%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC098+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:58:02 AM UTC 2026 % Result : Theorem 0.52s 0.72s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC098+1 : TPTP v9.2.1. Released v2.4.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n016.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 19:15:39 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.52/0.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.52/0.72 % SZS status Theorem % 0.52/0.72 % SZS output start Proof % 0.52/0.72 ( % 0.52/0.72 (declare-sort $$unsorted 0) % 0.52/0.72 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.52/0.72 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.52/0.72 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.72 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.52/0.72 (declare-const tptp.nil $$unsorted) % 0.52/0.72 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.52/0.72 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.52/0.72 (define @t1 () (@var "V" $$unsorted)) % 0.52/0.72 (define @t2 () (@var "U" $$unsorted)) % 0.52/0.72 (define @t3 () (= @t2 @t1)) % 0.52/0.72 (define @t4 () (not @t3)) % 0.52/0.72 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.52/0.72 (define @t6 () (tptp.ssItem @t1)) % 0.52/0.72 (define @t7 () (@list @t1)) % 0.52/0.72 (define @t8 () (tptp.ssItem @t2)) % 0.52/0.72 (define @t9 () (@list @t2)) % 0.52/0.72 (define @t10 () (@var "X" $$unsorted)) % 0.52/0.72 (define @t11 () (tptp.cons @t1 @t10)) % 0.52/0.72 (define @t12 () (@var "W" $$unsorted)) % 0.52/0.72 (define @t13 () (tptp.ssList @t10)) % 0.52/0.72 (define @t14 () (@list @t10)) % 0.52/0.72 (define @t15 () (tptp.ssList @t12)) % 0.52/0.72 (define @t16 () (@list @t12)) % 0.52/0.72 (define @t17 () (tptp.ssList @t2)) % 0.52/0.72 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.52/0.72 (define @t19 () (tptp.app @t1 @t12)) % 0.52/0.72 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.52/0.72 (define @t21 () (tptp.ssList @t1)) % 0.52/0.72 (define @t22 () (tptp.app @t12 @t1)) % 0.52/0.72 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.52/0.72 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.52/0.72 (define @t25 () (tptp.leq @t12 @t1)) % 0.52/0.72 (define @t26 () (tptp.leq @t1 @t12)) % 0.52/0.72 (define @t27 () (@var "Z" $$unsorted)) % 0.52/0.72 (define @t28 () (@var "Y" $$unsorted)) % 0.52/0.72 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.52/0.72 (define @t30 () (tptp.ssList @t27)) % 0.52/0.72 (define @t31 () (@list @t27)) % 0.52/0.72 (define @t32 () (tptp.ssList @t28)) % 0.52/0.72 (define @t33 () (@list @t28)) % 0.52/0.72 (define @t34 () (tptp.ssItem @t12)) % 0.52/0.72 (define @t35 () (tptp.lt @t1 @t12)) % 0.52/0.72 (define @t36 () (= @t1 @t12)) % 0.52/0.72 (define @t37 () (tptp.cons @t1 @t2)) % 0.52/0.72 (define @t38 () (= @t1 @t2)) % 0.52/0.72 (define @t39 () (tptp.cons @t12 @t1)) % 0.52/0.72 (define @t40 () (= tptp.nil @t2)) % 0.52/0.72 (define @t41 () (tptp.hd @t2)) % 0.52/0.72 (define @t42 () (not @t40)) % 0.52/0.72 (define @t43 () (tptp.tl @t2)) % 0.52/0.72 (define @t44 () (tptp.app @t2 @t1)) % 0.52/0.72 (define @t45 () (tptp.app @t1 @t2)) % 0.52/0.72 (define @t46 () (tptp.leq @t1 @t2)) % 0.52/0.72 (define @t47 () (tptp.leq @t2 @t1)) % 0.52/0.72 (define @t48 () (tptp.geq @t2 @t1)) % 0.52/0.72 (define @t49 () (tptp.lt @t1 @t2)) % 0.52/0.72 (define @t50 () (tptp.lt @t2 @t1)) % 0.52/0.72 (define @t51 () (tptp.lt @t2 @t12)) % 0.52/0.72 (define @t52 () (tptp.gt @t2 @t1)) % 0.52/0.72 (define @t53 () (tptp.memberP @t12 @t2)) % 0.52/0.72 (define @t54 () (tptp.app @t12 @t2)) % 0.52/0.72 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.52/0.72 (define @t56 () (tptp.hd @t1)) % 0.52/0.72 (define @t57 () (= tptp.nil @t1)) % 0.52/0.72 (define @t58 () (not @t57)) % 0.52/0.72 (define @t59 () (tptp.cons @t2 @t1)) % 0.52/0.72 (define @t60 () (= @t12 @t2)) % 0.52/0.72 (define @t61 () (and @t57 @t40)) % 0.52/0.72 (define @t62 () (not (= tptp.nil @t12))) % 0.52/0.72 (define @t63 () (not (= tptp.nil @t10))) % 0.52/0.72 (define @t64 () (or @t63 @t62)) % 0.52/0.72 (define @t65 () (@var "X2" $$unsorted)) % 0.52/0.72 (define @t66 () (@var "X1" $$unsorted)) % 0.52/0.72 (define @t67 () (tptp.leq @t66 @t65)) % 0.52/0.72 (define @t68 () (tptp.memberP @t10 @t65)) % 0.52/0.72 (define @t69 () (= @t66 @t65)) % 0.52/0.72 (define @t70 () (not @t69)) % 0.52/0.72 (define @t71 () (tptp.ssItem @t65)) % 0.52/0.72 (define @t72 () (and @t71 @t70 @t68 @t67)) % 0.52/0.72 (define @t73 () (@list @t65)) % 0.52/0.72 (define @t74 () (exists @t73 @t72)) % 0.52/0.72 (define @t75 () (not (tptp.memberP @t10 @t66))) % 0.52/0.72 (define @t76 () (tptp.cons @t66 tptp.nil)) % 0.52/0.72 (define @t77 () (not (= @t76 @t12))) % 0.52/0.72 (define @t78 () (or @t77 @t75 @t74)) % 0.52/0.72 (define @t79 () (tptp.ssItem @t66)) % 0.52/0.72 (define @t80 () (=> @t79 @t78)) % 0.52/0.72 (define @t81 () (@list @t66)) % 0.52/0.72 (define @t82 () (forall @t81 @t80)) % 0.52/0.72 (define @t83 () (and @t82 @t64)) % 0.52/0.72 (define @t84 () (tptp.memberP @t1 @t28)) % 0.52/0.72 (define @t85 () (= @t28 @t27)) % 0.52/0.72 (define @t86 () (not (tptp.leq @t28 @t27))) % 0.52/0.72 (define @t87 () (not (tptp.memberP @t1 @t27))) % 0.52/0.72 (define @t88 () (or @t87 @t86 @t85)) % 0.52/0.72 (define @t89 () (tptp.ssItem @t27)) % 0.52/0.72 (define @t90 () (forall @t31 (=> @t89 @t88))) % 0.52/0.72 (define @t91 () (tptp.cons @t28 tptp.nil)) % 0.52/0.72 (define @t92 () (tptp.ssItem @t28)) % 0.52/0.72 (define @t93 () (and @t92 (= @t91 @t2) @t90 @t84)) % 0.52/0.72 (define @t94 () (exists @t33 @t93)) % 0.52/0.72 (define @t95 () (not (= @t2 @t12))) % 0.52/0.72 (define @t96 () (not (= @t1 @t10))) % 0.52/0.72 (define @t97 () (or @t96 @t95 @t94 @t61 @t83)) % 0.52/0.72 (define @t98 () (=> @t13 @t97)) % 0.52/0.72 (define @t99 () (forall @t14 @t98)) % 0.52/0.72 (define @t100 () (=> @t15 @t99)) % 0.52/0.72 (define @t101 () (forall @t16 @t100)) % 0.52/0.72 (define @t102 () (=> @t21 @t101)) % 0.52/0.72 (define @t103 () (forall @t7 @t102)) % 0.52/0.72 (define @t104 () (=> @t17 @t103)) % 0.52/0.72 (define @t105 () (forall @t9 @t104)) % 0.52/0.72 (define @t106 () (not @t105)) % 0.52/0.72 (define @t107 () (= @t2 tptp.nil)) % 0.52/0.72 (define @t108 () (not @t107)) % 0.52/0.72 (define @t109 () (@var "BOUND_VARIABLE_11165" $$unsorted)) % 0.52/0.72 (define @t110 () (= @t109 tptp.nil)) % 0.52/0.72 (define @t111 () (not @t110)) % 0.52/0.72 (define @t112 () (or @t111 @t108)) % 0.52/0.72 (define @t113 () (@var "BOUND_VARIABLE_11167" $$unsorted)) % 0.52/0.72 (define @t114 () (not @t71)) % 0.52/0.72 (define @t115 () (or (not (tptp.ssItem @t113)) (not (= @t2 (tptp.cons @t113 tptp.nil))) (not (tptp.memberP @t109 @t113)) (not (forall @t73 (or @t114 (= @t65 @t113) (not (tptp.memberP @t109 @t65)) (not (tptp.leq @t113 @t65))))))) % 0.52/0.72 (define @t116 () (and @t115 @t112)) % 0.52/0.72 (define @t117 () (and @t110 @t107)) % 0.52/0.72 (define @t118 () (not @t89)) % 0.52/0.72 (define @t119 () (= @t2 @t91)) % 0.52/0.72 (define @t120 () (not @t119)) % 0.52/0.72 (define @t121 () (not @t92)) % 0.52/0.72 (define @t122 () (not (forall @t33 (or @t121 @t120 (not (forall @t31 (or @t118 (not (tptp.memberP @t109 @t27)) @t86 @t85))) (not (tptp.memberP @t109 @t28)))))) % 0.52/0.72 (define @t123 () (not (tptp.ssList @t109))) % 0.52/0.72 (define @t124 () (not @t17)) % 0.52/0.72 (define @t125 () (or @t124 @t123 @t122 @t117 @t116)) % 0.52/0.72 (define @t126 () (or @t123 @t122 @t117 @t116)) % 0.52/0.72 (define @t127 () (or @t124 @t126)) % 0.52/0.72 (define @t128 () (@list @t2 @t109 @t113)) % 0.52/0.72 (define @t129 () (forall @t128 @t127)) % 0.52/0.72 (define @t130 () (@list @t109 @t113)) % 0.52/0.72 (define @t131 () (forall @t130 @t127)) % 0.52/0.72 (define @t132 () (forall @t130 @t126)) % 0.52/0.72 (define @t133 () (@var "BOUND_VARIABLE_11141" $$unsorted)) % 0.52/0.72 (define @t134 () (or @t124 @t132)) % 0.52/0.72 (define @t135 () (= @t1 tptp.nil)) % 0.52/0.72 (define @t136 () (not @t135)) % 0.52/0.72 (define @t137 () (or @t136 @t108)) % 0.52/0.72 (define @t138 () (not (tptp.memberP @t1 @t65))) % 0.52/0.72 (define @t139 () (or (not (tptp.ssItem @t133)) (not (= @t2 (tptp.cons @t133 tptp.nil))) (not (tptp.memberP @t1 @t133)) (not (forall @t73 (or @t114 (= @t65 @t133) @t138 (not (tptp.leq @t133 @t65))))))) % 0.52/0.72 (define @t140 () (and @t139 @t137)) % 0.52/0.72 (define @t141 () (and @t135 @t107)) % 0.52/0.72 (define @t142 () (not @t84)) % 0.52/0.72 (define @t143 () (or @t118 @t87 @t86 @t85)) % 0.52/0.72 (define @t144 () (forall @t31 @t143)) % 0.52/0.72 (define @t145 () (not @t144)) % 0.52/0.72 (define @t146 () (or @t121 @t120 @t145 @t142)) % 0.52/0.72 (define @t147 () (not (forall @t33 @t146))) % 0.52/0.72 (define @t148 () (not @t21)) % 0.52/0.72 (define @t149 () (or @t148 @t147 @t141 @t140)) % 0.52/0.72 (define @t150 () (forall (@list @t1 @t133) @t149)) % 0.52/0.72 (define @t151 () (or @t124 @t150)) % 0.52/0.72 (define @t152 () (@list @t133)) % 0.52/0.72 (define @t153 () (forall @t152 @t149)) % 0.52/0.72 (define @t154 () (forall @t152 @t137)) % 0.52/0.72 (define @t155 () (forall @t152 @t139)) % 0.52/0.72 (define @t156 () (@var "BOUND_VARIABLE_11110" $$unsorted)) % 0.52/0.72 (define @t157 () (@list @t156)) % 0.52/0.72 (define @t158 () (and @t155 @t154)) % 0.52/0.72 (define @t159 () (forall @t152 @t140)) % 0.52/0.72 (define @t160 () (or @t148 @t147 @t141 @t159)) % 0.52/0.72 (define @t161 () (and (forall (@list @t156) (or (not (tptp.ssItem @t156)) (not (= @t2 (tptp.cons @t156 tptp.nil))) (not (tptp.memberP @t1 @t156)) (not (forall @t73 (or @t114 (= @t65 @t156) @t138 (not (tptp.leq @t156 @t65))))))) @t137)) % 0.52/0.72 (define @t162 () (or @t148 @t147 @t141 @t161)) % 0.52/0.72 (define @t163 () (forall @t7 @t162)) % 0.52/0.72 (define @t164 () (or @t124 @t163)) % 0.52/0.72 (define @t165 () (or @t124 @t162)) % 0.52/0.72 (define @t166 () (or @t148 @t147 @t141 @t124 @t161)) % 0.52/0.72 (define @t167 () (or @t147 @t141 @t148 @t124 @t161)) % 0.52/0.72 (define @t168 () (@var "BOUND_VARIABLE_11075" $$unsorted)) % 0.52/0.72 (define @t169 () (@list @t168)) % 0.52/0.72 (define @t170 () (forall @t169 @t137)) % 0.52/0.72 (define @t171 () (not (forall @t73 (or @t114 (= @t65 @t168) @t138 (not (tptp.leq @t168 @t65)))))) % 0.52/0.72 (define @t172 () (not (tptp.memberP @t1 @t168))) % 0.52/0.72 (define @t173 () (tptp.cons @t168 tptp.nil)) % 0.52/0.72 (define @t174 () (not (tptp.ssItem @t168))) % 0.52/0.72 (define @t175 () (or @t174 (not (= @t2 @t173)) @t172 @t171)) % 0.52/0.72 (define @t176 () (forall @t169 @t175)) % 0.52/0.72 (define @t177 () (@list @t168)) % 0.52/0.72 (define @t178 () (and @t176 @t170)) % 0.52/0.72 (define @t179 () (and @t175 @t137)) % 0.52/0.72 (define @t180 () (forall @t169 @t179)) % 0.52/0.72 (define @t181 () (or @t124 @t180)) % 0.52/0.72 (define @t182 () (or @t124 @t179)) % 0.52/0.72 (define @t183 () (not (= @t2 @t2))) % 0.52/0.72 (define @t184 () (or @t124 @t183 @t179)) % 0.52/0.72 (define @t185 () (not (= @t12 tptp.nil))) % 0.52/0.72 (define @t186 () (or @t136 @t185)) % 0.52/0.72 (define @t187 () (or @t174 (not (= @t12 @t173)) @t172 @t171)) % 0.52/0.72 (define @t188 () (and @t187 @t186)) % 0.52/0.72 (define @t189 () (not @t15)) % 0.52/0.72 (define @t190 () (or @t95 @t189 @t95 @t188)) % 0.52/0.72 (define @t191 () (or @t189 @t95 @t188)) % 0.52/0.72 (define @t192 () (forall @t16 @t191)) % 0.52/0.72 (define @t193 () (forall @t169 @t192)) % 0.52/0.72 (define @t194 () (forall (@list @t168 @t12) @t191)) % 0.52/0.72 (define @t195 () (forall (@list @t12 @t168) @t191)) % 0.52/0.72 (define @t196 () (forall @t169 @t191)) % 0.52/0.72 (define @t197 () (forall @t169 @t186)) % 0.52/0.72 (define @t198 () (forall @t169 @t187)) % 0.52/0.72 (define @t199 () (@var "BOUND_VARIABLE_11044" $$unsorted)) % 0.52/0.72 (define @t200 () (@list @t199)) % 0.52/0.72 (define @t201 () (and @t198 @t197)) % 0.52/0.72 (define @t202 () (forall @t169 @t188)) % 0.52/0.72 (define @t203 () (or @t189 @t95 @t202)) % 0.52/0.72 (define @t204 () (and (forall (@list @t199) (or (not (tptp.ssItem @t199)) (not (= @t12 (tptp.cons @t199 tptp.nil))) (not (tptp.memberP @t1 @t199)) (not (forall @t73 (or @t114 (= @t65 @t199) @t138 (not (tptp.leq @t199 @t65))))))) @t186)) % 0.52/0.72 (define @t205 () (or @t189 @t95 @t204)) % 0.52/0.72 (define @t206 () (forall @t16 @t205)) % 0.52/0.72 (define @t207 () (or @t147 @t141 @t148 @t206)) % 0.52/0.72 (define @t208 () (or @t147 @t141 @t148 @t205)) % 0.52/0.72 (define @t209 () (or @t189 @t95 @t147 @t141 @t148 @t204)) % 0.52/0.72 (define @t210 () (or @t95 @t147 @t141 @t148 @t204)) % 0.52/0.72 (define @t211 () (@var "BOUND_VARIABLE_10998" $$unsorted)) % 0.52/0.72 (define @t212 () (@list @t211)) % 0.52/0.72 (define @t213 () (forall @t212 @t186)) % 0.52/0.72 (define @t214 () (not (tptp.leq @t211 @t65))) % 0.52/0.72 (define @t215 () (= @t65 @t211)) % 0.52/0.72 (define @t216 () (not (= @t12 (tptp.cons @t211 tptp.nil)))) % 0.52/0.72 (define @t217 () (not (tptp.ssItem @t211))) % 0.52/0.72 (define @t218 () (or @t217 @t216 (not (tptp.memberP @t1 @t211)) (not (forall @t73 (or @t114 @t215 @t138 @t214))))) % 0.52/0.72 (define @t219 () (forall @t212 @t218)) % 0.52/0.72 (define @t220 () (@list @t211)) % 0.52/0.72 (define @t221 () (and @t219 @t213)) % 0.52/0.72 (define @t222 () (and @t218 @t186)) % 0.52/0.72 (define @t223 () (forall @t212 @t222)) % 0.52/0.72 (define @t224 () (or @t148 @t223)) % 0.52/0.72 (define @t225 () (or @t148 @t222)) % 0.52/0.72 (define @t226 () (not (= @t1 @t1))) % 0.52/0.72 (define @t227 () (or @t148 @t226 @t222)) % 0.52/0.72 (define @t228 () (or (not (= @t10 tptp.nil)) @t185)) % 0.52/0.72 (define @t229 () (not @t68)) % 0.52/0.72 (define @t230 () (not (tptp.memberP @t10 @t211))) % 0.52/0.72 (define @t231 () (and (or @t217 @t216 @t230 (not (forall @t73 (or @t114 @t215 @t229 @t214)))) @t228)) % 0.52/0.72 (define @t232 () (not @t13)) % 0.52/0.72 (define @t233 () (or @t96 @t232 @t96 @t231)) % 0.52/0.72 (define @t234 () (or @t232 @t96 @t231)) % 0.52/0.72 (define @t235 () (forall @t14 @t234)) % 0.52/0.72 (define @t236 () (forall @t212 @t235)) % 0.52/0.72 (define @t237 () (forall (@list @t211 @t10) @t234)) % 0.52/0.72 (define @t238 () (@list @t10 @t211)) % 0.52/0.72 (define @t239 () (or @t114 (= @t211 @t65) @t229 @t214)) % 0.52/0.72 (define @t240 () (forall @t73 @t239)) % 0.52/0.72 (define @t241 () (not @t240)) % 0.52/0.72 (define @t242 () (or @t217 @t216 @t230 @t241)) % 0.52/0.72 (define @t243 () (and @t242 @t228)) % 0.52/0.72 (define @t244 () (or @t232 @t96 @t243)) % 0.52/0.72 (define @t245 () (forall @t238 @t244)) % 0.52/0.72 (define @t246 () (forall @t212 @t244)) % 0.52/0.72 (define @t247 () (forall @t212 @t228)) % 0.52/0.72 (define @t248 () (forall @t212 @t242)) % 0.52/0.72 (define @t249 () (and @t248 @t247)) % 0.52/0.72 (define @t250 () (forall @t212 @t243)) % 0.52/0.72 (define @t251 () (or @t232 @t96 @t250)) % 0.52/0.72 (define @t252 () (not @t67)) % 0.52/0.72 (define @t253 () (not (forall @t73 (or @t114 @t69 @t229 @t252)))) % 0.52/0.72 (define @t254 () (not (= @t12 @t76))) % 0.52/0.72 (define @t255 () (not @t79)) % 0.52/0.72 (define @t256 () (or @t255 @t254 @t75 @t253)) % 0.52/0.72 (define @t257 () (and (forall @t81 @t256) @t228)) % 0.52/0.72 (define @t258 () (or @t232 @t96 @t257)) % 0.52/0.72 (define @t259 () (forall @t14 @t258)) % 0.52/0.72 (define @t260 () (or @t95 @t147 @t141 @t259)) % 0.52/0.72 (define @t261 () (or @t95 @t147 @t141 @t258)) % 0.52/0.72 (define @t262 () (or @t232 @t96 @t95 @t147 @t141 @t257)) % 0.52/0.72 (define @t263 () (or @t96 @t95 @t147 @t141 @t257)) % 0.52/0.72 (define @t264 () (or @t254 @t75 @t253)) % 0.52/0.72 (define @t265 () (not @t70)) % 0.52/0.72 (define @t266 () (or @t114 @t265 @t229 @t252)) % 0.52/0.72 (define @t267 () (forall @t73 (not @t72))) % 0.52/0.72 (define @t268 () (not @t267)) % 0.52/0.72 (define @t269 () (and @t92 @t119 @t144 @t84)) % 0.52/0.72 (define @t270 () (forall @t33 (not @t269))) % 0.52/0.72 (define @t271 () (not @t270)) % 0.52/0.72 (define @t272 () (= tptp.nil @t109)) % 0.52/0.72 (define @t273 () (forall @t128 (or @t124 @t123 @t122 (and @t272 @t107) (and @t115 (or (not @t272) @t108))))) % 0.52/0.72 (define @t274 () (@quantifiers_skolemize @t273 0)) % 0.52/0.72 (define @t275 () (= tptp.nil @t274)) % 0.52/0.72 (define @t276 () (not @t275)) % 0.52/0.72 (define @t277 () (@quantifiers_skolemize @t273 1)) % 0.52/0.72 (define @t278 () (= tptp.nil @t277)) % 0.52/0.72 (define @t279 () (not @t278)) % 0.52/0.72 (define @t280 () (or @t279 @t276)) % 0.52/0.72 (define @t281 () (@quantifiers_skolemize @t273 2)) % 0.52/0.72 (define @t282 () (forall @t73 (or @t114 (= @t65 @t281) (not (tptp.memberP @t277 @t65)) (not (tptp.leq @t281 @t65))))) % 0.52/0.72 (define @t283 () (not @t282)) % 0.52/0.72 (define @t284 () (tptp.memberP @t277 @t281)) % 0.52/0.72 (define @t285 () (not @t284)) % 0.52/0.72 (define @t286 () (tptp.cons @t281 tptp.nil)) % 0.52/0.72 (define @t287 () (= @t274 @t286)) % 0.52/0.72 (define @t288 () (not @t287)) % 0.52/0.72 (define @t289 () (tptp.ssItem @t281)) % 0.52/0.72 (define @t290 () (not @t289)) % 0.52/0.72 (define @t291 () (or @t290 @t288 @t285 @t283)) % 0.52/0.72 (define @t292 () (and @t291 @t280)) % 0.52/0.72 (define @t293 () (and @t278 @t275)) % 0.52/0.72 (define @t294 () (not (tptp.memberP @t277 @t28))) % 0.52/0.72 (define @t295 () (not (tptp.memberP @t277 @t27))) % 0.52/0.72 (define @t296 () (not (forall @t31 (or @t118 @t295 @t86 @t85)))) % 0.52/0.72 (define @t297 () (forall @t33 (or @t121 (not (= @t91 @t274)) @t296 @t294))) % 0.52/0.72 (define @t298 () (not @t297)) % 0.52/0.72 (define @t299 () (not (tptp.ssList @t277))) % 0.52/0.72 (define @t300 () (not (tptp.ssList @t274))) % 0.52/0.72 (define @t301 () (or @t300 @t299 @t298 @t293 @t292)) % 0.52/0.72 (define @t302 () (not @t301)) % 0.52/0.72 (define @t303 () (not @t273)) % 0.52/0.72 (define @t304 () (= @t274 tptp.nil)) % 0.52/0.72 (define @t305 () (not @t304)) % 0.52/0.72 (define @t306 () (or @t279 @t305)) % 0.52/0.72 (define @t307 () (and @t291 @t306)) % 0.52/0.72 (define @t308 () (and @t278 @t304)) % 0.52/0.72 (define @t309 () (not (= @t274 @t91))) % 0.52/0.72 (define @t310 () (or @t121 @t309 @t296 @t294)) % 0.52/0.72 (define @t311 () (forall @t33 @t310)) % 0.52/0.72 (define @t312 () (not @t311)) % 0.52/0.72 (define @t313 () (or @t300 @t299 @t312 @t308 @t307)) % 0.52/0.72 (define @t314 () (not @t313)) % 0.52/0.72 (define @t315 () (@list true)) % 0.52/0.72 (define @t316 () (@list @t301)) % 0.52/0.72 (define @t317 () (not (tptp.leq @t281 @t27))) % 0.52/0.72 (define @t318 () (or @t118 @t295 @t317 (= @t281 @t27))) % 0.52/0.72 (define @t319 () (forall @t31 @t318)) % 0.52/0.72 (define @t320 () (not @t319)) % 0.52/0.72 (define @t321 () (not (= @t286 @t274))) % 0.52/0.72 (define @t322 () (or @t290 @t321 @t320 @t285)) % 0.52/0.72 (define @t323 () (= @t27 @t281)) % 0.52/0.72 (define @t324 () (or @t118 @t295 @t317 @t323)) % 0.52/0.72 (define @t325 () (forall @t31 @t324)) % 0.52/0.72 (define @t326 () (not @t325)) % 0.52/0.72 (define @t327 () (or @t290 @t288 @t326 @t285)) % 0.52/0.72 (define @t328 () (or @t118 @t323 @t295 @t317)) % 0.52/0.72 (define @t329 () (forall @t31 @t328)) % 0.52/0.72 (define @t330 () (@list @t280)) % 0.52/0.72 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.52/0.72 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.52/0.72 (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))))))))))) % 0.52/0.72 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.52/0.72 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.52/0.72 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.52/0.72 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.52/0.72 (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))))))))))))))))) % 0.52/0.72 (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)))))))))))))))) % 0.52/0.72 (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))))))))))))))))) % 0.52/0.72 (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))))))))))))))) % 0.52/0.72 (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))))))))))))))) % 0.52/0.72 (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)))))))))))))))) % 0.52/0.72 (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))))))))))))) % 0.52/0.72 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.52/0.72 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.52/0.72 (assume @p17 (tptp.ssList tptp.nil)) % 0.52/0.72 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.52/0.72 (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) @t38))))))))))) % 0.52/0.72 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.52/0.72 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.52/0.72 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.52/0.72 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.52/0.72 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.52/0.72 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.52/0.72 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.52/0.72 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.52/0.72 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.52/0.72 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.52/0.72 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.52/0.72 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.52/0.72 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.52/0.72 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.52/0.72 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.52/0.72 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.52/0.72 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.52/0.72 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.52/0.72 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.52/0.72 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.52/0.72 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.52/0.72 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.52/0.72 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.52/0.72 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.52/0.72 (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)))))))))))) % 0.52/0.72 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.52/0.72 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.52/0.72 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.52/0.72 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.52/0.72 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.52/0.72 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.52/0.72 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.52/0.72 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.52/0.72 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.52/0.72 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.52/0.72 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.52/0.72 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.52/0.72 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.52/0.72 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.52/0.72 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.52/0.72 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.52/0.72 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.52/0.72 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.52/0.72 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.52/0.72 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.52/0.72 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.52/0.72 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.52/0.72 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.52/0.72 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.52/0.72 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.52/0.72 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.52/0.72 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.52/0.72 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.52/0.72 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.52/0.72 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.52/0.72 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.52/0.72 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.52/0.72 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.52/0.72 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.52/0.72 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.52/0.72 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.52/0.72 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.52/0.72 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.52/0.72 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) @t61)))))) % 0.52/0.72 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 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0.52/0.72 (step @p498 :rule reordering :premises (@p497) :args ((or @t279 @t293 @t276))) % 0.52/0.72 (step @p499 false :rule chain_m_resolution :premises (@p498 @p496 @p490 @p416) :args (false (@list false false true) (@list @t275 @t278 @t293))) % 0.52/0.72 ) % 0.52/0.72 % SZS output end Proof % 0.52/0.72 % cvc5 exiting %------------------------------------------------------------------------------