%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET760+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 0.63s 0.87s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET760+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.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 16:11:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.63/0.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.63/0.87 % SZS status Theorem % 0.63/0.87 % SZS output start Proof % 0.63/0.87 ( % 0.63/0.87 (declare-sort $$unsorted 0) % 0.63/0.87 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.empty_set $$unsorted) % 0.63/0.87 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.87 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.63/0.87 (define @t1 () (@var "B" $$unsorted)) % 0.63/0.87 (define @t2 () (@var "X" $$unsorted)) % 0.63/0.87 (define @t3 () (tptp.member @t2 @t1)) % 0.63/0.87 (define @t4 () (@var "A" $$unsorted)) % 0.63/0.87 (define @t5 () (tptp.member @t2 @t4)) % 0.63/0.87 (define @t6 () (@list @t2)) % 0.63/0.87 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.63/0.87 (define @t8 () (tptp.subset @t4 @t1)) % 0.63/0.87 (define @t9 () (= @t8 @t7)) % 0.63/0.87 (define @t10 () (@list @t4 @t1)) % 0.63/0.87 (define @t11 () (forall @t10 @t9)) % 0.63/0.87 (define @t12 () (@list @t2 @t4)) % 0.63/0.87 (define @t13 () (@list @t2 @t4 @t1)) % 0.63/0.87 (define @t14 () (@var "E" $$unsorted)) % 0.63/0.87 (define @t15 () (= @t2 @t4)) % 0.63/0.87 (define @t16 () (@var "Y" $$unsorted)) % 0.63/0.87 (define @t17 () (tptp.member @t2 @t16)) % 0.63/0.87 (define @t18 () (tptp.member @t16 @t4)) % 0.63/0.87 (define @t19 () (@list @t16)) % 0.63/0.87 (define @t20 () (@var "Y2" $$unsorted)) % 0.63/0.87 (define @t21 () (@var "Y1" $$unsorted)) % 0.63/0.87 (define @t22 () (= @t21 @t20)) % 0.63/0.87 (define @t23 () (@var "F" $$unsorted)) % 0.63/0.87 (define @t24 () (tptp.apply @t23 @t2 @t20)) % 0.63/0.87 (define @t25 () (tptp.apply @t23 @t2 @t21)) % 0.63/0.87 (define @t26 () (and @t25 @t24)) % 0.63/0.87 (define @t27 () (=> @t26 @t22)) % 0.63/0.87 (define @t28 () (tptp.member @t20 @t1)) % 0.63/0.87 (define @t29 () (tptp.member @t21 @t1)) % 0.63/0.87 (define @t30 () (and @t5 @t29 @t28)) % 0.63/0.87 (define @t31 () (@list @t2 @t21 @t20)) % 0.63/0.87 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.63/0.87 (define @t33 () (tptp.apply @t23 @t2 @t16)) % 0.63/0.87 (define @t34 () (tptp.member @t16 @t1)) % 0.63/0.87 (define @t35 () (and @t34 @t33)) % 0.63/0.87 (define @t36 () (exists @t19 @t35)) % 0.63/0.87 (define @t37 () (=> @t5 @t36)) % 0.63/0.87 (define @t38 () (forall @t6 @t37)) % 0.63/0.87 (define @t39 () (and @t38 @t32)) % 0.63/0.87 (define @t40 () (tptp.maps @t23 @t4 @t1)) % 0.63/0.87 (define @t41 () (= @t40 @t39)) % 0.63/0.87 (define @t42 () (@list @t23 @t4 @t1)) % 0.63/0.87 (define @t43 () (forall @t42 @t41)) % 0.63/0.87 (define @t44 () (@var "Z" $$unsorted)) % 0.63/0.87 (define @t45 () (@var "G" $$unsorted)) % 0.63/0.87 (define @t46 () (exists @t19 (and @t34 @t33 (tptp.apply @t45 @t16 @t44)))) % 0.63/0.87 (define @t47 () (@var "H" $$unsorted)) % 0.63/0.87 (define @t48 () (@var "C" $$unsorted)) % 0.63/0.87 (define @t49 () (and @t5 (tptp.member @t44 @t48))) % 0.63/0.87 (define @t50 () (@var "X2" $$unsorted)) % 0.63/0.87 (define @t51 () (@var "X1" $$unsorted)) % 0.63/0.87 (define @t52 () (tptp.member @t50 @t4)) % 0.63/0.87 (define @t53 () (tptp.member @t51 @t4)) % 0.63/0.87 (define @t54 () (tptp.injective @t23 @t4 @t1)) % 0.63/0.87 (define @t55 () (tptp.apply @t23 @t14 @t16)) % 0.63/0.87 (define @t56 () (tptp.member @t14 @t4)) % 0.63/0.87 (define @t57 () (and @t56 @t55)) % 0.63/0.87 (define @t58 () (@list @t14)) % 0.63/0.87 (define @t59 () (exists @t58 @t57)) % 0.63/0.87 (define @t60 () (=> @t34 @t59)) % 0.63/0.87 (define @t61 () (forall @t19 @t60)) % 0.63/0.87 (define @t62 () (tptp.surjective @t23 @t4 @t1)) % 0.63/0.87 (define @t63 () (= @t62 @t61)) % 0.63/0.87 (define @t64 () (forall @t42 @t63)) % 0.63/0.87 (define @t65 () (tptp.one_to_one @t23 @t4 @t1)) % 0.63/0.87 (define @t66 () (and @t5 @t34)) % 0.63/0.87 (define @t67 () (and @t5 @t33)) % 0.63/0.87 (define @t68 () (exists @t6 @t67)) % 0.63/0.87 (define @t69 () (and @t34 @t68)) % 0.63/0.87 (define @t70 () (tptp.member @t16 (tptp.image3 @t23 @t4 @t1))) % 0.63/0.87 (define @t71 () (= @t70 @t69)) % 0.63/0.87 (define @t72 () (@list @t23 @t4 @t1 @t16)) % 0.63/0.87 (define @t73 () (forall @t72 @t71)) % 0.63/0.87 (define @t74 () (and @t5 @t36)) % 0.63/0.87 (define @t75 () (tptp.member @t2 (tptp.inverse_image3 @t23 @t1 @t4))) % 0.63/0.87 (define @t76 () (= @t75 @t74)) % 0.63/0.87 (define @t77 () (forall (@list @t23 @t1 @t4 @t2) @t76)) % 0.63/0.87 (define @t78 () (@var "S" $$unsorted)) % 0.63/0.87 (define @t79 () (tptp.apply @t78 @t21 @t20)) % 0.63/0.87 (define @t80 () (tptp.apply @t23 @t50 @t20)) % 0.63/0.87 (define @t81 () (tptp.apply @t23 @t51 @t21)) % 0.63/0.87 (define @t82 () (@var "R" $$unsorted)) % 0.63/0.87 (define @t83 () (tptp.apply @t82 @t51 @t50)) % 0.63/0.87 (define @t84 () (and @t53 @t29 @t52 @t28 @t83 @t81 @t80)) % 0.63/0.87 (define @t85 () (@list @t51 @t21 @t50 @t20)) % 0.63/0.87 (define @t86 () (@list @t23 @t4 @t82 @t1 @t78)) % 0.63/0.87 (define @t87 () (tptp.equal_set (tptp.image3 @t23 (tptp.inverse_image3 @t23 @t16 @t4) @t1) @t16)) % 0.63/0.87 (define @t88 () (tptp.subset @t16 @t1)) % 0.63/0.87 (define @t89 () (and @t40 @t62 @t88)) % 0.63/0.87 (define @t90 () (forall @t72 (=> @t89 @t87))) % 0.63/0.87 (define @t91 () (not @t90)) % 0.63/0.87 (define @t92 () (forall @t6 (not @t67))) % 0.63/0.87 (define @t93 () (not @t92)) % 0.63/0.87 (define @t94 () (not @t88)) % 0.63/0.87 (define @t95 () (not @t62)) % 0.63/0.87 (define @t96 () (not @t40)) % 0.63/0.87 (define @t97 () (or @t96 @t95 @t94 @t87)) % 0.63/0.87 (define @t98 () (forall @t72 @t97)) % 0.63/0.87 (define @t99 () (@quantifiers_skolemize @t98 3)) % 0.63/0.87 (define @t100 () (tptp.member @t2 @t99)) % 0.63/0.87 (define @t101 () (@quantifiers_skolemize @t98 2)) % 0.63/0.87 (define @t102 () (@quantifiers_skolemize @t98 1)) % 0.63/0.87 (define @t103 () (@quantifiers_skolemize @t98 0)) % 0.63/0.87 (define @t104 () (tptp.inverse_image3 @t103 @t99 @t102)) % 0.63/0.87 (define @t105 () (tptp.image3 @t103 @t104 @t101)) % 0.63/0.87 (define @t106 () (tptp.member @t2 @t105)) % 0.63/0.87 (define @t107 () (forall @t6 (or (not @t106) @t100))) % 0.63/0.87 (define @t108 () (@quantifiers_skolemize @t107 0)) % 0.63/0.87 (define @t109 () (@list @t105 @t99)) % 0.63/0.87 (define @t110 () (not @t100)) % 0.63/0.87 (define @t111 () (forall @t6 (or @t110 @t106))) % 0.63/0.87 (define @t112 () (@quantifiers_skolemize @t111 0)) % 0.63/0.87 (define @t113 () (tptp.member @t112 @t99)) % 0.63/0.87 (define @t114 () (tptp.member @t112 @t105)) % 0.63/0.87 (define @t115 () (not @t113)) % 0.63/0.87 (define @t116 () (or @t115 @t114)) % 0.63/0.87 (define @t117 () (or @t96 @t95 @t94)) % 0.63/0.87 (define @t118 () (tptp.subset @t99 @t101)) % 0.63/0.87 (define @t119 () (tptp.equal_set @t105 @t99)) % 0.63/0.87 (define @t120 () (not @t118)) % 0.63/0.87 (define @t121 () (tptp.surjective @t103 @t102 @t101)) % 0.63/0.87 (define @t122 () (not @t121)) % 0.63/0.87 (define @t123 () (tptp.maps @t103 @t102 @t101)) % 0.63/0.87 (define @t124 () (not @t123)) % 0.63/0.87 (define @t125 () (or @t124 @t122 @t120 @t119)) % 0.63/0.87 (define @t126 () (@list true)) % 0.63/0.87 (define @t127 () (@list @t125)) % 0.63/0.87 (define @t128 () (forall @t6 (or @t110 (tptp.member @t2 @t101)))) % 0.63/0.87 (define @t129 () (= @t118 @t128)) % 0.63/0.87 (define @t130 () (@list false false)) % 0.63/0.87 (define @t131 () (@list @t112)) % 0.63/0.87 (define @t132 () (tptp.member @t112 @t101)) % 0.63/0.87 (define @t133 () (or @t115 @t132)) % 0.63/0.87 (define @t134 () (not (tptp.member @t2 @t104))) % 0.63/0.87 (define @t135 () (forall @t6 (or @t134 (not (tptp.apply @t103 @t2 @t112))))) % 0.63/0.87 (define @t136 () (not @t135)) % 0.63/0.87 (define @t137 () (and @t132 @t136)) % 0.63/0.87 (define @t138 () (= @t114 @t137)) % 0.63/0.87 (define @t139 () (not @t132)) % 0.63/0.87 (define @t140 () (not (forall @t58 (or (not @t56) (not @t55))))) % 0.63/0.87 (define @t141 () (forall @t58 (not @t57))) % 0.63/0.87 (define @t142 () (not @t141)) % 0.63/0.87 (define @t143 () (@list @t103 @t102 @t101)) % 0.63/0.87 (define @t144 () (not (tptp.member @t14 @t102))) % 0.63/0.87 (define @t145 () (not (tptp.member @t16 @t101))) % 0.63/0.87 (define @t146 () (forall @t19 (or @t145 (not (forall @t58 (or @t144 (not (tptp.apply @t103 @t14 @t16)))))))) % 0.63/0.87 (define @t147 () (= @t121 @t146)) % 0.63/0.87 (define @t148 () (forall @t58 (or @t144 (not (tptp.apply @t103 @t14 @t112))))) % 0.63/0.87 (define @t149 () (not @t148)) % 0.63/0.87 (define @t150 () (or @t139 @t149)) % 0.63/0.87 (define @t151 () (@quantifiers_skolemize @t148 0)) % 0.63/0.87 (define @t152 () (tptp.apply @t103 @t151 @t112)) % 0.63/0.87 (define @t153 () (not @t152)) % 0.63/0.87 (define @t154 () (tptp.member @t151 @t104)) % 0.63/0.87 (define @t155 () (not @t154)) % 0.63/0.87 (define @t156 () (or @t155 @t153)) % 0.63/0.87 (define @t157 () (tptp.member @t151 @t102)) % 0.63/0.87 (define @t158 () (not @t157)) % 0.63/0.87 (define @t159 () (or @t158 @t153)) % 0.63/0.87 (define @t160 () (not @t159)) % 0.63/0.87 (define @t161 () (not (tptp.member @t16 @t99))) % 0.63/0.87 (define @t162 () (forall @t19 (or @t161 (not (tptp.apply @t103 @t151 @t16))))) % 0.63/0.87 (define @t163 () (not @t162)) % 0.63/0.87 (define @t164 () (and @t157 @t163)) % 0.63/0.87 (define @t165 () (forall @t19 (not @t35))) % 0.63/0.87 (define @t166 () (not @t165)) % 0.63/0.87 (define @t167 () (= @t154 @t164)) % 0.63/0.87 (define @t168 () (or @t115 @t153)) % 0.63/0.87 (define @t169 () (not @t116)) % 0.63/0.87 (define @t170 () (not @t111)) % 0.63/0.87 (define @t171 () (@list false)) % 0.63/0.87 (define @t172 () (tptp.subset @t99 @t105)) % 0.63/0.87 (define @t173 () (= @t172 @t111)) % 0.63/0.87 (define @t174 () (tptp.subset @t105 @t99)) % 0.63/0.87 (define @t175 () (and @t174 @t172)) % 0.63/0.87 (define @t176 () (= @t119 @t175)) % 0.63/0.87 (define @t177 () (not @t175)) % 0.63/0.87 (define @t178 () (@list true false)) % 0.63/0.87 (define @t179 () (= @t174 @t107)) % 0.63/0.87 (define @t180 () (not @t107)) % 0.63/0.87 (define @t181 () (tptp.member @t108 @t99)) % 0.63/0.87 (define @t182 () (tptp.member @t108 @t105)) % 0.63/0.87 (define @t183 () (not @t182)) % 0.63/0.87 (define @t184 () (or @t183 @t181)) % 0.63/0.87 (define @t185 () (not @t184)) % 0.63/0.87 (define @t186 () (@list @t184)) % 0.63/0.87 (define @t187 () (forall @t6 (or @t134 (not (tptp.apply @t103 @t2 @t108))))) % 0.63/0.87 (define @t188 () (not @t187)) % 0.63/0.87 (define @t189 () (tptp.member @t108 @t101)) % 0.63/0.87 (define @t190 () (and @t189 @t188)) % 0.63/0.87 (define @t191 () (= @t182 @t190)) % 0.63/0.87 (define @t192 () (not @t190)) % 0.63/0.87 (define @t193 () (@list @t190)) % 0.63/0.87 (define @t194 () (@quantifiers_skolemize @t187 0)) % 0.63/0.87 (define @t195 () (tptp.apply @t103 @t194 @t108)) % 0.63/0.87 (define @t196 () (not @t195)) % 0.63/0.87 (define @t197 () (tptp.member @t194 @t104)) % 0.63/0.87 (define @t198 () (not @t197)) % 0.63/0.87 (define @t199 () (or @t198 @t196)) % 0.63/0.87 (define @t200 () (not @t199)) % 0.63/0.87 (define @t201 () (@list @t199)) % 0.63/0.87 (define @t202 () (forall @t19 (or @t161 (not (tptp.apply @t103 @t194 @t16))))) % 0.63/0.87 (define @t203 () (not @t202)) % 0.63/0.87 (define @t204 () (tptp.member @t194 @t102)) % 0.63/0.87 (define @t205 () (and @t204 @t203)) % 0.63/0.87 (define @t206 () (= @t197 @t205)) % 0.63/0.87 (define @t207 () (not @t205)) % 0.63/0.87 (define @t208 () (@list @t205)) % 0.63/0.87 (define @t209 () (@quantifiers_skolemize @t202 0)) % 0.63/0.87 (define @t210 () (tptp.apply @t103 @t194 @t209)) % 0.63/0.87 (define @t211 () (not @t210)) % 0.63/0.87 (define @t212 () (tptp.member @t209 @t99)) % 0.63/0.87 (define @t213 () (not @t212)) % 0.63/0.87 (define @t214 () (or @t213 @t211)) % 0.63/0.87 (define @t215 () (not @t214)) % 0.63/0.87 (define @t216 () (@list @t214)) % 0.63/0.87 (define @t217 () (not @t181)) % 0.63/0.87 (define @t218 () (= @t108 @t209)) % 0.63/0.87 (define @t219 () (not @t218)) % 0.63/0.87 (define @t220 () (and @t212 @t218 @t217)) % 0.63/0.87 (define @t221 () (not @t24)) % 0.63/0.87 (define @t222 () (not @t25)) % 0.63/0.87 (define @t223 () (not @t28)) % 0.63/0.87 (define @t224 () (not @t29)) % 0.63/0.87 (define @t225 () (not @t5)) % 0.63/0.87 (define @t226 () (or @t222 @t221 @t22)) % 0.63/0.87 (define @t227 () (or @t225 @t224 @t223)) % 0.63/0.87 (define @t228 () (not (forall @t19 (or (not @t34) (not @t33))))) % 0.63/0.87 (define @t229 () (not (tptp.member @t2 @t102))) % 0.63/0.87 (define @t230 () (forall @t31 (or @t229 (not (tptp.member @t21 @t101)) (not (tptp.member @t20 @t101)) (not (tptp.apply @t103 @t2 @t21)) (not (tptp.apply @t103 @t2 @t20)) @t22))) % 0.63/0.87 (define @t231 () (and (forall @t6 (or @t229 (not (forall @t19 (or @t145 (not (tptp.apply @t103 @t2 @t16))))))) @t230)) % 0.63/0.87 (define @t232 () (= @t123 @t231)) % 0.63/0.87 (define @t233 () (not @t189)) % 0.63/0.87 (define @t234 () (tptp.member @t209 @t101)) % 0.63/0.87 (define @t235 () (not @t234)) % 0.63/0.87 (define @t236 () (not @t204)) % 0.63/0.87 (define @t237 () (or @t236 @t235 @t233 @t211 @t196 (= @t209 @t108))) % 0.63/0.87 (define @t238 () (or @t236 @t235 @t233 @t211 @t196 @t218)) % 0.63/0.87 (define @t239 () (or @t213 @t234)) % 0.63/0.87 (assume @p1 @t11) % 0.63/0.87 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.63/0.87 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.63/0.87 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.63/0.87 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.63/0.87 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.63/0.87 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.63/0.87 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.63/0.87 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.63/0.87 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.63/0.87 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.63/0.87 (assume @p12 @t43) % 0.63/0.87 (assume @p13 (forall (@list @t47 @t45 @t23 @t4 @t1 @t48) (= (tptp.compose_predicate @t47 @t45 @t23 @t4 @t1 @t48) (forall (@list @t2 @t44) (=> @t49 (= (tptp.apply @t47 @t2 @t44) @t46)))))) % 0.63/0.87 (assume @p14 (forall (@list @t45 @t23 @t4 @t1 @t48 @t2 @t44) (=> @t49 (= (tptp.apply (tptp.compose_function @t45 @t23 @t4 @t1 @t48) @t2 @t44) @t46)))) % 0.63/0.87 (assume @p15 (forall (@list @t23 @t45 @t4 @t1) (= (tptp.equal_maps @t23 @t45 @t4 @t1) (forall @t31 (=> @t30 (=> (and @t25 (tptp.apply @t45 @t2 @t20)) @t22)))))) % 0.63/0.87 (assume @p16 (forall (@list @t23 @t4) (= (tptp.identity @t23 @t4) (forall @t6 (=> @t5 (tptp.apply @t23 @t2 @t2)))))) % 0.63/0.87 (assume @p17 (forall @t42 (= @t54 (forall (@list @t51 @t50 @t16) (=> (and @t53 @t52 @t34) (=> (and (tptp.apply @t23 @t51 @t16) (tptp.apply @t23 @t50 @t16)) (= @t51 @t50))))))) % 0.63/0.87 (assume @p18 @t64) % 0.63/0.87 (assume @p19 (forall @t42 (= @t65 (and @t54 @t62)))) % 0.63/0.87 (assume @p20 (forall (@list @t45 @t23 @t4 @t1) (= (tptp.inverse_predicate @t45 @t23 @t4 @t1) (forall (@list @t2 @t16) (=> @t66 (= @t33 (tptp.apply @t45 @t16 @t2))))))) % 0.63/0.87 (assume @p21 (forall (@list @t23 @t4 @t1 @t2 @t16) (=> @t66 (= @t33 (tptp.apply (tptp.inverse_function @t23 @t4 @t1) @t16 @t2))))) % 0.63/0.87 (assume @p22 (forall (@list @t23 @t4 @t16) (= (tptp.member @t16 (tptp.image2 @t23 @t4)) @t68))) % 0.63/0.87 (assume @p23 @t73) % 0.63/0.87 (assume @p24 (forall (@list @t23 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t23 @t1)) @t36))) % 0.63/0.87 (assume @p25 @t77) % 0.63/0.87 (assume @p26 (forall @t86 (= (tptp.increasing @t23 @t4 @t82 @t1 @t78) (forall @t85 (=> @t84 @t79))))) % 0.63/0.87 (assume @p27 (forall @t86 (= (tptp.decreasing @t23 @t4 @t82 @t1 @t78) (forall @t85 (=> @t84 (tptp.apply @t78 @t20 @t21)))))) % 0.63/0.87 (assume @p28 (forall @t86 (= (tptp.isomorphism @t23 @t4 @t82 @t1 @t78) (and @t40 @t65 (forall @t85 (=> (and @t53 @t29 @t52 @t28 @t81 @t80) (= @t83 @t79))))))) % 0.63/0.87 (assume @p29 @t91) % 0.63/0.87 (assume @p30 true) % 0.63/0.87 (step @p31 :rule bool-and-de-morgan :args (@t5 @t33 true)) % 0.63/0.87 (step @p32 :rule cong :premises (@p31) :args (@t92)) % 0.63/0.87 (step @p33 :rule cong :premises (@p32) :args (@t93)) % 0.63/0.87 (step @p34 :rule exists-elim :args ((= @t68 @t93))) % 0.63/0.87 (step @p35 :rule trans :premises (@p34 @p33)) % 0.63/0.87 (step @p36 :rule refl :args (@t34)) % 0.63/0.87 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t69)) % 0.63/0.87 (step @p38 :rule refl :args (@t70)) % 0.63/0.87 (step @p39 :rule cong :premises (@p38 @p37) :args (@t71)) % 0.63/0.87 (step @p40 :rule cong :premises (@p39) :args (@t73)) % 0.63/0.87 (step @p41 :rule eq_resolve :premises (@p23 @p40)) % 0.63/0.87 (step @p42 :rule instantiate :premises (@p41) :args ((@list @t103 @t104 @t101 @t108))) % 0.63/0.87 (step @p43 :rule bool-impl-elim :args (@t5 @t3)) % 0.63/0.87 (step @p44 :rule cong :premises (@p43) :args (@t7)) % 0.63/0.87 (step @p45 :rule refl :args (@t8)) % 0.63/0.87 (step @p46 :rule cong :premises (@p45 @p44) :args (@t9)) % 0.63/0.87 (step @p47 :rule cong :premises (@p46) :args (@t11)) % 0.63/0.87 (step @p48 :rule eq_resolve :premises (@p1 @p47)) % 0.63/0.87 (step @p49 :rule instantiate :premises (@p48) :args (@t109)) % 0.63/0.87 (step @p50 :rule instantiate :premises (@p48) :args ((@list @t99 @t105))) % 0.63/0.87 (step @p51 :rule bool-double-not-elim :args (@t113)) % 0.63/0.87 (step @p52 :rule refl :args (@t116)) % 0.63/0.87 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or @t116 (not @t115)))) % 0.63/0.87 (step @p54 :rule cnf_or_neg :args (@t116 0)) % 0.63/0.87 (step @p55 :rule eq_resolve :premises (@p54 @p53)) % 0.63/0.87 (step @p56 :rule reordering :premises (@p55) :args ((or @t113 @t116))) % 0.63/0.87 (step @p57 :rule cnf_or_neg :args (@t116 1)) % 0.63/0.87 (step @p58 :rule instantiate :premises (@p48) :args ((@list @t99 @t101))) % 0.63/0.87 (step @p59 :rule aci_norm :args ((= (or @t117 @t87) @t97))) % 0.63/0.87 (step @p60 :rule refl :args (@t87)) % 0.63/0.87 (step @p61 :rule aci_norm :args ((= (or @t96 (or @t95 @t94)) @t117))) % 0.63/0.87 (step @p62 :rule bool-and-de-morgan :args (@t62 @t88 true)) % 0.63/0.87 (step @p63 :rule refl :args (@t96)) % 0.63/0.87 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t96 (not (and @t62 @t88))))) % 0.63/0.87 (step @p65 :rule bool-and-de-morgan :args (@t40 @t62 (and @t88))) % 0.63/0.87 (step @p66 :rule trans :premises (@p65 @p64)) % 0.63/0.87 (step @p67 :rule trans :premises (@p66 @p61)) % 0.63/0.87 (step @p68 :rule nary_cong :premises (@p67 @p60) :args ((or (not @t89) @t87))) % 0.63/0.87 (step @p69 :rule trans :premises (@p68 @p59)) % 0.63/0.87 (step @p70 :rule bool-impl-elim :args (@t89 @t87)) % 0.63/0.87 (step @p71 :rule trans :premises (@p70 @p69)) % 0.63/0.87 (step @p72 :rule cong :premises (@p71) :args (@t90)) % 0.63/0.87 (step @p73 :rule cong :premises (@p72) :args (@t91)) % 0.63/0.87 (step @p74 :rule eq_resolve :premises (@p29 @p73)) % 0.63/0.87 (step @p75 :rule skolemize :premises (@p74)) % 0.63/0.87 (step @p76 :rule bool-double-not-elim :args (@t118)) % 0.63/0.87 (step @p77 :rule refl :args (@t125)) % 0.63/0.87 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t125 (not @t120)))) % 0.63/0.87 (step @p79 :rule cnf_or_neg :args (@t125 2)) % 0.63/0.87 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.63/0.87 (step @p81 :rule reordering :premises (@p80) :args ((or @t118 @t125))) % 0.63/0.87 (step @p82 :rule chain_m_resolution :premises (@p81 @p75) :args (@t118 @t126 @t127)) % 0.63/0.87 (step @p83 :rule cnf_equiv_pos1 :args (@t129)) % 0.63/0.87 (step @p84 :rule reordering :premises (@p83) :args ((or @t120 @t128 (not @t129)))) % 0.63/0.87 (step @p85 :rule chain_m_resolution :premises (@p84 @p82 @p58) :args (@t128 @t130 (@list @t118 @t129))) % 0.63/0.87 (step @p86 :rule instantiate :premises (@p85) :args (@t131)) % 0.63/0.87 (step @p87 :rule cnf_or_pos :args (@t133)) % 0.63/0.87 (step @p88 :rule reordering :premises (@p87) :args ((or @t115 @t132 (not @t133)))) % 0.63/0.87 (step @p89 :rule instantiate :premises (@p41) :args ((@list @t103 @t104 @t101 @t112))) % 0.63/0.87 (step @p90 :rule cnf_equiv_pos2 :args (@t138)) % 0.63/0.87 (step @p91 :rule reordering :premises (@p90) :args ((or @t114 (not @t137) (not @t138)))) % 0.63/0.87 (step @p92 :rule bool-double-not-elim :args (@t135)) % 0.63/0.87 (step @p93 :rule refl :args (@t139)) % 0.63/0.87 (step @p94 :rule refl :args (@t137)) % 0.63/0.87 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args ((or @t137 @t139 (not @t136)))) % 0.63/0.87 (step @p96 :rule cnf_and_neg :args (@t137)) % 0.63/0.87 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.63/0.87 (step @p98 :rule reordering :premises (@p97) :args ((or @t135 @t137 @t139))) % 0.63/0.87 (step @p99 :rule bool-impl-elim :args (@t34 @t140)) % 0.63/0.87 (step @p100 :rule cong :premises (@p99) :args ((forall @t19 (=> @t34 @t140)))) % 0.63/0.87 (step @p101 :rule bool-and-de-morgan :args (@t56 @t55 true)) % 0.63/0.87 (step @p102 :rule cong :premises (@p101) :args (@t141)) % 0.63/0.87 (step @p103 :rule cong :premises (@p102) :args (@t142)) % 0.63/0.87 (step @p104 :rule exists-elim :args ((= @t59 @t142))) % 0.63/0.87 (step @p105 :rule trans :premises (@p104 @p103)) % 0.63/0.87 (step @p106 :rule cong :premises (@p36 @p105) :args (@t60)) % 0.63/0.87 (step @p107 :rule cong :premises (@p106) :args (@t61)) % 0.63/0.87 (step @p108 :rule trans :premises (@p107 @p100)) % 0.63/0.87 (step @p109 :rule refl :args (@t62)) % 0.63/0.87 (step @p110 :rule cong :premises (@p109 @p108) :args (@t63)) % 0.63/0.87 (step @p111 :rule cong :premises (@p110) :args (@t64)) % 0.63/0.87 (step @p112 :rule eq_resolve :premises (@p18 @p111)) % 0.63/0.87 (step @p113 :rule instantiate :premises (@p112) :args (@t143)) % 0.63/0.87 (step @p114 :rule bool-double-not-elim :args (@t121)) % 0.63/0.87 (step @p115 :rule nary_cong :premises (@p77 @p114) :args ((or @t125 (not @t122)))) % 0.63/0.87 (step @p116 :rule cnf_or_neg :args (@t125 1)) % 0.63/0.87 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.63/0.87 (step @p118 :rule reordering :premises (@p117) :args ((or @t121 @t125))) % 0.63/0.87 (step @p119 :rule chain_m_resolution :premises (@p118 @p75) :args (@t121 @t126 @t127)) % 0.63/0.87 (step @p120 :rule cnf_equiv_pos1 :args (@t147)) % 0.63/0.87 (step @p121 :rule reordering :premises (@p120) :args ((or @t122 @t146 (not @t147)))) % 0.63/0.87 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p113) :args (@t146 @t130 (@list @t121 @t147))) % 0.63/0.87 (step @p123 :rule instantiate :premises (@p122) :args (@t131)) % 0.63/0.87 (step @p124 :rule cnf_or_pos :args (@t150)) % 0.63/0.87 (step @p125 :rule reordering :premises (@p124) :args ((or @t139 @t149 (not @t150)))) % 0.63/0.87 (assume-push @p389 @t135) % 0.63/0.87 (step @p127 :rule instantiate :premises (@p389) :args ((@list @t151))) % 0.63/0.87 (step-pop @p390 :rule scope :premises (@p127)) % 0.63/0.87 (step @p128 :rule process_scope :premises (@p390) :args (@t156)) % 0.63/0.87 (step @p130 :rule implies_elim :premises (@p128)) % 0.63/0.87 (step @p131 :rule refl :args (@t160)) % 0.63/0.87 (step @p132 :rule bool-double-not-elim :args (@t148)) % 0.63/0.87 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((or (not @t149) @t160))) % 0.63/0.87 (assume-push @p391 @t149) % 0.63/0.87 (step @p135 :rule skolemize :premises (@p391)) % 0.63/0.87 (step-pop @p392 :rule scope :premises (@p135)) % 0.63/0.87 (step @p136 :rule process_scope :premises (@p392) :args (@t160)) % 0.63/0.87 (step @p138 :rule implies_elim :premises (@p136)) % 0.63/0.87 (step @p139 :rule eq_resolve :premises (@p138 @p133)) % 0.63/0.87 (step @p140 :rule bool-double-not-elim :args (@t157)) % 0.63/0.87 (step @p141 :rule refl :args (@t159)) % 0.63/0.87 (step @p142 :rule nary_cong :premises (@p141 @p140) :args ((or @t159 (not @t158)))) % 0.63/0.87 (step @p143 :rule cnf_or_neg :args (@t159 0)) % 0.63/0.87 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.63/0.87 (step @p145 :rule reordering :premises (@p144) :args ((or @t157 @t159))) % 0.63/0.87 (step @p146 :rule bool-double-not-elim :args (@t152)) % 0.63/0.87 (step @p147 :rule nary_cong :premises (@p141 @p146) :args ((or @t159 (not @t153)))) % 0.63/0.87 (step @p148 :rule cnf_or_neg :args (@t159 1)) % 0.63/0.87 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.63/0.87 (step @p150 :rule reordering :premises (@p149) :args ((or @t152 @t159))) % 0.63/0.87 (step @p151 :rule bool-double-not-elim :args (@t162)) % 0.63/0.87 (step @p152 :rule refl :args (@t158)) % 0.63/0.87 (step @p153 :rule refl :args (@t164)) % 0.63/0.87 (step @p154 :rule nary_cong :premises (@p153 @p152 @p151) :args ((or @t164 @t158 (not @t163)))) % 0.63/0.87 (step @p155 :rule cnf_and_neg :args (@t164)) % 0.63/0.87 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.63/0.87 (step @p157 :rule reordering :premises (@p156) :args ((or @t158 @t162 @t164))) % 0.63/0.87 (step @p158 :rule cnf_or_pos :args (@t156)) % 0.63/0.87 (step @p159 :rule reordering :premises (@p158) :args ((or @t153 @t155 (not @t156)))) % 0.63/0.87 (step @p160 :rule bool-and-de-morgan :args (@t34 @t33 true)) % 0.63/0.87 (step @p161 :rule cong :premises (@p160) :args (@t165)) % 0.63/0.87 (step @p162 :rule cong :premises (@p161) :args (@t166)) % 0.63/0.87 (step @p163 :rule exists-elim :args ((= @t36 @t166))) % 0.63/0.87 (step @p164 :rule trans :premises (@p163 @p162)) % 0.63/0.87 (step @p165 :rule refl :args (@t5)) % 0.63/0.87 (step @p166 :rule nary_cong :premises (@p165 @p164) :args (@t74)) % 0.63/0.87 (step @p167 :rule refl :args (@t75)) % 0.63/0.87 (step @p168 :rule cong :premises (@p167 @p166) :args (@t76)) % 0.63/0.87 (step @p169 :rule cong :premises (@p168) :args (@t77)) % 0.63/0.87 (step @p170 :rule eq_resolve :premises (@p25 @p169)) % 0.63/0.87 (step @p171 :rule instantiate :premises (@p170) :args ((@list @t103 @t99 @t102 @t151))) % 0.63/0.87 (step @p172 :rule cnf_equiv_pos2 :args (@t167)) % 0.63/0.87 (step @p173 :rule reordering :premises (@p172) :args ((or @t154 (not @t164) (not @t167)))) % 0.63/0.87 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p159 @p157 @p150 @p145 @p139 @p130 @p125 @p123 @p98 @p91 @p89 @p88 @p86 @p57 @p56) :args ((or @t116 @t162) (@list false true false false false true false true false false true false false false true false) (@list @t167 @t154 @t164 @t152 @t157 @t159 @t156 @t148 @t150 @t135 @t137 @t138 @t132 @t133 @t114 @t113))) % 0.63/0.87 (assume-push @p393 @t162) % 0.63/0.87 (step @p176 :rule instantiate :premises (@p393) :args (@t131)) % 0.63/0.87 (step-pop @p394 :rule scope :premises (@p176)) % 0.63/0.87 (step @p177 :rule process_scope :premises (@p394) :args (@t168)) % 0.63/0.87 (step @p179 :rule implies_elim :premises (@p177)) % 0.63/0.87 (step @p180 :rule cnf_or_pos :args (@t168)) % 0.63/0.87 (step @p181 :rule reordering :premises (@p180) :args ((or @t115 @t153 (not @t168)))) % 0.63/0.87 (step @p182 :rule chain_m_resolution :premises (@p150 @p139 @p181 @p125 @p123 @p179 @p88 @p86 @p174 @p56) :args (@t116 (@list true true true false false false false false false) (@list @t159 @t152 @t148 @t150 @t168 @t132 @t133 @t162 @t113))) % 0.63/0.87 (step @p183 :rule refl :args (@t169)) % 0.63/0.87 (step @p184 :rule bool-double-not-elim :args (@t111)) % 0.63/0.87 (step @p185 :rule nary_cong :premises (@p184 @p183) :args ((or (not @t170) @t169))) % 0.63/0.87 (assume-push @p395 @t170) % 0.63/0.87 (step @p187 :rule skolemize :premises (@p395)) % 0.63/0.87 (step-pop @p396 :rule scope :premises (@p187)) % 0.63/0.87 (step @p188 :rule process_scope :premises (@p396) :args (@t169)) % 0.63/0.87 (step @p190 :rule implies_elim :premises (@p188)) % 0.63/0.87 (step @p191 :rule eq_resolve :premises (@p190 @p185)) % 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