%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET771+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 : n017.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 08:48:37 AM UTC 2026 % Result : Theorem 0.46s 0.67s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET771+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 : n017.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 16:10:01 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.67 % SZS status Theorem % 0.46/0.67 % SZS output start Proof % 0.46/0.67 ( % 0.46/0.67 (declare-sort $$unsorted 0) % 0.46/0.67 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.equivalence_class (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.empty_set $$unsorted) % 0.46/0.67 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.equivalence (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.pre_order (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.partition (-> $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.46/0.67 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.46/0.67 (define @t1 () (@var "B" $$unsorted)) % 0.46/0.67 (define @t2 () (@var "X" $$unsorted)) % 0.46/0.67 (define @t3 () (tptp.member @t2 @t1)) % 0.46/0.67 (define @t4 () (@var "A" $$unsorted)) % 0.46/0.67 (define @t5 () (tptp.member @t2 @t4)) % 0.46/0.67 (define @t6 () (@list @t2)) % 0.46/0.67 (define @t7 () (tptp.subset @t4 @t1)) % 0.46/0.67 (define @t8 () (@list @t4 @t1)) % 0.46/0.67 (define @t9 () (@list @t2 @t4)) % 0.46/0.67 (define @t10 () (and @t5 @t3)) % 0.46/0.67 (define @t11 () (@list @t2 @t4 @t1)) % 0.46/0.67 (define @t12 () (@var "E" $$unsorted)) % 0.46/0.67 (define @t13 () (= @t2 @t4)) % 0.46/0.67 (define @t14 () (@var "Y" $$unsorted)) % 0.46/0.67 (define @t15 () (tptp.member @t2 @t14)) % 0.46/0.67 (define @t16 () (tptp.member @t14 @t4)) % 0.46/0.67 (define @t17 () (@list @t14)) % 0.46/0.67 (define @t18 () (exists @t17 (and @t16 @t15))) % 0.46/0.67 (define @t19 () (@var "Y2" $$unsorted)) % 0.46/0.67 (define @t20 () (@var "Y1" $$unsorted)) % 0.46/0.67 (define @t21 () (= @t20 @t19)) % 0.46/0.67 (define @t22 () (@var "F" $$unsorted)) % 0.46/0.67 (define @t23 () (tptp.apply @t22 @t2 @t19)) % 0.46/0.67 (define @t24 () (tptp.apply @t22 @t2 @t20)) % 0.46/0.67 (define @t25 () (and @t24 @t23)) % 0.46/0.67 (define @t26 () (=> @t25 @t21)) % 0.46/0.67 (define @t27 () (tptp.member @t19 @t1)) % 0.46/0.67 (define @t28 () (tptp.member @t20 @t1)) % 0.46/0.67 (define @t29 () (and @t5 @t28 @t27)) % 0.46/0.67 (define @t30 () (@list @t2 @t20 @t19)) % 0.46/0.67 (define @t31 () (forall @t30 (=> @t29 @t26))) % 0.46/0.67 (define @t32 () (tptp.apply @t22 @t2 @t14)) % 0.46/0.67 (define @t33 () (tptp.member @t14 @t1)) % 0.46/0.67 (define @t34 () (and @t33 @t32)) % 0.46/0.67 (define @t35 () (exists @t17 @t34)) % 0.46/0.67 (define @t36 () (=> @t5 @t35)) % 0.46/0.67 (define @t37 () (forall @t6 @t36)) % 0.46/0.67 (define @t38 () (and @t37 @t31)) % 0.46/0.67 (define @t39 () (tptp.maps @t22 @t4 @t1)) % 0.46/0.67 (define @t40 () (= @t39 @t38)) % 0.46/0.67 (define @t41 () (@list @t22 @t4 @t1)) % 0.46/0.67 (define @t42 () (forall @t41 @t40)) % 0.46/0.67 (define @t43 () (@var "Z" $$unsorted)) % 0.46/0.67 (define @t44 () (@var "G" $$unsorted)) % 0.46/0.67 (define @t45 () (exists @t17 (and @t33 @t32 (tptp.apply @t44 @t14 @t43)))) % 0.46/0.67 (define @t46 () (@var "H" $$unsorted)) % 0.46/0.67 (define @t47 () (@var "C" $$unsorted)) % 0.46/0.67 (define @t48 () (and @t5 (tptp.member @t43 @t47))) % 0.46/0.67 (define @t49 () (@var "X2" $$unsorted)) % 0.46/0.67 (define @t50 () (@var "X1" $$unsorted)) % 0.46/0.67 (define @t51 () (tptp.apply @t22 @t49 @t14)) % 0.46/0.67 (define @t52 () (tptp.apply @t22 @t50 @t14)) % 0.46/0.67 (define @t53 () (and @t52 @t51)) % 0.46/0.67 (define @t54 () (tptp.member @t49 @t4)) % 0.46/0.67 (define @t55 () (tptp.member @t50 @t4)) % 0.46/0.67 (define @t56 () (tptp.injective @t22 @t4 @t1)) % 0.46/0.67 (define @t57 () (tptp.surjective @t22 @t4 @t1)) % 0.46/0.67 (define @t58 () (tptp.one_to_one @t22 @t4 @t1)) % 0.46/0.67 (define @t59 () (and @t5 @t33)) % 0.46/0.67 (define @t60 () (@list @t2 @t14)) % 0.46/0.67 (define @t61 () (exists @t6 (and @t5 @t32))) % 0.46/0.67 (define @t62 () (@var "S" $$unsorted)) % 0.46/0.67 (define @t63 () (tptp.apply @t62 @t20 @t19)) % 0.46/0.67 (define @t64 () (tptp.apply @t22 @t49 @t19)) % 0.46/0.67 (define @t65 () (tptp.apply @t22 @t50 @t20)) % 0.46/0.67 (define @t66 () (@var "R" $$unsorted)) % 0.46/0.67 (define @t67 () (tptp.apply @t66 @t50 @t49)) % 0.46/0.67 (define @t68 () (and @t55 @t28 @t54 @t27 @t67 @t65 @t64)) % 0.46/0.67 (define @t69 () (@list @t50 @t20 @t49 @t19)) % 0.46/0.67 (define @t70 () (@list @t22 @t4 @t66 @t1 @t62)) % 0.46/0.67 (define @t71 () (and @t5 @t16)) % 0.46/0.67 (define @t72 () (tptp.member @t2 @t12)) % 0.46/0.67 (define @t73 () (tptp.apply @t66 @t2 @t43)) % 0.46/0.67 (define @t74 () (tptp.apply @t66 @t14 @t43)) % 0.46/0.67 (define @t75 () (tptp.apply @t66 @t2 @t14)) % 0.46/0.67 (define @t76 () (and @t75 @t74)) % 0.46/0.67 (define @t77 () (=> @t76 @t73)) % 0.46/0.67 (define @t78 () (tptp.member @t43 @t4)) % 0.46/0.67 (define @t79 () (and @t5 @t16 @t78)) % 0.46/0.67 (define @t80 () (@list @t2 @t14 @t43)) % 0.46/0.67 (define @t81 () (forall @t80 (=> @t79 @t77))) % 0.46/0.67 (define @t82 () (tptp.apply @t66 @t14 @t2)) % 0.46/0.67 (define @t83 () (=> @t75 @t82)) % 0.46/0.67 (define @t84 () (forall @t60 (=> @t71 @t83))) % 0.46/0.67 (define @t85 () (tptp.apply @t66 @t2 @t2)) % 0.46/0.67 (define @t86 () (forall @t6 (=> @t5 @t85))) % 0.46/0.67 (define @t87 () (and @t86 @t84 @t81)) % 0.46/0.67 (define @t88 () (tptp.equivalence @t66 @t4)) % 0.46/0.67 (define @t89 () (= @t88 @t87)) % 0.46/0.67 (define @t90 () (forall (@list @t4 @t66) @t89)) % 0.46/0.67 (define @t91 () (and @t33 @t52 @t51)) % 0.46/0.67 (define @t92 () (exists @t17 @t91)) % 0.46/0.67 (define @t93 () (= @t67 @t92)) % 0.46/0.67 (define @t94 () (and @t55 @t54)) % 0.46/0.67 (define @t95 () (=> @t94 @t93)) % 0.46/0.67 (define @t96 () (@list @t50 @t49)) % 0.46/0.67 (define @t97 () (forall @t96 @t95)) % 0.46/0.67 (define @t98 () (and @t39 @t97)) % 0.46/0.67 (define @t99 () (=> @t98 @t88)) % 0.46/0.67 (define @t100 () (@list @t22 @t4 @t1 @t66)) % 0.46/0.67 (define @t101 () (forall @t100 @t99)) % 0.46/0.67 (define @t102 () (not @t101)) % 0.46/0.67 (define @t103 () (not @t23)) % 0.46/0.67 (define @t104 () (not @t24)) % 0.46/0.67 (define @t105 () (not @t27)) % 0.46/0.67 (define @t106 () (not @t28)) % 0.46/0.67 (define @t107 () (not @t5)) % 0.46/0.67 (define @t108 () (or @t104 @t103 @t21)) % 0.46/0.67 (define @t109 () (or @t107 @t106 @t105)) % 0.46/0.67 (define @t110 () (not @t33)) % 0.46/0.67 (define @t111 () (not (forall @t17 (or @t110 (not @t32))))) % 0.46/0.67 (define @t112 () (forall @t17 (not @t34))) % 0.46/0.67 (define @t113 () (not @t112)) % 0.46/0.67 (define @t114 () (not @t51)) % 0.46/0.67 (define @t115 () (not @t52)) % 0.46/0.67 (define @t116 () (or @t110 @t115 @t114)) % 0.46/0.67 (define @t117 () (= @t67 (not (forall @t17 @t116)))) % 0.46/0.67 (define @t118 () (not @t54)) % 0.46/0.67 (define @t119 () (not @t55)) % 0.46/0.67 (define @t120 () (or @t119 @t118 @t117)) % 0.46/0.67 (define @t121 () (forall @t96 @t120)) % 0.46/0.67 (define @t122 () (not @t121)) % 0.46/0.67 (define @t123 () (not @t39)) % 0.46/0.67 (define @t124 () (or @t123 @t122 @t88)) % 0.46/0.67 (define @t125 () (forall @t100 @t124)) % 0.46/0.67 (define @t126 () (@quantifiers_skolemize @t125 2)) % 0.46/0.67 (define @t127 () (@quantifiers_skolemize @t125 1)) % 0.46/0.67 (define @t128 () (@quantifiers_skolemize @t125 0)) % 0.46/0.67 (define @t129 () (and @t39 @t121)) % 0.46/0.67 (define @t130 () (forall @t17 (not @t91))) % 0.46/0.67 (define @t131 () (not @t130)) % 0.46/0.67 (define @t132 () (tptp.maps @t128 @t127 @t126)) % 0.46/0.67 (define @t133 () (@quantifiers_skolemize @t125 3)) % 0.46/0.67 (define @t134 () (tptp.equivalence @t133 @t127)) % 0.46/0.67 (define @t135 () (not (tptp.member @t14 @t126))) % 0.46/0.67 (define @t136 () (forall @t96 (or (not (tptp.member @t50 @t127)) (not (tptp.member @t49 @t127)) (= (tptp.apply @t133 @t50 @t49) (not (forall @t17 (or @t135 (not (tptp.apply @t128 @t50 @t14)) (not (tptp.apply @t128 @t49 @t14))))))))) % 0.46/0.67 (define @t137 () (not @t136)) % 0.46/0.67 (define @t138 () (not @t132)) % 0.46/0.67 (define @t139 () (or @t138 @t137 @t134)) % 0.46/0.67 (define @t140 () (@list true)) % 0.46/0.67 (define @t141 () (@list @t139)) % 0.46/0.67 (define @t142 () (not (tptp.member @t2 @t127))) % 0.46/0.67 (define @t143 () (forall @t30 (or @t142 (not (tptp.member @t20 @t126)) (not (tptp.member @t19 @t126)) (not (tptp.apply @t128 @t2 @t20)) (not (tptp.apply @t128 @t2 @t19)) @t21))) % 0.46/0.67 (define @t144 () (forall @t6 (or @t142 (not (forall @t17 (or @t135 (not (tptp.apply @t128 @t2 @t14)))))))) % 0.46/0.67 (define @t145 () (and @t144 @t143)) % 0.46/0.67 (define @t146 () (= @t132 @t145)) % 0.46/0.67 (define @t147 () (@list false false)) % 0.46/0.67 (define @t148 () (not @t145)) % 0.46/0.67 (define @t149 () (@list false)) % 0.46/0.67 (define @t150 () (@list @t145)) % 0.46/0.67 (define @t151 () (not (tptp.apply @t133 @t2 @t14))) % 0.46/0.67 (define @t152 () (not (tptp.member @t14 @t127))) % 0.46/0.67 (define @t153 () (forall @t80 (or @t142 @t152 (not (tptp.member @t43 @t127)) @t151 (not (tptp.apply @t133 @t14 @t43)) (tptp.apply @t133 @t2 @t43)))) % 0.46/0.67 (define @t154 () (@quantifiers_skolemize @t153 0)) % 0.46/0.67 (define @t155 () (forall @t60 (or @t142 @t152 @t151 (tptp.apply @t133 @t14 @t2)))) % 0.46/0.67 (define @t156 () (@quantifiers_skolemize @t155 0)) % 0.46/0.67 (define @t157 () (tptp.member @t156 @t127)) % 0.46/0.67 (define @t158 () (@quantifiers_skolemize @t155 1)) % 0.46/0.67 (define @t159 () (tptp.apply @t133 @t158 @t156)) % 0.46/0.67 (define @t160 () (tptp.apply @t133 @t156 @t158)) % 0.46/0.67 (define @t161 () (not @t160)) % 0.46/0.67 (define @t162 () (tptp.member @t158 @t127)) % 0.46/0.67 (define @t163 () (not @t162)) % 0.46/0.67 (define @t164 () (not @t157)) % 0.46/0.67 (define @t165 () (or @t164 @t163 @t161 @t159)) % 0.46/0.67 (define @t166 () (not (tptp.apply @t128 @t158 @t14))) % 0.46/0.67 (define @t167 () (not (tptp.apply @t128 @t156 @t14))) % 0.46/0.67 (define @t168 () (or @t135 @t167 @t166)) % 0.46/0.67 (define @t169 () (forall @t17 @t168)) % 0.46/0.67 (define @t170 () (not @t169)) % 0.46/0.67 (define @t171 () (= @t160 @t170)) % 0.46/0.67 (define @t172 () (or @t164 @t163 @t171)) % 0.46/0.67 (define @t173 () (or @t135 @t166 @t167)) % 0.46/0.67 (define @t174 () (forall @t17 @t173)) % 0.46/0.67 (define @t175 () (not @t174)) % 0.46/0.67 (define @t176 () (= @t159 @t175)) % 0.46/0.67 (define @t177 () (or @t163 @t164 @t176)) % 0.46/0.67 (define @t178 () (not @t176)) % 0.46/0.67 (define @t179 () (not @t165)) % 0.46/0.67 (define @t180 () (not @t155)) % 0.46/0.67 (define @t181 () (forall @t6 (or @t142 (tptp.apply @t133 @t2 @t2)))) % 0.46/0.67 (define @t182 () (@quantifiers_skolemize @t181 0)) % 0.46/0.67 (define @t183 () (tptp.member @t182 @t127)) % 0.46/0.67 (define @t184 () (tptp.apply @t133 @t182 @t182)) % 0.46/0.67 (define @t185 () (not @t183)) % 0.46/0.67 (define @t186 () (or @t185 @t184)) % 0.46/0.67 (define @t187 () (not (tptp.apply @t128 @t182 @t14))) % 0.46/0.67 (define @t188 () (or @t135 @t187)) % 0.46/0.67 (define @t189 () (or @t135 @t187 @t187)) % 0.46/0.67 (define @t190 () (forall @t17 @t189)) % 0.46/0.67 (define @t191 () (not @t190)) % 0.46/0.67 (define @t192 () (= @t184 @t191)) % 0.46/0.67 (define @t193 () (or @t185 @t185 @t192)) % 0.46/0.67 (define @t194 () (forall @t17 @t188)) % 0.46/0.67 (define @t195 () (not @t194)) % 0.46/0.67 (define @t196 () (= @t184 @t195)) % 0.46/0.67 (define @t197 () (or @t185 @t185 @t196)) % 0.46/0.67 (define @t198 () (or @t185 @t195)) % 0.46/0.67 (define @t199 () (not @t196)) % 0.46/0.67 (define @t200 () (not @t186)) % 0.46/0.67 (define @t201 () (not @t181)) % 0.46/0.67 (define @t202 () (not @t74)) % 0.46/0.67 (define @t203 () (not @t75)) % 0.46/0.67 (define @t204 () (not @t78)) % 0.46/0.67 (define @t205 () (not @t16)) % 0.46/0.67 (define @t206 () (or @t203 @t202 @t73)) % 0.46/0.67 (define @t207 () (or @t107 @t205 @t204)) % 0.46/0.67 (define @t208 () (and @t181 @t155 @t153)) % 0.46/0.67 (define @t209 () (= @t134 @t208)) % 0.46/0.67 (define @t210 () (not @t208)) % 0.46/0.67 (define @t211 () (@list true false)) % 0.46/0.67 (define @t212 () (not @t153)) % 0.46/0.67 (define @t213 () (@quantifiers_skolemize @t153 2)) % 0.46/0.67 (define @t214 () (tptp.apply @t133 @t154 @t213)) % 0.46/0.67 (define @t215 () (@quantifiers_skolemize @t153 1)) % 0.46/0.67 (define @t216 () (tptp.apply @t133 @t215 @t213)) % 0.46/0.67 (define @t217 () (not @t216)) % 0.46/0.67 (define @t218 () (tptp.apply @t133 @t154 @t215)) % 0.46/0.67 (define @t219 () (not @t218)) % 0.46/0.67 (define @t220 () (tptp.member @t213 @t127)) % 0.46/0.67 (define @t221 () (not @t220)) % 0.46/0.67 (define @t222 () (tptp.member @t215 @t127)) % 0.46/0.67 (define @t223 () (not @t222)) % 0.46/0.67 (define @t224 () (tptp.member @t154 @t127)) % 0.46/0.67 (define @t225 () (not @t224)) % 0.46/0.67 (define @t226 () (or @t225 @t223 @t221 @t219 @t217 @t214)) % 0.46/0.67 (define @t227 () (not @t226)) % 0.46/0.67 (define @t228 () (@list @t226)) % 0.46/0.67 (define @t229 () (not (tptp.apply @t128 @t154 @t14))) % 0.46/0.67 (define @t230 () (forall @t17 (or @t135 @t229))) % 0.46/0.67 (define @t231 () (not @t230)) % 0.46/0.67 (define @t232 () (or @t225 @t231)) % 0.46/0.67 (define @t233 () (@quantifiers_skolemize @t230 0)) % 0.46/0.67 (define @t234 () (tptp.apply @t128 @t154 @t233)) % 0.46/0.67 (define @t235 () (not @t234)) % 0.46/0.67 (define @t236 () (tptp.member @t233 @t126)) % 0.46/0.67 (define @t237 () (not @t236)) % 0.46/0.67 (define @t238 () (or @t237 @t235)) % 0.46/0.67 (define @t239 () (not @t238)) % 0.46/0.67 (define @t240 () (@list @t238)) % 0.46/0.67 (define @t241 () (not (tptp.apply @t128 @t213 @t14))) % 0.46/0.67 (define @t242 () (forall @t17 (or @t135 @t229 @t241))) % 0.46/0.67 (define @t243 () (not @t242)) % 0.46/0.67 (define @t244 () (= @t214 @t243)) % 0.46/0.67 (define @t245 () (or @t225 @t221 @t244)) % 0.46/0.67 (define @t246 () (@list false false false)) % 0.46/0.67 (define @t247 () (not @t244)) % 0.46/0.67 (define @t248 () (forall @t17 (or @t135 @t241))) % 0.46/0.67 (define @t249 () (@quantifiers_skolemize @t248 0)) % 0.46/0.67 (define @t250 () (tptp.apply @t128 @t213 @t249)) % 0.46/0.67 (define @t251 () (not @t250)) % 0.46/0.67 (define @t252 () (tptp.apply @t128 @t154 @t249)) % 0.46/0.67 (define @t253 () (not @t252)) % 0.46/0.67 (define @t254 () (tptp.member @t249 @t126)) % 0.46/0.67 (define @t255 () (not @t254)) % 0.46/0.67 (define @t256 () (or @t255 @t253 @t251)) % 0.46/0.67 (define @t257 () (not @t248)) % 0.46/0.67 (define @t258 () (or @t221 @t257)) % 0.46/0.67 (define @t259 () (or @t255 @t251)) % 0.46/0.67 (define @t260 () (not @t259)) % 0.46/0.67 (define @t261 () (@list @t259)) % 0.46/0.67 (define @t262 () (not (tptp.apply @t128 @t215 @t14))) % 0.46/0.67 (define @t263 () (forall @t17 (or @t135 @t262 @t241))) % 0.46/0.67 (define @t264 () (@quantifiers_skolemize @t263 0)) % 0.46/0.67 (define @t265 () (not @t263)) % 0.46/0.67 (define @t266 () (= @t216 @t265)) % 0.46/0.67 (define @t267 () (or @t223 @t221 @t266)) % 0.46/0.67 (define @t268 () (tptp.apply @t128 @t213 @t264)) % 0.46/0.67 (define @t269 () (not @t268)) % 0.46/0.67 (define @t270 () (tptp.apply @t128 @t215 @t264)) % 0.46/0.67 (define @t271 () (not @t270)) % 0.46/0.67 (define @t272 () (tptp.member @t264 @t126)) % 0.46/0.67 (define @t273 () (not @t272)) % 0.46/0.67 (define @t274 () (or @t273 @t271 @t269)) % 0.46/0.67 (define @t275 () (not @t274)) % 0.46/0.67 (define @t276 () (@list @t274)) % 0.46/0.67 (define @t277 () (= @t249 @t264)) % 0.46/0.67 (define @t278 () (or @t221 @t255 @t273 @t251 @t269 @t277)) % 0.46/0.67 (define @t279 () (@list false false false false false false)) % 0.46/0.67 (define @t280 () (forall @t17 (or @t135 @t262))) % 0.46/0.67 (define @t281 () (@quantifiers_skolemize @t280 0)) % 0.46/0.67 (define @t282 () (tptp.apply @t128 @t215 @t281)) % 0.46/0.67 (define @t283 () (not @t282)) % 0.46/0.67 (define @t284 () (tptp.apply @t128 @t215 @t233)) % 0.46/0.67 (define @t285 () (not @t284)) % 0.46/0.67 (define @t286 () (tptp.member @t281 @t126)) % 0.46/0.67 (define @t287 () (not @t286)) % 0.46/0.67 (define @t288 () (or @t223 @t237 @t287 @t285 @t283 (= @t233 @t281))) % 0.46/0.67 (define @t289 () (= @t281 @t233)) % 0.46/0.67 (define @t290 () (or @t223 @t237 @t287 @t285 @t283 @t289)) % 0.46/0.67 (define @t291 () (@list @t143)) % 0.46/0.67 (define @t292 () (forall @t17 (or @t135 @t229 @t262))) % 0.46/0.67 (define @t293 () (@quantifiers_skolemize @t292 0)) % 0.46/0.67 (define @t294 () (tptp.apply @t128 @t154 @t293)) % 0.46/0.67 (define @t295 () (not @t294)) % 0.46/0.67 (define @t296 () (tptp.member @t293 @t126)) % 0.46/0.67 (define @t297 () (not @t296)) % 0.46/0.67 (define @t298 () (or @t225 @t297 @t237 @t295 @t235 (= @t293 @t233))) % 0.46/0.67 (define @t299 () (= @t233 @t293)) % 0.46/0.67 (define @t300 () (or @t225 @t297 @t237 @t295 @t235 @t299)) % 0.46/0.67 (define @t301 () (not @t292)) % 0.46/0.67 (define @t302 () (= @t218 @t301)) % 0.46/0.67 (define @t303 () (or @t225 @t223 @t302)) % 0.46/0.67 (define @t304 () (tptp.apply @t128 @t215 @t293)) % 0.46/0.67 (define @t305 () (not @t304)) % 0.46/0.67 (define @t306 () (or @t297 @t295 @t305)) % 0.46/0.67 (define @t307 () (not @t306)) % 0.46/0.67 (define @t308 () (@list @t306)) % 0.46/0.67 (define @t309 () (and @t304 @t299)) % 0.46/0.67 (define @t310 () (not @t280)) % 0.46/0.67 (define @t311 () (or @t223 @t310)) % 0.46/0.67 (define @t312 () (or @t287 @t283)) % 0.46/0.67 (define @t313 () (not @t312)) % 0.46/0.67 (define @t314 () (@list @t312)) % 0.46/0.67 (define @t315 () (= @t281 @t264)) % 0.46/0.67 (define @t316 () (or @t223 @t287 @t273 @t283 @t271 @t315)) % 0.46/0.67 (define @t317 () (not @t315)) % 0.46/0.67 (define @t318 () (not @t277)) % 0.46/0.67 (define @t319 () (not @t289)) % 0.46/0.67 (define @t320 () (and @t234 @t289 @t315 @t277 @t253)) % 0.46/0.67 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.46/0.67 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.46/0.67 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.46/0.67 (assume @p4 (forall @t11 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) @t10))) % 0.46/0.67 (assume @p5 (forall @t11 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.46/0.67 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.46/0.67 (assume @p7 (forall (@list @t1 @t4 @t12) (= (tptp.member @t1 (tptp.difference @t12 @t4)) (and (tptp.member @t1 @t12) (not (tptp.member @t1 @t4)))))) % 0.46/0.67 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t13))) % 0.46/0.67 (assume @p9 (forall @t11 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t13 (= @t2 @t1))))) % 0.46/0.67 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) @t18))) % 0.46/0.67 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t17 (=> @t16 @t15))))) % 0.46/0.67 (assume @p12 @t42) % 0.46/0.67 (assume @p13 (forall (@list @t46 @t44 @t22 @t4 @t1 @t47) (= (tptp.compose_predicate @t46 @t44 @t22 @t4 @t1 @t47) (forall (@list @t2 @t43) (=> @t48 (= (tptp.apply @t46 @t2 @t43) @t45)))))) % 0.46/0.67 (assume @p14 (forall (@list @t44 @t22 @t4 @t1 @t47 @t2 @t43) (=> @t48 (= (tptp.apply (tptp.compose_function @t44 @t22 @t4 @t1 @t47) @t2 @t43) @t45)))) % 0.46/0.67 (assume @p15 (forall (@list @t22 @t44 @t4 @t1) (= (tptp.equal_maps @t22 @t44 @t4 @t1) (forall @t30 (=> @t29 (=> (and @t24 (tptp.apply @t44 @t2 @t19)) @t21)))))) % 0.46/0.67 (assume @p16 (forall (@list @t22 @t4) (= (tptp.identity @t22 @t4) (forall @t6 (=> @t5 (tptp.apply @t22 @t2 @t2)))))) % 0.46/0.67 (assume @p17 (forall @t41 (= @t56 (forall (@list @t50 @t49 @t14) (=> (and @t55 @t54 @t33) (=> @t53 (= @t50 @t49))))))) % 0.46/0.67 (assume @p18 (forall @t41 (= @t57 (forall @t17 (=> @t33 (exists (@list @t12) (and (tptp.member @t12 @t4) (tptp.apply @t22 @t12 @t14)))))))) % 0.46/0.67 (assume @p19 (forall @t41 (= @t58 (and @t56 @t57)))) % 0.46/0.67 (assume @p20 (forall (@list @t44 @t22 @t4 @t1) (= (tptp.inverse_predicate @t44 @t22 @t4 @t1) (forall @t60 (=> @t59 (= @t32 (tptp.apply @t44 @t14 @t2))))))) % 0.46/0.67 (assume @p21 (forall (@list @t22 @t4 @t1 @t2 @t14) (=> @t59 (= @t32 (tptp.apply (tptp.inverse_function @t22 @t4 @t1) @t14 @t2))))) % 0.46/0.67 (assume @p22 (forall (@list @t22 @t4 @t14) (= (tptp.member @t14 (tptp.image2 @t22 @t4)) @t61))) % 0.46/0.67 (assume @p23 (forall (@list @t22 @t4 @t1 @t14) (= (tptp.member @t14 (tptp.image3 @t22 @t4 @t1)) (and @t33 @t61)))) % 0.46/0.67 (assume @p24 (forall (@list @t22 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t22 @t1)) @t35))) % 0.46/0.67 (assume @p25 (forall (@list @t22 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t22 @t1 @t4)) (and @t5 @t35)))) % 0.46/0.67 (assume @p26 (forall @t70 (= (tptp.increasing @t22 @t4 @t66 @t1 @t62) (forall @t69 (=> @t68 @t63))))) % 0.46/0.67 (assume @p27 (forall @t70 (= (tptp.decreasing @t22 @t4 @t66 @t1 @t62) (forall @t69 (=> @t68 (tptp.apply @t62 @t19 @t20)))))) % 0.46/0.67 (assume @p28 (forall @t70 (= (tptp.isomorphism @t22 @t4 @t66 @t1 @t62) (and @t39 @t58 (forall @t69 (=> (and @t55 @t28 @t54 @t27 @t65 @t64) (= @t67 @t63))))))) % 0.46/0.67 (assume @p29 (forall @t8 (= (tptp.disjoint @t4 @t1) (not (exists @t6 @t10))))) % 0.46/0.67 (assume @p30 (forall (@list @t4 @t12) (= (tptp.partition @t4 @t12) (and (forall @t6 (=> @t5 (tptp.subset @t2 @t12))) (forall @t6 (=> @t72 @t18)) (forall @t60 (=> @t71 (=> (exists (@list @t43) (and (tptp.member @t43 @t2) (tptp.member @t43 @t14))) (= @t2 @t14)))))))) % 0.46/0.67 (assume @p31 @t90) % 0.46/0.67 (assume @p32 (forall (@list @t66 @t12 @t4 @t2) (= (tptp.member @t2 (tptp.equivalence_class @t4 @t12 @t66)) (and @t72 (tptp.apply @t66 @t4 @t2))))) % 0.46/0.67 (assume @p33 (forall (@list @t66 @t12) (= (tptp.pre_order @t66 @t12) (and (forall @t6 (=> @t72 @t85)) (forall @t80 (=> (and @t72 (tptp.member @t14 @t12) (tptp.member @t43 @t12)) @t77)))))) % 0.46/0.67 (assume @p34 @t102) % 0.46/0.67 (assume @p35 true) % 0.46/0.67 (step @p36 :rule aci_norm :args ((= (or @t109 @t108) (or @t107 @t106 @t105 @t104 @t103 @t21)))) % 0.46/0.67 (step @p37 :rule aci_norm :args ((= (or (or @t104 @t103) @t21) @t108))) % 0.46/0.67 (step @p38 :rule refl :args (@t21)) % 0.46/0.67 (step @p39 :rule bool-and-de-morgan :args (@t24 @t23 true)) % 0.46/0.67 (step @p40 :rule nary_cong :premises (@p39 @p38) :args ((or (not @t25) @t21))) % 0.46/0.67 (step @p41 :rule trans :premises (@p40 @p37)) % 0.46/0.67 (step @p42 :rule bool-impl-elim :args (@t25 @t21)) % 0.46/0.67 (step @p43 :rule trans :premises (@p42 @p41)) % 0.46/0.67 (step @p44 :rule aci_norm :args ((= (or @t107 (or @t106 @t105)) @t109))) % 0.46/0.67 (step @p45 :rule bool-and-de-morgan :args (@t28 @t27 true)) % 0.46/0.67 (step @p46 :rule refl :args (@t107)) % 0.46/0.67 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or @t107 (not (and @t28 @t27))))) % 0.46/0.67 (step @p48 :rule bool-and-de-morgan :args (@t5 @t28 (and @t27))) % 0.46/0.67 (step @p49 :rule trans :premises (@p48 @p47)) % 0.46/0.67 (step @p50 :rule trans :premises (@p49 @p44)) % 0.46/0.67 (step @p51 :rule nary_cong :premises (@p50 @p43) :args ((or (not @t29) @t26))) % 0.46/0.67 (step @p52 :rule trans :premises (@p51 @p36)) % 0.46/0.67 (step @p53 :rule bool-impl-elim :args (@t29 @t26)) % 0.46/0.67 (step @p54 :rule trans :premises (@p53 @p52)) % 0.46/0.67 (step @p55 :rule cong :premises (@p54) :args (@t31)) % 0.46/0.67 (step @p56 :rule bool-impl-elim :args (@t5 @t111)) % 0.46/0.67 (step @p57 :rule cong :premises (@p56) :args ((forall @t6 (=> @t5 @t111)))) % 0.46/0.67 (step @p58 :rule bool-and-de-morgan :args (@t33 @t32 true)) % 0.46/0.67 (step @p59 :rule cong :premises (@p58) :args (@t112)) % 0.46/0.67 (step @p60 :rule cong :premises (@p59) :args (@t113)) % 0.46/0.67 (step @p61 :rule exists-elim :args ((= @t35 @t113))) % 0.46/0.67 (step @p62 :rule trans :premises (@p61 @p60)) % 0.46/0.67 (step @p63 :rule refl :args (@t5)) % 0.46/0.67 (step @p64 :rule cong :premises (@p63 @p62) :args (@t36)) % 0.46/0.67 (step @p65 :rule cong :premises (@p64) :args (@t37)) % 0.46/0.67 (step @p66 :rule trans :premises (@p65 @p57)) % 0.46/0.67 (step @p67 :rule nary_cong :premises (@p66 @p55) :args (@t38)) % 0.46/0.67 (step @p68 :rule refl :args (@t39)) % 0.46/0.67 (step @p69 :rule cong :premises (@p68 @p67) :args (@t40)) % 0.46/0.67 (step @p70 :rule cong :premises (@p69) :args (@t42)) % 0.46/0.67 (step @p71 :rule eq_resolve :premises (@p12 @p70)) % 0.46/0.67 (step @p72 :rule instantiate :premises (@p71) :args ((@list @t128 @t127 @t126))) % 0.46/0.67 (step @p73 :rule aci_norm :args ((= (or (or @t123 @t122) @t88) @t124))) % 0.46/0.67 (step @p74 :rule refl :args (@t88)) % 0.46/0.67 (step @p75 :rule bool-and-de-morgan :args (@t39 @t121 true)) % 0.46/0.67 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or (not @t129) @t88))) % 0.46/0.67 (step @p77 :rule trans :premises (@p76 @p73)) % 0.46/0.67 (step @p78 :rule bool-impl-elim :args (@t129 @t88)) % 0.46/0.67 (step @p79 :rule trans :premises (@p78 @p77)) % 0.46/0.67 (step @p80 :rule cong :premises (@p79) :args ((forall @t100 (=> @t129 @t88)))) % 0.46/0.67 (step @p81 :rule refl :args (@t88)) % 0.46/0.67 (step @p82 :rule aci_norm :args ((= (or (or @t119 @t118) @t117) @t120))) % 0.46/0.67 (step @p83 :rule refl :args (@t117)) % 0.46/0.67 (step @p84 :rule bool-and-de-morgan :args (@t55 @t54 true)) % 0.46/0.67 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or (not @t94) @t117))) % 0.46/0.67 (step @p86 :rule trans :premises (@p85 @p82)) % 0.46/0.67 (step @p87 :rule bool-impl-elim :args (@t94 @t117)) % 0.46/0.67 (step @p88 :rule trans :premises (@p87 @p86)) % 0.46/0.67 (step @p89 :rule cong :premises (@p88) :args ((forall @t96 (=> @t94 @t117)))) % 0.46/0.67 (step @p90 :rule aci_norm :args ((= (or @t110 (or @t115 @t114)) @t116))) % 0.46/0.67 (step @p91 :rule bool-and-de-morgan :args (@t52 @t51 true)) % 0.46/0.67 (step @p92 :rule refl :args (@t110)) % 0.46/0.67 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t110 (not @t53)))) % 0.46/0.67 (step @p94 :rule bool-and-de-morgan :args (@t33 @t52 (and @t51))) % 0.46/0.67 (step @p95 :rule trans :premises (@p94 @p93)) % 0.46/0.67 (step @p96 :rule trans :premises (@p95 @p90)) % 0.46/0.67 (step @p97 :rule cong :premises (@p96) :args (@t130)) % 0.46/0.67 (step @p98 :rule cong :premises (@p97) :args (@t131)) % 0.46/0.67 (step @p99 :rule exists-elim :args ((= @t92 @t131))) % 0.46/0.67 (step @p100 :rule trans :premises (@p99 @p98)) % 0.46/0.67 (step @p101 :rule refl :args (@t67)) % 0.46/0.67 (step @p102 :rule cong :premises (@p101 @p100) :args (@t93)) % 0.46/0.67 (step @p103 :rule refl :args (@t94)) % 0.46/0.67 (step @p104 :rule cong :premises (@p103 @p102) :args (@t95)) % 0.46/0.67 (step @p105 :rule cong :premises (@p104) :args (@t97)) % 0.46/0.67 (step @p106 :rule trans :premises (@p105 @p89)) % 0.46/0.67 (step @p107 :rule nary_cong :premises (@p68 @p106) :args (@t98)) % 0.46/0.67 (step @p108 :rule 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chain_m_resolution :premises (@p555 @p374 @p543 @p537 @p409 @p553 @p547) :args (@t315 @t279 (@list @t222 @t286 @t282 @t272 @t270 @t316))) % 0.46/0.67 (step @p557 :rule refl :args (@t317)) % 0.46/0.67 (step @p558 :rule refl :args (@t318)) % 0.46/0.67 (step @p559 :rule bool-double-not-elim :args (@t252)) % 0.46/0.67 (step @p560 :rule refl :args (@t319)) % 0.46/0.67 (step @p561 :rule nary_cong :premises (@p430 @p560 @p559 @p558 @p557) :args ((or @t235 @t319 (not @t253) @t318 @t317))) % 0.46/0.67 (assume-push @p633 @t234) % 0.46/0.67 (assume-push @p634 @t289) % 0.46/0.67 (assume-push @p635 @t315) % 0.46/0.67 (assume-push @p636 @t277) % 0.46/0.67 (assume-push @p637 @t253) % 0.46/0.67 (step @p567 :rule evaluate :args ((= false true))) % 0.46/0.67 (step @p568 :rule true_intro :premises (@p633)) % 0.46/0.67 (step @p569 :rule symm :premises (@p635)) % 0.46/0.67 (step @p570 :rule trans :premises (@p636 @p569 @p634)) % 0.46/0.67 (step @p571 :rule refl :args (@t154)) % 0.46/0.67 (step @p500 :rule refl :args (@t128)) % 0.46/0.67 (step @p572 :rule cong :premises (@p500 @p571 @p570) :args (@t252)) % 0.46/0.67 (step @p573 :rule false_intro :premises (@p637)) % 0.46/0.67 (step @p574 :rule symm :premises (@p573)) % 0.46/0.67 (step @p575 :rule trans :premises (@p574 @p572 @p568)) % 0.46/0.67 (step @p576 false :rule eq_resolve :premises (@p575 @p567)) % 0.46/0.67 (step-pop @p638 :rule scope :premises (@p576)) % 0.46/0.67 (step-pop @p639 :rule scope :premises (@p638)) % 0.46/0.67 (step-pop @p640 :rule scope :premises (@p639)) % 0.46/0.67 (step-pop @p641 :rule scope :premises (@p640)) % 0.46/0.67 (step-pop @p642 :rule scope :premises (@p641)) % 0.46/0.67 (step @p577 :rule process_scope :premises (@p642) :args (false)) % 0.46/0.67 (assume-push @p643 @t234) % 0.46/0.67 (assume-push @p644 @t289) % 0.46/0.67 (assume-push @p645 @t253) % 0.46/0.67 (assume-push @p646 @t277) % 0.46/0.67 (assume-push @p647 @t315) % 0.46/0.67 (step @p588 :rule and_intro :premises (@p643 @p644 @p647 @p646 @p645)) % 0.46/0.67 (step-pop @p648 :rule scope :premises (@p588)) % 0.46/0.67 (step-pop @p649 :rule scope :premises (@p648)) % 0.46/0.67 (step-pop @p650 :rule scope :premises (@p649)) % 0.46/0.67 (step-pop @p651 :rule scope :premises (@p650)) % 0.46/0.67 (step-pop @p652 :rule scope :premises (@p651)) % 0.46/0.67 (step @p589 :rule process_scope :premises (@p652) :args (@t320)) % 0.46/0.67 (step @p595 :rule implies_elim :premises (@p589)) % 0.46/0.67 (step @p596 :rule resolution :premises (@p595 @p577) :args (true @t320)) % 0.46/0.67 (step @p597 :rule not_and :premises (@p596)) % 0.46/0.67 (step @p598 :rule eq_resolve :premises (@p597 @p561)) % 0.46/0.67 (step @p599 :rule reordering :premises (@p598) :args ((or @t235 @t252 @t319 @t318 @t317))) % 0.46/0.67 (step @p600 false :rule chain_m_resolution :premises (@p599 @p556 @p546 @p412 @p363 @p307) :args (false (@list false false false true false) (@list @t315 @t289 @t277 @t252 @t234))) % 0.46/0.67 ) % 0.46/0.67 % SZS output end Proof % 0.46/0.67 % cvc5 exiting %------------------------------------------------------------------------------