%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX044+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 : n024.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 09:07:02 AM UTC 2026 % Result : Theorem 33.84s 34.08s % Output : Proof 33.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SWX044+1 : TPTP v9.2.1. Released v9.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 17:54:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 33.84/34.08 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.84/34.08 --- Run --no-e-matching --full-saturate-quant at 6... % 33.84/34.08 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.84/34.08 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.84/34.08 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.84/34.08 % SZS status Theorem % 33.84/34.08 % SZS output start Proof % 33.84/34.08 ( % 33.84/34.08 (declare-sort $$unsorted 0) % 33.84/34.08 (declare-const tptp.nat_fails (-> $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 33.84/34.08 (declare-const |tptp.'@<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.gr (-> $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.plus_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'0'| $$unsorted) % 33.84/34.08 (declare-const |tptp.'@*'| (-> $$unsorted $$unsorted $$unsorted)) % 33.84/34.08 (declare-const tptp.plus_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.nat_terminates (-> $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@=<_terminates'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.times_fails (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.plus_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@<_terminates'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.times_succeeds (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const tptp.times_terminates (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@+'| (-> $$unsorted $$unsorted $$unsorted)) % 33.84/34.08 (declare-const tptp.nat_succeeds (-> $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@=<_fails'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@=<_succeeds'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (declare-const |tptp.'@<_fails'| (-> $$unsorted $$unsorted Bool)) % 33.84/34.08 (define @t1 () (@var "Xx3" $$unsorted)) % 33.84/34.08 (define @t2 () (tptp.s @t1)) % 33.84/34.08 (define @t3 () (forall (@list @t1) (not (= |tptp.'0'| @t2)))) % 33.84/34.08 (define @t4 () (@var "Xx5" $$unsorted)) % 33.84/34.08 (define @t5 () (@var "Xx4" $$unsorted)) % 33.84/34.08 (define @t6 () (= @t5 @t4)) % 33.84/34.08 (define @t7 () (tptp.s @t4)) % 33.84/34.08 (define @t8 () (tptp.s @t5)) % 33.84/34.08 (define @t9 () (= @t8 @t7)) % 33.84/34.08 (define @t10 () (@list @t5 @t4)) % 33.84/34.08 (define @t11 () (forall @t10 (=> @t9 @t6))) % 33.84/34.08 (define @t12 () (@var "Xx6" $$unsorted)) % 33.84/34.08 (define @t13 () (@var "Xx9" $$unsorted)) % 33.84/34.08 (define @t14 () (@var "Xx8" $$unsorted)) % 33.84/34.08 (define @t15 () (@var "Xx7" $$unsorted)) % 33.84/34.08 (define @t16 () (tptp.times_fails @t15 @t14 @t13)) % 33.84/34.08 (define @t17 () (tptp.times_succeeds @t15 @t14 @t13)) % 33.84/34.08 (define @t18 () (@list @t15 @t14 @t13)) % 33.84/34.08 (define @t19 () (@var "Xx12" $$unsorted)) % 33.84/34.08 (define @t20 () (@var "Xx11" $$unsorted)) % 33.84/34.08 (define @t21 () (@var "Xx10" $$unsorted)) % 33.84/34.08 (define @t22 () (tptp.plus_fails @t21 @t20 @t19)) % 33.84/34.08 (define @t23 () (tptp.plus_succeeds @t21 @t20 @t19)) % 33.84/34.08 (define @t24 () (@list @t21 @t20 @t19)) % 33.84/34.08 (define @t25 () (@var "Xx14" $$unsorted)) % 33.84/34.08 (define @t26 () (@var "Xx13" $$unsorted)) % 33.84/34.08 (define @t27 () (|tptp.'@=<_fails'| @t26 @t25)) % 33.84/34.08 (define @t28 () (|tptp.'@=<_succeeds'| @t26 @t25)) % 33.84/34.08 (define @t29 () (@list @t26 @t25)) % 33.84/34.08 (define @t30 () (@var "Xx16" $$unsorted)) % 33.84/34.08 (define @t31 () (@var "Xx15" $$unsorted)) % 33.84/34.08 (define @t32 () (|tptp.'@<_fails'| @t31 @t30)) % 33.84/34.09 (define @t33 () (|tptp.'@<_succeeds'| @t31 @t30)) % 33.84/34.09 (define @t34 () (@list @t31 @t30)) % 33.84/34.09 (define @t35 () (@var "Xx17" $$unsorted)) % 33.84/34.09 (define @t36 () (tptp.nat_fails @t35)) % 33.84/34.09 (define @t37 () (tptp.nat_succeeds @t35)) % 33.84/34.09 (define @t38 () (@list @t35)) % 33.84/34.09 (define @t39 () (= @t1 |tptp.'0'|)) % 33.84/34.09 (define @t40 () (@var "Xx1" $$unsorted)) % 33.84/34.09 (define @t41 () (= @t40 |tptp.'0'|)) % 33.84/34.09 (define @t42 () (@var "Xx2" $$unsorted)) % 33.84/34.09 (define @t43 () (= @t40 @t8)) % 33.84/34.09 (define @t44 () (@list @t40 @t42 @t1)) % 33.84/34.09 (define @t45 () (not @t41)) % 33.84/34.09 (define @t46 () (tptp.times_fails @t5 @t42 @t4)) % 33.84/34.09 (define @t47 () (not @t43)) % 33.84/34.09 (define @t48 () (or @t45 true)) % 33.84/34.09 (define @t49 () (= @t1 @t42)) % 33.84/34.09 (define @t50 () (= @t1 @t7)) % 33.84/34.09 (define @t51 () (not @t50)) % 33.84/34.09 (define @t52 () (= @t42 @t8)) % 33.84/34.09 (define @t53 () (= @t40 @t2)) % 33.84/34.09 (define @t54 () (@list @t1 @t5)) % 33.84/34.09 (define @t55 () (@list @t40 @t42)) % 33.84/34.09 (define @t56 () (not @t52)) % 33.84/34.09 (define @t57 () (not @t53)) % 33.84/34.09 (define @t58 () (= @t42 @t7)) % 33.84/34.09 (define @t59 () (and @t41 @t58)) % 33.84/34.09 (define @t60 () (@list @t4)) % 33.84/34.09 (define @t61 () (exists @t60 @t59)) % 33.84/34.09 (define @t62 () (|tptp.'@<_succeeds'| @t1 @t5)) % 33.84/34.09 (define @t63 () (and @t53 @t52 @t62)) % 33.84/34.09 (define @t64 () (exists @t54 @t63)) % 33.84/34.09 (define @t65 () (or @t64 @t61)) % 33.84/34.09 (define @t66 () (|tptp.'@<_succeeds'| @t40 @t42)) % 33.84/34.09 (define @t67 () (= @t66 @t65)) % 33.84/34.09 (define @t68 () (forall @t55 @t67)) % 33.84/34.09 (define @t69 () (tptp.nat_succeeds @t42)) % 33.84/34.09 (define @t70 () (tptp.s @t42)) % 33.84/34.09 (define @t71 () (= @t40 @t70)) % 33.84/34.09 (define @t72 () (@list @t42)) % 33.84/34.09 (define @t73 () (@list @t40)) % 33.84/34.09 (define @t74 () (not @t71)) % 33.84/34.09 (define @t75 () (@var "Xz" $$unsorted)) % 33.84/34.09 (define @t76 () (@var "Xy" $$unsorted)) % 33.84/34.09 (define @t77 () (@var "Xx" $$unsorted)) % 33.84/34.09 (define @t78 () (tptp.plus_succeeds @t77 @t76 @t75)) % 33.84/34.09 (define @t79 () (|tptp.'@+'| @t77 @t76)) % 33.84/34.09 (define @t80 () (tptp.nat_succeeds @t77)) % 33.84/34.09 (define @t81 () (@list @t77 @t76 @t75)) % 33.84/34.09 (define @t82 () (tptp.times_succeeds @t77 @t76 @t75)) % 33.84/34.09 (define @t83 () (|tptp.'@*'| @t77 @t76)) % 33.84/34.09 (define @t84 () (tptp.nat_succeeds @t76)) % 33.84/34.09 (define @t85 () (and @t80 @t84)) % 33.84/34.09 (define @t86 () (@list @t77)) % 33.84/34.09 (define @t87 () (tptp.gr @t77)) % 33.84/34.09 (define @t88 () (tptp.plus_terminates @t77 @t76 @t75)) % 33.84/34.09 (define @t89 () (tptp.nat_succeeds @t75)) % 33.84/34.09 (define @t90 () (tptp.gr @t75)) % 33.84/34.09 (define @t91 () (tptp.gr @t76)) % 33.84/34.09 (define @t92 () (@list @t75)) % 33.84/34.09 (define @t93 () (@list @t77 @t76)) % 33.84/34.09 (define @t94 () (@var "Xz2" $$unsorted)) % 33.84/34.09 (define @t95 () (@var "Xz1" $$unsorted)) % 33.84/34.09 (define @t96 () (= @t95 @t94)) % 33.84/34.09 (define @t97 () (@list @t77 @t76 @t95 @t94)) % 33.84/34.09 (define @t98 () (|tptp.'@+'| |tptp.'0'| @t76)) % 33.84/34.09 (define @t99 () (@list @t76)) % 33.84/34.09 (define @t100 () (forall @t99 (= @t98 @t76))) % 33.84/34.09 (define @t101 () (tptp.s @t77)) % 33.84/34.09 (define @t102 () (|tptp.'@+'| @t101 @t76)) % 33.84/34.09 (define @t103 () (= @t102 (tptp.s @t79))) % 33.84/34.09 (define @t104 () (forall @t93 (=> @t80 @t103))) % 33.84/34.09 (define @t105 () (|tptp.'@+'| @t76 @t75)) % 33.84/34.09 (define @t106 () (and @t80 @t84 @t89)) % 33.84/34.09 (define @t107 () (tptp.s @t76)) % 33.84/34.09 (define @t108 () (|tptp.'@+'| @t77 @t107)) % 33.84/34.09 (define @t109 () (|tptp.'@+'| @t76 @t77)) % 33.84/34.09 (define @t110 () (|tptp.'@+'| @t77 @t75)) % 33.84/34.09 (define @t111 () (|tptp.'@*'| @t76 @t75)) % 33.84/34.09 (define @t112 () (|tptp.'@*'| @t76 @t77)) % 33.84/34.09 (define @t113 () (tptp.s |tptp.'0'|)) % 33.84/34.09 (define @t114 () (|tptp.'@<_terminates'| @t77 @t76)) % 33.84/34.09 (define @t115 () (|tptp.'@<_succeeds'| @t77 @t76)) % 33.84/34.09 (define @t116 () (tptp.s @t75)) % 33.84/34.09 (define @t117 () (= @t76 @t116)) % 33.84/34.09 (define @t118 () (exists @t92 @t117)) % 33.84/34.09 (define @t119 () (=> @t115 @t118)) % 33.84/34.09 (define @t120 () (forall @t93 @t119)) % 33.84/34.09 (define @t121 () (|tptp.'@<_succeeds'| @t77 @t75)) % 33.84/34.09 (define @t122 () (|tptp.'@<_succeeds'| @t77 @t107)) % 33.84/34.09 (define @t123 () (|tptp.'@<_succeeds'| @t76 @t75)) % 33.84/34.09 (define @t124 () (= @t77 @t76)) % 33.84/34.09 (define @t125 () (or @t115 @t124)) % 33.84/34.09 (define @t126 () (= @t77 |tptp.'0'|)) % 33.84/34.09 (define @t127 () (|tptp.'@=<_terminates'| @t77 @t76)) % 33.84/34.09 (define @t128 () (|tptp.'@=<_succeeds'| @t77 @t76)) % 33.84/34.09 (define @t129 () (|tptp.'@=<_succeeds'| @t76 @t77)) % 33.84/34.09 (define @t130 () (|tptp.'@=<_succeeds'| @t76 @t75)) % 33.84/34.09 (define @t131 () (|tptp.'@<_succeeds'| @t79 @t110)) % 33.84/34.09 (define @t132 () (@list @t76 @t75)) % 33.84/34.09 (define @t133 () (forall @t132 (=> @t131 @t123))) % 33.84/34.09 (define @t134 () (=> @t80 @t133)) % 33.84/34.09 (define @t135 () (forall @t86 @t134)) % 33.84/34.09 (define @t136 () (|tptp.'@<_succeeds'| (|tptp.'@+'| @t42 @t76) (|tptp.'@+'| @t42 @t75))) % 33.84/34.09 (define @t137 () (forall @t132 (=> @t136 @t123))) % 33.84/34.09 (define @t138 () (and (= @t77 @t70) @t69 @t137)) % 33.84/34.09 (define @t139 () (exists @t72 @t138)) % 33.84/34.09 (define @t140 () (or @t139 @t126)) % 33.84/34.09 (define @t141 () (=> @t140 @t133)) % 33.84/34.09 (define @t142 () (forall @t86 @t141)) % 33.84/34.09 (define @t143 () (=> @t142 @t135)) % 33.84/34.09 (define @t144 () (and @t80 @t131)) % 33.84/34.09 (define @t145 () (forall @t81 (=> @t144 @t123))) % 33.84/34.09 (define @t146 () (not @t145)) % 33.84/34.09 (define @t147 () (not @t131)) % 33.84/34.09 (define @t148 () (not @t80)) % 33.84/34.09 (define @t149 () (or @t148 @t147 @t123)) % 33.84/34.09 (define @t150 () (@var "BOUND_VARIABLE_9603" $$unsorted)) % 33.84/34.09 (define @t151 () (@var "BOUND_VARIABLE_9602" $$unsorted)) % 33.84/34.09 (define @t152 () (@var "BOUND_VARIABLE_9601" $$unsorted)) % 33.84/34.09 (define @t153 () (@list @t152 @t151 @t150)) % 33.84/34.09 (define @t154 () (@var "BOUND_VARIABLE_8682" $$unsorted)) % 33.84/34.09 (define @t155 () (@var "BOUND_VARIABLE_8680" $$unsorted)) % 33.84/34.09 (define @t156 () (|tptp.'@<_succeeds'| @t155 @t154)) % 33.84/34.09 (define @t157 () (not (|tptp.'@<_succeeds'| (|tptp.'@+'| @t77 @t155) (|tptp.'@+'| @t77 @t154)))) % 33.84/34.09 (define @t158 () (or @t148 @t157 @t156)) % 33.84/34.09 (define @t159 () (@list @t77 @t155 @t154)) % 33.84/34.09 (define @t160 () (forall @t159 @t158)) % 33.84/34.09 (define @t161 () (not @t160)) % 33.84/34.09 (define @t162 () (forall @t81 @t149)) % 33.84/34.09 (define @t163 () (@list true)) % 33.84/34.09 (define @t164 () (or @t157 @t156)) % 33.84/34.09 (define @t165 () (or @t148 @t164)) % 33.84/34.09 (define @t166 () (forall @t159 @t165)) % 33.84/34.09 (define @t167 () (@list @t155 @t154)) % 33.84/34.09 (define @t168 () (forall @t167 @t165)) % 33.84/34.09 (define @t169 () (forall @t167 @t164)) % 33.84/34.09 (define @t170 () (@list @t76 @t75)) % 33.84/34.09 (define @t171 () (or @t148 @t169)) % 33.84/34.09 (define @t172 () (forall @t132 (or @t147 @t123))) % 33.84/34.09 (define @t173 () (@var "BOUND_VARIABLE_8658" $$unsorted)) % 33.84/34.09 (define @t174 () (@var "BOUND_VARIABLE_8656" $$unsorted)) % 33.84/34.09 (define @t175 () (|tptp.'@<_succeeds'| @t174 @t173)) % 33.84/34.09 (define @t176 () (not (|tptp.'@<_succeeds'| (|tptp.'@+'| @t77 @t174) (|tptp.'@+'| @t77 @t173)))) % 33.84/34.09 (define @t177 () (= |tptp.'0'| @t77)) % 33.84/34.09 (define @t178 () (not @t177)) % 33.84/34.09 (define @t179 () (@var "BOUND_VARIABLE_8640" $$unsorted)) % 33.84/34.09 (define @t180 () (not (forall @t132 (or (not (|tptp.'@<_succeeds'| (|tptp.'@+'| @t179 @t76) (|tptp.'@+'| @t179 @t75))) @t123)))) % 33.84/34.09 (define @t181 () (not (tptp.nat_succeeds @t179))) % 33.84/34.09 (define @t182 () (tptp.s @t179)) % 33.84/34.09 (define @t183 () (not (= @t182 @t77))) % 33.84/34.09 (define @t184 () (or @t183 @t181 @t180)) % 33.84/34.09 (define @t185 () (and @t184 @t178)) % 33.84/34.09 (define @t186 () (or @t185 @t176 @t175)) % 33.84/34.09 (define @t187 () (or @t176 @t175)) % 33.84/34.09 (define @t188 () (or @t185 @t187)) % 33.84/34.09 (define @t189 () (@list @t77 @t179 @t174 @t173)) % 33.84/34.09 (define @t190 () (forall @t189 @t188)) % 33.84/34.09 (define @t191 () (forall (@list @t179 @t174 @t173) @t188)) % 33.84/34.09 (define @t192 () (forall (@list @t174 @t173) @t187)) % 33.84/34.09 (define @t193 () (@list @t179)) % 33.84/34.09 (define @t194 () (forall @t193 @t178)) % 33.84/34.09 (define @t195 () (forall @t193 @t184)) % 33.84/34.09 (define @t196 () (and @t195 @t194)) % 33.84/34.09 (define @t197 () (forall @t193 @t185)) % 33.84/34.09 (define @t198 () (or @t197 @t192)) % 33.84/34.09 (define @t199 () (forall @t132 (or (not @t136) @t123))) % 33.84/34.09 (define @t200 () (not @t199)) % 33.84/34.09 (define @t201 () (not @t69)) % 33.84/34.09 (define @t202 () (= @t70 @t77)) % 33.84/34.09 (define @t203 () (not @t202)) % 33.84/34.09 (define @t204 () (or @t203 @t201 @t200)) % 33.84/34.09 (define @t205 () (forall @t72 @t204)) % 33.84/34.09 (define @t206 () (not @t205)) % 33.84/34.09 (define @t207 () (or @t206 @t177)) % 33.84/34.09 (define @t208 () (and @t202 @t69 @t199)) % 33.84/34.09 (define @t209 () (forall @t72 (not @t208))) % 33.84/34.09 (define @t210 () (not @t209)) % 33.84/34.09 (define @t211 () (forall @t189 (or (and (or (not (= @t77 @t182)) @t181 @t180) @t178) @t176 @t175))) % 33.84/34.09 (define @t212 () (not @t211)) % 33.84/34.09 (define @t213 () (@quantifiers_skolemize @t211 3)) % 33.84/34.09 (define @t214 () (@quantifiers_skolemize @t211 0)) % 33.84/34.09 (define @t215 () (|tptp.'@+'| @t214 @t213)) % 33.84/34.09 (define @t216 () (@quantifiers_skolemize @t211 2)) % 33.84/34.09 (define @t217 () (|tptp.'@+'| @t214 @t216)) % 33.84/34.09 (define @t218 () (|tptp.'@<_succeeds'| @t217 @t215)) % 33.84/34.09 (define @t219 () (|tptp.'@<_succeeds'| @t216 @t213)) % 33.84/34.09 (define @t220 () (not @t218)) % 33.84/34.09 (define @t221 () (= |tptp.'0'| @t214)) % 33.84/34.09 (define @t222 () (not @t221)) % 33.84/34.09 (define @t223 () (@quantifiers_skolemize @t211 1)) % 33.84/34.09 (define @t224 () (forall @t132 (or (not (|tptp.'@<_succeeds'| (|tptp.'@+'| @t223 @t76) (|tptp.'@+'| @t223 @t75))) @t123))) % 33.84/34.09 (define @t225 () (not @t224)) % 33.84/34.09 (define @t226 () (tptp.nat_succeeds @t223)) % 33.84/34.09 (define @t227 () (not @t226)) % 33.84/34.09 (define @t228 () (tptp.s @t223)) % 33.84/34.09 (define @t229 () (= @t214 @t228)) % 33.84/34.09 (define @t230 () (not @t229)) % 33.84/34.09 (define @t231 () (or @t230 @t227 @t225)) % 33.84/34.09 (define @t232 () (and @t231 @t222)) % 33.84/34.09 (define @t233 () (or @t232 @t220 @t219)) % 33.84/34.09 (define @t234 () (@list @t233)) % 33.84/34.09 (define @t235 () (not @t219)) % 33.84/34.09 (define @t236 () (= |tptp.'0'| @t228)) % 33.84/34.09 (define @t237 () (not @t236)) % 33.84/34.09 (define @t238 () (and @t229 @t237)) % 33.84/34.09 (define @t239 () (not @t233)) % 33.84/34.09 (define @t240 () (not @t231)) % 33.84/34.09 (define @t241 () (|tptp.'@+'| @t223 @t213)) % 33.84/34.09 (define @t242 () (|tptp.'@+'| @t223 @t216)) % 33.84/34.09 (define @t243 () (|tptp.'@<_succeeds'| @t242 @t241)) % 33.84/34.09 (define @t244 () (not @t243)) % 33.84/34.09 (define @t245 () (or @t244 @t219)) % 33.84/34.09 (define @t246 () (forall @t93 (or @t148 @t103))) % 33.84/34.09 (define @t247 () (@list @t223 @t216)) % 33.84/34.09 (define @t248 () (tptp.s @t242)) % 33.84/34.09 (define @t249 () (|tptp.'@+'| @t228 @t216)) % 33.84/34.09 (define @t250 () (= @t249 @t248)) % 33.84/34.09 (define @t251 () (or @t227 @t250)) % 33.84/34.09 (define @t252 () (tptp.s @t241)) % 33.84/34.09 (define @t253 () (|tptp.'@+'| @t228 @t213)) % 33.84/34.09 (define @t254 () (= @t253 @t252)) % 33.84/34.09 (define @t255 () (or @t227 @t254)) % 33.84/34.09 (define @t256 () (not @t62)) % 33.84/34.09 (define @t257 () (forall @t54 (or (not (= @t2 @t217)) (not (= @t8 @t215)) @t256))) % 33.84/34.09 (define @t258 () (@quantifiers_skolemize @t257 0)) % 33.84/34.09 (define @t259 () (tptp.s @t258)) % 33.84/34.09 (define @t260 () (= @t217 @t259)) % 33.84/34.09 (define @t261 () (@quantifiers_skolemize @t257 1)) % 33.84/34.09 (define @t262 () (|tptp.'@<_succeeds'| @t258 @t261)) % 33.84/34.09 (define @t263 () (not @t262)) % 33.84/34.09 (define @t264 () (tptp.s @t261)) % 33.84/34.09 (define @t265 () (= @t215 @t264)) % 33.84/34.09 (define @t266 () (not @t265)) % 33.84/34.09 (define @t267 () (not @t260)) % 33.84/34.09 (define @t268 () (or @t267 @t266 @t263)) % 33.84/34.09 (define @t269 () (not (forall @t92 (not @t117)))) % 33.84/34.09 (define @t270 () (not (= @t215 @t116))) % 33.84/34.09 (define @t271 () (forall @t92 @t270)) % 33.84/34.09 (define @t272 () (not @t271)) % 33.84/34.09 (define @t273 () (or @t220 @t272)) % 33.84/34.09 (define @t274 () (forall @t93 (or (not @t115) @t269))) % 33.84/34.09 (define @t275 () (@list @t217 @t215)) % 33.84/34.09 (define @t276 () (forall @t92 (not (= @t116 @t215)))) % 33.84/34.09 (define @t277 () (not @t276)) % 33.84/34.09 (define @t278 () (or @t220 @t277)) % 33.84/34.09 (define @t279 () (@list false false)) % 33.84/34.09 (define @t280 () (forall @t60 (not (= @t7 @t215)))) % 33.84/34.09 (define @t281 () (not @t280)) % 33.84/34.09 (define @t282 () (tptp.s (@quantifiers_skolemize @t280 0))) % 33.84/34.09 (define @t283 () (= @t215 @t282)) % 33.84/34.09 (define @t284 () (= @t282 @t215)) % 33.84/34.09 (define @t285 () (not (not @t284))) % 33.84/34.09 (define @t286 () (= @t252 @t282)) % 33.84/34.09 (define @t287 () (= @t252 @t264)) % 33.84/34.09 (define @t288 () (and @t229 @t254 @t283 @t265)) % 33.84/34.09 (define @t289 () (= @t248 @t259)) % 33.84/34.09 (define @t290 () (and @t229 @t250 @t260)) % 33.84/34.09 (define @t291 () (= @t241 @t261)) % 33.84/34.09 (define @t292 () (not @t287)) % 33.84/34.09 (define @t293 () (or @t292 @t291)) % 33.84/34.09 (define @t294 () (= @t242 @t258)) % 33.84/34.09 (define @t295 () (not @t289)) % 33.84/34.09 (define @t296 () (or @t295 @t294)) % 33.84/34.09 (define @t297 () (not @t291)) % 33.84/34.09 (define @t298 () (not @t294)) % 33.84/34.09 (define @t299 () (= false true)) % 33.84/34.09 (define @t300 () (not @t268)) % 33.84/34.09 (define @t301 () (not @t257)) % 33.84/34.09 (define @t302 () (not (= @t264 @t215))) % 33.84/34.09 (define @t303 () (not (= @t259 @t217))) % 33.84/34.09 (define @t304 () (or @t303 @t302 @t263)) % 33.84/34.09 (define @t305 () (not @t304)) % 33.84/34.09 (define @t306 () (= @t7 @t42)) % 33.84/34.09 (define @t307 () (not @t306)) % 33.84/34.09 (define @t308 () (forall @t60 @t307)) % 33.84/34.09 (define @t309 () (not @t308)) % 33.84/34.09 (define @t310 () (= |tptp.'0'| @t40)) % 33.84/34.09 (define @t311 () (not @t310)) % 33.84/34.09 (define @t312 () (= @t8 @t42)) % 33.84/34.09 (define @t313 () (not @t312)) % 33.84/34.09 (define @t314 () (= @t2 @t40)) % 33.84/34.09 (define @t315 () (not @t314)) % 33.84/34.09 (define @t316 () (or @t315 @t313 @t256)) % 33.84/34.09 (define @t317 () (not (forall @t54 @t316))) % 33.84/34.09 (define @t318 () (or @t311 @t308)) % 33.84/34.09 (define @t319 () (or @t317 (not @t318))) % 33.84/34.09 (define @t320 () (= @t66 @t319)) % 33.84/34.09 (define @t321 () (and @t310 @t306)) % 33.84/34.09 (define @t322 () (forall @t60 (not @t321))) % 33.84/34.09 (define @t323 () (not @t322)) % 33.84/34.09 (define @t324 () (and @t314 @t312 @t62)) % 33.84/34.09 (define @t325 () (forall @t54 (not @t324))) % 33.84/34.09 (define @t326 () (not @t325)) % 33.84/34.09 (define @t327 () (= |tptp.'0'| @t217)) % 33.84/34.09 (define @t328 () (and @t327 @t281)) % 33.84/34.09 (define @t329 () (or @t301 @t328)) % 33.84/34.09 (define @t330 () (= @t218 @t329)) % 33.84/34.09 (define @t331 () (not @t327)) % 33.84/34.09 (define @t332 () (= |tptp.'0'| @t248)) % 33.84/34.09 (define @t333 () (not @t250)) % 33.84/34.09 (define @t334 () (not @t332)) % 33.84/34.09 (define @t335 () (and @t229 @t250 @t334)) % 33.84/34.09 (define @t336 () (|tptp.'@+'| |tptp.'0'| @t213)) % 33.84/34.09 (define @t337 () (= @t213 @t336)) % 33.84/34.09 (define @t338 () (not @t337)) % 33.84/34.09 (define @t339 () (|tptp.'@+'| |tptp.'0'| @t216)) % 33.84/34.09 (define @t340 () (= @t216 @t339)) % 33.84/34.09 (define @t341 () (not @t340)) % 33.84/34.09 (define @t342 () (and @t218 @t221 @t340 @t337 @t235)) % 33.84/34.09 (assume @p1 @t3) % 33.84/34.09 (assume @p2 @t11) % 33.84/34.09 (assume @p3 (tptp.gr |tptp.'0'|)) % 33.84/34.09 (assume @p4 (forall (@list @t12) (= (tptp.gr @t12) (tptp.gr (tptp.s @t12))))) % 33.84/34.09 (assume @p5 (forall @t18 (not (and @t17 @t16)))) % 33.84/34.09 (assume @p6 (forall @t18 (=> (tptp.times_terminates @t15 @t14 @t13) (or @t17 @t16)))) % 33.84/34.09 (assume @p7 (forall @t24 (not (and @t23 @t22)))) % 33.84/34.09 (assume @p8 (forall @t24 (=> (tptp.plus_terminates @t21 @t20 @t19) (or @t23 @t22)))) % 33.84/34.09 (assume @p9 (forall @t29 (not (and @t28 @t27)))) % 33.84/34.09 (assume @p10 (forall @t29 (=> (|tptp.'@=<_terminates'| @t26 @t25) (or @t28 @t27)))) % 33.84/34.09 (assume @p11 (forall @t34 (not (and @t33 @t32)))) % 33.84/34.09 (assume @p12 (forall @t34 (=> (|tptp.'@<_terminates'| @t31 @t30) (or @t33 @t32)))) % 33.84/34.09 (assume @p13 (forall @t38 (not (and @t37 @t36)))) % 33.84/34.09 (assume @p14 (forall @t38 (=> (tptp.nat_terminates @t35) (or @t37 @t36)))) % 33.84/34.09 (assume @p15 (forall @t44 (= (tptp.times_succeeds @t40 @t42 @t1) (or (exists @t10 (and @t43 (tptp.times_succeeds @t5 @t42 @t4) (tptp.plus_succeeds @t42 @t4 @t1))) (and @t41 @t39))))) % 33.84/34.09 (assume @p16 (forall @t44 (= (tptp.times_fails @t40 @t42 @t1) (and (forall @t10 (or @t47 @t46 (tptp.plus_fails @t42 @t4 @t1))) (or @t45 (not @t39)))))) % 33.84/34.09 (assume @p17 (forall @t44 (= (tptp.times_terminates @t40 @t42 @t1) (and (forall @t10 (and true (or @t47 (and (tptp.times_terminates @t5 @t42 @t4) (or @t46 (tptp.plus_terminates @t42 @t4 @t1)))))) true @t48)))) % 33.84/34.09 (assume @p18 (forall @t44 (= (tptp.plus_succeeds @t40 @t42 @t1) (or (exists @t10 (and @t43 @t50 (tptp.plus_succeeds @t5 @t42 @t4))) (and @t41 @t49))))) % 33.84/34.09 (assume @p19 (forall @t44 (= (tptp.plus_fails @t40 @t42 @t1) (and (forall @t10 (or @t47 @t51 (tptp.plus_fails @t5 @t42 @t4))) (or @t45 (not @t49)))))) % 33.84/34.09 (assume @p20 (forall @t44 (= (tptp.plus_terminates @t40 @t42 @t1) (and (forall @t10 (and true (or @t47 (and true (or @t51 (tptp.plus_terminates @t5 @t42 @t4)))))) true @t48)))) % 33.84/34.09 (assume @p21 (forall @t55 (= (|tptp.'@=<_succeeds'| @t40 @t42) (or (exists @t54 (and @t53 @t52 (|tptp.'@=<_succeeds'| @t1 @t5))) @t41)))) % 33.84/34.09 (assume @p22 (forall @t55 (= (|tptp.'@=<_fails'| @t40 @t42) (and (forall @t54 (or @t57 @t56 (|tptp.'@=<_fails'| @t1 @t5))) @t45)))) % 33.84/34.09 (assume @p23 (forall @t55 (= (|tptp.'@=<_terminates'| @t40 @t42) (and (forall @t54 (and true (or @t57 (and true (or @t56 (|tptp.'@=<_terminates'| @t1 @t5)))))) true)))) % 33.84/34.09 (assume @p24 @t68) % 33.84/34.09 (assume @p25 (forall @t55 (= (|tptp.'@<_fails'| @t40 @t42) (and (forall @t54 (or @t57 @t56 (|tptp.'@<_fails'| @t1 @t5))) (forall @t60 (or @t45 (not @t58))))))) % 33.84/34.09 (assume @p26 (forall @t55 (= (|tptp.'@<_terminates'| @t40 @t42) (and (forall @t54 (and true (or @t57 (and true (or @t56 (|tptp.'@<_terminates'| @t1 @t5)))))) (forall @t60 (and true @t48)))))) % 33.84/34.09 (assume @p27 (forall @t73 (= (tptp.nat_succeeds @t40) (or (exists @t72 (and @t71 @t69)) @t41)))) % 33.84/34.09 (assume @p28 (forall @t73 (= (tptp.nat_fails @t40) (and (forall @t72 (or @t74 (tptp.nat_fails @t42))) @t45)))) % 33.84/34.09 (assume @p29 (forall @t73 (= (tptp.nat_terminates @t40) (and (forall @t72 (and true (or @t74 (tptp.nat_terminates @t42)))) true)))) % 33.84/34.09 (assume @p30 (forall @t81 (=> @t80 (= (= @t79 @t75) @t78)))) % 33.84/34.09 (assume @p31 (forall @t81 (=> @t85 (= (= @t83 @t75) @t82)))) % 33.84/34.09 (assume @p32 (forall @t86 (=> @t80 (tptp.nat_terminates @t77)))) % 33.84/34.09 (assume @p33 (forall @t86 (=> @t80 @t87))) % 33.84/34.09 (assume @p34 (forall @t81 (=> @t80 @t88))) % 33.84/34.09 (assume @p35 (forall @t81 (=> @t89 @t88))) % 33.84/34.09 (assume @p36 (forall @t81 (=> @t78 @t80))) % 33.84/34.09 (assume @p37 (forall @t81 (=> (and @t78 @t84) @t89))) % 33.84/34.09 (assume @p38 (forall @t81 (=> (and @t78 @t89) @t84))) % 33.84/34.09 (assume @p39 (forall @t81 (=> @t78 @t88))) % 33.84/34.09 (assume @p40 (forall @t81 (=> @t78 @t87))) % 33.84/34.09 (assume @p41 (forall @t81 (=> (and @t78 @t91) @t90))) % 33.84/34.09 (assume @p42 (forall @t81 (=> (and @t78 @t90) @t91))) % 33.84/34.09 (assume @p43 (forall @t93 (=> @t80 (exists @t92 @t78)))) % 33.84/34.09 (assume @p44 (forall @t97 (=> (and (tptp.plus_succeeds @t77 @t76 @t95) (tptp.plus_succeeds @t77 @t76 @t94)) @t96))) % 33.84/34.09 (assume @p45 @t100) % 33.84/34.09 (assume @p46 @t104) % 33.84/34.09 (assume @p47 (forall @t93 (=> @t85 (tptp.nat_succeeds @t79)))) % 33.84/34.09 (assume @p48 (forall @t81 (=> @t106 (= (|tptp.'@+'| @t79 @t75) (|tptp.'@+'| @t77 @t105))))) % 33.84/34.09 (assume @p49 (forall @t86 (=> @t80 (= (|tptp.'@+'| @t77 |tptp.'0'|) @t77)))) % 33.84/34.09 (assume @p50 (forall @t93 (=> @t85 (= @t108 @t102)))) % 33.84/34.09 (assume @p51 (forall @t93 (=> @t85 (= @t79 @t109)))) % 33.84/34.09 (assume @p52 (forall @t81 (=> (and @t80 (= @t79 @t110)) (= @t76 @t75)))) % 33.84/34.09 (assume @p53 (forall @t81 (=> @t82 @t80))) % 33.84/34.09 (assume @p54 (forall @t81 (=> (and @t82 @t84) @t89))) % 33.84/34.09 (assume @p55 (forall @t81 (=> @t82 @t87))) % 33.84/34.09 (assume @p56 (forall @t81 (=> (and @t82 @t91) @t90))) % 33.84/34.09 (assume @p57 (forall @t81 (=> @t85 (tptp.times_terminates @t77 @t76 @t75)))) % 33.84/34.09 (assume @p58 (forall @t93 (=> @t85 (exists @t92 @t82)))) % 33.84/34.09 (assume @p59 (forall @t97 (=> (and (tptp.times_succeeds @t77 @t76 @t95) (tptp.times_succeeds @t77 @t76 @t94)) @t96))) % 33.84/34.09 (assume @p60 (forall @t99 (=> @t84 (= (|tptp.'@*'| |tptp.'0'| @t76) |tptp.'0'|)))) % 33.84/34.09 (assume @p61 (forall @t93 (=> @t85 (= (|tptp.'@*'| @t101 @t76) (|tptp.'@+'| @t76 @t83))))) % 33.84/34.09 (assume @p62 (forall @t93 (=> @t85 (tptp.nat_succeeds @t83)))) % 33.84/34.09 (assume @p63 (forall @t81 (=> @t106 (= (|tptp.'@*'| @t79 @t75) (|tptp.'@+'| (|tptp.'@*'| @t77 @t75) @t111))))) % 33.84/34.09 (assume @p64 (forall @t81 (=> @t106 (= (|tptp.'@*'| @t83 @t75) (|tptp.'@*'| @t77 @t111))))) % 33.84/34.09 (assume @p65 (forall @t86 (=> @t80 (= (|tptp.'@*'| @t77 |tptp.'0'|) |tptp.'0'|)))) % 33.84/34.09 (assume @p66 (forall (@list @t76 @t77) (=> (and @t84 @t80) (= (|tptp.'@+'| @t112 @t76) (|tptp.'@*'| @t76 @t101))))) % 33.84/34.09 (assume @p67 (forall @t93 (=> @t85 (= @t83 @t112)))) % 33.84/34.09 (assume @p68 (forall @t86 (=> @t80 (= (|tptp.'@*'| @t113 @t77) @t77)))) % 33.84/34.09 (assume @p69 (forall @t86 (=> @t80 (= (|tptp.'@*'| @t77 @t113) @t77)))) % 33.84/34.09 (assume @p70 (forall @t81 (=> @t106 (= (|tptp.'@*'| @t75 @t79) (|tptp.'@+'| (|tptp.'@*'| @t75 @t77) (|tptp.'@*'| @t75 @t76)))))) % 33.84/34.09 (assume @p71 (forall @t93 (=> @t80 @t114))) % 33.84/34.09 (assume @p72 (forall @t93 (=> @t84 @t114))) % 33.84/34.09 (assume @p73 (forall @t93 (=> @t115 @t80))) % 33.84/34.09 (assume @p74 @t120) % 33.84/34.09 (assume @p75 (forall @t81 (=> (and @t115 (|tptp.'@<_succeeds'| @t76 @t116)) @t121))) % 33.84/34.09 (assume @p76 (forall @t93 (=> @t115 @t122))) % 33.84/34.09 (assume @p77 (forall @t81 (=> (and @t115 @t123) @t121))) % 33.84/34.09 (assume @p78 (forall @t86 (=> @t80 (|tptp.'@<_fails'| @t77 @t77)))) % 33.84/34.09 (assume @p79 (forall @t86 (=> @t80 (not (|tptp.'@<_succeeds'| @t77 @t77))))) % 33.84/34.09 (assume @p80 (forall @t86 (=> @t80 (|tptp.'@<_succeeds'| @t77 @t101)))) % 33.84/34.09 (assume @p81 (forall @t93 (=> (and @t84 @t122) @t125))) % 33.84/34.09 (assume @p82 (forall @t93 (=> @t85 (or @t115 @t124 (|tptp.'@<_succeeds'| @t76 @t77))))) % 33.84/34.09 (assume @p83 (forall @t86 (=> (and @t80 (not @t126)) (|tptp.'@<_succeeds'| |tptp.'0'| @t77)))) % 33.84/34.09 (assume @p84 (forall @t93 (=> @t80 @t127))) % 33.84/34.09 (assume @p85 (forall @t93 (=> @t84 @t127))) % 33.84/34.09 (assume @p86 (forall @t93 (=> @t128 @t80))) % 33.84/34.09 (assume @p87 (forall @t93 (=> @t128 (exists @t92 (tptp.plus_succeeds @t77 @t75 @t76))))) % 33.84/34.09 (assume @p88 (forall @t93 (=> @t128 (exists @t92 (= @t110 @t76))))) % 33.84/34.09 (assume @p89 (forall @t93 (=> @t115 (exists @t92 (tptp.plus_succeeds @t77 @t116 @t76))))) % 33.84/34.09 (assume @p90 (forall @t93 (=> @t115 (exists @t92 (= (|tptp.'@+'| @t77 @t116) @t76))))) % 33.84/34.09 (assume @p91 (forall @t93 (=> @t115 @t128))) % 33.84/34.09 (assume @p92 (forall @t86 (=> @t80 (|tptp.'@=<_succeeds'| @t77 @t77)))) % 33.84/34.09 (assume @p93 (forall @t93 (=> @t85 (or @t128 @t129)))) % 33.84/34.09 (assume @p94 (forall @t93 (=> @t85 (or @t115 @t129)))) % 33.84/34.09 (assume @p95 (forall @t93 (=> (and @t80 @t84 (|tptp.'@=<_fails'| @t77 @t76)) @t129))) % 33.84/34.09 (assume @p96 (forall @t93 (=> (and @t128 @t84) @t125))) % 33.84/34.09 (assume @p97 (forall @t81 (=> (and @t128 @t123) @t121))) % 33.84/34.09 (assume @p98 (forall @t81 (=> (and @t115 @t130) @t121))) % 33.84/34.09 (assume @p99 (forall @t81 (=> (and @t128 @t130) (|tptp.'@=<_succeeds'| @t77 @t75)))) % 33.84/34.09 (assume @p100 (forall @t93 (=> (and @t128 @t129) @t124))) % 33.84/34.09 (assume @p101 (forall @t86 (=> @t80 (|tptp.'@=<_succeeds'| @t77 @t101)))) % 33.84/34.09 (assume @p102 (forall @t86 (=> @t80 (|tptp.'@=<_fails'| @t101 @t77)))) % 33.84/34.09 (assume @p103 (forall @t81 (=> (and @t80 @t123) @t131))) % 33.84/34.09 (assume @p104 (forall @t93 (=> @t80 (|tptp.'@<_succeeds'| @t77 @t108)))) % 33.84/34.09 (assume @p105 (forall @t81 (=> (and @t115 @t84 @t89) (|tptp.'@<_succeeds'| @t110 @t105)))) % 33.84/34.09 (assume @p106 (forall @t93 (=> (and (|tptp.'@<_succeeds'| |tptp.'0'| @t76) @t80 @t84) (|tptp.'@<_succeeds'| @t77 @t109)))) % 33.84/34.09 (assume @p107 (forall @t81 (=> (and @t80 @t130) (|tptp.'@=<_succeeds'| @t79 @t110)))) % 33.84/34.09 (assume @p108 (forall @t81 (=> (and @t128 @t84 @t89) (|tptp.'@=<_succeeds'| @t110 @t105)))) % 33.84/34.09 (assume @p109 (forall @t93 (=> @t80 (|tptp.'@=<_succeeds'| @t77 @t79)))) % 33.84/34.09 (assume @p110 (forall @t93 (=> @t85 (|tptp.'@=<_succeeds'| @t76 @t79)))) % 33.84/34.09 (assume @p111 @t143) % 33.84/34.09 (assume @p112 @t146) % 33.84/34.09 (assume @p113 true) % 33.84/34.09 (step @p114 :rule aci_norm :args ((= (or (or @t148 @t147) @t123) @t149))) % 33.84/34.09 (step @p115 :rule refl :args (@t123)) % 33.84/34.09 (step @p116 :rule bool-and-de-morgan :args (@t80 @t131 true)) % 33.84/34.09 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t144) @t123))) % 33.84/34.09 (step @p118 :rule trans :premises (@p117 @p114)) % 33.84/34.09 (step @p119 :rule bool-impl-elim :args (@t144 @t123)) % 33.84/34.09 (step @p120 :rule trans :premises (@p119 @p118)) % 33.84/34.09 (step @p121 :rule cong :premises (@p120) :args (@t145)) % 33.84/34.09 (step @p122 :rule cong :premises (@p121) :args (@t146)) % 33.84/34.09 (step @p123 :rule eq_resolve :premises (@p112 @p122)) % 33.84/34.09 (step @p124 :rule alpha_equiv :args ((forall (@list @t152 @t151 @t150) (or (not (tptp.nat_succeeds @t152)) (not (|tptp.'@<_succeeds'| (|tptp.'@+'| @t152 @t151) (|tptp.'@+'| @t152 @t150))) (|tptp.'@<_succeeds'| @t151 @t150))) @t153 (@list @t77 @t76 @t75))) % 33.84/34.09 (step @p125 :rule alpha_equiv :args (@t160 (@list @t77 @t155 @t154) @t153)) % 33.84/34.09 (step @p126 :rule trans :premises (@p125 @p124)) % 33.84/34.09 (step @p127 :rule equiv_elim1 :premises (@p126)) % 33.84/34.09 (step @p128 :rule reordering :premises (@p127) :args ((or @t162 @t161))) % 33.84/34.09 (step @p129 :rule chain_m_resolution :premises (@p128 @p123) :args (@t161 @t163 (@list @t162))) % 33.84/34.09 (step @p130 :rule aci_norm :args ((= @t165 @t158))) % 33.84/34.09 (step @p131 :rule cong :premises (@p130) :args (@t166)) % 33.84/34.09 (step @p132 :rule quant-merge-prenex :args ((= (forall @t86 @t168) @t166))) % 33.84/34.09 (step @p133 :rule alpha_equiv :args (@t169 (@list @t155 @t154) @t170)) % 33.84/34.09 (step @p134 :rule refl :args (@t148)) % 33.84/34.09 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t171)) % 33.84/34.09 (step @p136 :rule quant-miniscope-or :args ((= @t168 @t171))) % 33.84/34.09 (step @p137 :rule trans :premises (@p136 @p135)) % 33.84/34.09 (step @p138 :rule symm :premises (@p137)) % 33.84/34.09 (step @p139 :rule cong :premises (@p138) :args ((forall @t86 (or @t148 @t172)))) % 33.84/34.09 (step @p140 :rule trans :premises (@p139 @p132)) % 33.84/34.09 (step @p141 :rule trans :premises (@p140 @p131)) % 33.84/34.09 (step @p142 :rule bool-impl-elim :args (@t80 @t172)) % 33.84/34.09 (step @p143 :rule cong :premises (@p142) :args ((forall @t86 (=> @t80 @t172)))) % 33.84/34.09 (step @p144 :rule trans :premises (@p143 @p141)) % 33.84/34.09 (step @p145 :rule bool-impl-elim :args (@t131 @t123)) % 33.84/34.09 (step @p146 :rule cong :premises (@p145) :args (@t133)) % 33.84/34.09 (step @p147 :rule refl :args (@t80)) % 33.84/34.09 (step @p148 :rule cong :premises (@p147 @p146) :args (@t134)) % 33.84/34.09 (step @p149 :rule cong :premises (@p148) :args (@t135)) % 33.84/34.09 (step @p150 :rule trans :premises (@p149 @p144)) % 33.84/34.09 (step @p151 :rule refl :args (@t175)) % 33.84/34.09 (step @p152 :rule refl :args (@t176)) % 33.84/34.09 (step @p153 :rule refl :args (@t178)) % 33.84/34.09 (step @p154 :rule refl :args (@t180)) % 33.84/34.09 (step @p155 :rule refl :args (@t181)) % 33.84/34.09 (step @p156 :rule eq-symm :args (@t182 @t77)) % 33.84/34.09 (step @p157 :rule cong :premises (@p156) :args (@t183)) % 33.84/34.09 (step @p158 :rule nary_cong :premises (@p157 @p155 @p154) :args (@t184)) % 33.84/34.09 (step @p159 :rule nary_cong :premises (@p158 @p153) :args (@t185)) % 33.84/34.09 (step @p160 :rule nary_cong :premises (@p159 @p152 @p151) :args (@t186)) % 33.84/34.09 (step @p161 :rule aci_norm :args ((= @t188 @t186))) % 33.84/34.09 (step @p162 :rule trans :premises (@p161 @p160)) % 33.84/34.09 (step @p163 :rule cong :premises (@p162) :args (@t190)) % 33.84/34.09 (step @p164 :rule quant-merge-prenex :args ((= (forall @t86 @t191) @t190))) % 33.84/34.09 (step @p165 :rule alpha_equiv :args (@t192 (@list @t174 @t173) @t170)) % 33.84/34.09 (step @p166 :rule quant-unused-vars :args ((= @t194 @t178))) % 33.84/34.09 (step @p167 :rule alpha_equiv :args (@t195 (@list @t179) (@list @t42))) % 33.84/34.09 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t196)) % 33.84/34.09 (step @p169 :rule quant-miniscope-and :args ((= @t197 @t196))) % 33.84/34.09 (step @p170 :rule trans :premises (@p169 @p168)) % 33.84/34.09 (step @p171 :rule nary_cong :premises (@p170 @p165) :args (@t198)) % 33.84/34.09 (step @p172 :rule quant-miniscope-or :args ((= @t191 @t198))) % 33.84/34.09 (step @p173 :rule trans :premises (@p172 @p171)) % 33.84/34.09 (step @p174 :rule symm :premises (@p173)) % 33.84/34.09 (step @p175 :rule cong :premises (@p174) :args ((forall @t86 (or (and @t205 @t178) @t172)))) % 33.84/34.09 (step @p176 :rule trans :premises (@p175 @p164)) % 33.84/34.09 (step @p177 :rule trans :premises (@p176 @p163)) % 33.84/34.09 (step @p178 :rule refl :args (@t172)) % 33.84/34.09 (step @p179 :rule refl :args (@t178)) % 33.84/34.09 (step @p180 :rule bool-double-not-elim :args (@t205)) % 33.84/34.09 (step @p181 :rule nary_cong :premises (@p180 @p179) :args ((and (not @t206) @t178))) % 33.84/34.09 (step @p182 :rule bool-or-de-morgan :args (@t206 @t177 false)) % 33.84/34.09 (step @p183 :rule trans :premises (@p182 @p181)) % 33.84/34.09 (step @p184 :rule nary_cong :premises (@p183 @p178) :args ((or (not @t207) @t172))) % 33.84/34.09 (step @p185 :rule bool-impl-elim :args (@t207 @t172)) % 33.84/34.09 (step @p186 :rule trans :premises (@p185 @p184)) % 33.84/34.09 (step @p187 :rule cong :premises (@p186) :args ((forall @t86 (=> @t207 @t172)))) % 33.84/34.09 (step @p188 :rule trans :premises (@p187 @p177)) % 33.84/34.09 (step @p189 :rule eq-symm :args (@t77 |tptp.'0'|)) % 33.84/34.09 (step @p190 :rule aci_norm :args ((= (or @t203 (or @t201 @t200)) @t204))) % 33.84/34.09 (step @p191 :rule bool-and-de-morgan :args (@t69 @t199 true)) % 33.84/34.09 (step @p192 :rule refl :args (@t203)) % 33.84/34.09 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or @t203 (not (and @t69 @t199))))) % 33.84/34.09 (step @p194 :rule bool-and-de-morgan :args (@t202 @t69 (and @t199))) % 33.84/34.09 (step @p195 :rule trans :premises (@p194 @p193)) % 33.84/34.09 (step @p196 :rule trans :premises (@p195 @p190)) % 33.84/34.09 (step @p197 :rule cong :premises (@p196) :args (@t209)) % 33.84/34.09 (step @p198 :rule cong :premises (@p197) :args (@t210)) % 33.84/34.09 (step @p199 :rule exists-elim :args ((= (exists @t72 @t208) @t210))) % 33.84/34.09 (step @p200 :rule trans :premises (@p199 @p198)) % 33.84/34.09 (step @p201 :rule bool-impl-elim :args (@t136 @t123)) % 33.84/34.09 (step @p202 :rule cong :premises (@p201) :args (@t137)) % 33.84/34.09 (step @p203 :rule refl :args (@t69)) % 33.84/34.09 (step @p204 :rule eq-symm :args (@t77 @t70)) % 33.84/34.09 (step @p205 :rule nary_cong :premises (@p204 @p203 @p202) :args (@t138)) % 33.84/34.09 (step @p206 :rule cong :premises (@p205) :args (@t139)) % 33.84/34.09 (step @p207 :rule trans :premises (@p206 @p200)) % 33.84/34.09 (step @p208 :rule nary_cong :premises (@p207 @p189) :args (@t140)) % 33.84/34.09 (step @p209 :rule cong :premises (@p208 @p146) :args (@t141)) % 33.84/34.09 (step @p210 :rule cong :premises (@p209) :args (@t142)) % 33.84/34.09 (step @p211 :rule trans :premises (@p210 @p188)) % 33.84/34.09 (step @p212 :rule cong :premises (@p211 @p150) :args (@t143)) % 33.84/34.09 (step @p213 :rule eq_resolve :premises (@p111 @p212)) % 33.84/34.09 (step @p214 :rule implies_elim :premises (@p213)) % 33.84/34.09 (step @p215 :rule reordering :premises (@p214) :args ((or @t160 @t212))) % 33.84/34.09 (step @p216 :rule chain_m_resolution :premises (@p215 @p129) :args (@t212 @t163 (@list @t160))) % 33.84/34.09 (step @p217 :rule skolemize :premises (@p216)) % 33.84/34.09 (step @p218 :rule bool-double-not-elim :args (@t218)) % 33.84/34.09 (step @p219 :rule refl :args (@t233)) % 33.84/34.09 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t233 (not @t220)))) % 33.84/34.09 (step @p221 :rule cnf_or_neg :args (@t233 1)) % 33.84/34.09 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 33.84/34.09 (step @p223 :rule reordering :premises (@p222) :args ((or @t218 @t233))) % 33.84/34.09 (step @p224 :rule chain_m_resolution :premises (@p223 @p217) :args (@t218 @t163 @t234)) % 33.84/34.09 (step @p225 :rule cnf_or_neg :args (@t233 2)) % 33.84/34.09 (step @p226 :rule chain_m_resolution :premises (@p225 @p217) :args (@t235 @t163 @t234)) % 33.84/34.09 (step @p227 :rule instantiate :premises (@p1) :args ((@list @t223))) % 33.84/34.09 (step @p228 :rule refl :args (@t222)) % 33.84/34.09 (step @p229 :rule bool-double-not-elim :args (@t236)) % 33.84/34.09 (step @p230 :rule refl :args (@t230)) % 33.84/34.09 (step @p231 :rule nary_cong :premises (@p230 @p229 @p228) :args ((or @t230 (not @t237) @t222))) % 33.84/34.09 (assume-push @p623 @t229) % 33.84/34.09 (assume-push @p624 @t237) % 33.84/34.09 (assume-push @p625 @t237) % 33.84/34.09 (assume-push @p626 @t229) % 33.84/34.09 (step @p236 :rule false_intro :premises (@p227)) % 33.84/34.09 (step @p237 :rule refl :args (|tptp.'0'|)) % 33.84/34.09 (step @p238 :rule cong :premises (@p237 @p623) :args (@t221)) % 33.84/34.09 (step @p239 :rule trans :premises (@p238 @p236)) % 33.84/34.09 (step @p240 :rule false_elim :premises (@p239)) % 33.84/34.09 (step-pop @p627 :rule scope :premises (@p240)) % 33.84/34.09 (step-pop @p628 :rule scope :premises (@p627)) % 33.84/34.09 (step @p241 :rule process_scope :premises (@p628) :args (@t222)) % 33.84/34.09 (step @p244 :rule and_intro :premises (@p227 @p623)) % 33.84/34.09 (step @p245 :rule modus_ponens :premises (@p244 @p241)) % 33.84/34.09 (step-pop @p629 :rule scope :premises (@p245)) % 33.84/34.09 (step-pop @p630 :rule scope :premises (@p629)) % 33.84/34.09 (step @p246 :rule process_scope :premises (@p630) :args (@t222)) % 33.84/34.09 (step @p249 :rule implies_elim :premises (@p246)) % 33.84/34.09 (step @p250 :rule cnf_and_neg :args (@t238)) % 33.84/34.09 (step @p251 :rule resolution :premises (@p250 @p249) :args (true @t238)) % 33.84/34.09 (step @p252 :rule eq_resolve :premises (@p251 @p231)) % 33.84/34.09 (step @p253 :rule reordering :premises (@p252) :args ((or @t230 @t222 @t236))) % 33.84/34.09 (assume-push @p631 @t3) % 33.84/34.09 (step-pop @p632 :rule scope :premises (@p227)) % 33.84/34.09 (step @p255 :rule process_scope :premises (@p632) :args (@t237)) % 33.84/34.09 (step @p257 :rule implies_elim :premises (@p255)) % 33.84/34.09 (step @p258 :rule refl :args (@t239)) % 33.84/34.09 (step @p259 :rule bool-double-not-elim :args (@t211)) % 33.84/34.09 (step @p260 :rule nary_cong :premises (@p259 @p258) :args ((or (not @t212) @t239))) % 33.84/34.09 (assume-push @p633 @t212) % 33.84/34.09 (step-pop @p634 :rule scope :premises (@p217)) % 33.84/34.09 (step @p262 :rule process_scope :premises (@p634) :args (@t239)) % 33.84/34.09 (step @p264 :rule implies_elim :premises (@p262)) % 33.84/34.09 (step @p265 :rule eq_resolve :premises (@p264 @p260)) % 33.84/34.09 (step @p266 :rule cnf_or_neg :args (@t233 0)) % 33.84/34.09 (step @p267 :rule bool-double-not-elim :args (@t221)) % 33.84/34.09 (step @p268 :rule refl :args (@t240)) % 33.84/34.09 (step @p269 :rule refl :args (@t232)) % 33.84/34.09 (step @p270 :rule nary_cong :premises (@p269 @p268 @p267) :args ((or @t232 @t240 (not @t222)))) % 33.84/34.09 (step @p271 :rule cnf_and_neg :args (@t232)) % 33.84/34.09 (step @p272 :rule eq_resolve :premises (@p271 @p270)) % 33.84/34.09 (step @p273 :rule reordering :premises (@p272) :args ((or @t221 @t232 @t240))) % 33.84/34.09 (step @p274 :rule bool-double-not-elim :args (@t224)) % 33.84/34.09 (step @p275 :rule refl :args (@t231)) % 33.84/34.09 (step @p276 :rule nary_cong :premises (@p275 @p274) :args ((or @t231 (not @t225)))) % 33.84/34.09 (step @p277 :rule cnf_or_neg :args (@t231 2)) % 33.84/34.09 (step @p278 :rule eq_resolve :premises (@p277 @p276)) % 33.84/34.09 (step @p279 :rule reordering :premises (@p278) :args ((or @t224 @t231))) % 33.84/34.09 (assume-push @p635 @t224) % 33.84/34.09 (step @p281 :rule instantiate :premises (@p635) :args ((@list @t216 @t213))) % 33.84/34.09 (step-pop @p636 :rule scope :premises (@p281)) % 33.84/34.09 (step @p282 :rule process_scope :premises (@p636) :args (@t245)) % 33.84/34.09 (step @p284 :rule implies_elim :premises (@p282)) % 33.84/34.09 (step @p285 :rule cnf_or_pos :args (@t245)) % 33.84/34.09 (step @p286 :rule reordering :premises (@p285) :args ((or @t219 @t244 (not @t245)))) % 33.84/34.09 (step @p287 :rule bool-double-not-elim :args (@t226)) % 33.84/34.09 (step @p288 :rule nary_cong :premises (@p275 @p287) :args ((or @t231 (not @t227)))) % 33.84/34.09 (step @p289 :rule cnf_or_neg :args 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@t218 @t330))) % 33.84/34.09 (step @p532 :rule cnf_or_pos :args (@t329)) % 33.84/34.09 (step @p533 :rule reordering :premises (@p532) :args ((or @t301 @t328 (not @t329)))) % 33.84/34.09 (step @p296 :rule instantiate :premises (@p294) :args (@t247)) % 33.84/34.09 (step @p534 :rule cnf_and_pos :args (@t328 0)) % 33.84/34.09 (step @p535 :rule reordering :premises (@p534) :args ((or @t327 (not @t328)))) % 33.84/34.09 (step @p536 :rule instantiate :premises (@p1) :args ((@list @t242))) % 33.84/34.09 (step @p537 :rule refl :args (@t331)) % 33.84/34.09 (step @p538 :rule bool-double-not-elim :args (@t332)) % 33.84/34.09 (step @p539 :rule refl :args (@t333)) % 33.84/34.09 (step @p540 :rule nary_cong :premises (@p230 @p539 @p538 @p537) :args ((or @t230 @t333 (not @t334) @t331))) % 33.84/34.09 (assume-push @p687 @t229) % 33.84/34.09 (assume-push @p688 @t250) % 33.84/34.09 (assume-push @p689 @t334) % 33.84/34.09 (assume-push @p690 @t334) % 33.84/34.09 (assume-push @p691 @t250) % 33.84/34.09 (assume-push @p692 @t229) % 33.84/34.09 (step @p547 :rule false_intro :premises (@p536)) % 33.84/34.09 (step @p413 :rule refl :args (@t216)) % 33.84/34.09 (step @p548 :rule cong :premises (@p687 @p413) :args (@t217)) % 33.84/34.09 (step @p549 :rule trans :premises (@p548 @p688)) % 33.84/34.09 (step @p237 :rule refl :args (|tptp.'0'|)) % 33.84/34.09 (step @p550 :rule cong :premises (@p237 @p549) :args (@t327)) % 33.84/34.09 (step @p551 :rule trans :premises (@p550 @p547)) % 33.84/34.09 (step @p552 :rule false_elim :premises (@p551)) % 33.84/34.09 (step-pop @p693 :rule scope :premises (@p552)) % 33.84/34.09 (step-pop @p694 :rule scope :premises (@p693)) % 33.84/34.09 (step-pop @p695 :rule scope :premises (@p694)) % 33.84/34.09 (step @p553 :rule process_scope :premises (@p695) :args (@t331)) % 33.84/34.09 (step @p557 :rule and_intro :premises (@p536 @p688 @p687)) % 33.84/34.09 (step @p558 :rule modus_ponens :premises (@p557 @p553)) % 33.84/34.09 (step-pop @p696 :rule scope :premises (@p558)) % 33.84/34.09 (step-pop @p697 :rule scope :premises (@p696)) % 33.84/34.09 (step-pop @p698 :rule scope :premises (@p697)) % 33.84/34.09 (step @p559 :rule process_scope :premises (@p698) :args (@t331)) % 33.84/34.09 (step @p563 :rule implies_elim :premises (@p559)) % 33.84/34.09 (step @p564 :rule cnf_and_neg :args (@t335)) % 33.84/34.09 (step @p565 :rule resolution :premises (@p564 @p563) :args (true @t335)) % 33.84/34.09 (step @p566 :rule eq_resolve :premises (@p565 @p540)) % 33.84/34.09 (step @p567 :rule reordering :premises (@p566) :args ((or @t230 @t331 @t333 @t332))) % 33.84/34.09 (step @p568 :rule chain_m_resolution :premises (@p567 @p536 @p535 @p301 @p296 @p533 @p531 @p291 @p482 @p273 @p464 @p463 @p253 @p227) :args (@t230 (@list true false false false false false false false true true false true true) (@list @t332 @t327 @t250 @t251 @t328 @t329 @t226 @t257 @t231 @t232 @t268 @t221 @t236))) % 33.84/34.09 (step @p569 :rule bool-double-not-elim :args (@t229)) % 33.84/34.09 (step @p570 :rule nary_cong :premises (@p275 @p569) :args ((or @t231 (not @t230)))) % 33.84/34.09 (step @p571 :rule cnf_or_neg :args (@t231 0)) % 33.84/34.09 (step @p572 :rule eq_resolve :premises (@p571 @p570)) % 33.84/34.09 (step @p573 :rule reordering :premises (@p572) :args ((or @t229 @t231))) % 33.84/34.09 (step @p574 :rule chain_m_resolution :premises (@p573 @p568) :args (@t231 @t163 (@list @t229))) % 33.84/34.09 (step @p575 :rule chain_m_resolution :premises (@p273 @p464 @p574) :args (@t221 (@list true false) (@list @t232 @t231))) % 33.84/34.09 (step @p576 :rule eq-symm :args (@t98 @t76)) % 33.84/34.09 (step @p577 :rule cong :premises (@p576) :args (@t100)) % 33.84/34.09 (step @p578 :rule eq_resolve :premises (@p45 @p577)) % 33.84/34.09 (step @p579 :rule instantiate :premises (@p578) :args ((@list @t216))) % 33.84/34.09 (step @p580 :rule instantiate :premises (@p578) :args ((@list @t213))) % 33.84/34.09 (step @p581 :rule refl :args (@t338)) % 33.84/34.09 (step @p582 :rule refl :args (@t341)) % 33.84/34.09 (step @p583 :rule bool-double-not-elim :args (@t219)) % 33.84/34.09 (step @p584 :rule nary_cong :premises (@p228 @p337 @p583 @p582 @p581) :args ((or @t222 @t220 (not @t235) @t341 @t338))) % 33.84/34.09 (assume-push @p699 @t218) % 33.84/34.09 (assume-push @p700 @t221) % 33.84/34.09 (assume-push @p701 @t340) % 33.84/34.09 (assume-push @p702 @t337) % 33.84/34.09 (assume-push @p703 @t235) % 33.84/34.09 (step @p449 :rule evaluate :args (@t299)) % 33.84/34.09 (step @p590 :rule true_intro :premises (@p224)) % 33.84/34.09 (step @p386 :rule refl :args (@t213)) % 33.84/34.09 (step @p591 :rule cong :premises (@p700 @p386) :args (@t336)) % 33.84/34.09 (step @p592 :rule trans :premises (@p580 @p591)) % 33.84/34.09 (step @p413 :rule refl :args (@t216)) % 33.84/34.09 (step @p593 :rule cong :premises (@p700 @p413) :args (@t339)) % 33.84/34.09 (step @p594 :rule trans :premises (@p579 @p593)) % 33.84/34.09 (step @p595 :rule cong :premises (@p594 @p592) :args (@t219)) % 33.84/34.09 (step @p596 :rule false_intro :premises (@p226)) % 33.84/34.09 (step @p597 :rule symm :premises (@p596)) % 33.84/34.09 (step @p598 :rule trans :premises (@p597 @p595 @p590)) % 33.84/34.09 (step @p599 false :rule eq_resolve :premises (@p598 @p449)) % 33.84/34.09 (step-pop @p704 :rule scope :premises (@p599)) % 33.84/34.09 (step-pop @p705 :rule scope :premises (@p704)) % 33.84/34.09 (step-pop @p706 :rule scope :premises (@p705)) % 33.84/34.09 (step-pop @p707 :rule scope :premises (@p706)) % 33.84/34.09 (step-pop @p708 :rule scope :premises (@p707)) % 33.84/34.09 (step @p600 :rule process_scope :premises (@p708) :args (false)) % 33.84/34.09 (assume-push @p709 @t221) % 33.84/34.09 (assume-push @p710 @t218) % 33.84/34.09 (assume-push @p711 @t235) % 33.84/34.09 (assume-push @p712 @t340) % 33.84/34.09 (assume-push @p713 @t337) % 33.84/34.09 (step @p611 :rule and_intro :premises (@p224 @p709 @p579 @p580 @p226)) % 33.84/34.09 (step-pop @p714 :rule scope :premises (@p611)) % 33.84/34.09 (step-pop @p715 :rule scope :premises (@p714)) % 33.84/34.09 (step-pop @p716 :rule scope :premises (@p715)) % 33.84/34.09 (step-pop @p717 :rule scope :premises (@p716)) % 33.84/34.09 (step-pop @p718 :rule scope :premises (@p717)) % 33.84/34.09 (step @p612 :rule process_scope :premises (@p718) :args (@t342)) % 33.84/34.09 (step @p618 :rule implies_elim :premises (@p612)) % 33.84/34.09 (step @p619 :rule resolution :premises (@p618 @p600) :args (true @t342)) % 33.84/34.09 (step @p620 :rule not_and :premises (@p619)) % 33.84/34.09 (step @p621 :rule eq_resolve :premises (@p620 @p584)) % 33.84/34.09 (step @p622 false :rule chain_m_resolution :premises (@p621 @p580 @p579 @p575 @p226 @p224) :args (false (@list false false false true false) (@list @t337 @t340 @t221 @t219 @t218))) % 33.84/34.09 ) % 33.84/34.09 % SZS output end Proof % 33.84/34.09 % cvc5 exiting %------------------------------------------------------------------------------