%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET761+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:48:35 AM UTC 2026 % Result : Theorem 0.46s 0.68s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET761+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n029.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:11:02 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.68 % SZS status Theorem % 0.46/0.68 % SZS output start Proof % 0.46/0.68 ( % 0.46/0.68 (declare-sort $$unsorted 0) % 0.46/0.68 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.empty_set $$unsorted) % 0.46/0.68 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.68 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.68 (define @t1 () (@var "B" $$unsorted)) % 0.46/0.68 (define @t2 () (@var "X" $$unsorted)) % 0.46/0.68 (define @t3 () (tptp.member @t2 @t1)) % 0.46/0.68 (define @t4 () (@var "A" $$unsorted)) % 0.46/0.68 (define @t5 () (tptp.member @t2 @t4)) % 0.46/0.68 (define @t6 () (@list @t2)) % 0.46/0.68 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.46/0.68 (define @t8 () (tptp.subset @t4 @t1)) % 0.46/0.68 (define @t9 () (= @t8 @t7)) % 0.46/0.68 (define @t10 () (@list @t4 @t1)) % 0.46/0.68 (define @t11 () (forall @t10 @t9)) % 0.46/0.68 (define @t12 () (tptp.subset @t2 @t4)) % 0.46/0.68 (define @t13 () (@list @t2 @t4)) % 0.46/0.68 (define @t14 () (@list @t2 @t4 @t1)) % 0.46/0.68 (define @t15 () (@var "E" $$unsorted)) % 0.46/0.68 (define @t16 () (= @t2 @t4)) % 0.46/0.68 (define @t17 () (@var "Y" $$unsorted)) % 0.46/0.68 (define @t18 () (tptp.member @t2 @t17)) % 0.46/0.68 (define @t19 () (tptp.member @t17 @t4)) % 0.46/0.68 (define @t20 () (@list @t17)) % 0.46/0.68 (define @t21 () (@var "Y2" $$unsorted)) % 0.46/0.68 (define @t22 () (@var "Y1" $$unsorted)) % 0.46/0.68 (define @t23 () (= @t22 @t21)) % 0.46/0.68 (define @t24 () (@var "F" $$unsorted)) % 0.46/0.68 (define @t25 () (tptp.apply @t24 @t2 @t22)) % 0.46/0.68 (define @t26 () (tptp.member @t21 @t1)) % 0.46/0.68 (define @t27 () (tptp.member @t22 @t1)) % 0.46/0.68 (define @t28 () (and @t5 @t27 @t26)) % 0.46/0.68 (define @t29 () (@list @t2 @t22 @t21)) % 0.46/0.68 (define @t30 () (tptp.apply @t24 @t2 @t17)) % 0.46/0.68 (define @t31 () (tptp.member @t17 @t1)) % 0.46/0.68 (define @t32 () (exists @t20 (and @t31 @t30))) % 0.46/0.68 (define @t33 () (tptp.maps @t24 @t4 @t1)) % 0.46/0.68 (define @t34 () (@list @t24 @t4 @t1)) % 0.46/0.68 (define @t35 () (@var "Z" $$unsorted)) % 0.46/0.68 (define @t36 () (@var "G" $$unsorted)) % 0.46/0.68 (define @t37 () (exists @t20 (and @t31 @t30 (tptp.apply @t36 @t17 @t35)))) % 0.46/0.68 (define @t38 () (@var "H" $$unsorted)) % 0.46/0.68 (define @t39 () (@var "C" $$unsorted)) % 0.46/0.68 (define @t40 () (and @t5 (tptp.member @t35 @t39))) % 0.46/0.68 (define @t41 () (@var "X2" $$unsorted)) % 0.46/0.68 (define @t42 () (@var "X1" $$unsorted)) % 0.46/0.68 (define @t43 () (= @t42 @t41)) % 0.46/0.68 (define @t44 () (tptp.apply @t24 @t41 @t17)) % 0.46/0.68 (define @t45 () (tptp.apply @t24 @t42 @t17)) % 0.46/0.68 (define @t46 () (and @t45 @t44)) % 0.46/0.68 (define @t47 () (=> @t46 @t43)) % 0.46/0.68 (define @t48 () (tptp.member @t41 @t4)) % 0.46/0.68 (define @t49 () (tptp.member @t42 @t4)) % 0.46/0.68 (define @t50 () (and @t49 @t48 @t31)) % 0.46/0.68 (define @t51 () (@list @t42 @t41 @t17)) % 0.46/0.68 (define @t52 () (forall @t51 (=> @t50 @t47))) % 0.46/0.68 (define @t53 () (tptp.injective @t24 @t4 @t1)) % 0.46/0.68 (define @t54 () (= @t53 @t52)) % 0.46/0.68 (define @t55 () (forall @t34 @t54)) % 0.46/0.68 (define @t56 () (tptp.surjective @t24 @t4 @t1)) % 0.46/0.68 (define @t57 () (tptp.one_to_one @t24 @t4 @t1)) % 0.46/0.68 (define @t58 () (and @t5 @t31)) % 0.46/0.68 (define @t59 () (@list @t24 @t4 @t1 @t2 @t17)) % 0.46/0.68 (define @t60 () (and @t5 @t30)) % 0.46/0.68 (define @t61 () (exists @t6 @t60)) % 0.46/0.68 (define @t62 () (and @t31 @t61)) % 0.46/0.68 (define @t63 () (tptp.member @t17 (tptp.image3 @t24 @t4 @t1))) % 0.46/0.68 (define @t64 () (= @t63 @t62)) % 0.46/0.68 (define @t65 () (forall (@list @t24 @t4 @t1 @t17) @t64)) % 0.46/0.68 (define @t66 () (@var "S" $$unsorted)) % 0.46/0.68 (define @t67 () (tptp.apply @t66 @t22 @t21)) % 0.46/0.68 (define @t68 () (tptp.apply @t24 @t41 @t21)) % 0.46/0.68 (define @t69 () (tptp.apply @t24 @t42 @t22)) % 0.46/0.68 (define @t70 () (@var "R" $$unsorted)) % 0.46/0.68 (define @t71 () (tptp.apply @t70 @t42 @t41)) % 0.46/0.68 (define @t72 () (and @t49 @t27 @t48 @t26 @t71 @t69 @t68)) % 0.46/0.68 (define @t73 () (@list @t42 @t22 @t41 @t21)) % 0.46/0.68 (define @t74 () (@list @t24 @t4 @t70 @t1 @t66)) % 0.46/0.68 (define @t75 () (tptp.equal_set (tptp.image3 @t24 (tptp.intersection @t2 @t17) @t1) (tptp.intersection (tptp.image3 @t24 @t2 @t1) (tptp.image3 @t24 @t17 @t1)))) % 0.46/0.68 (define @t76 () (tptp.subset @t17 @t4)) % 0.46/0.68 (define @t77 () (and @t33 @t53 @t12 @t76)) % 0.46/0.68 (define @t78 () (forall @t59 (=> @t77 @t75))) % 0.46/0.68 (define @t79 () (not @t78)) % 0.46/0.68 (define @t80 () (forall @t6 (not @t60))) % 0.46/0.68 (define @t81 () (not @t80)) % 0.46/0.68 (define @t82 () (not @t76)) % 0.46/0.68 (define @t83 () (not @t12)) % 0.46/0.68 (define @t84 () (not @t53)) % 0.46/0.68 (define @t85 () (not @t33)) % 0.46/0.68 (define @t86 () (or @t85 @t84 @t83 @t82 @t75)) % 0.46/0.68 (define @t87 () (forall @t59 @t86)) % 0.46/0.68 (define @t88 () (@quantifiers_skolemize @t87 2)) % 0.46/0.68 (define @t89 () (@quantifiers_skolemize @t87 4)) % 0.46/0.68 (define @t90 () (@quantifiers_skolemize @t87 0)) % 0.46/0.68 (define @t91 () (tptp.image3 @t90 @t89 @t88)) % 0.46/0.68 (define @t92 () (@quantifiers_skolemize @t87 3)) % 0.46/0.68 (define @t93 () (tptp.image3 @t90 @t92 @t88)) % 0.46/0.68 (define @t94 () (tptp.intersection @t93 @t91)) % 0.46/0.68 (define @t95 () (tptp.member @t2 @t94)) % 0.46/0.68 (define @t96 () (tptp.intersection @t92 @t89)) % 0.46/0.68 (define @t97 () (tptp.image3 @t90 @t96 @t88)) % 0.46/0.68 (define @t98 () (tptp.member @t2 @t97)) % 0.46/0.68 (define @t99 () (forall @t6 (or (not @t98) @t95))) % 0.46/0.68 (define @t100 () (@quantifiers_skolemize @t99 0)) % 0.46/0.68 (define @t101 () (not (tptp.apply @t90 @t2 @t100))) % 0.46/0.68 (define @t102 () (not (tptp.member @t2 @t96))) % 0.46/0.68 (define @t103 () (forall @t6 (or @t102 @t101))) % 0.46/0.68 (define @t104 () (@quantifiers_skolemize @t103 0)) % 0.46/0.68 (define @t105 () (@list @t97 @t94)) % 0.46/0.68 (define @t106 () (forall @t6 (or (not @t95) @t98))) % 0.46/0.68 (define @t107 () (@quantifiers_skolemize @t106 0)) % 0.46/0.68 (define @t108 () (tptp.member @t107 @t94)) % 0.46/0.68 (define @t109 () (tptp.member @t107 @t97)) % 0.46/0.68 (define @t110 () (not @t108)) % 0.46/0.68 (define @t111 () (or @t110 @t109)) % 0.46/0.68 (define @t112 () (tptp.member @t107 @t91)) % 0.46/0.68 (define @t113 () (tptp.member @t107 @t93)) % 0.46/0.68 (define @t114 () (and @t113 @t112)) % 0.46/0.68 (define @t115 () (= @t108 @t114)) % 0.46/0.68 (define @t116 () (not (tptp.apply @t90 @t2 @t107))) % 0.46/0.68 (define @t117 () (forall @t6 (or @t102 @t116))) % 0.46/0.68 (define @t118 () (not @t117)) % 0.46/0.68 (define @t119 () (tptp.member @t107 @t88)) % 0.46/0.68 (define @t120 () (and @t119 @t118)) % 0.46/0.68 (define @t121 () (= @t109 @t120)) % 0.46/0.68 (define @t122 () (not @t114)) % 0.46/0.68 (define @t123 () (not (tptp.member @t2 @t92))) % 0.46/0.68 (define @t124 () (forall @t6 (or @t123 @t116))) % 0.46/0.68 (define @t125 () (not @t124)) % 0.46/0.68 (define @t126 () (and @t119 @t125)) % 0.46/0.68 (define @t127 () (= @t113 @t126)) % 0.46/0.68 (define @t128 () (not (tptp.member @t2 @t89))) % 0.46/0.68 (define @t129 () (forall @t6 (or @t128 @t116))) % 0.46/0.68 (define @t130 () (not @t129)) % 0.46/0.68 (define @t131 () (and @t119 @t130)) % 0.46/0.68 (define @t132 () (= @t112 @t131)) % 0.46/0.68 (define @t133 () (not @t126)) % 0.46/0.68 (define @t134 () (not @t119)) % 0.46/0.68 (define @t135 () (@quantifiers_skolemize @t124 0)) % 0.46/0.68 (define @t136 () (tptp.apply @t90 @t135 @t107)) % 0.46/0.68 (define @t137 () (not @t136)) % 0.46/0.68 (define @t138 () (tptp.member @t135 @t92)) % 0.46/0.68 (define @t139 () (not @t138)) % 0.46/0.68 (define @t140 () (or @t139 @t137)) % 0.46/0.68 (define @t141 () (not @t140)) % 0.46/0.68 (define @t142 () (@quantifiers_skolemize @t129 0)) % 0.46/0.68 (define @t143 () (tptp.apply @t90 @t142 @t107)) % 0.46/0.68 (define @t144 () (not @t143)) % 0.46/0.68 (define @t145 () (tptp.member @t142 @t89)) % 0.46/0.68 (define @t146 () (not @t145)) % 0.46/0.68 (define @t147 () (or @t146 @t144)) % 0.46/0.68 (define @t148 () (not @t147)) % 0.46/0.68 (define @t149 () (@list @t135)) % 0.46/0.68 (define @t150 () (tptp.member @t135 @t96)) % 0.46/0.68 (define @t151 () (not @t150)) % 0.46/0.68 (define @t152 () (or @t151 @t137)) % 0.46/0.68 (define @t153 () (@quantifiers_skolemize @t87 1)) % 0.46/0.68 (define @t154 () (or @t85 @t84 @t83 @t82)) % 0.46/0.68 (define @t155 () (tptp.subset @t92 @t153)) % 0.46/0.68 (define @t156 () (tptp.equal_set @t97 @t94)) % 0.46/0.68 (define @t157 () (tptp.subset @t89 @t153)) % 0.46/0.68 (define @t158 () (not @t157)) % 0.46/0.68 (define @t159 () (not @t155)) % 0.46/0.68 (define @t160 () (tptp.injective @t90 @t153 @t88)) % 0.46/0.68 (define @t161 () (not @t160)) % 0.46/0.68 (define @t162 () (or (not (tptp.maps @t90 @t153 @t88)) @t161 @t159 @t158 @t156)) % 0.46/0.68 (define @t163 () (@list true)) % 0.46/0.68 (define @t164 () (@list @t162)) % 0.46/0.68 (define @t165 () (tptp.member @t2 @t153)) % 0.46/0.68 (define @t166 () (forall @t6 (or @t123 @t165))) % 0.46/0.68 (define @t167 () (= @t155 @t166)) % 0.46/0.68 (define @t168 () (@list false false)) % 0.46/0.68 (define @t169 () (tptp.member @t135 @t153)) % 0.46/0.68 (define @t170 () (or @t139 @t169)) % 0.46/0.68 (define @t171 () (forall @t6 (or @t128 @t165))) % 0.46/0.68 (define @t172 () (= @t157 @t171)) % 0.46/0.68 (define @t173 () (tptp.member @t142 @t153)) % 0.46/0.68 (define @t174 () (or @t146 @t173)) % 0.46/0.68 (define @t175 () (tptp.member @t135 @t89)) % 0.46/0.68 (define @t176 () (and @t138 @t175)) % 0.46/0.68 (define @t177 () (= @t150 @t176)) % 0.46/0.68 (define @t178 () (not @t44)) % 0.46/0.68 (define @t179 () (not @t45)) % 0.46/0.68 (define @t180 () (not @t31)) % 0.46/0.68 (define @t181 () (not @t48)) % 0.46/0.68 (define @t182 () (not @t49)) % 0.46/0.68 (define @t183 () (or @t179 @t178 @t43)) % 0.46/0.68 (define @t184 () (or @t182 @t181 @t180)) % 0.46/0.68 (define @t185 () (forall @t51 (or (not (tptp.member @t42 @t153)) (not (tptp.member @t41 @t153)) (not (tptp.member @t17 @t88)) (not (tptp.apply @t90 @t42 @t17)) (not (tptp.apply @t90 @t41 @t17)) @t43))) % 0.46/0.68 (define @t186 () (= @t160 @t185)) % 0.46/0.68 (define @t187 () (= @t135 @t142)) % 0.46/0.68 (define @t188 () (not @t173)) % 0.46/0.68 (define @t189 () (not @t169)) % 0.46/0.68 (define @t190 () (or @t189 @t188 @t134 @t137 @t144 @t187)) % 0.46/0.68 (define @t191 () (and @t145 @t187)) % 0.46/0.68 (define @t192 () (not @t111)) % 0.46/0.68 (define @t193 () (not @t106)) % 0.46/0.68 (define @t194 () (@list false)) % 0.46/0.68 (define @t195 () (tptp.subset @t94 @t97)) % 0.46/0.68 (define @t196 () (= @t195 @t106)) % 0.46/0.68 (define @t197 () (tptp.subset @t97 @t94)) % 0.46/0.68 (define @t198 () (and @t197 @t195)) % 0.46/0.68 (define @t199 () (= @t156 @t198)) % 0.46/0.68 (define @t200 () (not @t198)) % 0.46/0.68 (define @t201 () (@list true false)) % 0.46/0.68 (define @t202 () (= @t197 @t99)) % 0.46/0.68 (define @t203 () (not @t99)) % 0.46/0.68 (define @t204 () (tptp.member @t100 @t94)) % 0.46/0.68 (define @t205 () (tptp.member @t100 @t97)) % 0.46/0.68 (define @t206 () (not @t205)) % 0.46/0.68 (define @t207 () (or @t206 @t204)) % 0.46/0.68 (define @t208 () (not @t207)) % 0.46/0.68 (define @t209 () (@list @t207)) % 0.46/0.68 (define @t210 () (not @t103)) % 0.46/0.68 (define @t211 () (tptp.member @t100 @t88)) % 0.46/0.68 (define @t212 () (and @t211 @t210)) % 0.46/0.68 (define @t213 () (= @t205 @t212)) % 0.46/0.68 (define @t214 () (not @t212)) % 0.46/0.68 (define @t215 () (@list @t212)) % 0.46/0.68 (define @t216 () (tptp.apply @t90 @t104 @t100)) % 0.46/0.68 (define @t217 () (not @t216)) % 0.46/0.68 (define @t218 () (tptp.member @t104 @t96)) % 0.46/0.68 (define @t219 () (not @t218)) % 0.46/0.68 (define @t220 () (or @t219 @t217)) % 0.46/0.68 (define @t221 () (not @t220)) % 0.46/0.68 (define @t222 () (@list @t220)) % 0.46/0.68 (define @t223 () (tptp.member @t104 @t89)) % 0.46/0.68 (define @t224 () (tptp.member @t104 @t92)) % 0.46/0.68 (define @t225 () (and @t224 @t223)) % 0.46/0.68 (define @t226 () (= @t218 @t225)) % 0.46/0.68 (define @t227 () (not @t225)) % 0.46/0.68 (define @t228 () (@list @t225)) % 0.46/0.68 (define @t229 () (not @t224)) % 0.46/0.68 (define @t230 () (or @t229 @t217)) % 0.46/0.68 (define @t231 () (not @t230)) % 0.46/0.68 (define @t232 () (forall @t6 (or @t123 @t101))) % 0.46/0.68 (define @t233 () (@list @t104)) % 0.46/0.68 (define @t234 () (not @t232)) % 0.46/0.68 (define @t235 () (not @t211)) % 0.46/0.68 (define @t236 () (and @t211 @t234)) % 0.46/0.68 (define @t237 () (@list false true)) % 0.46/0.68 (define @t238 () (tptp.member @t100 @t93)) % 0.46/0.68 (define @t239 () (= @t238 @t236)) % 0.46/0.68 (define @t240 () (tptp.member @t100 @t91)) % 0.46/0.68 (define @t241 () (and @t238 @t240)) % 0.46/0.68 (define @t242 () (= @t204 @t241)) % 0.46/0.68 (define @t243 () (not @t241)) % 0.46/0.68 (define @t244 () (forall @t6 (or @t128 @t101))) % 0.46/0.68 (define @t245 () (not @t244)) % 0.46/0.68 (define @t246 () (and @t211 @t245)) % 0.46/0.68 (define @t247 () (= @t240 @t246)) % 0.46/0.68 (define @t248 () (not @t246)) % 0.46/0.68 (define @t249 () (not @t223)) % 0.46/0.68 (define @t250 () (or @t249 @t217)) % 0.46/0.68 (define @t251 () (not @t250)) % 0.46/0.68 (assume @p1 @t11) % 0.46/0.68 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.46/0.68 (assume @p3 (forall @t13 (= (tptp.member @t2 (tptp.power_set @t4)) @t12))) % 0.46/0.68 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.46/0.68 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.46/0.68 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.46/0.68 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.46/0.68 (assume @p8 (forall @t13 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.46/0.68 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.46/0.68 (assume @p10 (forall @t13 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.46/0.68 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.46/0.68 (assume @p12 (forall @t34 (= @t33 (and (forall @t6 (=> @t5 @t32)) (forall @t29 (=> @t28 (=> (and @t25 (tptp.apply @t24 @t2 @t21)) @t23))))))) % 0.46/0.68 (assume @p13 (forall (@list @t38 @t36 @t24 @t4 @t1 @t39) (= (tptp.compose_predicate @t38 @t36 @t24 @t4 @t1 @t39) (forall (@list @t2 @t35) (=> @t40 (= (tptp.apply @t38 @t2 @t35) @t37)))))) % 0.46/0.68 (assume @p14 (forall (@list @t36 @t24 @t4 @t1 @t39 @t2 @t35) (=> @t40 (= (tptp.apply (tptp.compose_function @t36 @t24 @t4 @t1 @t39) @t2 @t35) @t37)))) % 0.46/0.68 (assume @p15 (forall (@list @t24 @t36 @t4 @t1) (= (tptp.equal_maps @t24 @t36 @t4 @t1) (forall @t29 (=> @t28 (=> (and @t25 (tptp.apply @t36 @t2 @t21)) @t23)))))) % 0.46/0.68 (assume @p16 (forall (@list @t24 @t4) (= (tptp.identity @t24 @t4) (forall @t6 (=> @t5 (tptp.apply @t24 @t2 @t2)))))) % 0.46/0.68 (assume @p17 @t55) % 0.46/0.68 (assume @p18 (forall @t34 (= @t56 (forall @t20 (=> @t31 (exists (@list @t15) (and (tptp.member @t15 @t4) (tptp.apply @t24 @t15 @t17)))))))) % 0.46/0.68 (assume @p19 (forall @t34 (= @t57 (and @t53 @t56)))) % 0.46/0.68 (assume @p20 (forall (@list @t36 @t24 @t4 @t1) (= (tptp.inverse_predicate @t36 @t24 @t4 @t1) (forall (@list @t2 @t17) (=> @t58 (= @t30 (tptp.apply @t36 @t17 @t2))))))) % 0.46/0.68 (assume @p21 (forall @t59 (=> @t58 (= @t30 (tptp.apply (tptp.inverse_function @t24 @t4 @t1) @t17 @t2))))) % 0.46/0.68 (assume @p22 (forall (@list @t24 @t4 @t17) (= (tptp.member @t17 (tptp.image2 @t24 @t4)) @t61))) % 0.46/0.68 (assume @p23 @t65) % 0.46/0.68 (assume @p24 (forall (@list @t24 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t24 @t1)) @t32))) % 0.46/0.68 (assume @p25 (forall (@list @t24 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t24 @t1 @t4)) (and @t5 @t32)))) % 0.46/0.68 (assume @p26 (forall @t74 (= (tptp.increasing @t24 @t4 @t70 @t1 @t66) (forall @t73 (=> @t72 @t67))))) % 0.46/0.68 (assume @p27 (forall @t74 (= (tptp.decreasing @t24 @t4 @t70 @t1 @t66) (forall @t73 (=> @t72 (tptp.apply @t66 @t21 @t22)))))) % 0.46/0.68 (assume @p28 (forall @t74 (= (tptp.isomorphism @t24 @t4 @t70 @t1 @t66) (and @t33 @t57 (forall @t73 (=> (and @t49 @t27 @t48 @t26 @t69 @t68) (= @t71 @t67))))))) % 0.46/0.68 (assume @p29 @t79) % 0.46/0.68 (assume @p30 true) % 0.46/0.68 (step @p31 :rule bool-and-de-morgan :args (@t5 @t30 true)) % 0.46/0.68 (step @p32 :rule cong :premises (@p31) :args (@t80)) % 0.46/0.68 (step @p33 :rule cong :premises (@p32) :args (@t81)) % 0.46/0.68 (step @p34 :rule exists-elim :args ((= @t61 @t81))) % 0.46/0.68 (step @p35 :rule trans :premises (@p34 @p33)) % 0.46/0.68 (step @p36 :rule refl :args (@t31)) % 0.46/0.68 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t62)) % 0.46/0.68 (step @p38 :rule refl :args (@t63)) % 0.46/0.68 (step @p39 :rule cong :premises (@p38 @p37) :args (@t64)) % 0.46/0.68 (step @p40 :rule cong :premises (@p39) :args (@t65)) % 0.46/0.68 (step @p41 :rule eq_resolve :premises (@p23 @p40)) % 0.46/0.68 (step @p42 :rule instantiate :premises (@p41) :args ((@list @t90 @t89 @t88 @t100))) % 0.46/0.68 (step @p43 :rule instantiate :premises (@p41) :args ((@list @t90 @t92 @t88 @t100))) % 0.46/0.68 (step @p44 :rule instantiate :premises (@p4) :args ((@list @t104 @t92 @t89))) % 0.46/0.68 (step @p45 :rule instantiate :premises (@p41) :args ((@list @t90 @t96 @t88 @t100))) % 0.46/0.68 (step @p46 :rule bool-impl-elim :args (@t5 @t3)) % 0.46/0.68 (step @p47 :rule cong :premises (@p46) :args (@t7)) % 0.46/0.68 (step @p48 :rule refl :args (@t8)) % 0.46/0.68 (step @p49 :rule cong :premises (@p48 @p47) :args (@t9)) % 0.46/0.68 (step @p50 :rule cong :premises (@p49) :args (@t11)) % 0.46/0.68 (step @p51 :rule eq_resolve :premises (@p1 @p50)) % 0.46/0.68 (step @p52 :rule instantiate :premises (@p51) :args (@t105)) % 0.46/0.68 (step @p53 :rule instantiate :premises (@p51) :args ((@list @t94 @t97))) % 0.46/0.68 (step @p54 :rule bool-double-not-elim :args (@t108)) % 0.46/0.68 (step @p55 :rule refl :args (@t111)) % 0.46/0.68 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t111 (not @t110)))) % 0.46/0.68 (step @p57 :rule cnf_or_neg :args (@t111 0)) % 0.46/0.68 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 0.46/0.68 (step @p59 :rule reordering :premises (@p58) :args ((or @t108 @t111))) % 0.46/0.68 (step @p60 :rule cnf_or_neg :args (@t111 1)) % 0.46/0.68 (step @p61 :rule instantiate :premises (@p4) :args ((@list @t107 @t93 @t91))) % 0.46/0.68 (step @p62 :rule cnf_equiv_pos1 :args (@t115)) % 0.46/0.68 (step @p63 :rule reordering :premises (@p62) :args ((or @t110 @t114 (not @t115)))) % 0.46/0.68 (step @p64 :rule instantiate :premises (@p41) :args ((@list @t90 @t96 @t88 @t107))) % 0.46/0.68 (step @p65 :rule cnf_equiv_pos2 :args (@t121)) % 0.46/0.68 (step @p66 :rule reordering :premises (@p65) :args ((or @t109 (not @t120) (not @t121)))) % 0.46/0.68 (step @p67 :rule cnf_and_pos :args (@t114 0)) % 0.46/0.68 (step @p68 :rule reordering :premises (@p67) :args ((or @t113 @t122))) % 0.46/0.68 (step @p69 :rule cnf_and_pos :args (@t114 1)) % 0.46/0.68 (step @p70 :rule reordering :premises (@p69) :args ((or @t112 @t122))) % 0.46/0.68 (step @p71 :rule instantiate :premises (@p41) :args ((@list @t90 @t92 @t88 @t107))) % 0.46/0.68 (step @p72 :rule cnf_equiv_pos1 :args (@t127)) % 0.46/0.68 (step @p73 :rule reordering :premises (@p72) :args ((or (not @t113) @t126 (not @t127)))) % 0.46/0.68 (step @p74 :rule instantiate :premises (@p41) :args ((@list @t90 @t89 @t88 @t107))) % 0.46/0.68 (step @p75 :rule cnf_equiv_pos1 :args (@t132)) % 0.46/0.68 (step @p76 :rule reordering :premises (@p75) :args ((or (not @t112) @t131 (not @t132)))) % 0.46/0.68 (step @p77 :rule cnf_and_pos :args (@t126 0)) % 0.46/0.68 (step @p78 :rule reordering :premises (@p77) :args ((or @t119 @t133))) % 0.46/0.68 (step @p79 :rule cnf_and_pos :args (@t126 1)) % 0.46/0.68 (step @p80 :rule reordering :premises (@p79) :args ((or @t125 @t133))) % 0.46/0.68 (step @p81 :rule cnf_and_pos :args (@t131 1)) % 0.46/0.68 (step @p82 :rule reordering :premises (@p81) :args ((or @t130 (not @t131)))) % 0.46/0.68 (step @p83 :rule bool-double-not-elim :args (@t117)) % 0.46/0.68 (step @p84 :rule refl :args (@t134)) % 0.46/0.68 (step @p85 :rule refl :args (@t120)) % 0.46/0.68 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83) :args ((or @t120 @t134 (not @t118)))) % 0.46/0.68 (step @p87 :rule cnf_and_neg :args (@t120)) % 0.46/0.68 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.46/0.68 (step @p89 :rule reordering :premises (@p88) :args ((or @t117 @t120 @t134))) % 0.46/0.68 (step @p90 :rule refl :args (@t141)) % 0.46/0.68 (step @p91 :rule bool-double-not-elim :args (@t124)) % 0.46/0.68 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or (not @t125) @t141))) % 0.46/0.68 (assume-push @p378 @t125) % 0.46/0.68 (step @p94 :rule skolemize :premises (@p378)) % 0.46/0.68 (step-pop @p379 :rule scope :premises (@p94)) % 0.46/0.68 (step @p95 :rule process_scope :premises (@p379) :args (@t141)) % 0.46/0.68 (step @p97 :rule implies_elim :premises (@p95)) % 0.46/0.68 (step @p98 :rule eq_resolve :premises (@p97 @p92)) % 0.46/0.68 (step @p99 :rule refl :args (@t148)) % 0.46/0.68 (step @p100 :rule bool-double-not-elim :args (@t129)) % 0.46/0.68 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or (not @t130) @t148))) % 0.46/0.68 (assume-push @p380 @t130) % 0.46/0.68 (step @p103 :rule skolemize :premises (@p380)) % 0.46/0.68 (step-pop @p381 :rule scope :premises (@p103)) % 0.46/0.68 (step @p104 :rule process_scope :premises (@p381) :args (@t148)) % 0.46/0.68 (step @p106 :rule implies_elim :premises (@p104)) % 0.46/0.68 (step @p107 :rule eq_resolve :premises (@p106 @p101)) % 0.46/0.68 (assume-push @p382 @t117) % 0.46/0.68 (step @p109 :rule instantiate :premises (@p382) :args (@t149)) % 0.46/0.68 (step-pop @p383 :rule scope :premises (@p109)) % 0.46/0.68 (step @p110 :rule process_scope :premises (@p383) :args (@t152)) % 0.46/0.68 (step @p112 :rule implies_elim :premises (@p110)) % 0.46/0.68 (step @p113 :rule bool-double-not-elim :args (@t138)) % 0.46/0.68 (step @p114 :rule refl :args (@t140)) % 0.46/0.68 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t140 (not @t139)))) % 0.46/0.68 (step @p116 :rule cnf_or_neg :args (@t140 0)) % 0.46/0.68 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.46/0.68 (step @p118 :rule reordering :premises (@p117) :args ((or @t138 @t140))) % 0.46/0.68 (step @p119 :rule bool-double-not-elim :args (@t136)) % 0.46/0.68 (step @p120 :rule nary_cong :premises (@p114 @p119) :args ((or @t140 (not @t137)))) % 0.46/0.68 (step @p121 :rule cnf_or_neg :args (@t140 1)) % 0.46/0.68 (step @p122 :rule eq_resolve :premises (@p121 @p120)) % 0.46/0.68 (step @p123 :rule reordering :premises (@p122) :args ((or @t136 @t140))) % 0.46/0.68 (step @p124 :rule bool-double-not-elim :args (@t145)) % 0.46/0.68 (step @p125 :rule refl :args (@t147)) % 0.46/0.68 (step @p126 :rule nary_cong :premises (@p125 @p124) :args ((or @t147 (not @t146)))) % 0.46/0.68 (step @p127 :rule cnf_or_neg :args (@t147 0)) % 0.46/0.68 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.46/0.68 (step @p129 :rule reordering :premises (@p128) :args ((or @t145 @t147))) % 0.46/0.68 (step @p130 :rule bool-double-not-elim :args (@t143)) % 0.46/0.68 (step @p131 :rule nary_cong :premises (@p125 @p130) :args ((or @t147 (not @t144)))) % 0.46/0.68 (step @p132 :rule cnf_or_neg :args (@t147 1)) % 0.46/0.68 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.46/0.68 (step @p134 :rule reordering :premises (@p133) :args ((or @t143 @t147))) % 0.46/0.68 (step @p135 :rule cnf_or_pos :args (@t152)) % 0.46/0.68 (step @p136 :rule reordering :premises (@p135) :args ((or @t137 @t151 (not @t152)))) % 0.46/0.68 (step @p137 :rule instantiate :premises (@p51) :args ((@list @t92 @t153))) % 0.46/0.68 (step @p138 :rule aci_norm :args ((= (or @t154 @t75) @t86))) % 0.46/0.68 (step @p139 :rule refl :args (@t75)) % 0.46/0.68 (step @p140 :rule aci_norm :args ((= (or @t85 (or @t84 (or @t83 @t82))) @t154))) % 0.46/0.68 (step @p141 :rule bool-and-de-morgan :args (@t12 @t76 true)) % 0.46/0.68 (step @p142 :rule refl :args (@t84)) % 0.46/0.68 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t84 (not (and @t12 @t76))))) % 0.46/0.68 (step @p144 :rule bool-and-de-morgan :args (@t53 @t12 (and @t76))) % 0.46/0.68 (step @p145 :rule trans :premises (@p144 @p143)) % 0.46/0.68 (step @p146 :rule refl :args (@t85)) % 0.46/0.68 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t85 (not (and @t53 @t12 @t76))))) % 0.46/0.68 (step @p148 :rule bool-and-de-morgan :args (@t33 @t53 (and @t12 @t76))) % 0.46/0.68 (step @p149 :rule trans :premises (@p148 @p147)) % 0.46/0.68 (step @p150 :rule trans :premises (@p149 @p140)) % 0.46/0.68 (step @p151 :rule nary_cong :premises (@p150 @p139) :args ((or (not @t77) @t75))) % 0.46/0.68 (step @p152 :rule trans :premises (@p151 @p138)) % 0.46/0.68 (step @p153 :rule bool-impl-elim :args (@t77 @t75)) % 0.46/0.68 (step @p154 :rule trans :premises (@p153 @p152)) % 0.46/0.68 (step @p155 :rule cong :premises (@p154) :args (@t78)) % 0.46/0.68 (step @p156 :rule cong :premises (@p155) :args (@t79)) % 0.46/0.68 (step @p157 :rule eq_resolve :premises (@p29 @p156)) % 0.46/0.68 (step @p158 :rule skolemize :premises (@p157)) % 0.46/0.68 (step @p159 :rule bool-double-not-elim :args (@t155)) % 0.46/0.68 (step @p160 :rule refl :args (@t162)) % 0.46/0.68 (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((or @t162 (not @t159)))) % 0.46/0.68 (step 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