%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC041+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 08:57:48 AM UTC 2026 % Result : Theorem 0.40s 0.74s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SWC041+1 : TPTP v9.2.1. Released v2.4.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n023.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 19:11:58 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.74 % SZS status Theorem % 0.40/0.74 % SZS output start Proof % 0.40/0.74 ( % 0.40/0.74 (declare-sort $$unsorted 0) % 0.40/0.74 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.40/0.74 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.40/0.74 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.74 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.74 (declare-const tptp.nil $$unsorted) % 0.40/0.74 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.40/0.74 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.40/0.74 (define @t1 () (@var "V" $$unsorted)) % 0.40/0.74 (define @t2 () (@var "U" $$unsorted)) % 0.40/0.74 (define @t3 () (= @t2 @t1)) % 0.40/0.74 (define @t4 () (not @t3)) % 0.40/0.74 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.40/0.74 (define @t6 () (tptp.ssItem @t1)) % 0.40/0.74 (define @t7 () (@list @t1)) % 0.40/0.74 (define @t8 () (tptp.ssItem @t2)) % 0.40/0.74 (define @t9 () (@list @t2)) % 0.40/0.74 (define @t10 () (@var "X" $$unsorted)) % 0.40/0.74 (define @t11 () (tptp.cons @t1 @t10)) % 0.40/0.74 (define @t12 () (@var "W" $$unsorted)) % 0.40/0.74 (define @t13 () (tptp.ssList @t10)) % 0.40/0.74 (define @t14 () (@list @t10)) % 0.40/0.74 (define @t15 () (tptp.ssList @t12)) % 0.40/0.74 (define @t16 () (@list @t12)) % 0.40/0.74 (define @t17 () (tptp.ssList @t2)) % 0.40/0.74 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.40/0.74 (define @t19 () (tptp.app @t1 @t12)) % 0.40/0.74 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.40/0.74 (define @t21 () (tptp.ssList @t1)) % 0.40/0.74 (define @t22 () (tptp.app @t12 @t1)) % 0.40/0.74 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.40/0.74 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.40/0.74 (define @t25 () (tptp.leq @t12 @t1)) % 0.40/0.74 (define @t26 () (tptp.leq @t1 @t12)) % 0.40/0.74 (define @t27 () (@var "Z" $$unsorted)) % 0.40/0.74 (define @t28 () (@var "Y" $$unsorted)) % 0.40/0.74 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.40/0.74 (define @t30 () (tptp.ssList @t27)) % 0.40/0.74 (define @t31 () (@list @t27)) % 0.40/0.74 (define @t32 () (tptp.ssList @t28)) % 0.40/0.74 (define @t33 () (@list @t28)) % 0.40/0.74 (define @t34 () (tptp.ssItem @t12)) % 0.40/0.74 (define @t35 () (tptp.lt @t1 @t12)) % 0.40/0.74 (define @t36 () (= @t1 @t12)) % 0.40/0.74 (define @t37 () (tptp.equalelemsP @t2)) % 0.40/0.74 (define @t38 () (tptp.cons @t1 @t2)) % 0.40/0.74 (define @t39 () (tptp.ssList tptp.nil)) % 0.40/0.74 (define @t40 () (= @t1 @t2)) % 0.40/0.74 (define @t41 () (tptp.cons @t12 @t1)) % 0.40/0.74 (define @t42 () (= tptp.nil @t2)) % 0.40/0.74 (define @t43 () (tptp.hd @t2)) % 0.40/0.74 (define @t44 () (not @t42)) % 0.40/0.74 (define @t45 () (tptp.tl @t2)) % 0.40/0.74 (define @t46 () (tptp.app @t2 @t1)) % 0.40/0.74 (define @t47 () (tptp.app @t1 @t2)) % 0.40/0.74 (define @t48 () (tptp.leq @t1 @t2)) % 0.40/0.74 (define @t49 () (tptp.leq @t2 @t1)) % 0.40/0.74 (define @t50 () (tptp.geq @t2 @t1)) % 0.40/0.74 (define @t51 () (tptp.lt @t1 @t2)) % 0.40/0.74 (define @t52 () (tptp.lt @t2 @t1)) % 0.40/0.74 (define @t53 () (tptp.lt @t2 @t12)) % 0.40/0.74 (define @t54 () (tptp.gt @t2 @t1)) % 0.40/0.74 (define @t55 () (tptp.memberP @t12 @t2)) % 0.40/0.74 (define @t56 () (tptp.app @t12 @t2)) % 0.40/0.74 (define @t57 () (tptp.cons @t2 tptp.nil)) % 0.40/0.74 (define @t58 () (tptp.hd @t1)) % 0.40/0.74 (define @t59 () (= tptp.nil @t1)) % 0.40/0.74 (define @t60 () (not @t59)) % 0.40/0.74 (define @t61 () (tptp.cons @t2 @t1)) % 0.40/0.74 (define @t62 () (= @t12 @t2)) % 0.40/0.74 (define @t63 () (and @t59 @t42)) % 0.40/0.74 (define @t64 () (= tptp.nil @t46)) % 0.40/0.74 (define @t65 () (= @t64 @t63)) % 0.40/0.74 (define @t66 () (=> @t21 @t65)) % 0.40/0.74 (define @t67 () (forall @t7 @t66)) % 0.40/0.74 (define @t68 () (=> @t17 @t67)) % 0.40/0.74 (define @t69 () (forall @t9 @t68)) % 0.40/0.74 (define @t70 () (not (= tptp.nil @t10))) % 0.40/0.74 (define @t71 () (and @t70 (= tptp.nil @t12))) % 0.40/0.74 (define @t72 () (tptp.cons @t27 tptp.nil)) % 0.40/0.74 (define @t73 () (@var "X2" $$unsorted)) % 0.40/0.74 (define @t74 () (tptp.app @t73 @t72)) % 0.40/0.74 (define @t75 () (tptp.ssList @t73)) % 0.40/0.74 (define @t76 () (and @t75 (= @t74 @t12))) % 0.40/0.74 (define @t77 () (@list @t73)) % 0.40/0.74 (define @t78 () (exists @t77 @t76)) % 0.40/0.74 (define @t79 () (@var "X1" $$unsorted)) % 0.40/0.74 (define @t80 () (tptp.app @t72 @t79)) % 0.40/0.74 (define @t81 () (tptp.ssList @t79)) % 0.40/0.74 (define @t82 () (and @t81 (= @t80 @t28) @t78)) % 0.40/0.74 (define @t83 () (@list @t79)) % 0.40/0.74 (define @t84 () (exists @t83 @t82)) % 0.40/0.74 (define @t85 () (tptp.ssItem @t27)) % 0.40/0.74 (define @t86 () (and @t85 @t84)) % 0.40/0.74 (define @t87 () (exists @t31 @t86)) % 0.40/0.74 (define @t88 () (not (tptp.equalelemsP @t12))) % 0.40/0.74 (define @t89 () (tptp.app @t12 @t28)) % 0.40/0.74 (define @t90 () (not (= @t89 @t10))) % 0.40/0.74 (define @t91 () (or @t90 @t88 @t87)) % 0.40/0.74 (define @t92 () (=> @t32 @t91)) % 0.40/0.74 (define @t93 () (forall @t33 @t92)) % 0.40/0.74 (define @t94 () (not (= @t2 @t12))) % 0.40/0.74 (define @t95 () (not (= @t1 @t10))) % 0.40/0.74 (define @t96 () (or @t60 @t95 @t94 @t42 @t93 @t71)) % 0.40/0.74 (define @t97 () (=> @t13 @t96)) % 0.40/0.74 (define @t98 () (forall @t14 @t97)) % 0.40/0.74 (define @t99 () (=> @t15 @t98)) % 0.40/0.74 (define @t100 () (forall @t16 @t99)) % 0.40/0.74 (define @t101 () (=> @t21 @t100)) % 0.40/0.74 (define @t102 () (forall @t7 @t101)) % 0.40/0.74 (define @t103 () (=> @t17 @t102)) % 0.40/0.74 (define @t104 () (forall @t9 @t103)) % 0.40/0.74 (define @t105 () (not @t104)) % 0.40/0.74 (define @t106 () (@var "BOUND_VARIABLE_11154" $$unsorted)) % 0.40/0.74 (define @t107 () (@var "BOUND_VARIABLE_10983" $$unsorted)) % 0.40/0.74 (define @t108 () (tptp.app @t72 @t107)) % 0.40/0.74 (define @t109 () (not (tptp.ssList @t107))) % 0.40/0.74 (define @t110 () (@var "BOUND_VARIABLE_10975" $$unsorted)) % 0.40/0.74 (define @t111 () (tptp.app @t110 @t72)) % 0.40/0.74 (define @t112 () (not (= @t2 @t111))) % 0.40/0.74 (define @t113 () (not (tptp.ssList @t110))) % 0.40/0.74 (define @t114 () (not @t85)) % 0.40/0.74 (define @t115 () (@list @t27 @t110 @t107)) % 0.40/0.74 (define @t116 () (not (forall @t115 (or @t114 @t113 @t112 @t109 (not (= @t108 @t106)))))) % 0.40/0.74 (define @t117 () (not (= tptp.nil (tptp.app @t2 @t106)))) % 0.40/0.74 (define @t118 () (not (tptp.ssList @t106))) % 0.40/0.74 (define @t119 () (not @t37)) % 0.40/0.74 (define @t120 () (= @t2 tptp.nil)) % 0.40/0.74 (define @t121 () (not @t17)) % 0.40/0.74 (define @t122 () (or @t121 @t120 @t119 @t118 @t117 @t116)) % 0.40/0.74 (define @t123 () (or @t118 @t117 @t116)) % 0.40/0.74 (define @t124 () (or @t121 @t120 @t119 @t123)) % 0.40/0.74 (define @t125 () (@list @t2 @t106)) % 0.40/0.74 (define @t126 () (forall @t125 @t124)) % 0.40/0.74 (define @t127 () (@list @t106)) % 0.40/0.74 (define @t128 () (forall @t127 @t124)) % 0.40/0.74 (define @t129 () (forall @t127 @t123)) % 0.40/0.74 (define @t130 () (@var "BOUND_VARIABLE_11111" $$unsorted)) % 0.40/0.74 (define @t131 () (@list @t130)) % 0.40/0.74 (define @t132 () (or @t121 @t120 @t119 @t129)) % 0.40/0.74 (define @t133 () (not (forall @t115 (or @t114 @t113 @t112 @t109 (not (= @t108 @t130)))))) % 0.40/0.74 (define @t134 () (tptp.app @t2 @t130)) % 0.40/0.74 (define @t135 () (not (= tptp.nil @t134))) % 0.40/0.74 (define @t136 () (not (tptp.ssList @t130))) % 0.40/0.74 (define @t137 () (or @t136 @t135 @t133)) % 0.40/0.74 (define @t138 () (@list @t130)) % 0.40/0.74 (define @t139 () (forall @t138 @t137)) % 0.40/0.74 (define @t140 () (or @t121 @t120 @t119 @t139)) % 0.40/0.74 (define @t141 () (forall @t9 @t140)) % 0.40/0.74 (define @t142 () (not @t39)) % 0.40/0.74 (define @t143 () (or @t142 @t141)) % 0.40/0.74 (define @t144 () (or @t142 @t140)) % 0.40/0.74 (define @t145 () (or @t121 @t120 @t119 @t142 @t139)) % 0.40/0.74 (define @t146 () (or @t120 @t121 @t119 @t142 @t139)) % 0.40/0.74 (define @t147 () (or @t142 @t139)) % 0.40/0.74 (define @t148 () (or @t142 @t137)) % 0.40/0.74 (define @t149 () (or @t142 @t136 @t135 @t133)) % 0.40/0.74 (define @t150 () (not (= tptp.nil tptp.nil))) % 0.40/0.74 (define @t151 () (and @t150 @t120)) % 0.40/0.74 (define @t152 () (or @t142 @t150 @t151 @t136 @t135 @t133)) % 0.40/0.74 (define @t153 () (not (= @t1 @t134))) % 0.40/0.74 (define @t154 () (= @t1 tptp.nil)) % 0.40/0.74 (define @t155 () (not @t154)) % 0.40/0.74 (define @t156 () (and @t155 @t120)) % 0.40/0.74 (define @t157 () (not @t21)) % 0.40/0.74 (define @t158 () (or @t155 @t157 @t155 @t156 @t136 @t153 @t133)) % 0.40/0.74 (define @t159 () (or @t157 @t155 @t156 @t136 @t153 @t133)) % 0.40/0.74 (define @t160 () (forall @t7 @t159)) % 0.40/0.74 (define @t161 () (forall @t138 @t160)) % 0.40/0.74 (define @t162 () (forall (@list @t130 @t1) @t159)) % 0.40/0.74 (define @t163 () (@list @t1 @t130)) % 0.40/0.74 (define @t164 () (or @t136 @t153 @t133)) % 0.40/0.74 (define @t165 () (or @t157 @t155 @t156 @t164)) % 0.40/0.74 (define @t166 () (forall @t163 @t165)) % 0.40/0.74 (define @t167 () (forall @t138 @t165)) % 0.40/0.74 (define @t168 () (forall @t138 @t164)) % 0.40/0.74 (define @t169 () (@var "BOUND_VARIABLE_11063" $$unsorted)) % 0.40/0.74 (define @t170 () (@list @t169)) % 0.40/0.74 (define @t171 () (or @t157 @t155 @t156 @t168)) % 0.40/0.74 (define @t172 () (not (= @t108 @t169))) % 0.40/0.74 (define @t173 () (not (forall @t115 (or @t114 @t113 @t112 @t109 @t172)))) % 0.40/0.74 (define @t174 () (not (= @t1 (tptp.app @t2 @t169)))) % 0.40/0.74 (define @t175 () (not (tptp.ssList @t169))) % 0.40/0.74 (define @t176 () (or @t175 @t174 @t173)) % 0.40/0.74 (define @t177 () (@list @t169)) % 0.40/0.74 (define @t178 () (forall @t177 @t176)) % 0.40/0.74 (define @t179 () (or @t157 @t155 @t156 @t178)) % 0.40/0.74 (define @t180 () (forall @t7 @t179)) % 0.40/0.74 (define @t181 () (or @t120 @t121 @t119 @t180)) % 0.40/0.74 (define @t182 () (or @t120 @t121 @t119 @t179)) % 0.40/0.74 (define @t183 () (or @t157 @t155 @t120 @t121 @t119 @t156 @t178)) % 0.40/0.74 (define @t184 () (or @t155 @t120 @t157 @t121 @t119 @t156 @t178)) % 0.40/0.74 (define @t185 () (or @t121 @t119 @t156 @t178)) % 0.40/0.74 (define @t186 () (or @t121 @t119 @t156 @t176)) % 0.40/0.74 (define @t187 () (or @t121 @t119 @t156 @t175 @t174 @t173)) % 0.40/0.74 (define @t188 () (not (= @t2 @t2))) % 0.40/0.74 (define @t189 () (or @t121 @t188 @t119 @t156 @t175 @t174 @t173)) % 0.40/0.74 (define @t190 () (not (= @t12 @t111))) % 0.40/0.74 (define @t191 () (not (forall @t115 (or @t114 @t113 @t190 @t109 @t172)))) % 0.40/0.74 (define @t192 () (not (= @t1 (tptp.app @t12 @t169)))) % 0.40/0.74 (define @t193 () (= @t12 tptp.nil)) % 0.40/0.74 (define @t194 () (and @t155 @t193)) % 0.40/0.74 (define @t195 () (not @t15)) % 0.40/0.74 (define @t196 () (or @t94 @t195 @t94 @t88 @t194 @t175 @t192 @t191)) % 0.40/0.74 (define @t197 () (or @t195 @t94 @t88 @t194 @t175 @t192 @t191)) % 0.40/0.74 (define @t198 () (forall @t16 @t197)) % 0.40/0.74 (define @t199 () (forall @t177 @t198)) % 0.40/0.74 (define @t200 () (forall (@list @t169 @t12) @t197)) % 0.40/0.74 (define @t201 () (@list @t12 @t169)) % 0.40/0.74 (define @t202 () (or @t175 @t192 @t191)) % 0.40/0.74 (define @t203 () (or @t195 @t94 @t88 @t194 @t202)) % 0.40/0.74 (define @t204 () (forall @t201 @t203)) % 0.40/0.74 (define @t205 () (forall @t177 @t203)) % 0.40/0.74 (define @t206 () (forall @t177 @t202)) % 0.40/0.74 (define @t207 () (@var "BOUND_VARIABLE_11018" $$unsorted)) % 0.40/0.74 (define @t208 () (@list @t207)) % 0.40/0.74 (define @t209 () (or @t195 @t94 @t88 @t194 @t206)) % 0.40/0.74 (define @t210 () (not (forall @t115 (or @t114 @t113 @t190 @t109 (not (= @t108 @t207)))))) % 0.40/0.74 (define @t211 () (tptp.app @t12 @t207)) % 0.40/0.74 (define @t212 () (not (= @t1 @t211))) % 0.40/0.74 (define @t213 () (not (tptp.ssList @t207))) % 0.40/0.74 (define @t214 () (or @t213 @t212 @t210)) % 0.40/0.74 (define @t215 () (@list @t207)) % 0.40/0.74 (define @t216 () (forall @t215 @t214)) % 0.40/0.74 (define @t217 () (or @t195 @t94 @t88 @t194 @t216)) % 0.40/0.74 (define @t218 () (forall @t16 @t217)) % 0.40/0.74 (define @t219 () (or @t155 @t120 @t157 @t218)) % 0.40/0.74 (define @t220 () (or @t155 @t120 @t157 @t217)) % 0.40/0.74 (define @t221 () (or @t195 @t155 @t94 @t120 @t88 @t157 @t194 @t216)) % 0.40/0.74 (define @t222 () (or @t155 @t94 @t120 @t88 @t157 @t194 @t216)) % 0.40/0.74 (define @t223 () (or @t157 @t194 @t216)) % 0.40/0.74 (define @t224 () (or @t157 @t194 @t214)) % 0.40/0.74 (define @t225 () (or @t157 @t194 @t213 @t212 @t210)) % 0.40/0.74 (define @t226 () (not (= @t1 @t1))) % 0.40/0.74 (define @t227 () (or @t157 @t226 @t194 @t213 @t212 @t210)) % 0.40/0.74 (define @t228 () (not (= @t10 @t211))) % 0.40/0.74 (define @t229 () (and (not (= @t10 tptp.nil)) @t193)) % 0.40/0.74 (define @t230 () (not @t13)) % 0.40/0.74 (define @t231 () (or @t95 @t230 @t95 @t229 @t213 @t228 @t210)) % 0.40/0.74 (define @t232 () (or @t230 @t95 @t229 @t213 @t228 @t210)) % 0.40/0.74 (define @t233 () (forall @t14 @t232)) % 0.40/0.74 (define @t234 () (forall @t215 @t233)) % 0.40/0.74 (define @t235 () (forall (@list @t207 @t10) @t232)) % 0.40/0.74 (define @t236 () (@list @t10 @t207)) % 0.40/0.74 (define @t237 () (not (= @t207 @t108))) % 0.40/0.74 (define @t238 () (or @t114 @t113 @t190 @t109 @t237)) % 0.40/0.74 (define @t239 () (forall @t115 @t238)) % 0.40/0.74 (define @t240 () (not @t239)) % 0.40/0.74 (define @t241 () (or @t230 @t95 @t229 @t213 @t228 @t240)) % 0.40/0.74 (define @t242 () (or @t213 @t228 @t240)) % 0.40/0.74 (define @t243 () (or @t230 @t95 @t229 @t242)) % 0.40/0.74 (define @t244 () (forall @t236 @t243)) % 0.40/0.74 (define @t245 () (forall @t215 @t243)) % 0.40/0.74 (define @t246 () (forall @t215 @t242)) % 0.40/0.74 (define @t247 () (or @t230 @t95 @t229 @t246)) % 0.40/0.74 (define @t248 () (not (= @t28 @t108))) % 0.40/0.74 (define @t249 () (or @t114 @t113 @t190 @t109 @t248)) % 0.40/0.74 (define @t250 () (not (forall @t115 @t249))) % 0.40/0.74 (define @t251 () (not (= @t10 @t89))) % 0.40/0.74 (define @t252 () (not @t32)) % 0.40/0.74 (define @t253 () (or @t252 @t251 @t250)) % 0.40/0.74 (define @t254 () (forall @t33 @t253)) % 0.40/0.74 (define @t255 () (or @t230 @t95 @t229 @t254)) % 0.40/0.74 (define @t256 () (forall @t14 @t255)) % 0.40/0.74 (define @t257 () (or @t155 @t94 @t120 @t88 @t256)) % 0.40/0.74 (define @t258 () (or @t155 @t94 @t120 @t88 @t255)) % 0.40/0.74 (define @t259 () (or @t230 @t155 @t95 @t94 @t120 @t229 @t88 @t254)) % 0.40/0.74 (define @t260 () (or @t155 @t95 @t94 @t120 @t229 @t88 @t254)) % 0.40/0.74 (define @t261 () (or @t88 @t254)) % 0.40/0.74 (define @t262 () (or @t88 @t253)) % 0.40/0.74 (define @t263 () (or @t252 @t251 @t88 @t250)) % 0.40/0.74 (define @t264 () (or @t251 @t88 @t250)) % 0.40/0.74 (define @t265 () (or @t109 @t248)) % 0.40/0.74 (define @t266 () (or @t113 @t190)) % 0.40/0.74 (define @t267 () (or @t114 @t266 @t265)) % 0.40/0.74 (define @t268 () (forall @t115 @t267)) % 0.40/0.74 (define @t269 () (forall (@list @t110 @t107) @t267)) % 0.40/0.74 (define @t270 () (forall (@list @t107) @t265)) % 0.40/0.74 (define @t271 () (forall (@list @t110) @t266)) % 0.40/0.74 (define @t272 () (or @t114 @t271 @t270)) % 0.40/0.74 (define @t273 () (= @t28 @t80)) % 0.40/0.74 (define @t274 () (not @t273)) % 0.40/0.74 (define @t275 () (not @t81)) % 0.40/0.74 (define @t276 () (or @t275 @t274)) % 0.40/0.74 (define @t277 () (forall @t83 @t276)) % 0.40/0.74 (define @t278 () (= @t12 @t74)) % 0.40/0.74 (define @t279 () (forall @t77 (or (not @t75) (not @t278)))) % 0.40/0.74 (define @t280 () (or @t114 @t279 @t277)) % 0.40/0.74 (define @t281 () (or @t279 @t277)) % 0.40/0.74 (define @t282 () (not @t281)) % 0.40/0.74 (define @t283 () (and @t85 @t282)) % 0.40/0.74 (define @t284 () (forall @t31 (not @t283))) % 0.40/0.74 (define @t285 () (not @t284)) % 0.40/0.74 (define @t286 () (or @t279 @t276)) % 0.40/0.74 (define @t287 () (or @t275 @t274 @t279)) % 0.40/0.74 (define @t288 () (not @t279)) % 0.40/0.74 (define @t289 () (not @t288)) % 0.40/0.74 (define @t290 () (or @t275 @t274 @t289)) % 0.40/0.74 (define @t291 () (and @t81 @t273 @t288)) % 0.40/0.74 (define @t292 () (forall @t83 (not @t291))) % 0.40/0.74 (define @t293 () (not @t292)) % 0.40/0.74 (define @t294 () (and @t75 @t278)) % 0.40/0.74 (define @t295 () (forall @t77 (not @t294))) % 0.40/0.74 (define @t296 () (not @t295)) % 0.40/0.74 (define @t297 () (forall @t125 @t122)) % 0.40/0.74 (define @t298 () (@quantifiers_skolemize @t297 1)) % 0.40/0.74 (define @t299 () (not (= @t108 @t298))) % 0.40/0.74 (define @t300 () (@quantifiers_skolemize @t297 0)) % 0.40/0.74 (define @t301 () (= tptp.nil (tptp.app @t300 @t298))) % 0.40/0.74 (define @t302 () (not @t301)) % 0.40/0.74 (define @t303 () (tptp.ssList @t298)) % 0.40/0.74 (define @t304 () (not @t303)) % 0.40/0.74 (define @t305 () (not (tptp.equalelemsP @t300))) % 0.40/0.74 (define @t306 () (= tptp.nil @t300)) % 0.40/0.74 (define @t307 () (tptp.ssList @t300)) % 0.40/0.74 (define @t308 () (not @t307)) % 0.40/0.74 (define @t309 () (or @t308 @t306 @t305 @t304 @t302 (not (forall @t115 (or @t114 @t113 (not (= @t111 @t300)) @t109 @t299))))) % 0.40/0.74 (define @t310 () (not @t309)) % 0.40/0.74 (define @t311 () (not @t297)) % 0.40/0.74 (define @t312 () (not (= @t300 @t111))) % 0.40/0.74 (define @t313 () (or @t114 @t113 @t312 @t109 @t299)) % 0.40/0.74 (define @t314 () (forall @t115 @t313)) % 0.40/0.74 (define @t315 () (not @t314)) % 0.40/0.74 (define @t316 () (= @t300 tptp.nil)) % 0.40/0.74 (define @t317 () (or @t308 @t316 @t305 @t304 @t302 @t315)) % 0.40/0.74 (define @t318 () (not @t317)) % 0.40/0.74 (define @t319 () (@list true)) % 0.40/0.74 (define @t320 () (@list @t309)) % 0.40/0.74 (define @t321 () (@var "BOUND_VARIABLE_10610" $$unsorted)) % 0.40/0.74 (define @t322 () (and (= @t321 tptp.nil) @t120)) % 0.40/0.74 (define @t323 () (= tptp.nil (tptp.app @t2 @t321))) % 0.40/0.74 (define @t324 () (= @t323 @t322)) % 0.40/0.74 (define @t325 () (not (tptp.ssList @t321))) % 0.40/0.74 (define @t326 () (or @t121 @t325 @t324)) % 0.40/0.74 (define @t327 () (or @t325 @t324)) % 0.40/0.74 (define @t328 () (or @t121 @t327)) % 0.40/0.74 (define @t329 () (@list @t2 @t321)) % 0.40/0.74 (define @t330 () (forall @t329 @t328)) % 0.40/0.74 (define @t331 () (@list @t321)) % 0.40/0.74 (define @t332 () (forall @t331 @t328)) % 0.40/0.74 (define @t333 () (forall @t331 @t327)) % 0.40/0.74 (define @t334 () (or @t121 @t333)) % 0.40/0.74 (define @t335 () (= @t64 (and @t154 @t120))) % 0.40/0.74 (define @t336 () (forall @t7 (or @t157 @t335))) % 0.40/0.74 (define @t337 () (= tptp.nil @t298)) % 0.40/0.74 (define @t338 () (and @t337 @t316)) % 0.40/0.74 (define @t339 () (= @t301 @t338)) % 0.40/0.74 (define @t340 () (or @t308 @t304 @t339)) % 0.40/0.74 (define @t341 () (forall @t329 (or @t121 @t325 (= @t323 (and (= tptp.nil @t321) @t120))))) % 0.40/0.74 (define @t342 () (and @t337 @t306)) % 0.40/0.74 (define @t343 () (= @t301 @t342)) % 0.40/0.74 (define @t344 () (or @t308 @t304 @t343)) % 0.40/0.74 (define @t345 () (not @t342)) % 0.40/0.74 (define @t346 () (not @t343)) % 0.40/0.74 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.40/0.74 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.40/0.74 (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))))))))))) % 0.40/0.74 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.40/0.74 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.40/0.74 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.40/0.74 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.40/0.74 (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))))))))))))))))) % 0.40/0.74 (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)))))))))))))))) % 0.40/0.74 (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))))))))))))))))) % 0.40/0.74 (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))))))))))))))) % 0.40/0.74 (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))))))))))))))) % 0.40/0.74 (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)))))))))))))))) % 0.40/0.74 (assume @p14 (forall @t9 (=> @t17 (= @t37 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t28))) @t2) @t36))))))))))))) % 0.40/0.74 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.40/0.74 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.40/0.74 (assume @p17 @t39) % 0.40/0.74 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.40/0.74 (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) @t40))))))))))) % 0.40/0.74 (assume @p20 (forall @t9 (=> @t17 (or @t42 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t41 @t2))))))))) % 0.40/0.74 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.40/0.74 (assume @p22 (forall @t9 (=> @t17 (=> @t44 (tptp.ssItem @t43))))) % 0.40/0.74 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.40/0.74 (assume @p24 (forall @t9 (=> @t17 (=> @t44 (tptp.ssList @t45))))) % 0.40/0.74 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.40/0.74 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t46)))))) % 0.40/0.74 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t47) (tptp.app @t41 @t2))))))))) % 0.40/0.74 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.40/0.74 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 @t48) @t3)))))) % 0.40/0.74 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 @t26) (tptp.leq @t2 @t12))))))))) % 0.40/0.74 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.40/0.74 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 @t48)))))) % 0.40/0.74 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not @t51))))))) % 0.40/0.74 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 @t35) @t53)))))))) % 0.40/0.74 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 @t51)))))) % 0.40/0.74 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t55))))))))) % 0.40/0.74 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t55))))))))) % 0.40/0.74 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.40/0.74 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.40/0.74 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.40/0.74 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.40/0.74 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.40/0.74 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.40/0.74 (assume @p44 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (= (tptp.frontsegP (tptp.cons @t2 @t12) @t11) (and @t3 (tptp.frontsegP @t12 @t10)))))))))))) % 0.40/0.74 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.40/0.74 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t42)))) % 0.40/0.74 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.40/0.74 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.40/0.74 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.40/0.74 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t56 @t1))))))))) % 0.40/0.74 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.40/0.74 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t42)))) % 0.40/0.74 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.40/0.74 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.40/0.74 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.40/0.74 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t56 @t10) @t1))))))))))) % 0.40/0.74 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.40/0.74 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t42)))) % 0.40/0.74 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t57)))) % 0.40/0.74 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.40/0.74 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t57)))) % 0.40/0.74 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.40/0.74 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t57)))) % 0.40/0.74 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.40/0.74 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t57)))) % 0.40/0.74 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.40/0.74 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t61) (or @t59 (and @t60 (tptp.totalorderedP @t1) (tptp.leq @t2 @t58))))))))) % 0.40/0.74 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t57)))) % 0.40/0.74 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.40/0.74 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t61) (or @t59 (and @t60 (tptp.strictorderedP @t1) (tptp.lt @t2 @t58))))))))) % 0.40/0.74 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t57)))) % 0.40/0.74 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.40/0.74 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t57)))) % 0.40/0.74 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.40/0.74 (assume @p75 (forall @t9 (=> @t17 (=> @t44 (exists @t7 (and @t6 (= @t43 @t1))))))) % 0.40/0.74 (assume @p76 (forall @t9 (=> @t17 (=> @t44 (exists @t7 (and @t21 (= @t45 @t1))))))) % 0.40/0.74 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t60 @t44 (= @t58 @t43) (= (tptp.tl @t1) @t45)) @t40)))))) % 0.40/0.74 (assume @p78 (forall @t9 (=> @t17 (=> @t44 (= (tptp.cons @t43 @t45) @t2))))) % 0.40/0.74 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t46) @t62)))))))) % 0.40/0.74 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t47) @t62)))))))) % 0.40/0.74 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) 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(@p527 @p526)) % 0.40/0.74 (step @p529 :rule reordering :premises (@p528) :args ((or @t301 @t309))) % 0.40/0.74 (step @p530 :rule chain_m_resolution :premises (@p529 @p459) :args (@t301 @t319 @t320)) % 0.40/0.74 (step @p531 :rule cnf_equiv_pos1 :args (@t343)) % 0.40/0.74 (step @p532 :rule reordering :premises (@p531) :args ((or @t302 @t342 @t346))) % 0.40/0.74 (step @p533 :rule chain_m_resolution :premises (@p532 @p530 @p524) :args (@t346 (@list false true) (@list @t301 @t342))) % 0.40/0.74 (step @p534 :rule cnf_or_pos :args (@t344)) % 0.40/0.74 (step @p535 :rule reordering :premises (@p534) :args ((or @t308 @t304 @t343 (not @t344)))) % 0.40/0.74 (step @p536 false :rule chain_m_resolution :premises (@p535 @p533 @p519 @p472 @p466) :args (false (@list true false false false) (@list @t343 @t344 @t303 @t307))) % 0.40/0.74 ) % 0.40/0.74 % SZS output end Proof % 0.40/0.74 % cvc5 exiting %------------------------------------------------------------------------------