%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC218+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:58:29 AM UTC 2026 % Result : Theorem 0.53s 0.72s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC218+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n023.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 19:26:13 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.53/0.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.53/0.72 % SZS status Theorem % 0.53/0.72 % SZS output start Proof % 0.53/0.72 ( % 0.53/0.72 (declare-sort $$unsorted 0) % 0.53/0.72 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.72 (declare-const tptp.nil $$unsorted) % 0.53/0.72 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.53/0.72 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.53/0.72 (define @t1 () (@var "V" $$unsorted)) % 0.53/0.72 (define @t2 () (@var "U" $$unsorted)) % 0.53/0.72 (define @t3 () (= @t2 @t1)) % 0.53/0.72 (define @t4 () (not @t3)) % 0.53/0.72 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.53/0.72 (define @t6 () (tptp.ssItem @t1)) % 0.53/0.72 (define @t7 () (@list @t1)) % 0.53/0.72 (define @t8 () (tptp.ssItem @t2)) % 0.53/0.72 (define @t9 () (@list @t2)) % 0.53/0.72 (define @t10 () (@var "X" $$unsorted)) % 0.53/0.72 (define @t11 () (tptp.cons @t1 @t10)) % 0.53/0.72 (define @t12 () (@var "W" $$unsorted)) % 0.53/0.72 (define @t13 () (tptp.ssList @t10)) % 0.53/0.72 (define @t14 () (@list @t10)) % 0.53/0.72 (define @t15 () (tptp.ssList @t12)) % 0.53/0.72 (define @t16 () (@list @t12)) % 0.53/0.72 (define @t17 () (tptp.ssList @t2)) % 0.53/0.72 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.53/0.72 (define @t19 () (tptp.app @t1 @t12)) % 0.53/0.72 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.53/0.72 (define @t21 () (tptp.ssList @t1)) % 0.53/0.72 (define @t22 () (tptp.app @t12 @t1)) % 0.53/0.72 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.53/0.72 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.53/0.72 (define @t25 () (tptp.leq @t12 @t1)) % 0.53/0.72 (define @t26 () (tptp.leq @t1 @t12)) % 0.53/0.72 (define @t27 () (@var "Z" $$unsorted)) % 0.53/0.72 (define @t28 () (@var "Y" $$unsorted)) % 0.53/0.72 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.53/0.72 (define @t30 () (tptp.ssList @t27)) % 0.53/0.72 (define @t31 () (@list @t27)) % 0.53/0.72 (define @t32 () (tptp.ssList @t28)) % 0.53/0.72 (define @t33 () (@list @t28)) % 0.53/0.72 (define @t34 () (tptp.ssItem @t12)) % 0.53/0.72 (define @t35 () (tptp.lt @t1 @t12)) % 0.53/0.72 (define @t36 () (= @t1 @t12)) % 0.53/0.72 (define @t37 () (forall @t7 (=> @t21 @t5))) % 0.53/0.72 (define @t38 () (=> @t17 @t37)) % 0.53/0.72 (define @t39 () (forall @t9 @t38)) % 0.53/0.72 (define @t40 () (tptp.cons @t1 @t2)) % 0.53/0.72 (define @t41 () (tptp.ssList @t40)) % 0.53/0.72 (define @t42 () (forall @t7 (=> @t6 @t41))) % 0.53/0.72 (define @t43 () (=> @t17 @t42)) % 0.53/0.72 (define @t44 () (forall @t9 @t43)) % 0.53/0.72 (define @t45 () (tptp.ssList tptp.nil)) % 0.53/0.72 (define @t46 () (not (= @t40 @t2))) % 0.53/0.72 (define @t47 () (=> @t6 @t46)) % 0.53/0.72 (define @t48 () (forall @t7 @t47)) % 0.53/0.72 (define @t49 () (=> @t17 @t48)) % 0.53/0.72 (define @t50 () (forall @t9 @t49)) % 0.53/0.72 (define @t51 () (= @t1 @t2)) % 0.53/0.72 (define @t52 () (tptp.cons @t12 @t1)) % 0.53/0.72 (define @t53 () (= tptp.nil @t2)) % 0.53/0.72 (define @t54 () (tptp.hd @t2)) % 0.53/0.72 (define @t55 () (not @t53)) % 0.53/0.72 (define @t56 () (tptp.tl @t2)) % 0.53/0.72 (define @t57 () (tptp.app @t2 @t1)) % 0.53/0.72 (define @t58 () (tptp.ssList @t57)) % 0.53/0.72 (define @t59 () (forall @t7 (=> @t21 @t58))) % 0.53/0.72 (define @t60 () (=> @t17 @t59)) % 0.53/0.72 (define @t61 () (forall @t9 @t60)) % 0.53/0.72 (define @t62 () (tptp.app @t1 @t2)) % 0.53/0.72 (define @t63 () (tptp.leq @t1 @t2)) % 0.53/0.72 (define @t64 () (tptp.leq @t2 @t1)) % 0.53/0.72 (define @t65 () (tptp.geq @t2 @t1)) % 0.53/0.72 (define @t66 () (tptp.lt @t1 @t2)) % 0.53/0.72 (define @t67 () (tptp.lt @t2 @t1)) % 0.53/0.72 (define @t68 () (tptp.lt @t2 @t12)) % 0.53/0.72 (define @t69 () (tptp.gt @t2 @t1)) % 0.53/0.72 (define @t70 () (tptp.memberP @t12 @t2)) % 0.53/0.72 (define @t71 () (tptp.app @t12 @t2)) % 0.53/0.72 (define @t72 () (tptp.cons @t2 tptp.nil)) % 0.53/0.72 (define @t73 () (tptp.hd @t1)) % 0.53/0.72 (define @t74 () (= tptp.nil @t1)) % 0.53/0.72 (define @t75 () (not @t74)) % 0.53/0.72 (define @t76 () (tptp.cons @t2 @t1)) % 0.53/0.72 (define @t77 () (= @t12 @t2)) % 0.53/0.72 (define @t78 () (and @t74 @t53)) % 0.53/0.72 (define @t79 () (= tptp.nil @t57)) % 0.53/0.72 (define @t80 () (= @t79 @t78)) % 0.53/0.72 (define @t81 () (=> @t21 @t80)) % 0.53/0.72 (define @t82 () (forall @t7 @t81)) % 0.53/0.72 (define @t83 () (=> @t17 @t82)) % 0.53/0.72 (define @t84 () (forall @t9 @t83)) % 0.53/0.72 (define @t85 () (tptp.neq @t2 tptp.nil)) % 0.53/0.72 (define @t86 () (@var "X1" $$unsorted)) % 0.53/0.72 (define @t87 () (tptp.app (tptp.app @t28 (tptp.cons @t86 tptp.nil)) @t27)) % 0.53/0.72 (define @t88 () (not (= @t87 @t12))) % 0.53/0.72 (define @t89 () (tptp.ssItem @t86)) % 0.53/0.72 (define @t90 () (=> @t89 @t88)) % 0.53/0.72 (define @t91 () (@list @t86)) % 0.53/0.72 (define @t92 () (forall @t91 @t90)) % 0.53/0.72 (define @t93 () (tptp.app @t28 @t27)) % 0.53/0.72 (define @t94 () (not (= @t93 @t10))) % 0.53/0.72 (define @t95 () (or @t94 @t92)) % 0.53/0.72 (define @t96 () (=> @t30 @t95)) % 0.53/0.72 (define @t97 () (forall @t31 @t96)) % 0.53/0.72 (define @t98 () (=> @t32 @t97)) % 0.53/0.72 (define @t99 () (forall @t33 @t98)) % 0.53/0.72 (define @t100 () (not (= @t2 @t12))) % 0.53/0.72 (define @t101 () (not (= @t1 @t10))) % 0.53/0.72 (define @t102 () (or @t101 @t100 @t99 @t85)) % 0.53/0.72 (define @t103 () (=> @t13 @t102)) % 0.53/0.72 (define @t104 () (forall @t14 @t103)) % 0.53/0.72 (define @t105 () (=> @t15 @t104)) % 0.53/0.72 (define @t106 () (forall @t16 @t105)) % 0.53/0.72 (define @t107 () (=> @t21 @t106)) % 0.53/0.72 (define @t108 () (forall @t7 @t107)) % 0.53/0.72 (define @t109 () (=> @t17 @t108)) % 0.53/0.72 (define @t110 () (forall @t9 @t109)) % 0.53/0.72 (define @t111 () (not @t110)) % 0.53/0.72 (define @t112 () (= @t2 tptp.nil)) % 0.53/0.72 (define @t113 () (@var "BOUND_VARIABLE_10599" $$unsorted)) % 0.53/0.72 (define @t114 () (and (= @t113 tptp.nil) @t112)) % 0.53/0.72 (define @t115 () (= tptp.nil (tptp.app @t2 @t113))) % 0.53/0.72 (define @t116 () (= @t115 @t114)) % 0.53/0.72 (define @t117 () (not (tptp.ssList @t113))) % 0.53/0.72 (define @t118 () (not @t17)) % 0.53/0.72 (define @t119 () (or @t118 @t117 @t116)) % 0.53/0.72 (define @t120 () (or @t117 @t116)) % 0.53/0.72 (define @t121 () (or @t118 @t120)) % 0.53/0.72 (define @t122 () (@list @t2 @t113)) % 0.53/0.72 (define @t123 () (forall @t122 @t121)) % 0.53/0.72 (define @t124 () (@list @t113)) % 0.53/0.72 (define @t125 () (forall @t124 @t121)) % 0.53/0.72 (define @t126 () (forall @t124 @t120)) % 0.53/0.72 (define @t127 () (@list @t1)) % 0.53/0.72 (define @t128 () (or @t118 @t126)) % 0.53/0.72 (define @t129 () (= @t79 (and (= @t1 tptp.nil) @t112))) % 0.53/0.72 (define @t130 () (not @t21)) % 0.53/0.72 (define @t131 () (forall @t7 (or @t130 @t129))) % 0.53/0.72 (define @t132 () (@var "BOUND_VARIABLE_11131" $$unsorted)) % 0.53/0.72 (define @t133 () (not (tptp.ssItem @t132))) % 0.53/0.72 (define @t134 () (@var "BOUND_VARIABLE_11129" $$unsorted)) % 0.53/0.72 (define @t135 () (not (tptp.ssList @t134))) % 0.53/0.72 (define @t136 () (@var "BOUND_VARIABLE_11127" $$unsorted)) % 0.53/0.72 (define @t137 () (not (tptp.ssList @t136))) % 0.53/0.72 (define @t138 () (not (tptp.ssList (tptp.app @t136 @t134)))) % 0.53/0.72 (define @t139 () (tptp.app (tptp.app @t136 (tptp.cons @t132 tptp.nil)) @t134)) % 0.53/0.72 (define @t140 () (tptp.neq @t139 tptp.nil)) % 0.53/0.72 (define @t141 () (not (tptp.ssList @t139))) % 0.53/0.72 (define @t142 () (or @t141 @t140 @t138 @t137 @t135 @t133)) % 0.53/0.72 (define @t143 () (@list @t136 @t134 @t132)) % 0.53/0.72 (define @t144 () (forall @t143 @t142)) % 0.53/0.72 (define @t145 () (@quantifiers_skolemize @t144 0)) % 0.53/0.72 (define @t146 () (@quantifiers_skolemize @t144 2)) % 0.53/0.72 (define @t147 () (tptp.cons @t146 tptp.nil)) % 0.53/0.72 (define @t148 () (= tptp.nil @t147)) % 0.53/0.72 (define @t149 () (and @t148 (= @t145 tptp.nil))) % 0.53/0.72 (define @t150 () (tptp.app @t145 @t147)) % 0.53/0.72 (define @t151 () (= tptp.nil @t150)) % 0.53/0.72 (define @t152 () (= @t151 @t149)) % 0.53/0.72 (define @t153 () (tptp.ssList @t147)) % 0.53/0.72 (define @t154 () (not @t153)) % 0.53/0.72 (define @t155 () (tptp.ssList @t145)) % 0.53/0.72 (define @t156 () (not @t155)) % 0.53/0.72 (define @t157 () (or @t156 @t154 @t152)) % 0.53/0.72 (define @t158 () (forall @t122 (or @t118 @t117 (= @t115 (and (= tptp.nil @t113) @t112))))) % 0.53/0.72 (define @t159 () (@list @t145 @t147)) % 0.53/0.72 (define @t160 () (and @t148 (= tptp.nil @t145))) % 0.53/0.72 (define @t161 () (= @t151 @t160)) % 0.53/0.72 (define @t162 () (or @t156 @t154 @t161)) % 0.53/0.72 (define @t163 () (@list false)) % 0.53/0.72 (define @t164 () (@list @t158)) % 0.53/0.72 (define @t165 () (@var "BOUND_VARIABLE_9127" $$unsorted)) % 0.53/0.72 (define @t166 () (tptp.ssList (tptp.cons @t165 @t2))) % 0.53/0.72 (define @t167 () (not (tptp.ssItem @t165))) % 0.53/0.72 (define @t168 () (or @t167 @t166)) % 0.53/0.72 (define @t169 () (or @t118 @t168)) % 0.53/0.72 (define @t170 () (forall (@list @t2 @t165) @t169)) % 0.53/0.72 (define @t171 () (@list @t165)) % 0.53/0.72 (define @t172 () (forall @t171 @t169)) % 0.53/0.72 (define @t173 () (forall @t171 @t168)) % 0.53/0.72 (define @t174 () (or @t118 @t173)) % 0.53/0.72 (define @t175 () (not @t6)) % 0.53/0.72 (define @t176 () (forall @t7 (or @t175 @t41))) % 0.53/0.72 (define @t177 () (@list tptp.nil @t146)) % 0.53/0.72 (define @t178 () (not (= @t139 @t139))) % 0.53/0.72 (define @t179 () (or @t141 @t140 @t138 @t137 @t135 @t133 @t178)) % 0.53/0.72 (define @t180 () (not (= @t2 @t139))) % 0.53/0.72 (define @t181 () (or @t180 @t118 @t85 @t138 @t137 @t135 @t133 @t180)) % 0.53/0.72 (define @t182 () (or @t118 @t85 @t138 @t137 @t135 @t133 @t180)) % 0.53/0.72 (define @t183 () (forall @t9 @t182)) % 0.53/0.72 (define @t184 () (forall @t143 @t183)) % 0.53/0.72 (define @t185 () (forall (@list @t136 @t134 @t132 @t2) @t182)) % 0.53/0.72 (define @t186 () (@list @t2 @t136 @t134 @t132)) % 0.53/0.72 (define @t187 () (or @t138 @t137 @t135 @t133 @t180)) % 0.53/0.72 (define @t188 () (or @t118 @t85 @t187)) % 0.53/0.72 (define @t189 () (forall @t186 @t188)) % 0.53/0.72 (define @t190 () (forall @t143 @t188)) % 0.53/0.72 (define @t191 () (forall @t143 @t187)) % 0.53/0.72 (define @t192 () (@var "BOUND_VARIABLE_11090" $$unsorted)) % 0.53/0.72 (define @t193 () (@var "BOUND_VARIABLE_11088" $$unsorted)) % 0.53/0.72 (define @t194 () (@var "BOUND_VARIABLE_11086" $$unsorted)) % 0.53/0.72 (define @t195 () (@list @t194 @t193 @t192)) % 0.53/0.72 (define @t196 () (or @t118 @t85 @t191)) % 0.53/0.72 (define @t197 () (not (= @t2 (tptp.app (tptp.app @t194 (tptp.cons @t192 tptp.nil)) @t193)))) % 0.53/0.72 (define @t198 () (not (tptp.ssItem @t192))) % 0.53/0.72 (define @t199 () (not (tptp.ssList @t193))) % 0.53/0.72 (define @t200 () (not (tptp.ssList @t194))) % 0.53/0.72 (define @t201 () (tptp.app @t194 @t193)) % 0.53/0.72 (define @t202 () (not (tptp.ssList @t201))) % 0.53/0.72 (define @t203 () (or @t202 @t200 @t199 @t198 @t197)) % 0.53/0.72 (define @t204 () (@list @t194 @t193 @t192)) % 0.53/0.72 (define @t205 () (forall @t204 @t203)) % 0.53/0.72 (define @t206 () (or @t118 @t85 @t205)) % 0.53/0.72 (define @t207 () (or @t85 @t118 @t205)) % 0.53/0.72 (define @t208 () (not (= @t201 @t201))) % 0.53/0.72 (define @t209 () (or @t202 @t200 @t199 @t208 @t198 @t197)) % 0.53/0.72 (define @t210 () (not (= @t1 @t201))) % 0.53/0.72 (define @t211 () (or @t210 @t130 @t200 @t199 @t210 @t198 @t197)) % 0.53/0.72 (define @t212 () (or @t130 @t200 @t199 @t210 @t198 @t197)) % 0.53/0.72 (define @t213 () (forall @t7 @t212)) % 0.53/0.72 (define @t214 () (forall @t204 @t213)) % 0.53/0.72 (define @t215 () (forall (@list @t194 @t193 @t192 @t1) @t212)) % 0.53/0.72 (define @t216 () (@list @t1 @t194 @t193 @t192)) % 0.53/0.72 (define @t217 () (or @t200 @t199 @t210 @t198 @t197)) % 0.53/0.72 (define @t218 () (or @t130 @t217)) % 0.53/0.72 (define @t219 () (forall @t216 @t218)) % 0.53/0.72 (define @t220 () (forall @t204 @t218)) % 0.53/0.72 (define @t221 () (forall @t204 @t217)) % 0.53/0.72 (define @t222 () (@var "BOUND_VARIABLE_11042" $$unsorted)) % 0.53/0.72 (define @t223 () (@var "BOUND_VARIABLE_11040" $$unsorted)) % 0.53/0.72 (define @t224 () (@var "BOUND_VARIABLE_11038" $$unsorted)) % 0.53/0.72 (define @t225 () (@list @t224 @t223 @t222)) % 0.53/0.72 (define @t226 () (or @t130 @t221)) % 0.53/0.72 (define @t227 () (tptp.app (tptp.app @t224 (tptp.cons @t222 tptp.nil)) @t223)) % 0.53/0.72 (define @t228 () (not (= @t2 @t227))) % 0.53/0.72 (define @t229 () (not (tptp.ssItem @t222))) % 0.53/0.72 (define @t230 () (not (= @t1 (tptp.app @t224 @t223)))) % 0.53/0.72 (define @t231 () (not (tptp.ssList @t223))) % 0.53/0.72 (define @t232 () (not (tptp.ssList @t224))) % 0.53/0.72 (define @t233 () (or @t232 @t231 @t230 @t229 @t228)) % 0.53/0.72 (define @t234 () (@list @t224 @t223 @t222)) % 0.53/0.72 (define @t235 () (forall @t234 @t233)) % 0.53/0.72 (define @t236 () (or @t130 @t235)) % 0.53/0.72 (define @t237 () (forall @t7 @t236)) % 0.53/0.72 (define @t238 () (or @t85 @t118 @t237)) % 0.53/0.72 (define @t239 () (or @t85 @t118 @t236)) % 0.53/0.72 (define @t240 () (or @t130 @t85 @t118 @t235)) % 0.53/0.72 (define @t241 () (or @t85 @t130 @t118 @t235)) % 0.53/0.72 (define @t242 () (or @t118 @t235)) % 0.53/0.72 (define @t243 () (or @t118 @t233)) % 0.53/0.72 (define @t244 () (or @t118 @t232 @t231 @t230 @t229 @t228)) % 0.53/0.72 (define @t245 () (not (= @t2 @t2))) % 0.53/0.72 (define @t246 () (or @t118 @t245 @t232 @t231 @t230 @t229 @t228)) % 0.53/0.72 (define @t247 () (not (= @t12 @t227))) % 0.53/0.72 (define @t248 () (not @t15)) % 0.53/0.72 (define @t249 () (or @t100 @t248 @t100 @t232 @t231 @t230 @t229 @t247)) % 0.53/0.72 (define @t250 () (or @t248 @t100 @t232 @t231 @t230 @t229 @t247)) % 0.53/0.72 (define @t251 () (forall @t16 @t250)) % 0.53/0.72 (define @t252 () (forall @t234 @t251)) % 0.53/0.72 (define @t253 () (forall (@list @t224 @t223 @t222 @t12) @t250)) % 0.53/0.72 (define @t254 () (@list @t12 @t224 @t223 @t222)) % 0.53/0.72 (define @t255 () (or @t232 @t231 @t230 @t229 @t247)) % 0.53/0.72 (define @t256 () (or @t248 @t100 @t255)) % 0.53/0.72 (define @t257 () (forall @t254 @t256)) % 0.53/0.72 (define @t258 () (forall @t234 @t256)) % 0.53/0.72 (define @t259 () (forall @t234 @t255)) % 0.53/0.72 (define @t260 () (@var "BOUND_VARIABLE_10996" $$unsorted)) % 0.53/0.72 (define @t261 () (@var "BOUND_VARIABLE_10994" $$unsorted)) % 0.53/0.72 (define @t262 () (@var "BOUND_VARIABLE_10992" $$unsorted)) % 0.53/0.72 (define @t263 () (@list @t262 @t261 @t260)) % 0.53/0.72 (define @t264 () (or @t248 @t100 @t259)) % 0.53/0.72 (define @t265 () (not (= @t12 (tptp.app (tptp.app @t262 (tptp.cons @t260 tptp.nil)) @t261)))) % 0.53/0.72 (define @t266 () (not (tptp.ssItem @t260))) % 0.53/0.72 (define @t267 () (tptp.app @t262 @t261)) % 0.53/0.72 (define @t268 () (not (= @t1 @t267))) % 0.53/0.72 (define @t269 () (not (tptp.ssList @t261))) % 0.53/0.72 (define @t270 () (not (tptp.ssList @t262))) % 0.53/0.72 (define @t271 () (or @t270 @t269 @t268 @t266 @t265)) % 0.53/0.72 (define @t272 () (@list @t262 @t261 @t260)) % 0.53/0.72 (define @t273 () (forall @t272 @t271)) % 0.53/0.72 (define @t274 () (or @t248 @t100 @t273)) % 0.53/0.72 (define @t275 () (forall @t16 @t274)) % 0.53/0.72 (define @t276 () (or @t85 @t130 @t275)) % 0.53/0.72 (define @t277 () (or @t85 @t130 @t274)) % 0.53/0.72 (define @t278 () (or @t248 @t100 @t85 @t130 @t273)) % 0.53/0.72 (define @t279 () (or @t100 @t85 @t130 @t273)) % 0.53/0.72 (define @t280 () (or @t130 @t273)) % 0.53/0.72 (define @t281 () (or @t130 @t271)) % 0.53/0.72 (define @t282 () (or @t130 @t270 @t269 @t268 @t266 @t265)) % 0.53/0.72 (define @t283 () (not (= @t1 @t1))) % 0.53/0.72 (define @t284 () (or @t130 @t283 @t270 @t269 @t268 @t266 @t265)) % 0.53/0.72 (define @t285 () (not (= @t10 @t267))) % 0.53/0.72 (define @t286 () (not @t13)) % 0.53/0.72 (define @t287 () (or @t101 @t286 @t101 @t270 @t269 @t285 @t266 @t265)) % 0.53/0.72 (define @t288 () (or @t286 @t101 @t270 @t269 @t285 @t266 @t265)) % 0.53/0.72 (define @t289 () (forall @t14 @t288)) % 0.53/0.72 (define @t290 () (forall @t272 @t289)) % 0.53/0.72 (define @t291 () (forall (@list @t262 @t261 @t260 @t10) @t288)) % 0.53/0.72 (define @t292 () (@list @t10 @t262 @t261 @t260)) % 0.53/0.72 (define @t293 () (or @t270 @t269 @t285 @t266 @t265)) % 0.53/0.72 (define @t294 () (or @t286 @t101 @t293)) % 0.53/0.72 (define @t295 () (forall @t292 @t294)) % 0.53/0.72 (define @t296 () (forall @t272 @t294)) % 0.53/0.72 (define @t297 () (forall @t272 @t293)) % 0.53/0.72 (define @t298 () (@var "BOUND_VARIABLE_10964" $$unsorted)) % 0.53/0.72 (define @t299 () (@var "BOUND_VARIABLE_10962" $$unsorted)) % 0.53/0.72 (define @t300 () (or @t286 @t101 @t297)) % 0.53/0.72 (define @t301 () (not (= @t12 (tptp.app (tptp.app @t28 (tptp.cons @t298 tptp.nil)) @t299)))) % 0.53/0.72 (define @t302 () (not (tptp.ssItem @t298))) % 0.53/0.72 (define @t303 () (not (= @t10 (tptp.app @t28 @t299)))) % 0.53/0.72 (define @t304 () (not (tptp.ssList @t299))) % 0.53/0.72 (define @t305 () (not @t32)) % 0.53/0.72 (define @t306 () (or @t305 @t304 @t303 @t302 @t301)) % 0.53/0.72 (define @t307 () (@list @t28 @t299 @t298)) % 0.53/0.72 (define @t308 () (forall @t307 @t306)) % 0.53/0.72 (define @t309 () (or @t286 @t101 @t308)) % 0.53/0.72 (define @t310 () (forall @t14 @t309)) % 0.53/0.72 (define @t311 () (or @t100 @t85 @t310)) % 0.53/0.72 (define @t312 () (or @t100 @t85 @t309)) % 0.53/0.72 (define @t313 () (or @t286 @t101 @t100 @t308 @t85)) % 0.53/0.72 (define @t314 () (or @t101 @t100 @t308 @t85)) % 0.53/0.72 (define @t315 () (or @t304 @t303 @t302 @t301)) % 0.53/0.72 (define @t316 () (or @t305 @t315)) % 0.53/0.72 (define @t317 () (forall @t307 @t316)) % 0.53/0.72 (define @t318 () (@list @t299 @t298)) % 0.53/0.72 (define @t319 () (forall @t318 @t316)) % 0.53/0.72 (define @t320 () (forall @t318 @t315)) % 0.53/0.72 (define @t321 () (@var "BOUND_VARIABLE_10943" $$unsorted)) % 0.53/0.72 (define @t322 () (or @t305 @t320)) % 0.53/0.72 (define @t323 () (not (= @t12 (tptp.app (tptp.app @t28 (tptp.cons @t321 tptp.nil)) @t27)))) % 0.53/0.72 (define @t324 () (not (tptp.ssItem @t321))) % 0.53/0.72 (define @t325 () (not (= @t10 @t93))) % 0.53/0.72 (define @t326 () (not @t30)) % 0.53/0.72 (define @t327 () (or @t326 @t325 @t324 @t323)) % 0.53/0.72 (define @t328 () (@list @t27 @t321)) % 0.53/0.72 (define @t329 () (forall @t328 @t327)) % 0.53/0.72 (define @t330 () (or @t324 @t323)) % 0.53/0.72 (define @t331 () (or @t326 @t325 @t330)) % 0.53/0.72 (define @t332 () (forall @t328 @t331)) % 0.53/0.72 (define @t333 () (@list @t321)) % 0.53/0.72 (define @t334 () (forall @t333 @t331)) % 0.53/0.72 (define @t335 () (forall @t333 @t330)) % 0.53/0.72 (define @t336 () (or @t326 @t325 @t335)) % 0.53/0.72 (define @t337 () (not (= @t12 @t87))) % 0.53/0.72 (define @t338 () (forall @t91 (or (not @t89) @t337))) % 0.53/0.72 (define @t339 () (or @t326 @t325 @t338)) % 0.53/0.72 (define @t340 () (or @t325 @t338)) % 0.53/0.72 (define @t341 () (tptp.ssItem @t146)) % 0.53/0.72 (define @t342 () (not @t341)) % 0.53/0.72 (define @t343 () (@quantifiers_skolemize @t144 1)) % 0.53/0.72 (define @t344 () (tptp.ssList @t343)) % 0.53/0.72 (define @t345 () (not @t344)) % 0.53/0.72 (define @t346 () (tptp.app @t150 @t343)) % 0.53/0.72 (define @t347 () (tptp.neq @t346 tptp.nil)) % 0.53/0.72 (define @t348 () (tptp.ssList @t346)) % 0.53/0.72 (define @t349 () (not @t348)) % 0.53/0.72 (define @t350 () (or @t349 @t347 (not (tptp.ssList (tptp.app @t145 @t343))) @t156 @t345 @t342)) % 0.53/0.72 (define @t351 () (@list true)) % 0.53/0.72 (define @t352 () (@list @t350)) % 0.53/0.72 (define @t353 () (not @t45)) % 0.53/0.72 (define @t354 () (or @t353 @t342 @t153)) % 0.53/0.72 (define @t355 () (@list false false false)) % 0.53/0.72 (define @t356 () (@var "BOUND_VARIABLE_9150" $$unsorted)) % 0.53/0.72 (define @t357 () (not (= @t2 (tptp.cons @t356 @t2)))) % 0.53/0.72 (define @t358 () (not (tptp.ssItem @t356))) % 0.53/0.72 (define @t359 () (or @t358 @t357)) % 0.53/0.72 (define @t360 () (or @t118 @t359)) % 0.53/0.72 (define @t361 () (forall (@list @t2 @t356) @t360)) % 0.53/0.72 (define @t362 () (@list @t356)) % 0.53/0.72 (define @t363 () (forall @t362 @t360)) % 0.53/0.72 (define @t364 () (forall @t362 @t359)) % 0.53/0.72 (define @t365 () (or @t118 @t364)) % 0.53/0.72 (define @t366 () (not (= @t2 @t40))) % 0.53/0.72 (define @t367 () (forall @t7 (or @t175 @t366))) % 0.53/0.72 (define @t368 () (not @t148)) % 0.53/0.72 (define @t369 () (or @t353 @t342 @t368)) % 0.53/0.72 (define @t370 () (not @t160)) % 0.53/0.72 (define @t371 () (not @t151)) % 0.53/0.72 (define @t372 () (@list true false)) % 0.53/0.72 (define @t373 () (= tptp.nil @t343)) % 0.53/0.72 (define @t374 () (and @t373 (= @t150 tptp.nil))) % 0.53/0.72 (define @t375 () (= tptp.nil @t346)) % 0.53/0.72 (define @t376 () (= @t375 @t374)) % 0.53/0.72 (define @t377 () (tptp.ssList @t150)) % 0.53/0.72 (define @t378 () (not @t377)) % 0.53/0.72 (define @t379 () (or @t378 @t345 @t376)) % 0.53/0.72 (define @t380 () (and @t373 @t151)) % 0.53/0.72 (define @t381 () (= @t375 @t380)) % 0.53/0.72 (define @t382 () (or @t378 @t345 @t381)) % 0.53/0.72 (define @t383 () (@var "BOUND_VARIABLE_9371" $$unsorted)) % 0.53/0.72 (define @t384 () (tptp.ssList (tptp.app @t2 @t383))) % 0.53/0.72 (define @t385 () (not (tptp.ssList @t383))) % 0.53/0.72 (define @t386 () (or @t385 @t384)) % 0.53/0.72 (define @t387 () (or @t118 @t386)) % 0.53/0.72 (define @t388 () (forall (@list @t2 @t383) @t387)) % 0.53/0.72 (define @t389 () (@list @t383)) % 0.53/0.72 (define @t390 () (forall @t389 @t387)) % 0.53/0.72 (define @t391 () (forall @t389 @t386)) % 0.53/0.72 (define @t392 () (or @t118 @t391)) % 0.53/0.72 (define @t393 () (forall @t7 (or @t130 @t58))) % 0.53/0.72 (define @t394 () (or @t156 @t154 @t377)) % 0.53/0.72 (define @t395 () (@var "BOUND_VARIABLE_9106" $$unsorted)) % 0.53/0.72 (define @t396 () (= (tptp.neq @t2 @t395) (not (= @t2 @t395)))) % 0.53/0.72 (define @t397 () (not (tptp.ssList @t395))) % 0.53/0.72 (define @t398 () (or @t118 @t397 @t396)) % 0.53/0.72 (define @t399 () (or @t397 @t396)) % 0.53/0.72 (define @t400 () (or @t118 @t399)) % 0.53/0.72 (define @t401 () (@list @t2 @t395)) % 0.53/0.72 (define @t402 () (forall @t401 @t400)) % 0.53/0.72 (define @t403 () (@list @t395)) % 0.53/0.72 (define @t404 () (forall @t403 @t400)) % 0.53/0.72 (define @t405 () (forall @t403 @t399)) % 0.53/0.72 (define @t406 () (or @t118 @t405)) % 0.53/0.72 (define @t407 () (forall @t7 (or @t130 @t5))) % 0.53/0.72 (define @t408 () (not (= @t346 tptp.nil))) % 0.53/0.72 (define @t409 () (= @t347 @t408)) % 0.53/0.72 (define @t410 () (or @t349 @t353 @t409)) % 0.53/0.72 (define @t411 () (forall @t401 @t398)) % 0.53/0.72 (define @t412 () (not @t375)) % 0.53/0.72 (define @t413 () (= @t347 @t412)) % 0.53/0.72 (define @t414 () (or @t349 @t353 @t413)) % 0.53/0.72 (define @t415 () (not @t413)) % 0.53/0.72 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.53/0.72 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.53/0.72 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 0.53/0.72 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.53/0.72 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.53/0.72 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.53/0.72 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.53/0.72 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not (and @t26 @t25))))))))))))))))) % 0.53/0.72 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t26 @t25)))))))))))))))) % 0.53/0.72 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t35 (tptp.lt @t12 @t1))))))))))))))))) % 0.53/0.72 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t26))))))))))))))) % 0.53/0.72 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.53/0.72 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not @t36)))))))))))))))) % 0.53/0.72 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t28))) @t2) @t36))))))))))))) % 0.53/0.72 (assume @p15 @t39) % 0.53/0.72 (assume @p16 @t44) % 0.53/0.72 (assume @p17 @t45) % 0.53/0.72 (assume @p18 @t50) % 0.53/0.72 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t51))))))))))) % 0.53/0.72 (assume @p20 (forall @t9 (=> @t17 (or @t53 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t52 @t2))))))))) % 0.53/0.72 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t40))))))) % 0.53/0.72 (assume @p22 (forall @t9 (=> @t17 (=> @t55 (tptp.ssItem @t54))))) % 0.53/0.72 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t40) @t1)))))) % 0.53/0.72 (assume @p24 (forall @t9 (=> @t17 (=> @t55 (tptp.ssList @t56))))) % 0.53/0.72 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t40) @t2)))))) % 0.53/0.72 (assume @p26 @t61) % 0.53/0.72 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t62) (tptp.app @t52 @t2))))))))) % 0.53/0.72 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.53/0.72 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t64 @t63) @t3)))))) % 0.53/0.72 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t64 @t26) (tptp.leq @t2 @t12))))))))) % 0.53/0.72 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.53/0.72 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t65 @t63)))))) % 0.53/0.72 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t67 (not @t66))))))) % 0.53/0.72 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t67 @t35) @t68)))))))) % 0.53/0.72 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t69 @t66)))))) % 0.53/0.72 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t70))))))))) % 0.53/0.72 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t70))))))))) % 0.53/0.72 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.53/0.72 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.53/0.72 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.53/0.72 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.53/0.72 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.53/0.72 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 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@p611 :rule reordering :premises (@p610) :args ((or @t353 @t349 @t413 (not @t414)))) % 0.53/0.72 (step @p612 :rule chain_m_resolution :premises (@p611 @p17 @p609 @p603) :args (@t413 @t355 (@list @t45 @t348 @t414))) % 0.53/0.72 (step @p613 :rule cnf_or_neg :args (@t350 1)) % 0.53/0.72 (step @p614 :rule chain_m_resolution :premises (@p613 @p463) :args ((not @t347) @t351 @t352)) % 0.53/0.72 (step @p615 :rule bool-double-not-elim :args (@t375)) % 0.53/0.72 (step @p616 :rule refl :args (@t415)) % 0.53/0.72 (step @p617 :rule nary_cong :premises (@p616 @p590 @p615) :args ((or @t415 @t347 (not @t412)))) % 0.53/0.72 (step @p618 :rule cnf_equiv_pos2 :args (@t413)) % 0.53/0.72 (step @p619 :rule eq_resolve :premises (@p618 @p617)) % 0.53/0.72 (step @p620 :rule reordering :premises (@p619) :args ((or @t347 @t375 @t415))) % 0.53/0.72 (step @p621 :rule chain_m_resolution :premises (@p620 @p614 @p612) :args (@t375 @t372 (@list @t347 @t413))) % 0.53/0.72 (step @p622 :rule cnf_equiv_pos1 :args (@t381)) % 0.53/0.72 (step @p623 :rule reordering :premises (@p622) :args ((or @t412 @t380 (not @t381)))) % 0.53/0.72 (step @p624 :rule chain_m_resolution :premises (@p623 @p621 @p567) :args (@t380 (@list false false) (@list @t375 @t381))) % 0.53/0.72 (step @p625 :rule cnf_and_pos :args (@t380 1)) % 0.53/0.72 (step @p626 :rule reordering :premises (@p625) :args ((or @t151 (not @t380)))) % 0.53/0.72 (step @p627 false :rule chain_m_resolution :premises (@p626 @p624 @p518) :args (false (@list false true) (@list @t380 @t151))) % 0.53/0.72 ) % 0.53/0.72 % SZS output end Proof % 0.53/0.72 % cvc5 exiting %------------------------------------------------------------------------------