%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX022+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 : n027.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 09:06:59 AM UTC 2026 % Result : Theorem 5.42s 5.61s % Output : Proof 5.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWX022+1 : TPTP v9.2.1. Released v9.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n027.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 22:53:51 EDT 2026 % 0.14/0.35 % CPUTime : % 0.28/0.55 %----Proving TF0_NAR, FOF, or CNF % 5.42/5.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 5.42/5.61 % SZS status Theorem % 5.42/5.61 % SZS output start Proof % 5.42/5.61 ( % 5.42/5.61 (declare-sort $$unsorted 0) % 5.42/5.61 (declare-const tptp.sub (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'**'| (-> $$unsorted $$unsorted $$unsorted)) % 5.42/5.61 (declare-const tptp.nat_terminates (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nat_fails (-> $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@<_terminates'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@<_fails'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@=<_terminates'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@=<_fails'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nat_succeeds (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 5.42/5.61 (declare-const |tptp.'@*'| (-> $$unsorted $$unsorted $$unsorted)) % 5.42/5.61 (declare-const tptp.append_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.times_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.length_succeeds (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.delete_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.gr (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 5.42/5.61 (declare-const |tptp.'0'| $$unsorted) % 5.42/5.61 (declare-const tptp.delete_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.member_terminates (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nil $$unsorted) % 5.42/5.61 (declare-const tptp.list_terminates (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nat_list_fails (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.plus_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.member_succeeds (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.length_fails (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nat_list_succeeds (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.lh (-> $$unsorted $$unsorted)) % 5.42/5.61 (declare-const |tptp.'@=<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.list_fails (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.list_succeeds (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.append_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.times_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const |tptp.'@+'| (-> $$unsorted $$unsorted $$unsorted)) % 5.42/5.61 (declare-const tptp.length_terminates (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.nat_list_terminates (-> $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.append_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.times_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.member_fails (-> $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.plus_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.delete_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (declare-const tptp.plus_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 5.42/5.61 (define @t1 () (@var "Xx3" $$unsorted)) % 5.42/5.61 (define @t2 () (tptp.s @t1)) % 5.42/5.61 (define @t3 () (@var "Xx5" $$unsorted)) % 5.42/5.61 (define @t4 () (@var "Xx4" $$unsorted)) % 5.42/5.61 (define @t5 () (tptp.cons @t4 @t3)) % 5.42/5.61 (define @t6 () (@list @t4 @t3)) % 5.42/5.61 (define @t7 () (@var "Xx6" $$unsorted)) % 5.42/5.61 (define @t8 () (@var "Xx8" $$unsorted)) % 5.42/5.61 (define @t9 () (@var "Xx7" $$unsorted)) % 5.42/5.61 (define @t10 () (@var "Xx10" $$unsorted)) % 5.42/5.61 (define @t11 () (@var "Xx9" $$unsorted)) % 5.42/5.61 (define @t12 () (@var "Xx13" $$unsorted)) % 5.42/5.61 (define @t13 () (@var "Xx12" $$unsorted)) % 5.42/5.61 (define @t14 () (@var "Xx11" $$unsorted)) % 5.42/5.61 (define @t15 () (@var "Xx17" $$unsorted)) % 5.42/5.61 (define @t16 () (@var "Xx15" $$unsorted)) % 5.42/5.61 (define @t17 () (@var "Xx16" $$unsorted)) % 5.42/5.61 (define @t18 () (@var "Xx14" $$unsorted)) % 5.42/5.61 (define @t19 () (@var "Xx20" $$unsorted)) % 5.42/5.61 (define @t20 () (@var "Xx18" $$unsorted)) % 5.42/5.61 (define @t21 () (@var "Xx21" $$unsorted)) % 5.42/5.61 (define @t22 () (@var "Xx19" $$unsorted)) % 5.42/5.61 (define @t23 () (@var "Xx22" $$unsorted)) % 5.42/5.61 (define @t24 () (@var "Xx24" $$unsorted)) % 5.42/5.61 (define @t25 () (@var "Xx23" $$unsorted)) % 5.42/5.61 (define @t26 () (@var "Xx27" $$unsorted)) % 5.42/5.61 (define @t27 () (@var "Xx26" $$unsorted)) % 5.42/5.61 (define @t28 () (@var "Xx25" $$unsorted)) % 5.42/5.61 (define @t29 () (tptp.delete_fails @t28 @t27 @t26)) % 5.42/5.61 (define @t30 () (tptp.delete_succeeds @t28 @t27 @t26)) % 5.42/5.61 (define @t31 () (@list @t28 @t27 @t26)) % 5.42/5.61 (define @t32 () (@var "Xx29" $$unsorted)) % 5.42/5.61 (define @t33 () (@var "Xx28" $$unsorted)) % 5.42/5.61 (define @t34 () (tptp.length_fails @t33 @t32)) % 5.42/5.61 (define @t35 () (tptp.length_succeeds @t33 @t32)) % 5.42/5.61 (define @t36 () (@list @t33 @t32)) % 5.42/5.61 (define @t37 () (@var "Xx32" $$unsorted)) % 5.42/5.61 (define @t38 () (@var "Xx31" $$unsorted)) % 5.42/5.61 (define @t39 () (@var "Xx30" $$unsorted)) % 5.42/5.61 (define @t40 () (tptp.append_fails @t39 @t38 @t37)) % 5.42/5.61 (define @t41 () (tptp.append_succeeds @t39 @t38 @t37)) % 5.42/5.61 (define @t42 () (@list @t39 @t38 @t37)) % 5.42/5.61 (define @t43 () (@var "Xx34" $$unsorted)) % 5.42/5.61 (define @t44 () (@var "Xx33" $$unsorted)) % 5.42/5.61 (define @t45 () (tptp.member_fails @t44 @t43)) % 5.42/5.61 (define @t46 () (tptp.member_succeeds @t44 @t43)) % 5.42/5.61 (define @t47 () (@list @t44 @t43)) % 5.42/5.61 (define @t48 () (@var "Xx35" $$unsorted)) % 5.42/5.61 (define @t49 () (tptp.list_fails @t48)) % 5.42/5.61 (define @t50 () (tptp.list_succeeds @t48)) % 5.42/5.61 (define @t51 () (@list @t48)) % 5.42/5.61 (define @t52 () (@var "Xx36" $$unsorted)) % 5.42/5.61 (define @t53 () (tptp.nat_list_fails @t52)) % 5.42/5.61 (define @t54 () (tptp.nat_list_succeeds @t52)) % 5.42/5.61 (define @t55 () (@list @t52)) % 5.42/5.61 (define @t56 () (@var "Xx39" $$unsorted)) % 5.42/5.61 (define @t57 () (@var "Xx38" $$unsorted)) % 5.42/5.61 (define @t58 () (@var "Xx37" $$unsorted)) % 5.42/5.61 (define @t59 () (tptp.times_fails @t58 @t57 @t56)) % 5.42/5.61 (define @t60 () (tptp.times_succeeds @t58 @t57 @t56)) % 5.42/5.61 (define @t61 () (@list @t58 @t57 @t56)) % 5.42/5.61 (define @t62 () (@var "Xx42" $$unsorted)) % 5.42/5.61 (define @t63 () (@var "Xx41" $$unsorted)) % 5.42/5.61 (define @t64 () (@var "Xx40" $$unsorted)) % 5.42/5.61 (define @t65 () (tptp.plus_fails @t64 @t63 @t62)) % 5.42/5.61 (define @t66 () (tptp.plus_succeeds @t64 @t63 @t62)) % 5.42/5.61 (define @t67 () (@list @t64 @t63 @t62)) % 5.42/5.61 (define @t68 () (@var "Xx44" $$unsorted)) % 5.42/5.61 (define @t69 () (@var "Xx43" $$unsorted)) % 5.42/5.61 (define @t70 () (|tptp.'@=<_fails'| @t69 @t68)) % 5.42/5.61 (define @t71 () (|tptp.'@=<_succeeds'| @t69 @t68)) % 5.42/5.61 (define @t72 () (@list @t69 @t68)) % 5.42/5.61 (define @t73 () (@var "Xx46" $$unsorted)) % 5.42/5.61 (define @t74 () (@var "Xx45" $$unsorted)) % 5.42/5.61 (define @t75 () (|tptp.'@<_fails'| @t74 @t73)) % 5.42/5.61 (define @t76 () (|tptp.'@<_succeeds'| @t74 @t73)) % 5.42/5.61 (define @t77 () (@list @t74 @t73)) % 5.42/5.61 (define @t78 () (@var "Xx47" $$unsorted)) % 5.42/5.61 (define @t79 () (tptp.nat_fails @t78)) % 5.42/5.61 (define @t80 () (tptp.nat_succeeds @t78)) % 5.42/5.61 (define @t81 () (@list @t78)) % 5.42/5.61 (define @t82 () (@var "Xx1" $$unsorted)) % 5.42/5.61 (define @t83 () (@var "Xx2" $$unsorted)) % 5.42/5.61 (define @t84 () (= @t83 (tptp.cons @t82 @t1))) % 5.42/5.61 (define @t85 () (= @t1 (tptp.cons @t4 @t7))) % 5.42/5.61 (define @t86 () (= @t83 @t5)) % 5.42/5.61 (define @t87 () (@list @t4 @t3 @t7)) % 5.42/5.61 (define @t88 () (@list @t82 @t83 @t1)) % 5.42/5.61 (define @t89 () (not @t85)) % 5.42/5.61 (define @t90 () (not @t86)) % 5.42/5.61 (define @t91 () (= @t83 |tptp.'0'|)) % 5.42/5.61 (define @t92 () (= @t82 tptp.nil)) % 5.42/5.61 (define @t93 () (tptp.s @t3)) % 5.42/5.61 (define @t94 () (= @t83 @t93)) % 5.42/5.61 (define @t95 () (tptp.cons @t1 @t4)) % 5.42/5.61 (define @t96 () (= @t82 @t95)) % 5.42/5.61 (define @t97 () (@list @t1 @t4 @t3)) % 5.42/5.61 (define @t98 () (@list @t82 @t83)) % 5.42/5.61 (define @t99 () (not @t92)) % 5.42/5.61 (define @t100 () (not @t94)) % 5.42/5.61 (define @t101 () (not @t96)) % 5.42/5.61 (define @t102 () (or @t99 true)) % 5.42/5.61 (define @t103 () (= @t1 @t83)) % 5.42/5.61 (define @t104 () (= @t82 @t5)) % 5.42/5.61 (define @t105 () (not @t103)) % 5.42/5.61 (define @t106 () (not @t104)) % 5.42/5.61 (define @t107 () (= @t83 (tptp.cons @t82 @t3))) % 5.42/5.61 (define @t108 () (@list @t3)) % 5.42/5.61 (define @t109 () (= @t83 @t95)) % 5.42/5.61 (define @t110 () (@list @t1 @t4)) % 5.42/5.61 (define @t111 () (not @t109)) % 5.42/5.61 (define @t112 () (tptp.list_succeeds @t1)) % 5.42/5.61 (define @t113 () (tptp.cons @t83 @t1)) % 5.42/5.61 (define @t114 () (= @t82 @t113)) % 5.42/5.61 (define @t115 () (@list @t83 @t1)) % 5.42/5.61 (define @t116 () (@list @t82)) % 5.42/5.61 (define @t117 () (not @t114)) % 5.42/5.61 (define @t118 () (tptp.nat_succeeds @t83)) % 5.42/5.61 (define @t119 () (tptp.nat_fails @t83)) % 5.42/5.61 (define @t120 () (tptp.nat_terminates @t83)) % 5.42/5.61 (define @t121 () (= @t1 |tptp.'0'|)) % 5.42/5.61 (define @t122 () (= @t82 |tptp.'0'|)) % 5.42/5.61 (define @t123 () (tptp.s @t4)) % 5.42/5.61 (define @t124 () (= @t82 @t123)) % 5.42/5.61 (define @t125 () (not @t122)) % 5.42/5.61 (define @t126 () (tptp.times_fails @t4 @t83 @t3)) % 5.42/5.61 (define @t127 () (not @t124)) % 5.42/5.61 (define @t128 () (or @t125 true)) % 5.42/5.61 (define @t129 () (= @t1 @t93)) % 5.42/5.61 (define @t130 () (not @t129)) % 5.42/5.61 (define @t131 () (= @t83 @t123)) % 5.42/5.61 (define @t132 () (= @t82 @t2)) % 5.42/5.61 (define @t133 () (not @t131)) % 5.42/5.61 (define @t134 () (not @t132)) % 5.42/5.61 (define @t135 () (= @t82 (tptp.s @t83))) % 5.42/5.61 (define @t136 () (@list @t83)) % 5.42/5.61 (define @t137 () (tptp.nat_succeeds @t82)) % 5.42/5.61 (define @t138 () (not @t135)) % 5.42/5.61 (define @t139 () (@var "Xx" $$unsorted)) % 5.42/5.61 (define @t140 () (tptp.nat_succeeds @t139)) % 5.42/5.61 (define @t141 () (@list @t139)) % 5.42/5.61 (define @t142 () (tptp.gr @t139)) % 5.42/5.61 (define @t143 () (@var "Xz" $$unsorted)) % 5.42/5.61 (define @t144 () (@var "Xy" $$unsorted)) % 5.42/5.61 (define @t145 () (tptp.plus_terminates @t139 @t144 @t143)) % 5.42/5.61 (define @t146 () (@list @t139 @t144 @t143)) % 5.42/5.61 (define @t147 () (tptp.nat_succeeds @t143)) % 5.42/5.61 (define @t148 () (tptp.plus_succeeds @t139 @t144 @t143)) % 5.42/5.61 (define @t149 () (tptp.nat_succeeds @t144)) % 5.42/5.61 (define @t150 () (tptp.gr @t143)) % 5.42/5.61 (define @t151 () (tptp.gr @t144)) % 5.42/5.61 (define @t152 () (@list @t143)) % 5.42/5.61 (define @t153 () (@list @t139 @t144)) % 5.42/5.61 (define @t154 () (@var "Xz2" $$unsorted)) % 5.42/5.61 (define @t155 () (@var "Xz1" $$unsorted)) % 5.42/5.61 (define @t156 () (= @t155 @t154)) % 5.42/5.61 (define @t157 () (@list @t139 @t144 @t155 @t154)) % 5.42/5.61 (define @t158 () (@list @t144)) % 5.42/5.61 (define @t159 () (|tptp.'@+'| @t139 @t144)) % 5.42/5.61 (define @t160 () (tptp.s @t139)) % 5.42/5.61 (define @t161 () (|tptp.'@+'| @t160 @t144)) % 5.42/5.61 (define @t162 () (and @t140 @t149)) % 5.42/5.61 (define @t163 () (|tptp.'@+'| @t144 @t143)) % 5.42/5.61 (define @t164 () (and @t140 @t149 @t147)) % 5.42/5.61 (define @t165 () (tptp.s @t144)) % 5.42/5.61 (define @t166 () (|tptp.'@+'| @t139 @t165)) % 5.42/5.61 (define @t167 () (|tptp.'@+'| @t144 @t139)) % 5.42/5.61 (define @t168 () (|tptp.'@+'| @t139 @t143)) % 5.42/5.61 (define @t169 () (tptp.times_succeeds @t139 @t144 @t143)) % 5.42/5.61 (define @t170 () (|tptp.'@*'| @t139 @t144)) % 5.42/5.61 (define @t171 () (|tptp.'@*'| @t160 @t144)) % 5.42/5.61 (define @t172 () (|tptp.'@*'| @t144 @t143)) % 5.42/5.61 (define @t173 () (|tptp.'@*'| @t139 @t143)) % 5.42/5.61 (define @t174 () (|tptp.'@*'| @t144 @t139)) % 5.42/5.61 (define @t175 () (tptp.s |tptp.'0'|)) % 5.42/5.61 (define @t176 () (|tptp.'@<_terminates'| @t139 @t144)) % 5.42/5.61 (define @t177 () (|tptp.'@<_succeeds'| @t139 @t144)) % 5.42/5.61 (define @t178 () (tptp.s @t143)) % 5.42/5.61 (define @t179 () (|tptp.'@<_succeeds'| @t139 @t143)) % 5.42/5.61 (define @t180 () (|tptp.'@<_succeeds'| @t139 @t165)) % 5.42/5.61 (define @t181 () (|tptp.'@<_succeeds'| @t144 @t143)) % 5.42/5.61 (define @t182 () (= @t139 @t144)) % 5.42/5.61 (define @t183 () (or @t177 @t182)) % 5.42/5.61 (define @t184 () (not (= @t139 |tptp.'0'|))) % 5.42/5.61 (define @t185 () (|tptp.'@=<_succeeds'| @t139 @t144)) % 5.42/5.61 (define @t186 () (|tptp.'@=<_succeeds'| @t144 @t139)) % 5.42/5.61 (define @t187 () (|tptp.'@=<_succeeds'| @t144 @t143)) % 5.42/5.61 (define @t188 () (|tptp.'@<_succeeds'| @t159 @t168)) % 5.42/5.61 (define @t189 () (|tptp.'@<_succeeds'| @t168 @t163)) % 5.42/5.61 (define @t190 () (|tptp.'@=<_succeeds'| @t159 @t168)) % 5.42/5.61 (define @t191 () (and @t185 @t149 @t147)) % 5.42/5.61 (define @t192 () (@var "Xy2" $$unsorted)) % 5.42/5.61 (define @t193 () (@var "Xy1" $$unsorted)) % 5.42/5.61 (define @t194 () (|tptp.'@+'| @t193 @t192)) % 5.42/5.61 (define @t195 () (|tptp.'@+'| @t82 @t83)) % 5.42/5.61 (define @t196 () (tptp.nat_succeeds @t193)) % 5.42/5.61 (define @t197 () (|tptp.'@=<_succeeds'| @t83 @t192)) % 5.42/5.61 (define @t198 () (|tptp.'@=<_succeeds'| @t82 @t193)) % 5.42/5.61 (define @t199 () (@list @t82 @t83 @t193 @t192)) % 5.42/5.61 (define @t200 () (|tptp.'@<_succeeds'| @t195 @t194)) % 5.42/5.61 (define @t201 () (|tptp.'@<_succeeds'| @t82 @t193)) % 5.42/5.61 (define @t202 () (|tptp.'@<_succeeds'| @t83 @t192)) % 5.42/5.61 (define @t203 () (@var "Xl3" $$unsorted)) % 5.42/5.61 (define @t204 () (@var "Xl2" $$unsorted)) % 5.42/5.61 (define @t205 () (@var "Xl1" $$unsorted)) % 5.42/5.61 (define @t206 () (tptp.append_succeeds @t205 @t204 @t203)) % 5.42/5.61 (define @t207 () (|tptp.'**'| @t205 @t204)) % 5.42/5.61 (define @t208 () (tptp.list_succeeds @t205)) % 5.42/5.61 (define @t209 () (@list @t205 @t204 @t203)) % 5.42/5.61 (define @t210 () (@var "Xn" $$unsorted)) % 5.42/5.61 (define @t211 () (@var "Xl" $$unsorted)) % 5.42/5.61 (define @t212 () (tptp.list_succeeds @t211)) % 5.42/5.61 (define @t213 () (@list @t205 @t204)) % 5.42/5.61 (define @t214 () (@list @t139 @t211)) % 5.42/5.61 (define @t215 () (@list @t211)) % 5.42/5.61 (define @t216 () (tptp.member_succeeds @t139 @t211)) % 5.42/5.61 (define @t217 () (tptp.list_succeeds @t203)) % 5.42/5.61 (define @t218 () (tptp.list_succeeds @t204)) % 5.42/5.61 (define @t219 () (and @t206 @t217)) % 5.42/5.61 (define @t220 () (and @t208 @t218)) % 5.42/5.61 (define @t221 () (tptp.append_terminates @t205 @t204 @t203)) % 5.42/5.61 (define @t222 () (tptp.gr @t203)) % 5.42/5.61 (define @t223 () (tptp.gr @t204)) % 5.42/5.61 (define @t224 () (tptp.gr @t205)) % 5.42/5.61 (define @t225 () (and @t224 @t223)) % 5.42/5.61 (define @t226 () (@var "Xl4" $$unsorted)) % 5.42/5.61 (define @t227 () (|tptp.'**'| tptp.nil @t211)) % 5.42/5.61 (define @t228 () (forall @t215 (= @t227 @t211))) % 5.42/5.61 (define @t229 () (= (|tptp.'**'| (tptp.cons @t139 @t205) @t204) (tptp.cons @t139 @t207))) % 5.42/5.61 (define @t230 () (forall (@list @t139 @t205 @t204) (=> @t208 @t229))) % 5.42/5.61 (define @t231 () (tptp.list_succeeds @t207)) % 5.42/5.61 (define @t232 () (forall @t213 (=> @t220 @t231))) % 5.42/5.61 (define @t233 () (tptp.gr @t207)) % 5.42/5.61 (define @t234 () (|tptp.'**'| @t204 @t203)) % 5.42/5.61 (define @t235 () (= (|tptp.'**'| @t207 @t203) (|tptp.'**'| @t205 @t234))) % 5.42/5.61 (define @t236 () (@list @t204 @t203)) % 5.42/5.61 (define @t237 () (forall @t236 (=> @t218 @t235))) % 5.42/5.61 (define @t238 () (=> @t208 @t237)) % 5.42/5.61 (define @t239 () (@list @t205)) % 5.42/5.61 (define @t240 () (forall @t239 @t238)) % 5.42/5.61 (define @t241 () (= (|tptp.'**'| (|tptp.'**'| @t1 @t204) @t203) (|tptp.'**'| @t1 @t234))) % 5.42/5.61 (define @t242 () (forall @t236 (=> @t218 @t241))) % 5.42/5.61 (define @t243 () (and (= @t205 @t113) @t112 @t242)) % 5.42/5.61 (define @t244 () (exists @t115 @t243)) % 5.42/5.61 (define @t245 () (or @t244 (= @t205 tptp.nil))) % 5.42/5.61 (define @t246 () (=> @t245 @t237)) % 5.42/5.61 (define @t247 () (forall @t239 @t246)) % 5.42/5.61 (define @t248 () (=> @t247 @t240)) % 5.42/5.61 (define @t249 () (forall @t209 (=> @t220 @t235))) % 5.42/5.61 (define @t250 () (not @t249)) % 5.42/5.61 (define @t251 () (not @t218)) % 5.42/5.61 (define @t252 () (not @t208)) % 5.42/5.61 (define @t253 () (or @t252 @t251 @t235)) % 5.42/5.61 (define @t254 () (or @t252 @t251)) % 5.42/5.61 (define @t255 () (not @t220)) % 5.42/5.61 (define @t256 () (@var "BOUND_VARIABLE_11182" $$unsorted)) % 5.42/5.61 (define @t257 () (@var "BOUND_VARIABLE_11181" $$unsorted)) % 5.42/5.61 (define @t258 () (@var "BOUND_VARIABLE_11180" $$unsorted)) % 5.42/5.61 (define @t259 () (@list @t258 @t257 @t256)) % 5.42/5.61 (define @t260 () (@var "BOUND_VARIABLE_9580" $$unsorted)) % 5.42/5.61 (define @t261 () (@var "BOUND_VARIABLE_9578" $$unsorted)) % 5.42/5.61 (define @t262 () (= (|tptp.'**'| (|tptp.'**'| @t205 @t261) @t260) (|tptp.'**'| @t205 (|tptp.'**'| @t261 @t260)))) % 5.42/5.61 (define @t263 () (not (tptp.list_succeeds @t261))) % 5.42/5.61 (define @t264 () (or @t252 @t263 @t262)) % 5.42/5.61 (define @t265 () (@list @t205 @t261 @t260)) % 5.42/5.61 (define @t266 () (forall @t265 @t264)) % 5.42/5.61 (define @t267 () (not @t266)) % 5.42/5.61 (define @t268 () (forall @t209 @t253)) % 5.42/5.61 (define @t269 () (@list true)) % 5.42/5.61 (define @t270 () (or @t263 @t262)) % 5.42/5.61 (define @t271 () (or @t252 @t270)) % 5.42/5.61 (define @t272 () (forall @t265 @t271)) % 5.42/5.61 (define @t273 () (@list @t261 @t260)) % 5.42/5.61 (define @t274 () (forall @t273 @t271)) % 5.42/5.61 (define @t275 () (forall @t273 @t270)) % 5.42/5.61 (define @t276 () (@list @t204 @t203)) % 5.42/5.61 (define @t277 () (or @t252 @t275)) % 5.42/5.61 (define @t278 () (forall @t236 (or @t251 @t235))) % 5.42/5.61 (define @t279 () (@var "BOUND_VARIABLE_9554" $$unsorted)) % 5.42/5.61 (define @t280 () (@var "BOUND_VARIABLE_9552" $$unsorted)) % 5.42/5.61 (define @t281 () (= (|tptp.'**'| (|tptp.'**'| @t205 @t280) @t279) (|tptp.'**'| @t205 (|tptp.'**'| @t280 @t279)))) % 5.42/5.61 (define @t282 () (not (tptp.list_succeeds @t280))) % 5.42/5.61 (define @t283 () (= tptp.nil @t205)) % 5.42/5.61 (define @t284 () (not @t283)) % 5.42/5.61 (define @t285 () (@var "BOUND_VARIABLE_9536" $$unsorted)) % 5.42/5.61 (define @t286 () (not (forall @t236 (or @t251 (= (|tptp.'**'| (|tptp.'**'| @t285 @t204) @t203) (|tptp.'**'| @t285 @t234)))))) % 5.42/5.61 (define @t287 () (not (tptp.list_succeeds @t285))) % 5.42/5.61 (define @t288 () (@var "BOUND_VARIABLE_9534" $$unsorted)) % 5.42/5.61 (define @t289 () (tptp.cons @t288 @t285)) % 5.42/5.61 (define @t290 () (not (= @t289 @t205))) % 5.42/5.61 (define @t291 () (or @t290 @t287 @t286)) % 5.42/5.61 (define @t292 () (and @t291 @t284)) % 5.42/5.61 (define @t293 () (or @t292 @t282 @t281)) % 5.42/5.61 (define @t294 () (or @t282 @t281)) % 5.42/5.61 (define @t295 () (or @t292 @t294)) % 5.42/5.61 (define @t296 () (@list @t205 @t288 @t285 @t280 @t279)) % 5.42/5.61 (define @t297 () (forall @t296 @t295)) % 5.42/5.61 (define @t298 () (forall (@list @t288 @t285 @t280 @t279) @t295)) % 5.42/5.61 (define @t299 () (forall (@list @t280 @t279) @t294)) % 5.42/5.61 (define @t300 () (@list @t288 @t285)) % 5.42/5.61 (define @t301 () (forall @t300 @t284)) % 5.42/5.61 (define @t302 () (forall @t300 @t291)) % 5.42/5.61 (define @t303 () (and @t302 @t301)) % 5.42/5.61 (define @t304 () (forall @t300 @t292)) % 5.42/5.61 (define @t305 () (or @t304 @t299)) % 5.42/5.61 (define @t306 () (forall @t236 (or @t251 @t241))) % 5.42/5.61 (define @t307 () (not @t306)) % 5.42/5.61 (define @t308 () (not @t112)) % 5.42/5.61 (define @t309 () (= @t113 @t205)) % 5.42/5.61 (define @t310 () (not @t309)) % 5.42/5.61 (define @t311 () (or @t310 @t308 @t307)) % 5.42/5.61 (define @t312 () (forall @t115 @t311)) % 5.42/5.61 (define @t313 () (not @t312)) % 5.42/5.61 (define @t314 () (or @t313 @t283)) % 5.42/5.61 (define @t315 () (and @t309 @t112 @t306)) % 5.42/5.61 (define @t316 () (forall @t115 (not @t315))) % 5.42/5.61 (define @t317 () (not @t316)) % 5.42/5.61 (define @t318 () (forall @t296 (or (and (or (not (= @t205 @t289)) @t287 @t286) @t284) @t282 @t281))) % 5.42/5.61 (define @t319 () (not @t318)) % 5.42/5.61 (define @t320 () (@quantifiers_skolemize @t318 4)) % 5.42/5.61 (define @t321 () (@quantifiers_skolemize @t318 3)) % 5.42/5.61 (define @t322 () (|tptp.'**'| @t321 @t320)) % 5.42/5.61 (define @t323 () (@quantifiers_skolemize @t318 0)) % 5.42/5.61 (define @t324 () (|tptp.'**'| @t323 @t321)) % 5.42/5.61 (define @t325 () (|tptp.'**'| @t324 @t320)) % 5.42/5.61 (define @t326 () (= @t325 (|tptp.'**'| @t323 @t322))) % 5.42/5.61 (define @t327 () (tptp.list_succeeds @t321)) % 5.42/5.61 (define @t328 () (not @t327)) % 5.42/5.61 (define @t329 () (= tptp.nil @t323)) % 5.42/5.61 (define @t330 () (not @t329)) % 5.42/5.61 (define @t331 () (@quantifiers_skolemize @t318 2)) % 5.42/5.61 (define @t332 () (forall @t236 (or @t251 (= (|tptp.'**'| (|tptp.'**'| @t331 @t204) @t203) (|tptp.'**'| @t331 @t234))))) % 5.42/5.61 (define @t333 () (not @t332)) % 5.42/5.61 (define @t334 () (tptp.list_succeeds @t331)) % 5.42/5.61 (define @t335 () (not @t334)) % 5.42/5.61 (define @t336 () (@quantifiers_skolemize @t318 1)) % 5.42/5.61 (define @t337 () (tptp.cons @t336 @t331)) % 5.42/5.61 (define @t338 () (= @t323 @t337)) % 5.42/5.61 (define @t339 () (not @t338)) % 5.42/5.61 (define @t340 () (or @t339 @t335 @t333)) % 5.42/5.61 (define @t341 () (and @t340 @t330)) % 5.42/5.61 (define @t342 () (or @t341 @t328 @t326)) % 5.42/5.61 (define @t343 () (not @t326)) % 5.42/5.61 (define @t344 () (@list @t342)) % 5.42/5.61 (define @t345 () (= @t321 (|tptp.'**'| tptp.nil @t321))) % 5.42/5.61 (define @t346 () (|tptp.'**'| tptp.nil @t322)) % 5.42/5.61 (define @t347 () (= @t322 @t346)) % 5.42/5.61 (define @t348 () (and @t329 @t345 @t347)) % 5.42/5.61 (define @t349 () (not @t340)) % 5.42/5.61 (define @t350 () (@list @t340)) % 5.42/5.61 (define @t351 () (|tptp.'**'| @t331 @t322)) % 5.42/5.61 (define @t352 () (|tptp.'**'| @t337 @t322)) % 5.42/5.61 (define @t353 () (= @t352 (tptp.cons @t336 @t351))) % 5.42/5.61 (define @t354 () (or @t335 @t353)) % 5.42/5.61 (define @t355 () (@list false false)) % 5.42/5.61 (define @t356 () (|tptp.'**'| @t331 @t321)) % 5.42/5.61 (define @t357 () (tptp.cons @t336 @t356)) % 5.42/5.61 (define @t358 () (|tptp.'**'| @t337 @t321)) % 5.42/5.61 (define @t359 () (= @t358 @t357)) % 5.42/5.61 (define @t360 () (or @t335 @t359)) % 5.42/5.61 (define @t361 () (|tptp.'**'| @t356 @t320)) % 5.42/5.61 (define @t362 () (or @t328 (= @t361 @t351))) % 5.42/5.61 (define @t363 () (= @t351 @t361)) % 5.42/5.61 (define @t364 () (or @t328 @t363)) % 5.42/5.61 (define @t365 () (tptp.list_succeeds @t356)) % 5.42/5.61 (define @t366 () (or @t335 @t328 @t365)) % 5.42/5.61 (define @t367 () (tptp.cons @t336 @t361)) % 5.42/5.61 (define @t368 () (|tptp.'**'| @t357 @t320)) % 5.42/5.61 (define @t369 () (= @t368 @t367)) % 5.42/5.61 (define @t370 () (not @t365)) % 5.42/5.61 (define @t371 () (or @t370 @t369)) % 5.42/5.61 (define @t372 () (not @t369)) % 5.42/5.61 (define @t373 () (not @t363)) % 5.42/5.61 (define @t374 () (not @t359)) % 5.42/5.61 (define @t375 () (not @t353)) % 5.42/5.61 (define @t376 () (and @t369 @t372)) % 5.42/5.61 (assume @p1 (not (= |tptp.'0'| tptp.nil))) % 5.42/5.61 (assume @p2 (forall (@list @t1) (not (= |tptp.'0'| @t2)))) % 5.42/5.61 (assume @p3 (forall @t6 (not (= |tptp.'0'| @t5)))) % 5.42/5.61 (assume @p4 (forall (@list @t7) (not (= tptp.nil (tptp.s @t7))))) % 5.42/5.61 (assume @p5 (forall (@list @t9 @t8) (not (= tptp.nil (tptp.cons @t9 @t8))))) % 5.42/5.61 (assume @p6 (forall (@list @t11 @t10) (=> (= (tptp.s @t11) (tptp.s @t10)) (= @t11 @t10)))) % 5.42/5.61 (assume @p7 (forall (@list @t14 @t13 @t12) (not (= (tptp.s @t14) (tptp.cons @t13 @t12))))) % 5.42/5.61 (assume @p8 (forall (@list @t18 @t16 @t17 @t15) (=> (= (tptp.cons @t18 @t16) (tptp.cons @t17 @t15)) (= @t16 @t15)))) % 5.42/5.61 (assume @p9 (forall (@list @t20 @t22 @t19 @t21) (=> (= (tptp.cons @t20 @t22) (tptp.cons @t19 @t21)) (= @t20 @t19)))) % 5.42/5.61 (assume @p10 (tptp.gr |tptp.'0'|)) % 5.42/5.61 (assume @p11 (tptp.gr tptp.nil)) % 5.42/5.61 (assume @p12 (forall (@list @t23) (= (tptp.gr @t23) (tptp.gr (tptp.s @t23))))) % 5.42/5.61 (assume @p13 (forall (@list @t25 @t24) (= (and (tptp.gr @t25) (tptp.gr @t24)) (tptp.gr (tptp.cons @t25 @t24))))) % 5.42/5.61 (assume @p14 (forall @t31 (not (and @t30 @t29)))) % 5.42/5.61 (assume @p15 (forall @t31 (=> (tptp.delete_terminates @t28 @t27 @t26) (or @t30 @t29)))) % 5.42/5.61 (assume @p16 (forall @t36 (not (and @t35 @t34)))) % 5.42/5.61 (assume @p17 (forall @t36 (=> (tptp.length_terminates @t33 @t32) (or @t35 @t34)))) % 5.42/5.61 (assume @p18 (forall @t42 (not (and @t41 @t40)))) % 5.42/5.61 (assume @p19 (forall @t42 (=> (tptp.append_terminates @t39 @t38 @t37) (or @t41 @t40)))) % 5.42/5.61 (assume @p20 (forall @t47 (not (and @t46 @t45)))) % 5.42/5.61 (assume @p21 (forall @t47 (=> (tptp.member_terminates @t44 @t43) (or @t46 @t45)))) % 5.42/5.61 (assume @p22 (forall @t51 (not (and @t50 @t49)))) % 5.42/5.61 (assume @p23 (forall @t51 (=> (tptp.list_terminates @t48) (or @t50 @t49)))) % 5.42/5.61 (assume @p24 (forall @t55 (not (and @t54 @t53)))) % 5.42/5.61 (assume @p25 (forall @t55 (=> (tptp.nat_list_terminates @t52) (or @t54 @t53)))) % 5.42/5.61 (assume @p26 (forall @t61 (not (and @t60 @t59)))) % 5.42/5.61 (assume @p27 (forall @t61 (=> (tptp.times_terminates @t58 @t57 @t56) (or @t60 @t59)))) % 5.42/5.61 (assume @p28 (forall @t67 (not (and @t66 @t65)))) % 5.42/5.61 (assume @p29 (forall @t67 (=> (tptp.plus_terminates @t64 @t63 @t62) (or @t66 @t65)))) % 5.42/5.61 (assume @p30 (forall @t72 (not (and @t71 @t70)))) % 5.42/5.61 (assume @p31 (forall @t72 (=> (|tptp.'@=<_terminates'| @t69 @t68) (or @t71 @t70)))) % 5.42/5.61 (assume @p32 (forall @t77 (not (and @t76 @t75)))) % 5.42/5.61 (assume @p33 (forall @t77 (=> (|tptp.'@<_terminates'| @t74 @t73) (or @t76 @t75)))) % 5.42/5.61 (assume @p34 (forall @t81 (not (and @t80 @t79)))) % 5.42/5.61 (assume @p35 (forall @t81 (=> (tptp.nat_terminates @t78) (or @t80 @t79)))) % 5.42/5.61 (assume @p36 (forall @t88 (= (tptp.delete_succeeds @t82 @t83 @t1) (or (exists @t87 (and @t86 @t85 (tptp.delete_succeeds @t82 @t3 @t7))) @t84)))) % 5.42/5.61 (assume @p37 (forall @t88 (= (tptp.delete_fails @t82 @t83 @t1) (and (forall @t87 (or @t90 @t89 (tptp.delete_fails @t82 @t3 @t7))) (not @t84))))) % 5.42/5.61 (assume @p38 (forall @t88 (= (tptp.delete_terminates @t82 @t83 @t1) (and (forall @t87 (and true (or @t90 (and true (or @t89 (tptp.delete_terminates @t82 @t3 @t7)))))) true)))) % 5.42/5.61 (assume @p39 (forall @t98 (= (tptp.length_succeeds @t82 @t83) (or (exists @t97 (and @t96 @t94 (tptp.length_succeeds @t4 @t3))) (and @t92 @t91))))) % 5.42/5.61 (assume @p40 (forall @t98 (= (tptp.length_fails @t82 @t83) (and (forall @t97 (or @t101 @t100 (tptp.length_fails @t4 @t3))) (or @t99 (not @t91)))))) % 5.42/5.61 (assume @p41 (forall @t98 (= (tptp.length_terminates @t82 @t83) (and (forall @t97 (and true (or @t101 (and true (or @t100 (tptp.length_terminates @t4 @t3)))))) true @t102)))) % 5.42/5.61 (assume @p42 (forall @t88 (= (tptp.append_succeeds @t82 @t83 @t1) (or (exists @t87 (and @t104 @t85 (tptp.append_succeeds @t3 @t83 @t7))) (and @t92 @t103))))) % 5.42/5.61 (assume @p43 (forall @t88 (= (tptp.append_fails @t82 @t83 @t1) (and (forall @t87 (or @t106 @t89 (tptp.append_fails @t3 @t83 @t7))) (or @t99 @t105))))) % 5.42/5.61 (assume @p44 (forall @t88 (= (tptp.append_terminates @t82 @t83 @t1) (and (forall @t87 (and true (or @t106 (and true (or @t89 (tptp.append_terminates @t3 @t83 @t7)))))) true @t102)))) % 5.42/5.61 (assume @p45 (forall @t98 (= (tptp.member_succeeds @t82 @t83) (or (exists @t110 (and @t109 (tptp.member_succeeds @t82 @t4))) (exists @t108 @t107))))) % 5.42/5.61 (assume @p46 (forall @t98 (= (tptp.member_fails @t82 @t83) (and (forall @t110 (or @t111 (tptp.member_fails @t82 @t4))) (forall @t108 (not @t107)))))) % 5.42/5.61 (assume @p47 (forall @t98 (= (tptp.member_terminates @t82 @t83) (and (forall @t110 (and true (or @t111 (tptp.member_terminates @t82 @t4)))) (forall @t108 true))))) % 5.42/5.61 (assume @p48 (forall @t116 (= (tptp.list_succeeds @t82) (or (exists @t115 (and @t114 @t112)) @t92)))) % 5.42/5.61 (assume @p49 (forall @t116 (= (tptp.list_fails @t82) (and (forall @t115 (or @t117 (tptp.list_fails @t1))) @t99)))) % 5.42/5.61 (assume @p50 (forall @t116 (= (tptp.list_terminates @t82) (and (forall @t115 (and true (or @t117 (tptp.list_terminates @t1)))) true)))) % 5.42/5.61 (assume @p51 (forall @t116 (= (tptp.nat_list_succeeds @t82) (or (exists @t115 (and @t114 @t118 (tptp.nat_list_succeeds @t1))) @t92)))) % 5.42/5.61 (assume @p52 (forall @t116 (= (tptp.nat_list_fails @t82) (and (forall @t115 (or @t117 @t119 (tptp.nat_list_fails @t1))) @t99)))) % 5.42/5.61 (assume @p53 (forall @t116 (= (tptp.nat_list_terminates @t82) (and (forall @t115 (and true (or @t117 (and @t120 (or @t119 (tptp.nat_list_terminates @t1)))))) true)))) % 5.42/5.61 (assume @p54 (forall @t88 (= (tptp.times_succeeds @t82 @t83 @t1) (or (exists @t6 (and @t124 (tptp.times_succeeds @t4 @t83 @t3) (tptp.plus_succeeds @t83 @t3 @t1))) (and @t122 @t121))))) % 5.42/5.61 (assume @p55 (forall @t88 (= (tptp.times_fails @t82 @t83 @t1) (and (forall @t6 (or @t127 @t126 (tptp.plus_fails @t83 @t3 @t1))) (or @t125 (not @t121)))))) % 5.42/5.61 (assume @p56 (forall @t88 (= (tptp.times_terminates @t82 @t83 @t1) (and (forall @t6 (and true (or @t127 (and (tptp.times_terminates @t4 @t83 @t3) (or @t126 (tptp.plus_terminates @t83 @t3 @t1)))))) true @t128)))) % 5.42/5.61 (assume @p57 (forall @t88 (= (tptp.plus_succeeds @t82 @t83 @t1) (or (exists @t6 (and @t124 @t129 (tptp.plus_succeeds @t4 @t83 @t3))) (and @t122 @t103))))) % 5.42/5.61 (assume @p58 (forall @t88 (= (tptp.plus_fails @t82 @t83 @t1) (and (forall @t6 (or @t127 @t130 (tptp.plus_fails @t4 @t83 @t3))) (or @t125 @t105))))) % 5.42/5.61 (assume @p59 (forall @t88 (= (tptp.plus_terminates @t82 @t83 @t1) (and (forall @t6 (and true (or @t127 (and true (or @t130 (tptp.plus_terminates @t4 @t83 @t3)))))) true @t128)))) % 5.42/5.61 (assume @p60 (forall @t98 (= (|tptp.'@=<_succeeds'| @t82 @t83) (or (exists @t110 (and @t132 @t131 (|tptp.'@=<_succeeds'| @t1 @t4))) @t122)))) % 5.42/5.61 (assume @p61 (forall @t98 (= (|tptp.'@=<_fails'| @t82 @t83) (and (forall @t110 (or @t134 @t133 (|tptp.'@=<_fails'| @t1 @t4))) @t125)))) % 5.42/5.61 (assume @p62 (forall @t98 (= (|tptp.'@=<_terminates'| @t82 @t83) (and (forall @t110 (and true (or @t134 (and true (or @t133 (|tptp.'@=<_terminates'| @t1 @t4)))))) true)))) % 5.42/5.61 (assume @p63 (forall @t98 (= (|tptp.'@<_succeeds'| @t82 @t83) (or (exists @t110 (and @t132 @t131 (|tptp.'@<_succeeds'| @t1 @t4))) (exists @t108 (and @t122 @t94)))))) % 5.42/5.61 (assume @p64 (forall @t98 (= (|tptp.'@<_fails'| @t82 @t83) (and (forall @t110 (or @t134 @t133 (|tptp.'@<_fails'| @t1 @t4))) (forall @t108 (or @t125 @t100)))))) % 5.42/5.61 (assume @p65 (forall @t98 (= (|tptp.'@<_terminates'| @t82 @t83) (and (forall @t110 (and true (or @t134 (and true (or @t133 (|tptp.'@<_terminates'| @t1 @t4)))))) (forall @t108 (and true @t128)))))) % 5.42/5.61 (assume @p66 (forall @t116 (= @t137 (or (exists @t136 (and @t135 @t118)) @t122)))) % 5.42/5.61 (assume @p67 (forall @t116 (= (tptp.nat_fails @t82) (and (forall @t136 (or @t138 @t119)) @t125)))) % 5.42/5.61 (assume @p68 (forall @t116 (= (tptp.nat_terminates @t82) (and (forall @t136 (and true (or @t138 @t120))) true)))) % 5.42/5.61 (assume @p69 (forall @t141 (=> @t140 (tptp.nat_terminates @t139)))) % 5.42/5.61 (assume @p70 (forall @t141 (=> @t140 @t142))) % 5.42/5.61 (assume @p71 (forall @t146 (=> @t140 @t145))) % 5.42/5.61 (assume @p72 (forall @t146 (=> @t147 @t145))) % 5.42/5.61 (assume @p73 (forall @t146 (=> @t148 @t140))) % 5.42/5.61 (assume @p74 (forall @t146 (=> (and @t148 @t149) @t147))) % 5.42/5.61 (assume @p75 (forall @t146 (=> (and @t148 @t147) @t149))) % 5.42/5.61 (assume @p76 (forall @t146 (=> @t148 @t145))) % 5.42/5.61 (assume @p77 (forall @t146 (=> @t148 @t142))) % 5.42/5.61 (assume @p78 (forall @t146 (=> (and @t148 @t151) @t150))) % 5.42/5.61 (assume @p79 (forall @t146 (=> (and @t148 @t150) @t151))) % 5.42/5.61 (assume @p80 (forall @t153 (=> @t140 (exists @t152 @t148)))) % 5.42/5.61 (assume @p81 (forall @t157 (=> (and (tptp.plus_succeeds @t139 @t144 @t155) (tptp.plus_succeeds @t139 @t144 @t154)) @t156))) % 5.42/5.61 (assume @p82 (forall @t158 (= (|tptp.'@+'| |tptp.'0'| @t144) @t144))) % 5.42/5.61 (assume @p83 (forall @t153 (=> @t140 (= @t161 (tptp.s @t159))))) % 5.42/5.61 (assume @p84 (forall @t153 (=> @t162 (tptp.nat_succeeds @t159)))) % 5.42/5.61 (assume @p85 (forall @t146 (=> @t164 (= (|tptp.'@+'| @t159 @t143) (|tptp.'@+'| @t139 @t163))))) % 5.42/5.61 (assume @p86 (forall @t141 (=> @t140 (= (|tptp.'@+'| @t139 |tptp.'0'|) @t139)))) % 5.42/5.61 (assume @p87 (forall @t153 (=> @t162 (= @t166 @t161)))) % 5.42/5.61 (assume @p88 (forall @t153 (=> @t162 (= @t159 @t167)))) % 5.42/5.61 (assume @p89 (forall @t146 (=> (and @t140 (= @t159 @t168)) (= @t144 @t143)))) % 5.42/5.61 (assume @p90 (forall @t146 (=> @t169 @t140))) % 5.42/5.61 (assume @p91 (forall @t146 (=> (and @t169 @t149) @t147))) % 5.42/5.61 (assume @p92 (forall @t146 (=> @t169 @t142))) % 5.42/5.61 (assume @p93 (forall @t146 (=> (and @t169 @t151) @t150))) % 5.42/5.61 (assume @p94 (forall @t146 (=> @t162 (tptp.times_terminates @t139 @t144 @t143)))) % 5.42/5.61 (assume @p95 (forall @t153 (=> @t162 (exists @t152 @t169)))) % 5.42/5.61 (assume @p96 (forall @t157 (=> (and (tptp.times_succeeds @t139 @t144 @t155) (tptp.times_succeeds @t139 @t144 @t154)) @t156))) % 5.42/5.61 (assume @p97 (forall @t158 (=> @t149 (= (|tptp.'@*'| |tptp.'0'| @t144) |tptp.'0'|)))) % 5.42/5.61 (assume @p98 (forall @t153 (=> @t162 (= @t171 (|tptp.'@+'| @t144 @t170))))) % 5.42/5.61 (assume @p99 (forall @t153 (=> @t162 (tptp.nat_succeeds @t170)))) % 5.42/5.61 (assume @p100 (forall @t146 (=> @t164 (= (|tptp.'@*'| @t159 @t143) (|tptp.'@+'| @t173 @t172))))) % 5.42/5.61 (assume @p101 (forall @t146 (=> @t164 (= (|tptp.'@*'| @t170 @t143) (|tptp.'@*'| @t139 @t172))))) % 5.42/5.61 (assume @p102 (forall @t141 (=> @t140 (= (|tptp.'@*'| @t139 |tptp.'0'|) |tptp.'0'|)))) % 5.42/5.61 (assume @p103 (forall (@list @t144 @t139) (=> (and @t149 @t140) (= (|tptp.'@+'| @t174 @t144) (|tptp.'@*'| @t144 @t160))))) % 5.42/5.61 (assume @p104 (forall @t153 (=> @t162 (= @t170 @t174)))) % 5.42/5.61 (assume @p105 (forall @t141 (=> @t140 (= (|tptp.'@*'| @t175 @t139) @t139)))) % 5.42/5.61 (assume @p106 (forall @t141 (=> @t140 (= (|tptp.'@*'| @t139 @t175) @t139)))) % 5.42/5.61 (assume @p107 (forall @t146 (=> @t164 (= (|tptp.'@*'| @t143 @t159) (|tptp.'@+'| (|tptp.'@*'| @t143 @t139) (|tptp.'@*'| @t143 @t144)))))) % 5.42/5.61 (assume @p108 (forall @t153 (=> @t140 @t176))) % 5.42/5.61 (assume @p109 (forall @t153 (=> @t149 @t176))) % 5.42/5.61 (assume @p110 (forall @t153 (=> @t177 @t140))) % 5.42/5.61 (assume @p111 (forall @t153 (=> @t177 (exists @t152 (= @t144 @t178))))) % 5.42/5.61 (assume @p112 (forall @t146 (=> (and @t177 (|tptp.'@<_succeeds'| @t144 @t178)) @t179))) % 5.42/5.61 (assume @p113 (forall @t153 (=> @t177 @t180))) % 5.42/5.61 (assume @p114 (forall @t146 (=> (and @t177 @t181) @t179))) % 5.42/5.61 (assume @p115 (forall @t141 (=> @t140 (|tptp.'@<_fails'| @t139 @t139)))) % 5.42/5.61 (assume @p116 (forall @t141 (=> @t140 (not (|tptp.'@<_succeeds'| @t139 @t139))))) % 5.42/5.61 (assume @p117 (forall @t141 (=> @t140 (|tptp.'@<_succeeds'| @t139 @t160)))) % 5.42/5.61 (assume @p118 (forall @t153 (=> (and @t149 @t180) @t183))) % 5.42/5.61 (assume @p119 (forall @t153 (=> @t162 (or @t177 @t182 (|tptp.'@<_succeeds'| @t144 @t139))))) % 5.42/5.61 (assume @p120 (forall @t141 (=> (and @t140 @t184) (|tptp.'@<_succeeds'| |tptp.'0'| @t139)))) % 5.42/5.61 (assume @p121 (forall @t153 (=> @t140 (|tptp.'@=<_terminates'| @t139 @t144)))) % 5.42/5.61 (assume @p122 (forall @t153 (=> @t185 @t140))) % 5.42/5.61 (assume @p123 (forall @t153 (=> @t185 (exists @t152 (tptp.plus_succeeds @t139 @t143 @t144))))) % 5.42/5.61 (assume @p124 (forall @t153 (=> @t185 (exists @t152 (= @t168 @t144))))) % 5.42/5.61 (assume @p125 (forall @t153 (=> @t177 (exists @t152 (tptp.plus_succeeds @t139 @t178 @t144))))) % 5.42/5.61 (assume @p126 (forall @t153 (=> @t177 (exists @t152 (= (|tptp.'@+'| @t139 @t178) @t144))))) % 5.42/5.61 (assume @p127 (forall @t153 (=> @t177 @t185))) % 5.42/5.61 (assume @p128 (forall @t141 (=> @t140 (|tptp.'@=<_succeeds'| @t139 @t139)))) % 5.42/5.61 (assume @p129 (forall @t153 (=> @t162 (or @t185 @t186)))) % 5.42/5.61 (assume @p130 (forall @t153 (=> @t162 (or @t177 @t186)))) % 5.42/5.61 (assume @p131 (forall @t153 (=> (and @t140 @t149 (|tptp.'@=<_fails'| @t139 @t144)) @t186))) % 5.42/5.61 (assume @p132 (forall @t153 (=> (and @t185 @t149) @t183))) % 5.42/5.61 (assume @p133 (forall @t146 (=> (and @t185 @t181) @t179))) % 5.42/5.61 (assume @p134 (forall @t146 (=> (and @t177 @t187) @t179))) % 5.42/5.61 (assume @p135 (forall @t146 (=> (and @t185 @t187) (|tptp.'@=<_succeeds'| @t139 @t143)))) % 5.42/5.61 (assume @p136 (forall @t153 (=> (and @t185 @t186) @t182))) % 5.42/5.61 (assume @p137 (forall @t141 (=> @t140 (|tptp.'@=<_succeeds'| @t139 @t160)))) % 5.42/5.61 (assume @p138 (forall @t141 (=> @t140 (|tptp.'@=<_fails'| @t160 @t139)))) % 5.42/5.61 (assume @p139 (forall @t146 (=> (and @t140 @t181) @t188))) % 5.42/5.61 (assume @p140 (forall @t153 (=> @t140 (|tptp.'@<_succeeds'| @t139 @t166)))) % 5.42/5.61 (assume @p141 (forall @t146 (=> (and @t177 @t149 @t147) @t189))) % 5.42/5.61 (assume @p142 (forall @t153 (=> (and (|tptp.'@<_succeeds'| |tptp.'0'| @t144) @t140 @t149) (|tptp.'@<_succeeds'| @t139 @t167)))) % 5.42/5.61 (assume @p143 (forall @t146 (=> (and @t140 @t187) @t190))) % 5.42/5.61 (assume @p144 (forall @t146 (=> @t191 (|tptp.'@=<_succeeds'| @t168 @t163)))) % 5.42/5.61 (assume @p145 (forall @t153 (=> @t140 (|tptp.'@=<_succeeds'| @t139 @t159)))) % 5.42/5.61 (assume @p146 (forall @t153 (=> @t162 (|tptp.'@=<_succeeds'| @t144 @t159)))) % 5.42/5.61 (assume @p147 (forall @t146 (=> (and @t140 @t188) @t181))) % 5.42/5.61 (assume @p148 (forall @t146 (=> (and @t140 @t149 @t147 @t189) @t177))) % 5.42/5.61 (assume @p149 (forall @t146 (=> (and @t140 @t190) @t187))) % 5.42/5.61 (assume @p150 (forall @t199 (=> (and @t198 @t197 @t196) (|tptp.'@=<_succeeds'| @t195 @t194)))) % 5.42/5.61 (assume @p151 (forall @t199 (=> (and @t201 @t197 @t196) @t200))) % 5.42/5.61 (assume @p152 (forall @t199 (=> (and @t198 @t202 @t196) @t200))) % 5.42/5.61 (assume @p153 (forall @t199 (=> (and @t201 @t202 @t196) @t200))) % 5.42/5.61 (assume @p154 (forall @t146 (=> (and @t140 @t187 @t147) (|tptp.'@=<_succeeds'| @t170 @t173)))) % 5.42/5.61 (assume @p155 (forall @t146 (=> @t191 (|tptp.'@=<_succeeds'| @t173 @t172)))) % 5.42/5.61 (assume @p156 (forall @t146 (=> (and @t140 @t184 @t181 @t147) (|tptp.'@<_succeeds'| @t170 @t173)))) % 5.42/5.61 (assume @p157 (forall @t146 (=> (and @t140 @t149 @t147 (|tptp.'@=<_succeeds'| @t171 (|tptp.'@*'| @t160 @t143))) @t187))) % 5.42/5.61 (assume @p158 (forall (@list @t82 @t83 @t144) (=> (and @t137 @t118 @t149 (= (|tptp.'@+'| @t82 @t144) (|tptp.'@+'| @t83 @t144))) (= @t82 @t83)))) % 5.42/5.61 (assume @p159 (forall @t209 (=> @t208 (= (= @t207 @t203) @t206)))) % 5.42/5.61 (assume @p160 (forall (@list @t211 @t210) (=> @t212 (= (= (tptp.lh @t211) @t210) (tptp.length_succeeds @t211 @t210))))) % 5.42/5.61 (assume @p161 (forall @t213 (= (tptp.sub @t205 @t204) (forall @t141 (=> (tptp.member_succeeds @t139 @t205) (tptp.member_succeeds @t139 @t204)))))) % 5.42/5.61 (assume @p162 (forall @t141 (tptp.list_succeeds (tptp.cons @t139 tptp.nil)))) % 5.42/5.61 (assume @p163 (forall @t153 (tptp.list_succeeds (tptp.cons @t139 (tptp.cons @t144 tptp.nil))))) % 5.42/5.61 (assume @p164 (forall @t146 (tptp.list_succeeds (tptp.cons @t139 (tptp.cons @t144 (tptp.cons @t143 tptp.nil)))))) % 5.42/5.61 (assume @p165 (forall @t214 (=> (tptp.list_succeeds (tptp.cons @t139 @t211)) @t212))) % 5.42/5.61 (assume @p166 (forall @t215 (=> @t212 (tptp.list_terminates @t211)))) % 5.42/5.61 (assume @p167 (forall @t214 (=> @t212 (tptp.member_terminates @t139 @t211)))) % 5.42/5.61 (assume @p168 (forall @t214 (=> @t212 (or @t216 (tptp.member_fails @t139 @t211))))) % 5.42/5.61 (assume @p169 (forall @t214 (=> (and @t216 (tptp.gr @t211)) @t142))) % 5.42/5.61 (assume @p170 (forall (@list @t139 @t144 @t143 @t211) (=> (and (tptp.member_succeeds @t139 (tptp.cons @t144 @t211)) (not @t182)) @t216))) % 5.42/5.61 (assume @p171 (forall @t209 (=> @t206 @t208))) % 5.42/5.61 (assume @p172 (forall @t209 (=> (and @t206 @t218) @t217))) % 5.42/5.61 (assume @p173 (forall @t209 (=> @t219 @t218))) % 5.42/5.61 (assume @p174 (forall @t209 (=> @t219 @t220))) % 5.42/5.61 (assume @p175 (forall @t209 (=> @t208 @t221))) % 5.42/5.61 (assume @p176 (forall @t209 (=> @t217 @t221))) % 5.42/5.61 (assume @p177 (forall @t209 (=> (and @t206 @t224 @t223) @t222))) % 5.42/5.61 (assume @p178 (forall @t209 (=> (and @t206 @t222) @t225))) % 5.42/5.61 (assume @p179 (forall @t213 (=> @t208 (exists (@list @t203) @t206)))) % 5.42/5.61 (assume @p180 (forall (@list @t205 @t204 @t203 @t226) (=> (and @t206 (tptp.append_succeeds @t205 @t204 @t226)) (= @t203 @t226)))) % 5.42/5.61 (assume @p181 @t228) % 5.42/5.61 (assume @p182 @t230) % 5.42/5.61 (assume @p183 @t232) % 5.42/5.61 (assume @p184 (forall @t213 (=> (and @t208 @t231) @t218))) % 5.42/5.61 (assume @p185 (forall @t213 (=> (and @t208 @t224 @t223) @t233))) % 5.42/5.61 (assume @p186 (forall @t213 (=> (and @t208 @t233) @t225))) % 5.42/5.61 (assume @p187 @t248) % 5.42/5.61 (assume @p188 @t250) % 5.42/5.61 (assume @p189 true) % 5.42/5.61 (step @p190 :rule aci_norm :args ((= (or @t254 @t235) @t253))) % 5.42/5.61 (step @p191 :rule refl :args (@t235)) % 5.42/5.61 (step @p192 :rule bool-and-de-morgan :args (@t208 @t218 true)) % 5.42/5.61 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or @t255 @t235))) % 5.42/5.61 (step @p194 :rule trans :premises (@p193 @p190)) % 5.42/5.61 (step @p195 :rule bool-impl-elim :args (@t220 @t235)) % 5.42/5.61 (step @p196 :rule trans :premises (@p195 @p194)) % 5.42/5.61 (step @p197 :rule cong :premises (@p196) :args (@t249)) % 5.42/5.61 (step @p198 :rule cong :premises (@p197) :args (@t250)) % 5.42/5.61 (step @p199 :rule eq_resolve :premises (@p188 @p198)) % 5.42/5.61 (step @p200 :rule alpha_equiv :args ((forall (@list @t258 @t257 @t256) (or (not (tptp.list_succeeds @t258)) (not (tptp.list_succeeds @t257)) (= (|tptp.'**'| (|tptp.'**'| @t258 @t257) @t256) (|tptp.'**'| @t258 (|tptp.'**'| @t257 @t256))))) @t259 (@list @t205 @t204 @t203))) % 5.42/5.61 (step @p201 :rule 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@t231)))) % 5.42/5.61 (step @p396 :rule refl :args (@t231)) % 5.42/5.61 (step @p397 :rule nary_cong :premises (@p192 @p396) :args ((or @t255 @t231))) % 5.42/5.61 (step @p398 :rule trans :premises (@p397 @p395)) % 5.42/5.61 (step @p399 :rule bool-impl-elim :args (@t220 @t231)) % 5.42/5.61 (step @p400 :rule trans :premises (@p399 @p398)) % 5.42/5.61 (step @p401 :rule cong :premises (@p400) :args (@t232)) % 5.42/5.61 (step @p402 :rule eq_resolve :premises (@p183 @p401)) % 5.42/5.61 (step @p403 :rule instantiate :premises (@p402) :args ((@list @t331 @t321))) % 5.42/5.61 (step @p404 :rule cnf_or_pos :args (@t366)) % 5.42/5.61 (step @p405 :rule reordering :premises (@p404) :args ((or @t335 @t328 @t365 (not @t366)))) % 5.42/5.61 (step @p406 :rule chain_m_resolution :premises (@p405 @p358 @p390 @p403) :args (@t365 (@list false false false) (@list @t334 @t327 @t366))) % 5.42/5.61 (step @p407 :rule cnf_or_pos :args (@t371)) % 5.42/5.61 (step @p408 :rule reordering :premises (@p407) :args ((or @t370 @t369 (not @t371)))) % 5.42/5.61 (step @p409 :rule chain_m_resolution :premises (@p408 @p406 @p394) :args (@t369 @t355 (@list @t365 @t371))) % 5.42/5.61 (step @p410 :rule refl :args (@t372)) % 5.42/5.61 (step @p411 :rule refl :args (@t373)) % 5.42/5.61 (step @p412 :rule refl :args (@t374)) % 5.42/5.61 (step @p413 :rule refl :args (@t375)) % 5.42/5.61 (step @p414 :rule bool-double-not-elim :args (@t326)) % 5.42/5.61 (step @p415 :rule refl :args (@t339)) % 5.42/5.61 (step @p416 :rule nary_cong :premises (@p415 @p414 @p413 @p412 @p411 @p410) :args ((or @t339 (not @t343) @t375 @t374 @t373 @t372))) % 5.42/5.61 (assume-push @p489 @t369) % 5.42/5.61 (assume-push @p490 @t372) % 5.42/5.61 (step @p419 :rule evaluate :args ((= false true))) % 5.42/5.61 (step @p420 :rule true_intro :premises (@p489)) % 5.42/5.61 (step @p421 :rule false_intro :premises (@p490)) % 5.42/5.61 (step @p422 :rule symm :premises (@p421)) % 5.42/5.61 (step @p423 :rule trans :premises (@p422 @p420)) % 5.42/5.61 (step @p424 false :rule eq_resolve :premises (@p423 @p419)) % 5.42/5.62 (step-pop @p491 :rule scope :premises (@p424)) % 5.42/5.62 (step-pop @p492 :rule scope :premises (@p491)) % 5.42/5.62 (step @p425 :rule process_scope :premises (@p492) :args (false)) % 5.42/5.62 (assume-push @p493 @t338) % 5.42/5.62 (assume-push @p494 @t343) % 5.42/5.62 (assume-push @p495 @t353) % 5.42/5.62 (assume-push @p496 @t359) % 5.42/5.62 (assume-push @p497 @t363) % 5.42/5.62 (assume-push @p498 @t369) % 5.42/5.62 (assume-push @p499 @t338) % 5.42/5.62 (assume-push @p500 @t359) % 5.42/5.62 (assume-push @p501 @t343) % 5.42/5.62 (assume-push @p502 @t353) % 5.42/5.62 (assume-push @p503 @t363) % 5.42/5.62 (step @p439 :rule false_intro :premises (@p295)) % 5.42/5.62 (step @p309 :rule refl :args (@t322)) % 5.42/5.62 (step @p440 :rule symm :premises (@p493)) % 5.42/5.62 (step @p441 :rule cong :premises (@p440 @p309) :args (@t352)) % 5.42/5.62 (step @p442 :rule symm :premises (@p495)) % 5.42/5.62 (step @p443 :rule symm :premises (@p497)) % 5.42/5.62 (step @p444 :rule refl :args (@t336)) % 5.42/5.62 (step @p445 :rule cong :premises (@p444 @p443) :args (@t367)) % 5.42/5.62 (step @p446 :rule trans :premises (@p445 @p442 @p441)) % 5.42/5.62 (step @p311 :rule refl :args (@t320)) % 5.42/5.62 (step @p313 :rule refl :args (@t321)) % 5.42/5.62 (step @p447 :rule cong :premises (@p440 @p313) :args (@t358)) % 5.42/5.62 (step @p448 :rule symm :premises (@p496)) % 5.42/5.62 (step @p449 :rule trans :premises (@p448 @p447)) % 5.42/5.62 (step @p450 :rule cong :premises (@p449 @p311) :args (@t368)) % 5.42/5.62 (step @p451 :rule cong :premises (@p450 @p446) :args (@t369)) % 5.42/5.62 (step @p452 :rule trans :premises (@p451 @p439)) % 5.42/5.62 (step @p453 :rule false_elim :premises (@p452)) % 5.42/5.62 (step-pop @p504 :rule scope :premises (@p453)) % 5.42/5.62 (step-pop @p505 :rule scope :premises (@p504)) % 5.42/5.62 (step-pop @p506 :rule scope :premises (@p505)) % 5.42/5.62 (step-pop @p507 :rule scope :premises (@p506)) % 5.42/5.62 (step-pop @p508 :rule scope :premises (@p507)) % 5.42/5.62 (step @p454 :rule process_scope :premises (@p508) :args (@t372)) % 5.42/5.62 (step @p460 :rule and_intro :premises (@p493 @p496 @p295 @p495 @p497)) % 5.42/5.62 (step @p461 :rule modus_ponens :premises (@p460 @p454)) % 5.42/5.62 (step @p462 :rule and_intro :premises (@p498 @p461)) % 5.42/5.62 (step-pop @p509 :rule scope :premises (@p462)) % 5.42/5.62 (step-pop @p510 :rule scope :premises (@p509)) % 5.42/5.62 (step-pop @p511 :rule scope :premises (@p510)) % 5.42/5.62 (step-pop @p512 :rule scope :premises (@p511)) % 5.42/5.62 (step-pop @p513 :rule scope :premises (@p512)) % 5.42/5.62 (step-pop @p514 :rule scope :premises (@p513)) % 5.42/5.62 (step @p463 :rule process_scope :premises (@p514) :args (@t376)) % 5.42/5.62 (step @p470 :rule implies_elim :premises (@p463)) % 5.42/5.62 (step @p471 :rule resolution :premises (@p470 @p425) :args (true @t376)) % 5.42/5.62 (step @p472 :rule not_and :premises (@p471)) % 5.42/5.62 (step @p473 :rule eq_resolve :premises (@p472 @p416)) % 5.42/5.62 (step @p474 false :rule chain_m_resolution :premises (@p473 @p409 @p393 @p365 @p361 @p348 @p295) :args (false (@list false false false false false true) (@list @t369 @t363 @t359 @t353 @t338 @t326))) % 5.42/5.62 ) % 5.42/5.62 % SZS output end Proof % 5.42/5.62 % cvc5 exiting %------------------------------------------------------------------------------