)) % 0.72/0.99 (step @p48 :rule cong :premises (@p47) :args ((forall @t17 (=> @t39 @t102)))) % 0.72/0.99 (step @p49 :rule trans :premises (@p48 @p46)) % 0.72/0.99 (step @p50 :rule aci_norm :args ((= (or @t103 @t23) @t101))) % 0.72/0.99 (step @p51 :rule refl :args (@t23)) % 0.72/0.99 (step @p52 :rule aci_norm :args ((= (or @t100 (or @t99 (or @t98 (or @t89 @t88)))) @t103))) % 0.72/0.99 (step @p53 :rule bool-and-de-morgan :args (@t28 @t26 true)) % 0.72/0.99 (step @p54 :rule refl :args (@t98)) % 0.72/0.99 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t98 (not (and @t28 @t26))))) % 0.72/0.99 (step @p56 :rule bool-and-de-morgan :args (@t29 @t28 (and @t26))) % 0.72/0.99 (step @p57 :rule trans :premises (@p56 @p55)) % 0.72/0.99 (step @p58 :rule refl :args (@t99)) % 0.72/0.99 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or @t99 (not (and @t29 @t28 @t26))))) % 0.72/0.99 (step @p60 :rule bool-and-de-morgan :args (@t30 @t29 (and @t28 @t26))) % 0.72/0.99 (step @p61 :rule trans :premises (@p60 @p59)) % 0.72/0.99 (step @p62 :rule refl :args (@t100)) % 0.72/0.99 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t100 (not (and @t30 @t29 @t28 @t26))))) % 0.72/0.99 (step @p64 :rule bool-and-de-morgan :args (@t31 @t30 (and @t29 @t28 @t26))) % 0.72/0.99 (step @p65 :rule trans :premises (@p64 @p63)) % 0.72/0.99 (step @p66 :rule trans :premises (@p65 @p52)) % 0.72/0.99 (step @p67 :rule nary_cong :premises (@p66 @p51) :args ((or (not @t32) @t23))) % 0.72/0.99 (step @p68 :rule trans :premises (@p67 @p50)) % 0.72/0.99 (step @p69 :rule bool-impl-elim :args (@t32 @t23)) % 0.72/0.99 (step @p70 :rule trans :premises (@p69 @p68)) % 0.72/0.99 (step @p71 :rule cong :premises (@p70) :args (@t34)) % 0.72/0.99 (step @p72 :rule refl :args (@t35)) % 0.72/0.99 (step @p73 :rule cong :premises (@p72 @p71) :args (@t36)) % 0.72/0.99 (step @p74 :rule cong :premises (@p73) :args (@t38)) % 0.72/0.99 (step @p75 :rule refl :args (@t39)) % 0.72/0.99 (step @p76 :rule cong :premises (@p75 @p74) :args (@t40)) % 0.72/0.99 (step @p77 :rule cong :premises (@p76) :args (@t41)) % 0.72/0.99 (step @p78 :rule trans :premises (@p77 @p49)) % 0.72/0.99 (step @p79 :rule eq_resolve :premises (@p6 @p78)) % 0.72/0.99 (step @p80 :rule instantiate :premises (@p79) :args ((@list @t120 @t119))) % 0.72/0.99 (step @p81 :rule bool-impl-elim :args (@t8 @t6)) % 0.72/0.99 (step @p82 :rule cong :premises (@p81) :args (@t10)) % 0.72/0.99 (step @p83 :rule eq_resolve :premises (@p2 @p82)) % 0.72/0.99 (step @p84 :rule instantiate :premises (@p83) :args (@t121)) % 0.72/0.99 (step @p85 :rule bool-impl-elim :args (@t53 @t8)) % 0.72/0.99 (step @p86 :rule cong :premises (@p85) :args (@t54)) % 0.72/0.99 (step @p87 :rule eq_resolve :premises (@p10 @p86)) % 0.72/0.99 (step @p88 :rule instantiate :premises (@p87) :args (@t121)) % 0.72/0.99 (step @p89 :rule bool-impl-elim :args (@t16 @t55)) % 0.72/0.99 (step @p90 :rule cong :premises (@p89) :args (@t56)) % 0.72/0.99 (step @p91 :rule eq_resolve :premises (@p11 @p90)) % 0.72/0.99 (step @p92 :rule instantiate :premises (@p91) :args (@t122)) % 0.72/0.99 (step @p93 :rule aci_norm :args ((= @t124 @t115))) % 0.72/0.99 (step @p94 :rule cong :premises (@p93) :args (@t125)) % 0.72/0.99 (step @p95 :rule quant-merge-prenex :args ((= (forall @t17 @t127) @t125))) % 0.72/0.99 (step @p96 :rule alpha_equiv :args (@t128 (@list @t105 @t107 @t104) (@list @t2 @t130 @t129))) % 0.72/0.99 (step @p97 :rule refl :args (@t113)) % 0.72/0.99 (step @p98 :rule refl :args (@t114)) % 0.72/0.99 (step @p99 :rule nary_cong :premises (@p98 @p97 @p96) :args (@t131)) % 0.72/0.99 (step @p100 :rule quant-miniscope-or :args ((= @t127 @t131))) % 0.72/0.99 (step @p101 :rule trans :premises (@p100 @p99)) % 0.72/0.99 (step @p102 :rule symm :premises (@p101)) % 0.72/0.99 (step @p103 :rule cong :premises (@p102) :args ((forall @t17 @t141))) % 0.72/0.99 (step @p104 :rule trans :premises (@p103 @p95)) % 0.72/0.99 (step @p105 :rule trans :premises (@p104 @p94)) % 0.72/0.99 (step @p106 :rule aci_norm :args ((= (or (or @t114 @t113) @t140) @t141))) % 0.72/0.99 (step @p107 :rule refl :args (@t140)) % 0.72/0.99 (step @p108 :rule bool-and-de-morgan :args (@t14 @t16 true)) % 0.72/0.99 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or (not @t76) @t140))) % 0.72/0.99 (step @p110 :rule trans :premises (@p109 @p106)) % 0.72/0.99 (step @p111 :rule bool-impl-elim :args (@t76 @t140)) % 0.72/0.99 (step @p112 :rule trans :premises (@p111 @p110)) % 0.72/0.99 (step @p113 :rule cong :premises (@p112) :args ((forall @t17 (=> @t76 @t140)))) % 0.72/0.99 (step @p114 :rule trans :premises (@p113 @p105)) % 0.72/0.99 (step @p115 :rule aci_norm :args ((= @t143 @t138))) % 0.72/0.99 (step @p116 :rule cong :premises (@p115) :args (@t144)) % 0.72/0.99 (step @p117 :rule quant-merge-prenex :args ((= (forall @t37 @t146) @t144))) % 0.72/0.99 (step @p118 :rule alpha_equiv :args (@t147 (@list @t130 @t129) (@list @t5 @t148))) % 0.72/0.99 (step @p119 :rule refl :args (@t137)) % 0.72/0.99 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t149)) % 0.72/0.99 (step @p121 :rule quant-miniscope-or :args ((= @t146 @t149))) % 0.72/0.99 (step @p122 :rule trans :premises (@p121 @p120)) % 0.72/0.99 (step @p123 :rule symm :premises (@p122)) % 0.72/0.99 (step @p124 :rule cong :premises (@p123) :args ((forall @t37 (or @t137 @t157)))) % 0.72/0.99 (step @p125 :rule trans :premises (@p124 @p117)) % 0.72/0.99 (step @p126 :rule trans :premises (@p125 @p116)) % 0.72/0.99 (step @p127 :rule bool-impl-elim :args (@t47 @t157)) % 0.72/0.99 (step @p128 :rule cong :premises (@p127) :args ((forall @t37 (=> @t47 @t157)))) % 0.72/0.99 (step @p129 :rule trans :premises (@p128 @p126)) % 0.72/0.99 (step @p130 :rule aci_norm :args ((= @t159 @t155))) % 0.72/0.99 (step @p131 :rule cong :premises (@p130) :args (@t160)) % 0.72/0.99 (step @p132 :rule quant-merge-prenex :args ((= (forall @t45 @t162) @t160))) % 0.72/0.99 (step @p133 :rule alpha_equiv :args (@t163 (@list @t148) (@list @t24))) % 0.72/0.99 (step @p134 :rule refl :args (@t153)) % 0.72/0.99 (step @p135 :rule refl :args (@t154)) % 0.72/0.99 (step @p136 :rule nary_cong :premises (@p135 @p134 @p133) :args (@t164)) % 0.72/0.99 (step @p137 :rule quant-miniscope-or :args ((= @t162 @t164))) % 0.72/0.99 (step @p138 :rule trans :premises (@p137 @p136)) % 0.72/0.99 (step @p139 :rule symm :premises (@p138)) % 0.72/0.99 (step @p140 :rule cong :premises (@p139) :args ((forall @t45 @t169))) % 0.72/0.99 (step @p141 :rule trans :premises (@p140 @p132)) % 0.72/0.99 (step @p142 :rule trans :premises (@p141 @p131)) % 0.72/0.99 (step @p143 :rule aci_norm :args ((= (or @t154 @t170) @t169))) % 0.72/0.99 (step @p144 :rule bool-impl-elim :args (@t44 @t170)) % 0.72/0.99 (step @p145 :rule trans :premises (@p144 @p143)) % 0.72/0.99 (step @p146 :rule cong :premises (@p145) :args ((forall @t45 (=> @t44 @t170)))) % 0.72/0.99 (step @p147 :rule trans :premises (@p146 @p142)) % 0.72/0.99 (step @p148 :rule quant-miniscope-or :args ((= (forall @t70 @t171) @t170))) % 0.72/0.99 (step @p149 :rule aci_norm :args ((= @t172 @t171))) % 0.72/0.99 (step @p150 :rule cong :premises (@p149) :args ((forall @t70 @t172))) % 0.72/0.99 (step @p151 :rule trans :premises (@p150 @p148)) % 0.72/0.99 (step @p152 :rule aci_norm :args ((= (or @t166 @t173) @t172))) % 0.72/0.99 (step @p153 :rule aci_norm :args ((= (or (or @t153 @t165) @t65) @t173))) % 0.72/0.99 (step @p154 :rule refl :args (@t65)) % 0.72/0.99 (step @p155 :rule bool-and-de-morgan :args (@t42 @t66 true)) % 0.72/0.99 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t67) @t65))) % 0.72/0.99 (step @p157 :rule trans :premises (@p156 @p153)) % 0.72/0.99 (step @p158 :rule bool-impl-elim :args (@t67 @t65)) % 0.72/0.99 (step @p159 :rule trans :premises (@p158 @p157)) % 0.72/0.99 (step @p160 :rule refl :args (@t166)) % 0.72/0.99 (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((or @t166 @t68))) % 0.72/0.99 (step @p162 :rule trans :premises (@p161 @p152)) % 0.72/0.99 (step @p163 :rule bool-impl-elim :args (@t69 @t68)) % 0.72/0.99 (step @p164 :rule trans :premises (@p163 @p162)) % 0.72/0.99 (step @p165 :rule cong :premises (@p164) :args (@t71)) % 0.72/0.99 (step @p166 :rule trans :premises (@p165 @p151)) % 0.72/0.99 (step @p167 :rule refl :args (@t44)) % 0.72/0.99 (step @p168 :rule cong :premises (@p167 @p166) :args (@t72)) % 0.72/0.99 (step @p169 :rule cong :premises (@p168) :args (@t73)) % 0.72/0.99 (step @p170 :rule trans :premises (@p169 @p147)) % 0.72/0.99 (step @p171 :rule refl :args (@t47)) % 0.72/0.99 (step @p172 :rule cong :premises (@p171 @p170) :args (@t74)) % 0.72/0.99 (step @p173 :rule cong :premises (@p172) :args (@t75)) % 0.72/0.99 (step @p174 :rule trans :premises (@p173 @p129)) % 0.72/0.99 (step @p175 :rule refl :args (@t76)) % 0.72/0.99 (step @p176 :rule cong :premises (@p175 @p174) :args (@t77)) % 0.72/0.99 (step @p177 :rule cong :premises (@p176) :args (@t78)) % 0.72/0.99 (step @p178 :rule trans :premises (@p177 @p114)) % 0.72/0.99 (step @p179 :rule cong :premises (@p178) :args (@t79)) % 0.72/0.99 (step @p180 :rule eq_resolve :premises (@p30 @p179)) % 0.72/0.99 (step @p181 :rule skolemize :premises (@p180)) % 0.72/0.99 (step @p182 :rule bool-double-not-elim :args (@t174)) % 0.72/0.99 (step @p183 :rule refl :args (@t192)) % 0.72/0.99 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t192 (not @t189)))) % 0.72/0.99 (step @p185 :rule cnf_or_neg :args (@t192 1)) % 0.72/0.99 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.72/0.99 (step @p187 :rule reordering :premises (@p186) :args ((or @t174 @t192))) % 0.72/0.99 (step @p188 :rule chain_m_resolution :premises (@p187 @p181) :args (@t174 @t193 @t194)) % 0.72/0.99 (step @p189 :rule cnf_or_pos :args (@t196)) % 0.72/0.99 (step @p190 :rule reordering :premises (@p189) :args ((or @t189 @t195 (not @t196)))) % 0.72/0.99 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p92) :args (@t195 @t197 (@list @t174 @t196))) % 0.72/0.99 (step @p192 :rule cnf_or_pos :args (@t201)) % 0.72/0.99 (step @p193 :rule reordering :premises (@p192) :args ((or @t200 @t199 (not @t201)))) % 0.72/0.99 (step @p194 :rule chain_m_resolution :premises (@p193 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0.72/1.00 (step-pop @p381 :rule scope :premises (@p375)) % 0.72/1.00 (step @p376 :rule process_scope :premises (@p381) :args (@t287)) % 0.72/1.00 (step @p378 :rule implies_elim :premises (@p376)) % 0.72/1.00 (step @p379 false :rule chain_m_resolution :premises (@p378 @p373 @p219) :args (false @t283 (@list @t287 @t205))) % 0.72/1.00 ) % 0.72/1.00 % SZS output end Proof % 0.72/1.00 % cvc5 exiting %------------------------------------------------------------------------------