%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX024+1 : TPTP v9.2.1. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n025.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 09:07:00 AM UTC 2026 % Result : Theorem 0.41s 0.97s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWX024+1 : TPTP v9.2.1. Released v9.1.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n025.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 22:53:46 EDT 2026 % 0.17/0.35 % CPUTime : % 0.38/0.56 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.97 % SZS status Theorem % 0.41/0.97 % SZS output start Proof % 0.41/0.97 ( % 0.41/0.97 (declare-sort $$unsorted 0) % 0.41/0.97 (declare-const tptp.sub (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'**'| (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.97 (declare-const tptp.nat_terminates (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nat_fails (-> $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@<_terminates'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@<_fails'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@=<_terminates'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@=<_fails'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nat_succeeds (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.97 (declare-const |tptp.'@*'| (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.97 (declare-const tptp.append_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.times_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.length_succeeds (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.delete_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.gr (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.41/0.97 (declare-const |tptp.'0'| $$unsorted) % 0.41/0.97 (declare-const tptp.delete_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.member_terminates (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nil $$unsorted) % 0.41/0.97 (declare-const tptp.list_terminates (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nat_list_fails (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.plus_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.member_succeeds (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.length_fails (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nat_list_succeeds (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.lh (-> $$unsorted $$unsorted)) % 0.41/0.97 (declare-const |tptp.'@=<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.list_fails (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.list_succeeds (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.append_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.times_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const |tptp.'@+'| (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.97 (declare-const tptp.length_terminates (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.nat_list_terminates (-> $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.append_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.times_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.member_fails (-> $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.plus_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.delete_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (declare-const tptp.plus_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.97 (define @t1 () (@var "Xx3" $$unsorted)) % 0.41/0.97 (define @t2 () (tptp.s @t1)) % 0.41/0.97 (define @t3 () (@var "Xx5" $$unsorted)) % 0.41/0.97 (define @t4 () (@var "Xx4" $$unsorted)) % 0.41/0.97 (define @t5 () (tptp.cons @t4 @t3)) % 0.41/0.97 (define @t6 () (@list @t4 @t3)) % 0.41/0.97 (define @t7 () (@var "Xx6" $$unsorted)) % 0.41/0.97 (define @t8 () (@var "Xx8" $$unsorted)) % 0.41/0.97 (define @t9 () (@var "Xx7" $$unsorted)) % 0.41/0.97 (define @t10 () (@var "Xx10" $$unsorted)) % 0.41/0.97 (define @t11 () (@var "Xx9" $$unsorted)) % 0.41/0.97 (define @t12 () (@var "Xx13" $$unsorted)) % 0.41/0.97 (define @t13 () (@var "Xx12" $$unsorted)) % 0.41/0.97 (define @t14 () (@var "Xx11" $$unsorted)) % 0.41/0.97 (define @t15 () (@var "Xx17" $$unsorted)) % 0.41/0.97 (define @t16 () (@var "Xx15" $$unsorted)) % 0.41/0.97 (define @t17 () (@var "Xx16" $$unsorted)) % 0.41/0.97 (define @t18 () (@var "Xx14" $$unsorted)) % 0.41/0.97 (define @t19 () (@var "Xx20" $$unsorted)) % 0.41/0.97 (define @t20 () (@var "Xx18" $$unsorted)) % 0.41/0.97 (define @t21 () (@var "Xx21" $$unsorted)) % 0.41/0.97 (define @t22 () (@var "Xx19" $$unsorted)) % 0.41/0.97 (define @t23 () (@var "Xx22" $$unsorted)) % 0.41/0.97 (define @t24 () (@var "Xx24" $$unsorted)) % 0.41/0.97 (define @t25 () (@var "Xx23" $$unsorted)) % 0.41/0.97 (define @t26 () (@var "Xx27" $$unsorted)) % 0.41/0.97 (define @t27 () (@var "Xx26" $$unsorted)) % 0.41/0.97 (define @t28 () (@var "Xx25" $$unsorted)) % 0.41/0.97 (define @t29 () (tptp.delete_fails @t28 @t27 @t26)) % 0.41/0.97 (define @t30 () (tptp.delete_succeeds @t28 @t27 @t26)) % 0.41/0.97 (define @t31 () (@list @t28 @t27 @t26)) % 0.41/0.97 (define @t32 () (@var "Xx29" $$unsorted)) % 0.41/0.97 (define @t33 () (@var "Xx28" $$unsorted)) % 0.41/0.97 (define @t34 () (tptp.length_fails @t33 @t32)) % 0.41/0.97 (define @t35 () (tptp.length_succeeds @t33 @t32)) % 0.41/0.97 (define @t36 () (@list @t33 @t32)) % 0.41/0.97 (define @t37 () (@var "Xx32" $$unsorted)) % 0.41/0.97 (define @t38 () (@var "Xx31" $$unsorted)) % 0.41/0.97 (define @t39 () (@var "Xx30" $$unsorted)) % 0.41/0.97 (define @t40 () (tptp.append_fails @t39 @t38 @t37)) % 0.41/0.97 (define @t41 () (tptp.append_succeeds @t39 @t38 @t37)) % 0.41/0.97 (define @t42 () (@list @t39 @t38 @t37)) % 0.41/0.97 (define @t43 () (@var "Xx34" $$unsorted)) % 0.41/0.97 (define @t44 () (@var "Xx33" $$unsorted)) % 0.41/0.97 (define @t45 () (tptp.member_fails @t44 @t43)) % 0.41/0.97 (define @t46 () (tptp.member_succeeds @t44 @t43)) % 0.41/0.97 (define @t47 () (@list @t44 @t43)) % 0.41/0.97 (define @t48 () (@var "Xx35" $$unsorted)) % 0.41/0.97 (define @t49 () (tptp.list_fails @t48)) % 0.41/0.97 (define @t50 () (tptp.list_succeeds @t48)) % 0.41/0.97 (define @t51 () (@list @t48)) % 0.41/0.97 (define @t52 () (@var "Xx36" $$unsorted)) % 0.41/0.97 (define @t53 () (tptp.nat_list_fails @t52)) % 0.41/0.97 (define @t54 () (tptp.nat_list_succeeds @t52)) % 0.41/0.97 (define @t55 () (@list @t52)) % 0.41/0.97 (define @t56 () (@var "Xx39" $$unsorted)) % 0.41/0.97 (define @t57 () (@var "Xx38" $$unsorted)) % 0.41/0.97 (define @t58 () (@var "Xx37" $$unsorted)) % 0.41/0.97 (define @t59 () (tptp.times_fails @t58 @t57 @t56)) % 0.41/0.97 (define @t60 () (tptp.times_succeeds @t58 @t57 @t56)) % 0.41/0.97 (define @t61 () (@list @t58 @t57 @t56)) % 0.41/0.97 (define @t62 () (@var "Xx42" $$unsorted)) % 0.41/0.97 (define @t63 () (@var "Xx41" $$unsorted)) % 0.41/0.97 (define @t64 () (@var "Xx40" $$unsorted)) % 0.41/0.97 (define @t65 () (tptp.plus_fails @t64 @t63 @t62)) % 0.41/0.97 (define @t66 () (tptp.plus_succeeds @t64 @t63 @t62)) % 0.41/0.97 (define @t67 () (@list @t64 @t63 @t62)) % 0.41/0.97 (define @t68 () (@var "Xx44" $$unsorted)) % 0.41/0.97 (define @t69 () (@var "Xx43" $$unsorted)) % 0.41/0.97 (define @t70 () (|tptp.'@=<_fails'| @t69 @t68)) % 0.41/0.97 (define @t71 () (|tptp.'@=<_succeeds'| @t69 @t68)) % 0.41/0.97 (define @t72 () (@list @t69 @t68)) % 0.41/0.97 (define @t73 () (@var "Xx46" $$unsorted)) % 0.41/0.97 (define @t74 () (@var "Xx45" $$unsorted)) % 0.41/0.97 (define @t75 () (|tptp.'@<_fails'| @t74 @t73)) % 0.41/0.97 (define @t76 () (|tptp.'@<_succeeds'| @t74 @t73)) % 0.41/0.97 (define @t77 () (@list @t74 @t73)) % 0.41/0.97 (define @t78 () (@var "Xx47" $$unsorted)) % 0.41/0.97 (define @t79 () (tptp.nat_fails @t78)) % 0.41/0.97 (define @t80 () (tptp.nat_succeeds @t78)) % 0.41/0.97 (define @t81 () (@list @t78)) % 0.41/0.97 (define @t82 () (@var "Xx1" $$unsorted)) % 0.41/0.97 (define @t83 () (@var "Xx2" $$unsorted)) % 0.41/0.97 (define @t84 () (= @t83 (tptp.cons @t82 @t1))) % 0.41/0.97 (define @t85 () (tptp.cons @t4 @t7)) % 0.41/0.97 (define @t86 () (= @t1 @t85)) % 0.41/0.97 (define @t87 () (= @t83 @t5)) % 0.41/0.97 (define @t88 () (@list @t4 @t3 @t7)) % 0.41/0.97 (define @t89 () (@list @t82 @t83 @t1)) % 0.41/0.97 (define @t90 () (not @t86)) % 0.41/0.97 (define @t91 () (not @t87)) % 0.41/0.97 (define @t92 () (= @t83 |tptp.'0'|)) % 0.41/0.97 (define @t93 () (= @t82 tptp.nil)) % 0.41/0.97 (define @t94 () (tptp.s @t3)) % 0.41/0.97 (define @t95 () (= @t83 @t94)) % 0.41/0.97 (define @t96 () (tptp.cons @t1 @t4)) % 0.41/0.97 (define @t97 () (= @t82 @t96)) % 0.41/0.97 (define @t98 () (@list @t1 @t4 @t3)) % 0.41/0.97 (define @t99 () (@list @t82 @t83)) % 0.41/0.97 (define @t100 () (not @t93)) % 0.41/0.97 (define @t101 () (not @t95)) % 0.41/0.97 (define @t102 () (not @t97)) % 0.41/0.97 (define @t103 () (or @t100 true)) % 0.41/0.97 (define @t104 () (= @t1 @t83)) % 0.41/0.97 (define @t105 () (= @t82 @t5)) % 0.41/0.97 (define @t106 () (not @t104)) % 0.41/0.97 (define @t107 () (not @t105)) % 0.41/0.97 (define @t108 () (= @t83 (tptp.cons @t82 @t3))) % 0.41/0.97 (define @t109 () (@list @t3)) % 0.41/0.97 (define @t110 () (exists @t109 @t108)) % 0.41/0.97 (define @t111 () (tptp.member_succeeds @t82 @t4)) % 0.41/0.97 (define @t112 () (= @t83 @t96)) % 0.41/0.97 (define @t113 () (and @t112 @t111)) % 0.41/0.97 (define @t114 () (@list @t1 @t4)) % 0.41/0.97 (define @t115 () (exists @t114 @t113)) % 0.41/0.97 (define @t116 () (or @t115 @t110)) % 0.41/0.97 (define @t117 () (tptp.member_succeeds @t82 @t83)) % 0.41/0.97 (define @t118 () (= @t117 @t116)) % 0.41/0.97 (define @t119 () (forall @t99 @t118)) % 0.41/0.97 (define @t120 () (forall @t109 (not @t108))) % 0.41/0.97 (define @t121 () (not @t112)) % 0.41/0.97 (define @t122 () (= @t82 (tptp.cons @t83 @t1))) % 0.41/0.97 (define @t123 () (@list @t83 @t1)) % 0.41/0.97 (define @t124 () (@list @t82)) % 0.41/0.97 (define @t125 () (not @t122)) % 0.41/0.97 (define @t126 () (tptp.nat_succeeds @t83)) % 0.41/0.97 (define @t127 () (tptp.nat_fails @t83)) % 0.41/0.97 (define @t128 () (tptp.nat_terminates @t83)) % 0.41/0.97 (define @t129 () (= @t1 |tptp.'0'|)) % 0.41/0.97 (define @t130 () (= @t82 |tptp.'0'|)) % 0.41/0.97 (define @t131 () (tptp.s @t4)) % 0.41/0.97 (define @t132 () (= @t82 @t131)) % 0.41/0.97 (define @t133 () (not @t130)) % 0.41/0.97 (define @t134 () (tptp.times_fails @t4 @t83 @t3)) % 0.41/0.97 (define @t135 () (not @t132)) % 0.41/0.97 (define @t136 () (or @t133 true)) % 0.41/0.97 (define @t137 () (= @t1 @t94)) % 0.41/0.97 (define @t138 () (not @t137)) % 0.41/0.97 (define @t139 () (= @t83 @t131)) % 0.41/0.97 (define @t140 () (= @t82 @t2)) % 0.41/0.97 (define @t141 () (not @t139)) % 0.41/0.97 (define @t142 () (not @t140)) % 0.41/0.97 (define @t143 () (= @t82 (tptp.s @t83))) % 0.41/0.97 (define @t144 () (@list @t83)) % 0.41/0.97 (define @t145 () (tptp.nat_succeeds @t82)) % 0.41/0.97 (define @t146 () (not @t143)) % 0.41/0.97 (define @t147 () (@var "Xx" $$unsorted)) % 0.41/0.97 (define @t148 () (tptp.nat_succeeds @t147)) % 0.41/0.97 (define @t149 () (@list @t147)) % 0.41/0.97 (define @t150 () (tptp.gr @t147)) % 0.41/0.97 (define @t151 () (@var "Xz" $$unsorted)) % 0.41/0.97 (define @t152 () (@var "Xy" $$unsorted)) % 0.41/0.97 (define @t153 () (tptp.plus_terminates @t147 @t152 @t151)) % 0.41/0.97 (define @t154 () (@list @t147 @t152 @t151)) % 0.41/0.97 (define @t155 () (tptp.nat_succeeds @t151)) % 0.41/0.97 (define @t156 () (tptp.plus_succeeds @t147 @t152 @t151)) % 0.41/0.97 (define @t157 () (tptp.nat_succeeds @t152)) % 0.41/0.97 (define @t158 () (tptp.gr @t151)) % 0.41/0.97 (define @t159 () (tptp.gr @t152)) % 0.41/0.97 (define @t160 () (@list @t151)) % 0.41/0.97 (define @t161 () (@list @t147 @t152)) % 0.41/0.97 (define @t162 () (@var "Xz2" $$unsorted)) % 0.41/0.97 (define @t163 () (@var "Xz1" $$unsorted)) % 0.41/0.97 (define @t164 () (= @t163 @t162)) % 0.41/0.97 (define @t165 () (@list @t147 @t152 @t163 @t162)) % 0.41/0.97 (define @t166 () (@list @t152)) % 0.41/0.97 (define @t167 () (|tptp.'@+'| @t147 @t152)) % 0.41/0.97 (define @t168 () (tptp.s @t147)) % 0.41/0.97 (define @t169 () (|tptp.'@+'| @t168 @t152)) % 0.41/0.97 (define @t170 () (and @t148 @t157)) % 0.41/0.97 (define @t171 () (|tptp.'@+'| @t152 @t151)) % 0.41/0.97 (define @t172 () (and @t148 @t157 @t155)) % 0.41/0.97 (define @t173 () (tptp.s @t152)) % 0.41/0.97 (define @t174 () (|tptp.'@+'| @t147 @t173)) % 0.41/0.97 (define @t175 () (|tptp.'@+'| @t152 @t147)) % 0.41/0.97 (define @t176 () (|tptp.'@+'| @t147 @t151)) % 0.41/0.97 (define @t177 () (tptp.times_succeeds @t147 @t152 @t151)) % 0.41/0.97 (define @t178 () (|tptp.'@*'| @t147 @t152)) % 0.41/0.97 (define @t179 () (|tptp.'@*'| @t168 @t152)) % 0.41/0.97 (define @t180 () (|tptp.'@*'| @t152 @t151)) % 0.41/0.97 (define @t181 () (|tptp.'@*'| @t147 @t151)) % 0.41/0.97 (define @t182 () (|tptp.'@*'| @t152 @t147)) % 0.41/0.97 (define @t183 () (tptp.s |tptp.'0'|)) % 0.41/0.97 (define @t184 () (|tptp.'@<_terminates'| @t147 @t152)) % 0.41/0.97 (define @t185 () (|tptp.'@<_succeeds'| @t147 @t152)) % 0.41/0.97 (define @t186 () (tptp.s @t151)) % 0.41/0.97 (define @t187 () (|tptp.'@<_succeeds'| @t147 @t151)) % 0.41/0.97 (define @t188 () (|tptp.'@<_succeeds'| @t147 @t173)) % 0.41/0.97 (define @t189 () (|tptp.'@<_succeeds'| @t152 @t151)) % 0.41/0.97 (define @t190 () (= @t147 @t152)) % 0.41/0.97 (define @t191 () (or @t185 @t190)) % 0.41/0.97 (define @t192 () (not (= @t147 |tptp.'0'|))) % 0.41/0.97 (define @t193 () (|tptp.'@=<_succeeds'| @t147 @t152)) % 0.41/0.97 (define @t194 () (|tptp.'@=<_succeeds'| @t152 @t147)) % 0.41/0.97 (define @t195 () (|tptp.'@=<_succeeds'| @t152 @t151)) % 0.41/0.97 (define @t196 () (|tptp.'@<_succeeds'| @t167 @t176)) % 0.41/0.97 (define @t197 () (|tptp.'@<_succeeds'| @t176 @t171)) % 0.41/0.97 (define @t198 () (|tptp.'@=<_succeeds'| @t167 @t176)) % 0.41/0.97 (define @t199 () (and @t193 @t157 @t155)) % 0.41/0.97 (define @t200 () (@var "Xy2" $$unsorted)) % 0.41/0.97 (define @t201 () (@var "Xy1" $$unsorted)) % 0.41/0.97 (define @t202 () (|tptp.'@+'| @t201 @t200)) % 0.41/0.97 (define @t203 () (|tptp.'@+'| @t82 @t83)) % 0.41/0.97 (define @t204 () (tptp.nat_succeeds @t201)) % 0.41/0.97 (define @t205 () (|tptp.'@=<_succeeds'| @t83 @t200)) % 0.41/0.97 (define @t206 () (|tptp.'@=<_succeeds'| @t82 @t201)) % 0.41/0.97 (define @t207 () (@list @t82 @t83 @t201 @t200)) % 0.41/0.97 (define @t208 () (|tptp.'@<_succeeds'| @t203 @t202)) % 0.41/0.97 (define @t209 () (|tptp.'@<_succeeds'| @t82 @t201)) % 0.41/0.97 (define @t210 () (|tptp.'@<_succeeds'| @t83 @t200)) % 0.41/0.97 (define @t211 () (@var "Xl3" $$unsorted)) % 0.41/0.97 (define @t212 () (@var "Xl2" $$unsorted)) % 0.41/0.97 (define @t213 () (@var "Xl1" $$unsorted)) % 0.41/0.97 (define @t214 () (tptp.append_succeeds @t213 @t212 @t211)) % 0.41/0.97 (define @t215 () (|tptp.'**'| @t213 @t212)) % 0.41/0.97 (define @t216 () (tptp.list_succeeds @t213)) % 0.41/0.97 (define @t217 () (@list @t213 @t212 @t211)) % 0.41/0.97 (define @t218 () (@var "Xn" $$unsorted)) % 0.41/0.97 (define @t219 () (@var "Xl" $$unsorted)) % 0.41/0.97 (define @t220 () (tptp.length_succeeds @t219 @t218)) % 0.41/0.97 (define @t221 () (tptp.lh @t219)) % 0.41/0.97 (define @t222 () (tptp.list_succeeds @t219)) % 0.41/0.97 (define @t223 () (@list @t219 @t218)) % 0.41/0.97 (define @t224 () (tptp.member_succeeds @t147 @t212)) % 0.41/0.97 (define @t225 () (tptp.member_succeeds @t147 @t213)) % 0.41/0.97 (define @t226 () (@list @t213 @t212)) % 0.41/0.97 (define @t227 () (tptp.cons @t147 @t219)) % 0.41/0.97 (define @t228 () (@list @t147 @t219)) % 0.41/0.97 (define @t229 () (@list @t219)) % 0.41/0.97 (define @t230 () (tptp.member_succeeds @t147 @t219)) % 0.41/0.97 (define @t231 () (not @t190)) % 0.41/0.97 (define @t232 () (tptp.member_succeeds @t147 (tptp.cons @t152 @t219))) % 0.41/0.97 (define @t233 () (and @t232 @t231)) % 0.41/0.97 (define @t234 () (@list @t147 @t152 @t151 @t219)) % 0.41/0.97 (define @t235 () (forall @t234 (=> @t233 @t230))) % 0.41/0.97 (define @t236 () (tptp.list_succeeds @t211)) % 0.41/0.97 (define @t237 () (tptp.list_succeeds @t212)) % 0.41/0.97 (define @t238 () (and @t214 @t236)) % 0.41/0.97 (define @t239 () (and @t216 @t237)) % 0.41/0.97 (define @t240 () (tptp.append_terminates @t213 @t212 @t211)) % 0.41/0.97 (define @t241 () (tptp.gr @t211)) % 0.41/0.97 (define @t242 () (tptp.gr @t212)) % 0.41/0.97 (define @t243 () (tptp.gr @t213)) % 0.41/0.97 (define @t244 () (and @t243 @t242)) % 0.41/0.97 (define @t245 () (@var "Xl4" $$unsorted)) % 0.41/0.97 (define @t246 () (@list @t147 @t213 @t212)) % 0.41/0.97 (define @t247 () (tptp.list_succeeds @t215)) % 0.41/0.97 (define @t248 () (tptp.gr @t215)) % 0.41/0.97 (define @t249 () (@var "Xm" $$unsorted)) % 0.41/0.97 (define @t250 () (tptp.lh @t227)) % 0.41/0.97 (define @t251 () (tptp.cons @t147 @t212)) % 0.41/0.97 (define @t252 () (tptp.lh @t213)) % 0.41/0.97 (define @t253 () (tptp.lh @t212)) % 0.41/0.97 (define @t254 () (|tptp.'@+'| @t252 @t253)) % 0.41/0.97 (define @t255 () (tptp.lh @t215)) % 0.41/0.97 (define @t256 () (tptp.lh @t211)) % 0.41/0.97 (define @t257 () (@var "Xi" $$unsorted)) % 0.41/0.97 (define @t258 () (tptp.cons @t147 @t257)) % 0.41/0.97 (define @t259 () (@var "Xk" $$unsorted)) % 0.41/0.97 (define @t260 () (@var "Xj" $$unsorted)) % 0.41/0.97 (define @t261 () (tptp.sub @t257 @t260)) % 0.41/0.97 (define @t262 () (@list @t147 @t257 @t260)) % 0.41/0.97 (define @t263 () (tptp.append_succeeds @t213 @t251 @t211)) % 0.41/0.97 (define @t264 () (tptp.member_succeeds @t147 @t211)) % 0.41/0.97 (define @t265 () (@list @t147 @t213 @t212 @t211)) % 0.41/0.97 (define @t266 () (tptp.member_succeeds @t147 @t215)) % 0.41/0.97 (define @t267 () (or @t225 @t224)) % 0.41/0.97 (define @t268 () (forall @t149 (=> @t264 @t267))) % 0.41/0.97 (define @t269 () (=> @t214 @t268)) % 0.41/0.97 (define @t270 () (forall @t217 @t269)) % 0.41/0.97 (define @t271 () (and (= @t213 tptp.nil) (= @t211 @t212))) % 0.41/0.97 (define @t272 () (tptp.member_succeeds @t147 @t3)) % 0.41/0.97 (define @t273 () (or @t272 @t224)) % 0.41/0.97 (define @t274 () (tptp.member_succeeds @t147 @t7)) % 0.41/0.97 (define @t275 () (forall @t149 (=> @t274 @t273))) % 0.41/0.97 (define @t276 () (tptp.append_succeeds @t3 @t212 @t7)) % 0.41/0.97 (define @t277 () (and (= @t213 @t5) (= @t211 @t85) @t276 @t275)) % 0.41/0.97 (define @t278 () (exists @t88 @t277)) % 0.41/0.97 (define @t279 () (or @t278 @t271)) % 0.41/0.97 (define @t280 () (=> @t279 @t268)) % 0.41/0.97 (define @t281 () (forall @t217 @t280)) % 0.41/0.97 (define @t282 () (=> @t281 @t270)) % 0.41/0.97 (define @t283 () (and @t214 @t264)) % 0.41/0.97 (define @t284 () (forall @t265 (=> @t283 @t267))) % 0.41/0.97 (define @t285 () (not @t284)) % 0.41/0.97 (define @t286 () (not @t120)) % 0.41/0.97 (define @t287 () (forall @t114 (not @t113))) % 0.41/0.97 (define @t288 () (not @t287)) % 0.41/0.97 (define @t289 () (@var "BOUND_VARIABLE_9831" $$unsorted)) % 0.41/0.97 (define @t290 () (tptp.member_succeeds @t289 @t212)) % 0.41/0.97 (define @t291 () (tptp.member_succeeds @t289 @t213)) % 0.41/0.97 (define @t292 () (not (tptp.member_succeeds @t289 @t211))) % 0.41/0.97 (define @t293 () (= @t212 @t211)) % 0.41/0.97 (define @t294 () (= tptp.nil @t213)) % 0.41/0.97 (define @t295 () (or (not @t294) (not @t293))) % 0.41/0.97 (define @t296 () (@var "BOUND_VARIABLE_9811" $$unsorted)) % 0.41/0.97 (define @t297 () (@var "BOUND_VARIABLE_9813" $$unsorted)) % 0.41/0.97 (define @t298 () (not (forall @t149 (or (not (tptp.member_succeeds @t147 @t297)) (tptp.member_succeeds @t147 @t296) @t224)))) % 0.41/0.97 (define @t299 () (not (tptp.append_succeeds @t296 @t212 @t297))) % 0.41/0.97 (define @t300 () (@var "BOUND_VARIABLE_9809" $$unsorted)) % 0.41/0.97 (define @t301 () (tptp.cons @t300 @t297)) % 0.41/0.97 (define @t302 () (tptp.cons @t300 @t296)) % 0.41/0.97 (define @t303 () (@list @t213 @t212 @t211 @t300 @t296 @t297 @t289)) % 0.41/0.97 (define @t304 () (forall @t303 (or (and (or (not (= @t213 @t302)) (not (= @t211 @t301)) @t299 @t298) @t295) @t292 @t291 @t290))) % 0.41/0.97 (define @t305 () (@quantifiers_skolemize @t304 6)) % 0.41/0.97 (define @t306 () (@quantifiers_skolemize @t304 0)) % 0.41/0.97 (define @t307 () (forall @t109 (not (= @t306 (tptp.cons @t305 @t3))))) % 0.41/0.97 (define @t308 () (not @t307)) % 0.41/0.97 (define @t309 () (not (tptp.member_succeeds @t305 @t4))) % 0.41/0.97 (define @t310 () (not (= @t306 @t96))) % 0.41/0.97 (define @t311 () (or @t310 @t309)) % 0.41/0.97 (define @t312 () (forall @t114 @t311)) % 0.41/0.97 (define @t313 () (not @t312)) % 0.41/0.97 (define @t314 () (or @t313 @t308)) % 0.41/0.97 (define @t315 () (tptp.member_succeeds @t305 @t306)) % 0.41/0.97 (define @t316 () (= @t315 @t314)) % 0.41/0.97 (define @t317 () (forall @t99 (= @t117 (or (not (forall @t114 (or @t121 (not @t111)))) @t286)))) % 0.41/0.97 (define @t318 () (forall @t114 (or (not (= @t96 @t306)) @t309))) % 0.41/0.97 (define @t319 () (not @t318)) % 0.41/0.97 (define @t320 () (or @t319 @t308)) % 0.41/0.97 (define @t321 () (= @t315 @t320)) % 0.41/0.97 (define @t322 () (@list false)) % 0.41/0.97 (define @t323 () (not @t264)) % 0.41/0.97 (define @t324 () (not @t214)) % 0.41/0.97 (define @t325 () (or @t324 @t323 @t225 @t224)) % 0.41/0.97 (define @t326 () (forall @t265 @t325)) % 0.41/0.97 (define @t327 () (@var "BOUND_VARIABLE_11685" $$unsorted)) % 0.41/0.97 (define @t328 () (@var "BOUND_VARIABLE_11687" $$unsorted)) % 0.41/0.97 (define @t329 () (@var "BOUND_VARIABLE_11684" $$unsorted)) % 0.41/0.97 (define @t330 () (@var "BOUND_VARIABLE_11686" $$unsorted)) % 0.41/0.97 (define @t331 () (@list @t329 @t327 @t330 @t328)) % 0.41/0.97 (define @t332 () (@var "BOUND_VARIABLE_9854" $$unsorted)) % 0.41/0.97 (define @t333 () (tptp.member_succeeds @t332 @t212)) % 0.41/0.97 (define @t334 () (tptp.member_succeeds @t332 @t213)) % 0.41/0.97 (define @t335 () (not (tptp.member_succeeds @t332 @t211))) % 0.41/0.97 (define @t336 () (or @t324 @t335 @t334 @t333)) % 0.41/0.97 (define @t337 () (@list @t213 @t212 @t211 @t332)) % 0.41/0.97 (define @t338 () (forall @t337 @t336)) % 0.41/0.97 (define @t339 () (not @t338)) % 0.41/0.97 (define @t340 () (@list true)) % 0.41/0.97 (define @t341 () (or @t335 @t334 @t333)) % 0.41/0.97 (define @t342 () (or @t324 @t341)) % 0.41/0.97 (define @t343 () (forall @t337 @t342)) % 0.41/0.97 (define @t344 () (@list @t332)) % 0.41/0.97 (define @t345 () (forall @t344 @t342)) % 0.41/0.97 (define @t346 () (forall @t344 @t341)) % 0.41/0.97 (define @t347 () (@list @t147)) % 0.41/0.97 (define @t348 () (or @t324 @t346)) % 0.41/0.97 (define @t349 () (or @t323 @t225 @t224)) % 0.41/0.97 (define @t350 () (forall @t149 @t349)) % 0.41/0.97 (define @t351 () (not (= @t301 @t211))) % 0.41/0.97 (define @t352 () (not (= @t302 @t213))) % 0.41/0.97 (define @t353 () (or @t352 @t351 @t299 @t298)) % 0.41/0.97 (define @t354 () (and @t353 @t295)) % 0.41/0.97 (define @t355 () (or @t354 @t292 @t291 @t290)) % 0.41/0.97 (define @t356 () (or @t292 @t291 @t290)) % 0.41/0.97 (define @t357 () (or @t354 @t356)) % 0.41/0.97 (define @t358 () (forall @t303 @t357)) % 0.41/0.97 (define @t359 () (forall (@list @t300 @t296 @t297 @t289) @t357)) % 0.41/0.97 (define @t360 () (forall (@list @t289) @t356)) % 0.41/0.97 (define @t361 () (@list @t300 @t296 @t297)) % 0.41/0.97 (define @t362 () (forall @t361 @t295)) % 0.41/0.97 (define @t363 () (forall @t361 @t353)) % 0.41/0.97 (define @t364 () (and @t363 @t362)) % 0.41/0.97 (define @t365 () (forall @t361 @t354)) % 0.41/0.97 (define @t366 () (or @t365 @t360)) % 0.41/0.97 (define @t367 () (not @t274)) % 0.41/0.97 (define @t368 () (or @t367 @t272 @t224)) % 0.41/0.97 (define @t369 () (forall @t149 @t368)) % 0.41/0.97 (define @t370 () (not @t369)) % 0.41/0.97 (define @t371 () (not @t276)) % 0.41/0.97 (define @t372 () (= @t85 @t211)) % 0.41/0.97 (define @t373 () (not @t372)) % 0.41/0.97 (define @t374 () (= @t5 @t213)) % 0.41/0.97 (define @t375 () (not @t374)) % 0.41/0.97 (define @t376 () (or @t375 @t373 @t371 @t370)) % 0.41/0.97 (define @t377 () (forall @t88 @t376)) % 0.41/0.97 (define @t378 () (and @t294 @t293)) % 0.41/0.97 (define @t379 () (not @t378)) % 0.41/0.97 (define @t380 () (not @t377)) % 0.41/0.97 (define @t381 () (or @t380 @t378)) % 0.41/0.97 (define @t382 () (and @t374 @t372 @t276 @t369)) % 0.41/0.97 (define @t383 () (forall @t88 (not @t382))) % 0.41/0.97 (define @t384 () (not @t383)) % 0.41/0.97 (define @t385 () (not @t304)) % 0.41/0.97 (define @t386 () (@quantifiers_skolemize @t304 1)) % 0.41/0.97 (define @t387 () (tptp.member_succeeds @t305 @t386)) % 0.41/0.97 (define @t388 () (@quantifiers_skolemize @t304 2)) % 0.41/0.97 (define @t389 () (tptp.member_succeeds @t305 @t388)) % 0.41/0.97 (define @t390 () (not @t389)) % 0.41/0.97 (define @t391 () (= @t386 @t388)) % 0.41/0.97 (define @t392 () (not @t391)) % 0.41/0.97 (define @t393 () (or (not (= tptp.nil @t306)) @t392)) % 0.41/0.97 (define @t394 () (@quantifiers_skolemize @t304 4)) % 0.41/0.97 (define @t395 () (@quantifiers_skolemize @t304 5)) % 0.41/0.97 (define @t396 () (forall @t149 (or (not (tptp.member_succeeds @t147 @t395)) (tptp.member_succeeds @t147 @t394) (tptp.member_succeeds @t147 @t386)))) % 0.41/0.97 (define @t397 () (not @t396)) % 0.41/0.97 (define @t398 () (@quantifiers_skolemize @t304 3)) % 0.41/0.97 (define @t399 () (tptp.cons @t398 @t395)) % 0.41/0.97 (define @t400 () (= @t388 @t399)) % 0.41/0.97 (define @t401 () (not @t400)) % 0.41/0.97 (define @t402 () (tptp.cons @t398 @t394)) % 0.41/0.97 (define @t403 () (= @t306 @t402)) % 0.41/0.97 (define @t404 () (not @t403)) % 0.41/0.97 (define @t405 () (or @t404 @t401 (not (tptp.append_succeeds @t394 @t386 @t395)) @t397)) % 0.41/0.97 (define @t406 () (and @t405 @t393)) % 0.41/0.97 (define @t407 () (or @t406 @t390 @t315 @t387)) % 0.41/0.97 (define @t408 () (@list @t407)) % 0.41/0.97 (define @t409 () (not @t320)) % 0.41/0.97 (define @t410 () (@list true false)) % 0.41/0.97 (define @t411 () (@list @t320)) % 0.41/0.97 (define @t412 () (not @t387)) % 0.41/0.97 (define @t413 () (and @t412 @t391 @t389)) % 0.41/0.97 (define @t414 () (@list false true)) % 0.41/0.97 (define @t415 () (@list @t405)) % 0.41/0.97 (define @t416 () (tptp.member_succeeds @t305 @t394)) % 0.41/0.97 (define @t417 () (tptp.member_succeeds @t305 @t395)) % 0.41/0.97 (define @t418 () (not @t417)) % 0.41/0.97 (define @t419 () (or @t418 @t416 @t387)) % 0.41/0.97 (define @t420 () (not @t232)) % 0.41/0.97 (define @t421 () (or @t420 @t190 @t230)) % 0.41/0.97 (define @t422 () (forall (@list @t147 @t152 @t219) @t421)) % 0.41/0.97 (define @t423 () (tptp.member_succeeds @t305 @t399)) % 0.41/0.97 (define @t424 () (not @t423)) % 0.41/0.97 (define @t425 () (or @t424 (= @t305 @t398) @t417)) % 0.41/0.97 (define @t426 () (= @t398 @t305)) % 0.41/0.97 (define @t427 () (or @t424 @t426 @t417)) % 0.41/0.97 (define @t428 () (= @t306 (tptp.cons @t305 @t394))) % 0.41/0.97 (define @t429 () (and @t403 @t426)) % 0.41/0.97 (define @t430 () (and @t400 @t389)) % 0.41/0.97 (define @t431 () (@list false false)) % 0.41/0.97 (define @t432 () (not @t416)) % 0.41/0.97 (define @t433 () (or @t404 @t432)) % 0.41/0.97 (define @t434 () (not @t433)) % 0.41/0.97 (define @t435 () (not (= @t402 @t306))) % 0.41/0.97 (define @t436 () (or @t435 @t432)) % 0.41/0.97 (assume @p1 (not (= |tptp.'0'| tptp.nil))) % 0.41/0.97 (assume @p2 (forall (@list @t1) (not (= |tptp.'0'| @t2)))) % 0.41/0.97 (assume @p3 (forall @t6 (not (= |tptp.'0'| @t5)))) % 0.41/0.97 (assume @p4 (forall (@list @t7) (not (= tptp.nil (tptp.s @t7))))) % 0.41/0.97 (assume @p5 (forall (@list @t9 @t8) (not (= tptp.nil (tptp.cons @t9 @t8))))) % 0.41/0.97 (assume @p6 (forall (@list @t11 @t10) (=> (= (tptp.s @t11) (tptp.s @t10)) (= @t11 @t10)))) % 0.41/0.97 (assume @p7 (forall (@list @t14 @t13 @t12) (not (= (tptp.s @t14) (tptp.cons @t13 @t12))))) % 0.41/0.97 (assume @p8 (forall (@list @t18 @t16 @t17 @t15) (=> (= (tptp.cons @t18 @t16) (tptp.cons @t17 @t15)) (= @t16 @t15)))) % 0.41/0.97 (assume @p9 (forall (@list @t20 @t22 @t19 @t21) (=> (= (tptp.cons @t20 @t22) (tptp.cons @t19 @t21)) (= @t20 @t19)))) % 0.41/0.97 (assume @p10 (tptp.gr |tptp.'0'|)) % 0.41/0.97 (assume @p11 (tptp.gr tptp.nil)) % 0.41/0.97 (assume @p12 (forall (@list @t23) (= (tptp.gr @t23) (tptp.gr (tptp.s @t23))))) % 0.41/0.97 (assume @p13 (forall (@list @t25 @t24) (= (and (tptp.gr @t25) (tptp.gr @t24)) (tptp.gr (tptp.cons @t25 @t24))))) % 0.41/0.97 (assume @p14 (forall @t31 (not (and @t30 @t29)))) % 0.41/0.97 (assume @p15 (forall @t31 (=> (tptp.delete_terminates @t28 @t27 @t26) (or @t30 @t29)))) % 0.41/0.97 (assume @p16 (forall @t36 (not (and @t35 @t34)))) % 0.41/0.97 (assume @p17 (forall @t36 (=> (tptp.length_terminates @t33 @t32) (or @t35 @t34)))) % 0.41/0.97 (assume @p18 (forall @t42 (not (and @t41 @t40)))) % 0.41/0.97 (assume @p19 (forall @t42 (=> (tptp.append_terminates @t39 @t38 @t37) (or @t41 @t40)))) % 0.41/0.97 (assume @p20 (forall @t47 (not (and @t46 @t45)))) % 0.41/0.97 (assume @p21 (forall @t47 (=> (tptp.member_terminates @t44 @t43) (or @t46 @t45)))) % 0.41/0.97 (assume @p22 (forall @t51 (not (and @t50 @t49)))) % 0.41/0.97 (assume @p23 (forall @t51 (=> (tptp.list_terminates @t48) (or @t50 @t49)))) % 0.41/0.97 (assume @p24 (forall @t55 (not (and @t54 @t53)))) % 0.41/0.97 (assume @p25 (forall @t55 (=> (tptp.nat_list_terminates @t52) (or @t54 @t53)))) % 0.41/0.97 (assume @p26 (forall @t61 (not (and @t60 @t59)))) % 0.41/0.97 (assume @p27 (forall @t61 (=> (tptp.times_terminates @t58 @t57 @t56) (or @t60 @t59)))) % 0.41/0.97 (assume @p28 (forall @t67 (not (and @t66 @t65)))) % 0.41/0.97 (assume @p29 (forall @t67 (=> (tptp.plus_terminates @t64 @t63 @t62) (or @t66 @t65)))) % 0.41/0.97 (assume @p30 (forall @t72 (not (and @t71 @t70)))) % 0.41/0.97 (assume @p31 (forall @t72 (=> (|tptp.'@=<_terminates'| @t69 @t68) (or @t71 @t70)))) % 0.41/0.97 (assume @p32 (forall @t77 (not (and @t76 @t75)))) % 0.41/0.97 (assume @p33 (forall @t77 (=> (|tptp.'@<_terminates'| @t74 @t73) (or @t76 @t75)))) % 0.41/0.97 (assume @p34 (forall @t81 (not (and @t80 @t79)))) % 0.41/0.97 (assume @p35 (forall @t81 (=> (tptp.nat_terminates @t78) (or @t80 @t79)))) % 0.41/0.97 (assume @p36 (forall @t89 (= (tptp.delete_succeeds @t82 @t83 @t1) (or (exists @t88 (and @t87 @t86 (tptp.delete_succeeds @t82 @t3 @t7))) @t84)))) % 0.41/0.97 (assume @p37 (forall @t89 (= (tptp.delete_fails @t82 @t83 @t1) (and (forall @t88 (or @t91 @t90 (tptp.delete_fails @t82 @t3 @t7))) (not @t84))))) % 0.41/0.97 (assume @p38 (forall @t89 (= (tptp.delete_terminates @t82 @t83 @t1) (and (forall @t88 (and true (or @t91 (and true (or @t90 (tptp.delete_terminates @t82 @t3 @t7)))))) true)))) % 0.41/0.97 (assume @p39 (forall @t99 (= (tptp.length_succeeds @t82 @t83) (or (exists @t98 (and @t97 @t95 (tptp.length_succeeds @t4 @t3))) (and @t93 @t92))))) % 0.41/0.97 (assume @p40 (forall @t99 (= (tptp.length_fails @t82 @t83) (and (forall @t98 (or @t102 @t101 (tptp.length_fails @t4 @t3))) (or @t100 (not @t92)))))) % 0.41/0.97 (assume @p41 (forall @t99 (= (tptp.length_terminates @t82 @t83) (and (forall @t98 (and true (or @t102 (and true (or @t101 (tptp.length_terminates @t4 @t3)))))) true @t103)))) % 0.41/0.97 (assume @p42 (forall @t89 (= (tptp.append_succeeds @t82 @t83 @t1) (or (exists @t88 (and @t105 @t86 (tptp.append_succeeds @t3 @t83 @t7))) (and @t93 @t104))))) % 0.41/0.97 (assume @p43 (forall @t89 (= (tptp.append_fails @t82 @t83 @t1) (and (forall @t88 (or @t107 @t90 (tptp.append_fails @t3 @t83 @t7))) (or @t100 @t106))))) % 0.41/0.97 (assume @p44 (forall @t89 (= (tptp.append_terminates @t82 @t83 @t1) (and (forall @t88 (and true (or @t107 (and true (or @t90 (tptp.append_terminates @t3 @t83 @t7)))))) true @t103)))) % 0.41/0.97 (assume @p45 @t119) % 0.41/0.97 (assume @p46 (forall @t99 (= (tptp.member_fails @t82 @t83) (and (forall @t114 (or @t121 (tptp.member_fails @t82 @t4))) @t120)))) % 0.41/0.97 (assume @p47 (forall @t99 (= (tptp.member_terminates @t82 @t83) (and (forall @t114 (and true (or @t121 (tptp.member_terminates @t82 @t4)))) (forall @t109 true))))) % 0.41/0.97 (assume @p48 (forall @t124 (= (tptp.list_succeeds @t82) (or (exists @t123 (and @t122 (tptp.list_succeeds @t1))) @t93)))) % 0.41/0.97 (assume @p49 (forall @t124 (= (tptp.list_fails @t82) (and (forall @t123 (or @t125 (tptp.list_fails @t1))) @t100)))) % 0.41/0.97 (assume @p50 (forall @t124 (= (tptp.list_terminates @t82) (and (forall @t123 (and true (or @t125 (tptp.list_terminates @t1)))) true)))) % 0.41/0.97 (assume @p51 (forall @t124 (= (tptp.nat_list_succeeds @t82) (or (exists @t123 (and @t122 @t126 (tptp.nat_list_succeeds @t1))) @t93)))) % 0.41/0.97 (assume @p52 (forall @t124 (= (tptp.nat_list_fails @t82) (and (forall @t123 (or @t125 @t127 (tptp.nat_list_fails @t1))) @t100)))) % 0.41/0.97 (assume @p53 (forall @t124 (= (tptp.nat_list_terminates @t82) (and (forall @t123 (and true (or @t125 (and @t128 (or @t127 (tptp.nat_list_terminates @t1)))))) true)))) % 0.41/0.97 (assume @p54 (forall @t89 (= (tptp.times_succeeds @t82 @t83 @t1) (or (exists @t6 (and @t132 (tptp.times_succeeds @t4 @t83 @t3) (tptp.plus_succeeds @t83 @t3 @t1))) (and @t130 @t129))))) % 0.41/0.97 (assume @p55 (forall @t89 (= (tptp.times_fails @t82 @t83 @t1) (and (forall @t6 (or @t135 @t134 (tptp.plus_fails @t83 @t3 @t1))) (or @t133 (not @t129)))))) % 0.41/0.97 (assume @p56 (forall @t89 (= (tptp.times_terminates @t82 @t83 @t1) (and (forall @t6 (and true (or @t135 (and (tptp.times_terminates @t4 @t83 @t3) (or @t134 (tptp.plus_terminates @t83 @t3 @t1)))))) true @t136)))) % 0.41/0.97 (assume @p57 (forall @t89 (= (tptp.plus_succeeds @t82 @t83 @t1) (or (exists @t6 (and @t132 @t137 (tptp.plus_succeeds @t4 @t83 @t3))) (and @t130 @t104))))) % 0.41/0.97 (assume @p58 (forall @t89 (= (tptp.plus_fails @t82 @t83 @t1) (and (forall @t6 (or @t135 @t138 (tptp.plus_fails @t4 @t83 @t3))) (or @t133 @t106))))) % 0.41/0.97 (assume @p59 (forall @t89 (= (tptp.plus_terminates @t82 @t83 @t1) (and (forall @t6 (and true (or @t135 (and true (or @t138 (tptp.plus_terminates @t4 @t83 @t3)))))) true @t136)))) % 0.41/0.97 (assume @p60 (forall @t99 (= (|tptp.'@=<_succeeds'| @t82 @t83) (or (exists @t114 (and @t140 @t139 (|tptp.'@=<_succeeds'| @t1 @t4))) @t130)))) % 0.41/0.97 (assume @p61 (forall @t99 (= (|tptp.'@=<_fails'| @t82 @t83) (and (forall @t114 (or @t142 @t141 (|tptp.'@=<_fails'| @t1 @t4))) @t133)))) % 0.41/0.97 (assume @p62 (forall @t99 (= (|tptp.'@=<_terminates'| @t82 @t83) (and (forall @t114 (and true (or @t142 (and true (or @t141 (|tptp.'@=<_terminates'| @t1 @t4)))))) true)))) % 0.41/0.97 (assume @p63 (forall @t99 (= (|tptp.'@<_succeeds'| @t82 @t83) (or (exists @t114 (and @t140 @t139 (|tptp.'@<_succeeds'| @t1 @t4))) (exists @t109 (and @t130 @t95)))))) % 0.41/0.97 (assume @p64 (forall @t99 (= (|tptp.'@<_fails'| @t82 @t83) (and (forall @t114 (or @t142 @t141 (|tptp.'@<_fails'| @t1 @t4))) (forall @t109 (or @t133 @t101)))))) % 0.41/0.97 (assume @p65 (forall @t99 (= (|tptp.'@<_terminates'| @t82 @t83) (and (forall @t114 (and true (or @t142 (and true (or @t141 (|tptp.'@<_terminates'| @t1 @t4)))))) (forall @t109 (and true @t136)))))) % 0.41/0.97 (assume @p66 (forall @t124 (= @t145 (or (exists @t144 (and @t143 @t126)) @t130)))) % 0.41/0.97 (assume @p67 (forall @t124 (= (tptp.nat_fails @t82) (and (forall @t144 (or @t146 @t127)) @t133)))) % 0.41/0.97 (assume @p68 (forall @t124 (= (tptp.nat_terminates @t82) (and (forall @t144 (and true (or @t146 @t128))) true)))) % 0.41/0.97 (assume @p69 (forall @t149 (=> @t148 (tptp.nat_terminates @t147)))) % 0.41/0.97 (assume @p70 (forall @t149 (=> @t148 @t150))) % 0.41/0.97 (assume @p71 (forall @t154 (=> @t148 @t153))) % 0.41/0.97 (assume @p72 (forall @t154 (=> @t155 @t153))) % 0.41/0.97 (assume @p73 (forall @t154 (=> @t156 @t148))) % 0.41/0.97 (assume @p74 (forall @t154 (=> (and @t156 @t157) @t155))) % 0.41/0.97 (assume @p75 (forall @t154 (=> (and @t156 @t155) @t157))) % 0.41/0.97 (assume @p76 (forall @t154 (=> @t156 @t153))) % 0.41/0.97 (assume @p77 (forall @t154 (=> @t156 @t150))) % 0.41/0.97 (assume @p78 (forall @t154 (=> (and @t156 @t159) @t158))) % 0.41/0.97 (assume @p79 (forall @t154 (=> (and @t156 @t158) @t159))) % 0.41/0.97 (assume @p80 (forall @t161 (=> @t148 (exists @t160 @t156)))) % 0.41/0.97 (assume @p81 (forall @t165 (=> (and (tptp.plus_succeeds @t147 @t152 @t163) (tptp.plus_succeeds @t147 @t152 @t162)) @t164))) % 0.41/0.97 (assume @p82 (forall @t166 (= (|tptp.'@+'| |tptp.'0'| @t152) @t152))) % 0.41/0.97 (assume @p83 (forall @t161 (=> @t148 (= @t169 (tptp.s @t167))))) % 0.41/0.97 (assume @p84 (forall @t161 (=> @t170 (tptp.nat_succeeds @t167)))) % 0.41/0.97 (assume @p85 (forall @t154 (=> @t172 (= (|tptp.'@+'| @t167 @t151) (|tptp.'@+'| @t147 @t171))))) % 0.41/0.97 (assume @p86 (forall @t149 (=> @t148 (= (|tptp.'@+'| @t147 |tptp.'0'|) @t147)))) % 0.41/0.97 (assume @p87 (forall @t161 (=> @t170 (= @t174 @t169)))) % 0.41/0.97 (assume @p88 (forall @t161 (=> @t170 (= @t167 @t175)))) % 0.41/0.97 (assume @p89 (forall @t154 (=> (and @t148 (= @t167 @t176)) (= @t152 @t151)))) % 0.41/0.97 (assume @p90 (forall @t154 (=> @t177 @t148))) % 0.41/0.97 (assume @p91 (forall @t154 (=> (and @t177 @t157) @t155))) % 0.41/0.97 (assume @p92 (forall @t154 (=> @t177 @t150))) % 0.41/0.97 (assume @p93 (forall @t154 (=> (and @t177 @t159) @t158))) % 0.41/0.97 (assume @p94 (forall @t154 (=> @t170 (tptp.times_terminates @t147 @t152 @t151)))) % 0.41/0.97 (assume @p95 (forall @t161 (=> @t170 (exists @t160 @t177)))) % 0.41/0.97 (assume @p96 (forall @t165 (=> (and (tptp.times_succeeds @t147 @t152 @t163) (tptp.times_succeeds @t147 @t152 @t162)) @t164))) % 0.41/0.97 (assume @p97 (forall @t166 (=> @t157 (= (|tptp.'@*'| |tptp.'0'| @t152) |tptp.'0'|)))) % 0.41/0.97 (assume @p98 (forall @t161 (=> @t170 (= @t179 (|tptp.'@+'| @t152 @t178))))) % 0.41/0.97 (assume @p99 (forall @t161 (=> @t170 (tptp.nat_succeeds @t178)))) % 0.41/0.97 (assume @p100 (forall @t154 (=> @t172 (= (|tptp.'@*'| @t167 @t151) (|tptp.'@+'| @t181 @t180))))) % 0.41/0.97 (assume @p101 (forall @t154 (=> @t172 (= (|tptp.'@*'| @t178 @t151) (|tptp.'@*'| @t147 @t180))))) % 0.41/0.97 (assume @p102 (forall @t149 (=> @t148 (= (|tptp.'@*'| @t147 |tptp.'0'|) |tptp.'0'|)))) % 0.41/0.97 (assume @p103 (forall (@list @t152 @t147) (=> (and @t157 @t148) (= (|tptp.'@+'| @t182 @t152) (|tptp.'@*'| @t152 @t168))))) % 0.41/0.97 (assume @p104 (forall @t161 (=> @t170 (= @t178 @t182)))) % 0.41/0.97 (assume @p105 (forall @t149 (=> @t148 (= (|tptp.'@*'| @t183 @t147) @t147)))) % 0.41/0.97 (assume @p106 (forall @t149 (=> @t148 (= (|tptp.'@*'| @t147 @t183) @t147)))) % 0.41/0.97 (assume @p107 (forall @t154 (=> @t172 (= (|tptp.'@*'| @t151 @t167) (|tptp.'@+'| (|tptp.'@*'| @t151 @t147) (|tptp.'@*'| @t151 @t152)))))) % 0.41/0.97 (assume @p108 (forall @t161 (=> @t148 @t184))) % 0.41/0.97 (assume @p109 (forall @t161 (=> @t157 @t184))) % 0.41/0.97 (assume @p110 (forall @t161 (=> @t185 @t148))) % 0.41/0.97 (assume @p111 (forall @t161 (=> @t185 (exists @t160 (= @t152 @t186))))) % 0.41/0.97 (assume @p112 (forall @t154 (=> (and @t185 (|tptp.'@<_succeeds'| @t152 @t186)) @t187))) % 0.41/0.97 (assume @p113 (forall @t161 (=> @t185 @t188))) % 0.41/0.97 (assume @p114 (forall @t154 (=> (and @t185 @t189) @t187))) % 0.41/0.97 (assume @p115 (forall @t149 (=> @t148 (|tptp.'@<_fails'| @t147 @t147)))) % 0.41/0.97 (assume @p116 (forall @t149 (=> @t148 (not (|tptp.'@<_succeeds'| @t147 @t147))))) % 0.41/0.97 (assume @p117 (forall @t149 (=> @t148 (|tptp.'@<_succeeds'| @t147 @t168)))) % 0.41/0.97 (assume @p118 (forall @t161 (=> (and @t157 @t188) @t191))) % 0.41/0.97 (assume @p119 (forall @t161 (=> @t170 (or @t185 @t190 (|tptp.'@<_succeeds'| @t152 @t147))))) % 0.41/0.97 (assume @p120 (forall @t149 (=> (and @t148 @t192) (|tptp.'@<_succeeds'| |tptp.'0'| @t147)))) % 0.41/0.97 (assume @p121 (forall @t161 (=> @t148 (|tptp.'@=<_terminates'| @t147 @t152)))) % 0.41/0.97 (assume @p122 (forall @t161 (=> @t193 @t148))) % 0.41/0.97 (assume @p123 (forall @t161 (=> @t193 (exists @t160 (tptp.plus_succeeds @t147 @t151 @t152))))) % 0.41/0.97 (assume @p124 (forall @t161 (=> @t193 (exists @t160 (= @t176 @t152))))) % 0.41/0.97 (assume @p125 (forall @t161 (=> @t185 (exists @t160 (tptp.plus_succeeds @t147 @t186 @t152))))) % 0.41/0.97 (assume @p126 (forall @t161 (=> @t185 (exists @t160 (= (|tptp.'@+'| @t147 @t186) @t152))))) % 0.41/0.97 (assume @p127 (forall @t161 (=> @t185 @t193))) % 0.41/0.97 (assume @p128 (forall @t149 (=> @t148 (|tptp.'@=<_succeeds'| @t147 @t147)))) % 0.41/0.97 (assume @p129 (forall @t161 (=> @t170 (or @t193 @t194)))) % 0.41/0.97 (assume @p130 (forall @t161 (=> @t170 (or @t185 @t194)))) % 0.41/0.97 (assume @p131 (forall @t161 (=> (and @t148 @t157 (|tptp.'@=<_fails'| @t147 @t152)) @t194))) % 0.41/0.97 (assume @p132 (forall @t161 (=> (and @t193 @t157) @t191))) % 0.41/0.97 (assume @p133 (forall @t154 (=> (and @t193 @t189) @t187))) % 0.41/0.97 (assume @p134 (forall @t154 (=> (and @t185 @t195) @t187))) % 0.41/0.97 (assume @p135 (forall @t154 (=> (and @t193 @t195) (|tptp.'@=<_succeeds'| @t147 @t151)))) % 0.41/0.97 (assume @p136 (forall @t161 (=> (and @t193 @t194) @t190))) % 0.41/0.97 (assume @p137 (forall @t149 (=> @t148 (|tptp.'@=<_succeeds'| @t147 @t168)))) % 0.41/0.97 (assume @p138 (forall @t149 (=> @t148 (|tptp.'@=<_fails'| @t168 @t147)))) % 0.41/0.97 (assume @p139 (forall @t154 (=> (and @t148 @t189) @t196))) % 0.41/0.97 (assume @p140 (forall @t161 (=> @t148 (|tptp.'@<_succeeds'| @t147 @t174)))) % 0.41/0.97 (assume @p141 (forall @t154 (=> (and @t185 @t157 @t155) @t197))) % 0.41/0.97 (assume @p142 (forall @t161 (=> (and (|tptp.'@<_succeeds'| |tptp.'0'| @t152) @t148 @t157) (|tptp.'@<_succeeds'| @t147 @t175)))) % 0.41/0.97 (assume @p143 (forall @t154 (=> (and @t148 @t195) @t198))) % 0.41/0.97 (assume @p144 (forall @t154 (=> @t199 (|tptp.'@=<_succeeds'| @t176 @t171)))) % 0.41/0.97 (assume @p145 (forall @t161 (=> @t148 (|tptp.'@=<_succeeds'| @t147 @t167)))) % 0.41/0.97 (assume @p146 (forall @t161 (=> @t170 (|tptp.'@=<_succeeds'| @t152 @t167)))) % 0.41/0.97 (assume @p147 (forall @t154 (=> (and @t148 @t196) @t189))) % 0.41/0.97 (assume @p148 (forall @t154 (=> (and @t148 @t157 @t155 @t197) @t185))) % 0.41/0.97 (assume @p149 (forall @t154 (=> (and @t148 @t198) @t195))) % 0.41/0.97 (assume @p150 (forall @t207 (=> (and @t206 @t205 @t204) (|tptp.'@=<_succeeds'| @t203 @t202)))) % 0.41/0.97 (assume @p151 (forall @t207 (=> (and @t209 @t205 @t204) @t208))) % 0.41/0.97 (assume @p152 (forall @t207 (=> (and @t206 @t210 @t204) @t208))) % 0.41/0.97 (assume @p153 (forall @t207 (=> (and @t209 @t210 @t204) @t208))) % 0.41/0.97 (assume @p154 (forall @t154 (=> (and @t148 @t195 @t155) (|tptp.'@=<_succeeds'| @t178 @t181)))) % 0.41/0.97 (assume @p155 (forall @t154 (=> @t199 (|tptp.'@=<_succeeds'| @t181 @t180)))) % 0.41/0.97 (assume @p156 (forall @t154 (=> (and @t148 @t192 @t189 @t155) (|tptp.'@<_succeeds'| @t178 @t181)))) % 0.41/0.97 (assume @p157 (forall @t154 (=> (and @t148 @t157 @t155 (|tptp.'@=<_succeeds'| @t179 (|tptp.'@*'| @t168 @t151))) @t195))) % 0.41/0.97 (assume @p158 (forall (@list @t82 @t83 @t152) (=> (and @t145 @t126 @t157 (= (|tptp.'@+'| @t82 @t152) (|tptp.'@+'| @t83 @t152))) (= @t82 @t83)))) % 0.41/0.97 (assume @p159 (forall @t217 (=> @t216 (= (= @t215 @t211) @t214)))) % 0.41/0.97 (assume @p160 (forall @t223 (=> @t222 (= (= @t221 @t218) @t220)))) % 0.41/0.97 (assume @p161 (forall @t226 (= (tptp.sub @t213 @t212) 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(step-pop @p584 :rule scope :premises (@p504)) % 0.41/0.97 (step-pop @p585 :rule scope :premises (@p584)) % 0.41/0.97 (step @p505 :rule process_scope :premises (@p585) :args (@t428)) % 0.41/0.97 (step @p508 :rule implies_elim :premises (@p505)) % 0.41/0.97 (step @p509 :rule cnf_and_neg :args (@t429)) % 0.41/0.97 (step @p510 :rule resolution :premises (@p509 @p508) :args (true @t429)) % 0.41/0.97 (step @p511 :rule chain_m_resolution :premises (@p510 @p492 @p486) :args ((not @t426) @t414 (@list @t403 @t428))) % 0.41/0.97 (step @p512 :rule bool-double-not-elim :args (@t400)) % 0.41/0.97 (step @p513 :rule nary_cong :premises (@p440 @p512) :args ((or @t405 (not @t401)))) % 0.41/0.97 (step @p514 :rule cnf_or_neg :args (@t405 1)) % 0.41/0.97 (step @p515 :rule eq_resolve :premises (@p514 @p513)) % 0.41/0.97 (step @p516 :rule reordering :premises (@p515) :args ((or @t400 @t405))) % 0.41/0.97 (step @p517 :rule chain_m_resolution :premises (@p516 @p438) :args (@t400 @t340 @t415)) % 0.41/0.97 (assume-push @p586 @t400) % 0.41/0.97 (assume-push @p587 @t389) % 0.41/0.97 (assume-push @p588 @t389) % 0.41/0.97 (assume-push @p589 @t400) % 0.41/0.97 (step @p407 :rule true_intro :premises (@p394)) % 0.41/0.97 (step @p522 :rule symm :premises (@p586)) % 0.41/0.97 (step @p405 :rule refl :args (@t305)) % 0.41/0.97 (step @p523 :rule cong :premises (@p405 @p522) :args (@t423)) % 0.41/0.97 (step @p524 :rule trans :premises (@p523 @p407)) % 0.41/0.97 (step @p525 :rule true_elim :premises (@p524)) % 0.41/0.97 (step-pop @p590 :rule scope :premises (@p525)) % 0.41/0.97 (step-pop @p591 :rule scope :premises (@p590)) % 0.41/0.97 (step @p526 :rule process_scope :premises (@p591) :args (@t423)) % 0.41/0.97 (step @p529 :rule and_intro :premises (@p394 @p586)) % 0.41/0.97 (step @p530 :rule modus_ponens :premises (@p529 @p526)) % 0.41/0.97 (step-pop @p592 :rule scope :premises (@p530)) % 0.41/0.97 (step-pop @p593 :rule scope :premises (@p592)) % 0.41/0.97 (step @p531 :rule process_scope :premises 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:premises (@p557)) % 0.41/0.97 (step @p559 false :rule chain_m_resolution :premises (@p558 @p546 @p385) :args (false @t410 (@list @t433 @t318))) % 0.41/0.97 ) % 0.41/0.97 % SZS output end Proof % 0.41/0.97 % cvc5 exiting %------------------------------------------------------------------------------