%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET724+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 08:48:31 AM UTC 2026 % Result : Theorem 0.52s 0.70s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET724+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 16:10:19 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.52/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.52/0.70 % SZS status Theorem % 0.52/0.70 % SZS output start Proof % 0.52/0.70 ( % 0.52/0.70 (declare-sort $$unsorted 0) % 0.52/0.70 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.empty_set $$unsorted) % 0.52/0.70 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.52/0.70 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.52/0.70 (define @t1 () (@var "B" $$unsorted)) % 0.52/0.70 (define @t2 () (@var "X" $$unsorted)) % 0.52/0.70 (define @t3 () (tptp.member @t2 @t1)) % 0.52/0.70 (define @t4 () (@var "A" $$unsorted)) % 0.52/0.70 (define @t5 () (tptp.member @t2 @t4)) % 0.52/0.70 (define @t6 () (@list @t2)) % 0.52/0.70 (define @t7 () (tptp.subset @t4 @t1)) % 0.52/0.70 (define @t8 () (@list @t4 @t1)) % 0.52/0.70 (define @t9 () (@list @t2 @t4)) % 0.52/0.70 (define @t10 () (@list @t2 @t4 @t1)) % 0.52/0.70 (define @t11 () (@var "E" $$unsorted)) % 0.52/0.70 (define @t12 () (= @t2 @t4)) % 0.52/0.70 (define @t13 () (@var "Y" $$unsorted)) % 0.52/0.70 (define @t14 () (tptp.member @t2 @t13)) % 0.52/0.70 (define @t15 () (tptp.member @t13 @t4)) % 0.52/0.70 (define @t16 () (@list @t13)) % 0.52/0.70 (define @t17 () (@var "Y2" $$unsorted)) % 0.52/0.70 (define @t18 () (@var "Y1" $$unsorted)) % 0.52/0.70 (define @t19 () (= @t18 @t17)) % 0.52/0.70 (define @t20 () (@var "F" $$unsorted)) % 0.52/0.70 (define @t21 () (tptp.apply @t20 @t2 @t18)) % 0.52/0.70 (define @t22 () (tptp.member @t17 @t1)) % 0.52/0.70 (define @t23 () (tptp.member @t18 @t1)) % 0.52/0.70 (define @t24 () (and @t5 @t23 @t22)) % 0.52/0.70 (define @t25 () (@list @t2 @t18 @t17)) % 0.52/0.70 (define @t26 () (tptp.apply @t20 @t2 @t13)) % 0.52/0.70 (define @t27 () (tptp.member @t13 @t1)) % 0.52/0.70 (define @t28 () (exists @t16 (and @t27 @t26))) % 0.52/0.70 (define @t29 () (tptp.maps @t20 @t4 @t1)) % 0.52/0.70 (define @t30 () (@list @t20 @t4 @t1)) % 0.52/0.70 (define @t31 () (@var "Z" $$unsorted)) % 0.52/0.70 (define @t32 () (@var "G" $$unsorted)) % 0.52/0.70 (define @t33 () (tptp.apply @t32 @t13 @t31)) % 0.52/0.70 (define @t34 () (and @t27 @t26 @t33)) % 0.52/0.70 (define @t35 () (exists @t16 @t34)) % 0.52/0.70 (define @t36 () (@var "H" $$unsorted)) % 0.52/0.70 (define @t37 () (@var "C" $$unsorted)) % 0.52/0.70 (define @t38 () (tptp.member @t31 @t37)) % 0.52/0.70 (define @t39 () (and @t5 @t38)) % 0.52/0.70 (define @t40 () (tptp.compose_function @t32 @t20 @t4 @t1 @t37)) % 0.52/0.70 (define @t41 () (tptp.apply @t40 @t2 @t31)) % 0.52/0.70 (define @t42 () (=> @t39 (= @t41 @t35))) % 0.52/0.70 (define @t43 () (@list @t32 @t20 @t4 @t1 @t37 @t2 @t31)) % 0.52/0.70 (define @t44 () (forall @t43 @t42)) % 0.52/0.70 (define @t45 () (tptp.apply @t32 @t2 @t17)) % 0.52/0.70 (define @t46 () (and @t21 @t45)) % 0.52/0.70 (define @t47 () (=> @t46 @t19)) % 0.52/0.70 (define @t48 () (forall @t25 (=> @t24 @t47))) % 0.52/0.70 (define @t49 () (tptp.equal_maps @t20 @t32 @t4 @t1)) % 0.52/0.70 (define @t50 () (= @t49 @t48)) % 0.52/0.70 (define @t51 () (forall (@list @t20 @t32 @t4 @t1) @t50)) % 0.52/0.70 (define @t52 () (@var "X2" $$unsorted)) % 0.52/0.70 (define @t53 () (@var "X1" $$unsorted)) % 0.52/0.70 (define @t54 () (tptp.member @t52 @t4)) % 0.52/0.70 (define @t55 () (tptp.member @t53 @t4)) % 0.52/0.70 (define @t56 () (tptp.injective @t20 @t4 @t1)) % 0.52/0.70 (define @t57 () (tptp.apply @t20 @t11 @t13)) % 0.52/0.70 (define @t58 () (tptp.member @t11 @t4)) % 0.52/0.70 (define @t59 () (and @t58 @t57)) % 0.52/0.70 (define @t60 () (@list @t11)) % 0.52/0.70 (define @t61 () (exists @t60 @t59)) % 0.52/0.70 (define @t62 () (=> @t27 @t61)) % 0.52/0.70 (define @t63 () (forall @t16 @t62)) % 0.52/0.70 (define @t64 () (tptp.surjective @t20 @t4 @t1)) % 0.52/0.70 (define @t65 () (= @t64 @t63)) % 0.52/0.70 (define @t66 () (forall @t30 @t65)) % 0.52/0.70 (define @t67 () (tptp.one_to_one @t20 @t4 @t1)) % 0.52/0.70 (define @t68 () (and @t5 @t27)) % 0.52/0.70 (define @t69 () (exists @t6 (and @t5 @t26))) % 0.52/0.70 (define @t70 () (@var "S" $$unsorted)) % 0.52/0.70 (define @t71 () (tptp.apply @t70 @t18 @t17)) % 0.52/0.70 (define @t72 () (tptp.apply @t20 @t52 @t17)) % 0.52/0.70 (define @t73 () (tptp.apply @t20 @t53 @t18)) % 0.52/0.70 (define @t74 () (@var "R" $$unsorted)) % 0.52/0.70 (define @t75 () (tptp.apply @t74 @t53 @t52)) % 0.52/0.70 (define @t76 () (and @t55 @t23 @t54 @t22 @t75 @t73 @t72)) % 0.52/0.70 (define @t77 () (@list @t53 @t18 @t52 @t17)) % 0.52/0.70 (define @t78 () (@list @t20 @t4 @t74 @t1 @t70)) % 0.52/0.70 (define @t79 () (tptp.equal_maps @t32 @t36 @t1 @t37)) % 0.52/0.70 (define @t80 () (tptp.equal_maps @t40 (tptp.compose_function @t36 @t20 @t4 @t1 @t37) @t4 @t37)) % 0.52/0.70 (define @t81 () (tptp.maps @t36 @t1 @t37)) % 0.52/0.70 (define @t82 () (tptp.maps @t32 @t1 @t37)) % 0.52/0.70 (define @t83 () (and @t29 @t82 @t81 @t64 @t80)) % 0.52/0.70 (define @t84 () (@list @t20 @t32 @t36 @t4 @t1 @t37)) % 0.52/0.70 (define @t85 () (forall @t84 (=> @t83 @t79))) % 0.52/0.70 (define @t86 () (not @t85)) % 0.52/0.70 (define @t87 () (not @t33)) % 0.52/0.70 (define @t88 () (not @t26)) % 0.52/0.70 (define @t89 () (not @t27)) % 0.52/0.70 (define @t90 () (or @t89 @t88 @t87)) % 0.52/0.70 (define @t91 () (not (forall @t16 @t90))) % 0.52/0.70 (define @t92 () (= @t41 @t91)) % 0.52/0.70 (define @t93 () (not @t38)) % 0.52/0.70 (define @t94 () (not @t5)) % 0.52/0.70 (define @t95 () (forall @t16 (not @t34))) % 0.52/0.70 (define @t96 () (not @t95)) % 0.52/0.70 (define @t97 () (not @t80)) % 0.52/0.70 (define @t98 () (not @t64)) % 0.52/0.70 (define @t99 () (not @t81)) % 0.52/0.70 (define @t100 () (not @t82)) % 0.52/0.70 (define @t101 () (not @t29)) % 0.52/0.70 (define @t102 () (or @t101 @t100 @t99 @t98 @t97 @t79)) % 0.52/0.70 (define @t103 () (forall @t84 @t102)) % 0.52/0.70 (define @t104 () (@quantifiers_skolemize @t103 2)) % 0.52/0.70 (define @t105 () (@quantifiers_skolemize @t103 1)) % 0.52/0.70 (define @t106 () (@quantifiers_skolemize @t103 5)) % 0.52/0.70 (define @t107 () (not (tptp.member @t17 @t106))) % 0.52/0.70 (define @t108 () (not (tptp.member @t18 @t106))) % 0.52/0.70 (define @t109 () (@quantifiers_skolemize @t103 4)) % 0.52/0.70 (define @t110 () (forall @t25 (or (not (tptp.member @t2 @t109)) @t108 @t107 (not (tptp.apply @t105 @t2 @t18)) (not (tptp.apply @t104 @t2 @t17)) @t19))) % 0.52/0.70 (define @t111 () (@quantifiers_skolemize @t110 1)) % 0.52/0.70 (define @t112 () (@quantifiers_skolemize @t110 0)) % 0.52/0.70 (define @t113 () (@quantifiers_skolemize @t103 0)) % 0.52/0.70 (define @t114 () (@quantifiers_skolemize @t103 3)) % 0.52/0.70 (define @t115 () (not (tptp.member @t11 @t114))) % 0.52/0.70 (define @t116 () (forall @t60 (or @t115 (not (tptp.apply @t113 @t11 @t112))))) % 0.52/0.70 (define @t117 () (@quantifiers_skolemize @t116 0)) % 0.52/0.70 (define @t118 () (not (forall @t60 (or (not @t58) (not @t57))))) % 0.52/0.70 (define @t119 () (forall @t60 (not @t59))) % 0.52/0.70 (define @t120 () (not @t119)) % 0.52/0.70 (define @t121 () (or @t101 @t100 @t99 @t98 @t97)) % 0.52/0.70 (define @t122 () (tptp.surjective @t113 @t114 @t109)) % 0.52/0.70 (define @t123 () (tptp.equal_maps @t105 @t104 @t109 @t106)) % 0.52/0.70 (define @t124 () (tptp.compose_function @t104 @t113 @t114 @t109 @t106)) % 0.52/0.70 (define @t125 () (tptp.compose_function @t105 @t113 @t114 @t109 @t106)) % 0.52/0.70 (define @t126 () (tptp.equal_maps @t125 @t124 @t114 @t106)) % 0.52/0.70 (define @t127 () (not @t126)) % 0.52/0.70 (define @t128 () (not @t122)) % 0.52/0.70 (define @t129 () (or (not (tptp.maps @t113 @t114 @t109)) (not (tptp.maps @t105 @t109 @t106)) (not (tptp.maps @t104 @t109 @t106)) @t128 @t127 @t123)) % 0.52/0.70 (define @t130 () (@list true)) % 0.52/0.70 (define @t131 () (@list @t129)) % 0.52/0.70 (define @t132 () (not (tptp.member @t13 @t109))) % 0.52/0.70 (define @t133 () (forall @t16 (or @t132 (not (forall @t60 (or @t115 (not (tptp.apply @t113 @t11 @t13)))))))) % 0.52/0.70 (define @t134 () (= @t122 @t133)) % 0.52/0.70 (define @t135 () (@list false false)) % 0.52/0.70 (define @t136 () (@list @t112)) % 0.52/0.70 (define @t137 () (not @t45)) % 0.52/0.70 (define @t138 () (not @t21)) % 0.52/0.70 (define @t139 () (not @t22)) % 0.52/0.70 (define @t140 () (not @t23)) % 0.52/0.70 (define @t141 () (or @t138 @t137 @t19)) % 0.52/0.70 (define @t142 () (or @t94 @t140 @t139)) % 0.52/0.70 (define @t143 () (= @t123 @t110)) % 0.52/0.70 (define @t144 () (not @t110)) % 0.52/0.70 (define @t145 () (@list true false)) % 0.52/0.70 (define @t146 () (tptp.member @t112 @t109)) % 0.52/0.70 (define @t147 () (@quantifiers_skolemize @t110 2)) % 0.52/0.70 (define @t148 () (= @t111 @t147)) % 0.52/0.70 (define @t149 () (tptp.apply @t104 @t112 @t147)) % 0.52/0.70 (define @t150 () (not @t149)) % 0.52/0.70 (define @t151 () (tptp.apply @t105 @t112 @t111)) % 0.52/0.70 (define @t152 () (not @t151)) % 0.52/0.70 (define @t153 () (tptp.member @t147 @t106)) % 0.52/0.70 (define @t154 () (not @t153)) % 0.52/0.70 (define @t155 () (tptp.member @t111 @t106)) % 0.52/0.70 (define @t156 () (not @t155)) % 0.52/0.70 (define @t157 () (not @t146)) % 0.52/0.70 (define @t158 () (or @t157 @t156 @t154 @t152 @t150 @t148)) % 0.52/0.70 (define @t159 () (@list @t158)) % 0.52/0.70 (define @t160 () (not @t116)) % 0.52/0.70 (define @t161 () (or @t157 @t160)) % 0.52/0.70 (define @t162 () (tptp.member @t117 @t114)) % 0.52/0.70 (define @t163 () (tptp.apply @t113 @t117 @t112)) % 0.52/0.70 (define @t164 () (not @t163)) % 0.52/0.70 (define @t165 () (not @t162)) % 0.52/0.70 (define @t166 () (or @t165 @t164)) % 0.52/0.70 (define @t167 () (@list @t166)) % 0.52/0.70 (define @t168 () (not (tptp.apply @t113 @t117 @t13))) % 0.52/0.70 (define @t169 () (forall @t16 (or @t132 @t168 (not (tptp.apply @t105 @t13 @t111))))) % 0.52/0.70 (define @t170 () (not @t169)) % 0.52/0.70 (define @t171 () (tptp.apply @t125 @t117 @t111)) % 0.52/0.70 (define @t172 () (= @t171 @t170)) % 0.52/0.70 (define @t173 () (or @t165 @t156 @t172)) % 0.52/0.70 (define @t174 () (@list false false false)) % 0.52/0.70 (define @t175 () (forall @t25 (or (not (tptp.member @t2 @t114)) @t108 @t107 (not (tptp.apply @t125 @t2 @t18)) (not (tptp.apply @t124 @t2 @t17)) @t19))) % 0.52/0.70 (define @t176 () (= @t126 @t175)) % 0.52/0.70 (define @t177 () (forall @t16 (or @t132 @t168 (not (tptp.apply @t104 @t13 @t147))))) % 0.52/0.70 (define @t178 () (not @t177)) % 0.52/0.70 (define @t179 () (tptp.apply @t124 @t117 @t147)) % 0.52/0.70 (define @t180 () (= @t179 @t178)) % 0.52/0.70 (define @t181 () (or @t165 @t154 @t180)) % 0.52/0.70 (define @t182 () (or @t157 @t164 @t150)) % 0.52/0.70 (define @t183 () (not @t182)) % 0.52/0.70 (define @t184 () (not @t180)) % 0.52/0.70 (define @t185 () (not @t179)) % 0.52/0.70 (define @t186 () (not @t171)) % 0.52/0.70 (define @t187 () (or @t165 @t156 @t154 @t186 @t185 @t148)) % 0.52/0.70 (define @t188 () (not @t172)) % 0.52/0.70 (define @t189 () (or @t157 @t164 @t152)) % 0.52/0.70 (define @t190 () (not @t189)) % 0.52/0.70 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.52/0.70 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.52/0.70 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.52/0.70 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.52/0.70 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.52/0.70 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.52/0.70 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.52/0.70 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.52/0.70 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.52/0.70 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.52/0.70 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.52/0.70 (assume @p12 (forall @t30 (= @t29 (and (forall @t6 (=> @t5 @t28)) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t20 @t2 @t17)) @t19))))))) % 0.52/0.70 (assume @p13 (forall (@list @t36 @t32 @t20 @t4 @t1 @t37) (= (tptp.compose_predicate @t36 @t32 @t20 @t4 @t1 @t37) (forall (@list @t2 @t31) (=> @t39 (= (tptp.apply @t36 @t2 @t31) @t35)))))) % 0.52/0.70 (assume @p14 @t44) % 0.52/0.70 (assume @p15 @t51) % 0.52/0.70 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.52/0.70 (assume @p17 (forall @t30 (= @t56 (forall (@list @t53 @t52 @t13) (=> (and @t55 @t54 @t27) (=> (and (tptp.apply @t20 @t53 @t13) (tptp.apply @t20 @t52 @t13)) (= @t53 @t52))))))) % 0.52/0.70 (assume @p18 @t66) % 0.52/0.70 (assume @p19 (forall @t30 (= @t67 (and @t56 @t64)))) % 0.52/0.70 (assume @p20 (forall (@list @t32 @t20 @t4 @t1) (= (tptp.inverse_predicate @t32 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t68 (= @t26 (tptp.apply @t32 @t13 @t2))))))) % 0.52/0.70 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t68 (= @t26 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.52/0.70 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t69))) % 0.52/0.70 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t27 @t69)))) % 0.52/0.70 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t28))) % 0.52/0.70 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t28)))) % 0.52/0.70 (assume @p26 (forall @t78 (= (tptp.increasing @t20 @t4 @t74 @t1 @t70) (forall @t77 (=> @t76 @t71))))) % 0.52/0.70 (assume @p27 (forall @t78 (= (tptp.decreasing @t20 @t4 @t74 @t1 @t70) (forall @t77 (=> @t76 (tptp.apply @t70 @t17 @t18)))))) % 0.52/0.70 (assume @p28 (forall @t78 (= (tptp.isomorphism @t20 @t4 @t74 @t1 @t70) (and @t29 @t67 (forall @t77 (=> (and @t55 @t23 @t54 @t22 @t73 @t72) (= @t75 @t71))))))) % 0.52/0.70 (assume @p29 @t86) % 0.52/0.70 (assume @p30 true) % 0.52/0.70 (step @p31 :rule aci_norm :args ((= (or (or @t94 @t93) @t92) (or @t94 @t93 @t92)))) % 0.52/0.70 (step @p32 :rule refl :args (@t92)) % 0.52/0.70 (step @p33 :rule bool-and-de-morgan :args (@t5 @t38 true)) % 0.52/0.70 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or (not @t39) @t92))) % 0.52/0.70 (step @p35 :rule trans :premises (@p34 @p31)) % 0.52/0.70 (step @p36 :rule bool-impl-elim :args (@t39 @t92)) % 0.52/0.70 (step @p37 :rule trans :premises (@p36 @p35)) % 0.52/0.70 (step @p38 :rule cong :premises (@p37) :args ((forall @t43 (=> @t39 @t92)))) % 0.52/0.70 (step @p39 :rule eq-symm :args (@t91 @t41)) % 0.52/0.70 (step @p40 :rule refl :args (@t41)) % 0.52/0.70 (step @p41 :rule aci_norm :args ((= (or @t89 (or @t88 @t87)) @t90))) % 0.52/0.70 (step @p42 :rule bool-and-de-morgan :args (@t26 @t33 true)) % 0.52/0.70 (step @p43 :rule refl :args (@t89)) % 0.52/0.70 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t89 (not (and @t26 @t33))))) % 0.52/0.70 (step @p45 :rule bool-and-de-morgan :args (@t27 @t26 (and @t33))) % 0.52/0.70 (step @p46 :rule trans :premises (@p45 @p44)) % 0.52/0.70 (step @p47 :rule trans :premises (@p46 @p41)) % 0.52/0.70 (step @p48 :rule cong :premises (@p47) :args (@t95)) % 0.52/0.70 (step @p49 :rule cong :premises (@p48) :args (@t96)) % 0.52/0.70 (step @p50 :rule exists-elim :args ((= @t35 @t96))) % 0.52/0.70 (step @p51 :rule trans :premises (@p50 @p49)) % 0.52/0.70 (step @p52 :rule cong :premises (@p51 @p40) :args ((= @t35 @t41))) % 0.52/0.70 (step @p53 :rule trans :premises (@p52 @p39)) % 0.52/0.70 (step @p54 :rule eq-symm :args (@t41 @t35)) % 0.52/0.70 (step @p55 :rule trans :premises (@p54 @p53)) % 0.52/0.70 (step @p56 :rule refl :args (@t39)) % 0.52/0.70 (step @p57 :rule cong :premises (@p56 @p55) :args (@t42)) % 0.52/0.70 (step @p58 :rule cong :premises (@p57) :args (@t44)) % 0.52/0.70 (step @p59 :rule trans :premises (@p58 @p38)) % 0.52/0.70 (step @p60 :rule eq_resolve :premises (@p14 @p59)) % 0.52/0.70 (step @p61 :rule instantiate :premises (@p60) :args ((@list @t105 @t113 @t114 @t109 @t106 @t117 @t111))) % 0.52/0.70 (step @p62 :rule bool-impl-elim :args (@t27 @t118)) % 0.52/0.70 (step @p63 :rule cong :premises (@p62) :args ((forall @t16 (=> @t27 @t118)))) % 0.52/0.70 (step @p64 :rule bool-and-de-morgan :args (@t58 @t57 true)) % 0.52/0.70 (step @p65 :rule cong :premises (@p64) :args (@t119)) % 0.52/0.70 (step @p66 :rule cong :premises (@p65) :args (@t120)) % 0.52/0.70 (step @p67 :rule exists-elim :args ((= @t61 @t120))) % 0.52/0.70 (step @p68 :rule trans :premises (@p67 @p66)) % 0.52/0.70 (step @p69 :rule refl :args (@t27)) % 0.52/0.70 (step @p70 :rule cong :premises (@p69 @p68) :args (@t62)) % 0.52/0.70 (step @p71 :rule cong :premises (@p70) :args (@t63)) % 0.52/0.70 (step @p72 :rule trans :premises (@p71 @p63)) % 0.52/0.70 (step @p73 :rule refl :args (@t64)) % 0.52/0.70 (step @p74 :rule cong :premises (@p73 @p72) :args (@t65)) % 0.52/0.70 (step @p75 :rule cong :premises (@p74) :args (@t66)) % 0.52/0.70 (step @p76 :rule eq_resolve :premises (@p18 @p75)) % 0.52/0.70 (step @p77 :rule instantiate :premises (@p76) :args ((@list @t113 @t114 @t109))) % 0.52/0.70 (step @p78 :rule aci_norm :args ((= (or @t121 @t79) @t102))) % 0.52/0.70 (step @p79 :rule refl :args (@t79)) % 0.52/0.70 (step @p80 :rule aci_norm :args ((= (or @t101 (or @t100 (or @t99 (or @t98 @t97)))) @t121))) % 0.52/0.70 (step @p81 :rule bool-and-de-morgan :args (@t64 @t80 true)) % 0.52/0.70 (step @p82 :rule refl :args (@t99)) % 0.52/0.70 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t99 (not (and @t64 @t80))))) % 0.52/0.70 (step @p84 :rule bool-and-de-morgan :args (@t81 @t64 (and @t80))) % 0.52/0.70 (step @p85 :rule trans :premises (@p84 @p83)) % 0.52/0.70 (step @p86 :rule refl :args (@t100)) % 0.52/0.70 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t100 (not (and @t81 @t64 @t80))))) % 0.52/0.70 (step @p88 :rule bool-and-de-morgan :args (@t82 @t81 (and @t64 @t80))) % 0.52/0.70 (step @p89 :rule trans :premises (@p88 @p87)) % 0.52/0.70 (step @p90 :rule refl :args (@t101)) % 0.52/0.70 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or @t101 (not (and @t82 @t81 @t64 @t80))))) % 0.52/0.70 (step @p92 :rule bool-and-de-morgan :args (@t29 @t82 (and @t81 @t64 @t80))) % 0.52/0.70 (step @p93 :rule trans :premises (@p92 @p91)) % 0.52/0.70 (step @p94 :rule trans :premises (@p93 @p80)) % 0.52/0.70 (step @p95 :rule nary_cong :premises (@p94 @p79) :args ((or (not @t83) @t79))) % 0.52/0.70 (step @p96 :rule trans :premises (@p95 @p78)) % 0.52/0.70 (step @p97 :rule bool-impl-elim :args (@t83 @t79)) % 0.52/0.70 (step @p98 :rule trans :premises (@p97 @p96)) % 0.52/0.70 (step @p99 :rule cong :premises (@p98) :args (@t85)) % 0.52/0.70 (step @p100 :rule cong :premises (@p99) :args (@t86)) % 0.52/0.70 (step @p101 :rule eq_resolve :premises (@p29 @p100)) % 0.52/0.70 (step @p102 :rule skolemize :premises (@p101)) % 0.52/0.70 (step @p103 :rule bool-double-not-elim :args (@t122)) % 0.52/0.70 (step @p104 :rule refl :args (@t129)) % 0.52/0.70 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t129 (not @t128)))) % 0.52/0.70 (step @p106 :rule cnf_or_neg :args (@t129 3)) % 0.52/0.70 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.52/0.70 (step @p108 :rule reordering :premises (@p107) :args ((or @t122 @t129))) % 0.52/0.70 (step @p109 :rule chain_m_resolution :premises (@p108 @p102) :args (@t122 @t130 @t131)) % 0.52/0.70 (step @p110 :rule cnf_equiv_pos1 :args (@t134)) % 0.52/0.70 (step @p111 :rule reordering :premises (@p110) :args ((or @t128 @t133 (not @t134)))) % 0.52/0.70 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p77) :args (@t133 @t135 (@list @t122 @t134))) % 0.52/0.70 (step @p113 :rule instantiate :premises (@p112) :args (@t136)) % 0.52/0.70 (step @p114 :rule aci_norm :args ((= (or @t142 @t141) (or @t94 @t140 @t139 @t138 @t137 @t19)))) % 0.52/0.70 (step @p115 :rule aci_norm :args ((= (or (or @t138 @t137) @t19) @t141))) % 0.52/0.70 (step @p116 :rule refl :args (@t19)) % 0.52/0.70 (step @p117 :rule bool-and-de-morgan :args (@t21 @t45 true)) % 0.52/0.70 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or (not @t46) @t19))) % 0.52/0.70 (step @p119 :rule trans :premises (@p118 @p115)) % 0.52/0.70 (step @p120 :rule bool-impl-elim :args (@t46 @t19)) % 0.52/0.70 (step @p121 :rule trans :premises (@p120 @p119)) % 0.52/0.70 (step @p122 :rule aci_norm :args ((= (or @t94 (or @t140 @t139)) @t142))) % 0.52/0.70 (step @p123 :rule bool-and-de-morgan :args (@t23 @t22 true)) % 0.52/0.70 (step @p124 :rule refl :args (@t94)) % 0.52/0.70 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or @t94 (not (and @t23 @t22))))) % 0.52/0.70 (step @p126 :rule bool-and-de-morgan :args (@t5 @t23 (and @t22))) % 0.52/0.70 (step @p127 :rule trans :premises (@p126 @p125)) % 0.52/0.70 (step @p128 :rule trans :premises (@p127 @p122)) % 0.52/0.70 (step @p129 :rule nary_cong :premises (@p128 @p121) :args ((or (not @t24) @t47))) % 0.52/0.70 (step @p130 :rule trans :premises (@p129 @p114)) % 0.52/0.70 (step @p131 :rule bool-impl-elim :args (@t24 @t47)) % 0.52/0.70 (step @p132 :rule trans :premises (@p131 @p130)) % 0.52/0.70 (step @p133 :rule cong :premises (@p132) :args (@t48)) % 0.52/0.70 (step @p134 :rule refl :args (@t49)) % 0.52/0.70 (step @p135 :rule cong :premises (@p134 @p133) :args (@t50)) % 0.52/0.70 (step @p136 :rule cong :premises (@p135) :args (@t51)) % 0.52/0.70 (step @p137 :rule eq_resolve :premises (@p15 @p136)) % 0.52/0.70 (step @p138 :rule instantiate :premises (@p137) :args ((@list @t105 @t104 @t109 @t106))) % 0.52/0.70 (step @p139 :rule cnf_or_neg :args (@t129 5)) % 0.52/0.70 (step @p140 :rule chain_m_resolution :premises (@p139 @p102) :args ((not @t123) @t130 @t131)) % 0.52/0.70 (step @p141 :rule cnf_equiv_pos2 :args (@t143)) % 0.52/0.70 (step @p142 :rule reordering :premises (@p141) :args ((or @t123 @t144 (not @t143)))) % 0.52/0.70 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p138) :args (@t144 @t145 (@list @t123 @t143))) % 0.52/0.70 (step @p144 :rule skolemize :premises (@p143)) % 0.52/0.70 (step @p145 :rule bool-double-not-elim :args (@t146)) % 0.52/0.70 (step @p146 :rule refl :args (@t158)) % 0.52/0.70 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t158 (not @t157)))) % 0.52/0.70 (step @p148 :rule cnf_or_neg :args (@t158 0)) % 0.52/0.70 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.52/0.70 (step @p150 :rule reordering :premises (@p149) :args ((or @t146 @t158))) % 0.52/0.70 (step @p151 :rule chain_m_resolution :premises (@p150 @p144) :args (@t146 @t130 @t159)) % 0.52/0.70 (step @p152 :rule cnf_or_pos :args (@t161)) % 0.52/0.70 (step @p153 :rule reordering :premises (@p152) :args ((or @t157 @t160 (not @t161)))) % 0.52/0.70 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p113) :args (@t160 @t135 (@list @t146 @t161))) % 0.52/0.70 (step @p155 :rule skolemize :premises (@p154)) % 0.52/0.70 (step @p156 :rule bool-double-not-elim :args (@t162)) % 0.52/0.70 (step @p157 :rule refl :args (@t166)) % 0.52/0.70 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t166 (not @t165)))) % 0.52/0.70 (step @p159 :rule cnf_or_neg :args (@t166 0)) % 0.52/0.70 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.52/0.70 (step @p161 :rule reordering :premises (@p160) :args ((or @t162 @t166))) % 0.52/0.70 (step @p162 :rule chain_m_resolution :premises (@p161 @p155) :args (@t162 @t130 @t167)) % 0.52/0.70 (step @p163 :rule bool-double-not-elim :args (@t155)) % 0.52/0.70 (step @p164 :rule nary_cong :premises (@p146 @p163) :args ((or @t158 (not @t156)))) % 0.52/0.70 (step @p165 :rule cnf_or_neg :args (@t158 1)) % 0.52/0.70 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.52/0.70 (step @p167 :rule reordering :premises (@p166) :args ((or @t155 @t158))) % 0.52/0.70 (step @p168 :rule chain_m_resolution :premises (@p167 @p144) :args (@t155 @t130 @t159)) % 0.52/0.70 (step @p169 :rule cnf_or_pos :args (@t173)) % 0.52/0.70 (step @p170 :rule reordering :premises (@p169) :args ((or @t156 @t165 @t172 (not @t173)))) % 0.52/0.70 (step @p171 :rule chain_m_resolution :premises (@p170 @p168 @p162 @p61) :args (@t172 @t174 (@list @t155 @t162 @t173))) % 0.52/0.70 (step @p172 :rule instantiate :premises (@p137) :args ((@list @t125 @t124 @t114 @t106))) % 0.52/0.70 (step @p173 :rule bool-double-not-elim :args (@t126)) % 0.52/0.70 (step @p174 :rule nary_cong :premises (@p104 @p173) :args ((or @t129 (not @t127)))) % 0.52/0.70 (step @p175 :rule cnf_or_neg :args (@t129 4)) % 0.52/0.70 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.52/0.70 (step @p177 :rule reordering :premises (@p176) :args ((or @t126 @t129))) % 0.52/0.70 (step @p178 :rule chain_m_resolution :premises (@p177 @p102) :args (@t126 @t130 @t131)) % 0.52/0.70 (step @p179 :rule cnf_equiv_pos1 :args (@t176)) % 0.52/0.70 (step @p180 :rule reordering :premises (@p179) :args ((or @t127 @t175 (not @t176)))) % 0.52/0.70 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p172) :args (@t175 @t135 (@list @t126 @t176))) % 0.52/0.70 (step @p182 :rule instantiate :premises (@p181) :args ((@list @t117 @t111 @t147))) % 0.52/0.70 (step @p183 :rule instantiate :premises (@p60) :args ((@list @t104 @t113 @t114 @t109 @t106 @t117 @t147))) % 0.52/0.70 (step @p184 :rule bool-double-not-elim :args (@t153)) % 0.52/0.70 (step @p185 :rule nary_cong :premises (@p146 @p184) :args ((or @t158 (not @t154)))) % 0.52/0.70 (step @p186 :rule cnf_or_neg :args (@t158 2)) % 0.52/0.70 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 0.52/0.70 (step @p188 :rule reordering :premises (@p187) :args ((or @t153 @t158))) % 0.52/0.70 (step @p189 :rule chain_m_resolution :premises (@p188 @p144) :args (@t153 @t130 @t159)) % 0.52/0.70 (step @p190 :rule cnf_or_pos :args (@t181)) % 0.52/0.70 (step @p191 :rule reordering :premises (@p190) :args ((or @t154 @t165 @t180 (not @t181)))) % 0.52/0.70 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p162 @p183) :args (@t180 @t174 (@list @t153 @t162 @t181))) % 0.52/0.70 (step @p193 :rule bool-double-not-elim :args (@t163)) % 0.52/0.70 (step @p194 :rule nary_cong :premises (@p157 @p193) :args ((or @t166 (not @t164)))) % 0.52/0.70 (step @p195 :rule cnf_or_neg :args (@t166 1)) % 0.52/0.70 (step @p196 :rule eq_resolve :premises (@p195 @p194)) % 0.52/0.70 (step @p197 :rule reordering :premises (@p196) :args ((or @t163 @t166))) % 0.52/0.70 (step @p198 :rule chain_m_resolution :premises (@p197 @p155) :args (@t163 @t130 @t167)) % 0.52/0.70 (step @p199 :rule bool-double-not-elim :args (@t149)) % 0.52/0.70 (step @p200 :rule nary_cong :premises (@p146 @p199) :args ((or @t158 (not @t150)))) % 0.52/0.70 (step @p201 :rule cnf_or_neg :args (@t158 4)) % 0.52/0.70 (step @p202 :rule eq_resolve :premises (@p201 @p200)) % 0.52/0.70 (step @p203 :rule reordering :premises (@p202) :args ((or @t149 @t158))) % 0.52/0.70 (step @p204 :rule chain_m_resolution :premises (@p203 @p144) :args (@t149 @t130 @t159)) % 0.52/0.70 (step @p205 :rule cnf_or_pos :args (@t182)) % 0.52/0.70 (step @p206 :rule reordering :premises (@p205) :args ((or @t157 @t150 @t164 @t183))) % 0.52/0.70 (step @p207 :rule chain_m_resolution :premises (@p206 @p151 @p204 @p198) :args (@t183 @t174 (@list @t146 @t149 @t163))) % 0.52/0.70 (assume-push @p250 @t177) % 0.52/0.70 (step @p209 :rule instantiate :premises (@p250) :args (@t136)) % 0.52/0.70 (step-pop @p251 :rule scope :premises (@p209)) % 0.52/0.70 (step @p210 :rule process_scope :premises (@p251) :args (@t182)) % 0.52/0.70 (step @p212 :rule implies_elim :premises (@p210)) % 0.52/0.70 (step @p213 :rule chain_m_resolution :premises (@p212 @p207) :args (@t178 @t130 (@list @t182))) % 0.52/0.70 (step @p214 :rule bool-double-not-elim :args (@t177)) % 0.52/0.70 (step @p215 :rule refl :args (@t179)) % 0.52/0.70 (step @p216 :rule refl :args (@t184)) % 0.52/0.70 (step @p217 :rule nary_cong :premises (@p216 @p215 @p214) :args ((or @t184 @t179 (not @t178)))) % 0.52/0.70 (step @p218 :rule cnf_equiv_pos2 :args (@t180)) % 0.52/0.70 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 0.52/0.70 (step @p220 :rule reordering :premises (@p219) :args ((or @t179 @t177 @t184))) % 0.52/0.70 (step @p221 :rule chain_m_resolution :premises (@p220 @p213 @p192) :args (@t179 @t145 (@list @t177 @t180))) % 0.52/0.70 (step @p222 :rule cnf_or_neg :args (@t158 5)) % 0.52/0.70 (step @p223 :rule chain_m_resolution :premises (@p222 @p144) :args ((not @t148) @t130 @t159)) % 0.52/0.70 (step @p224 :rule cnf_or_pos :args (@t187)) % 0.52/0.70 (step @p225 :rule reordering :premises (@p224) :args ((or @t156 @t154 @t148 @t165 @t186 @t185 (not @t187)))) % 0.52/0.70 (step @p226 :rule chain_m_resolution :premises (@p225 @p168 @p189 @p223 @p162 @p221 @p182) :args (@t186 (@list false false true false false false) (@list @t155 @t153 @t148 @t162 @t179 @t187))) % 0.52/0.70 (step @p227 :rule bool-double-not-elim :args (@t169)) % 0.52/0.70 (step @p228 :rule refl :args (@t171)) % 0.52/0.70 (step @p229 :rule refl :args (@t188)) % 0.52/0.70 (step @p230 :rule nary_cong :premises (@p229 @p228 @p227) :args ((or @t188 @t171 (not @t170)))) % 0.52/0.70 (step @p231 :rule cnf_equiv_pos2 :args (@t172)) % 0.52/0.70 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 0.52/0.70 (step @p233 :rule reordering :premises (@p232) :args ((or @t171 @t169 @t188))) % 0.52/0.70 (step @p234 :rule chain_m_resolution :premises (@p233 @p226 @p171) :args (@t169 @t145 (@list @t171 @t172))) % 0.52/0.70 (step @p235 :rule bool-double-not-elim :args (@t151)) % 0.52/0.70 (step @p236 :rule nary_cong :premises (@p146 @p235) :args ((or @t158 (not @t152)))) % 0.52/0.70 (step @p237 :rule cnf_or_neg :args (@t158 3)) % 0.52/0.70 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 0.52/0.70 (step @p239 :rule reordering :premises (@p238) :args ((or @t151 @t158))) % 0.52/0.70 (step @p240 :rule chain_m_resolution :premises (@p239 @p144) :args (@t151 @t130 @t159)) % 0.52/0.70 (step @p241 :rule cnf_or_pos :args (@t189)) % 0.52/0.70 (step @p242 :rule reordering :premises (@p241) :args ((or @t157 @t152 @t164 @t190))) % 0.52/0.70 (step @p243 :rule chain_m_resolution :premises (@p242 @p151 @p240 @p198) :args (@t190 @t174 (@list @t146 @t151 @t163))) % 0.52/0.70 (assume-push @p252 @t169) % 0.52/0.70 (step @p245 :rule instantiate :premises (@p252) :args (@t136)) % 0.52/0.70 (step-pop @p253 :rule scope :premises (@p245)) % 0.52/0.70 (step @p246 :rule process_scope :premises (@p253) :args (@t189)) % 0.52/0.70 (step @p248 :rule implies_elim :premises (@p246)) % 0.52/0.70 (step @p249 false :rule chain_m_resolution :premises (@p248 @p243 @p234) :args (false @t145 (@list @t189 @t169))) % 0.52/0.70 ) % 0.52/0.70 % SZS output end Proof % 0.52/0.70 % cvc5 exiting %------------------------------------------------------------------------------