%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC207+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 : n018.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 08:58:27 AM UTC 2026 % Result : Theorem 0.36s 0.94s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC207+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 : n018.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 19:24:20 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.94 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.94 % SZS status Theorem % 0.36/0.94 % SZS output start Proof % 0.36/0.94 ( % 0.36/0.94 (declare-sort $$unsorted 0) % 0.36/0.94 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.94 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.94 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.94 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.94 (declare-const tptp.nil $$unsorted) % 0.36/0.94 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.94 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.94 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.94 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.94 (define @t3 () (= @t2 @t1)) % 0.36/0.94 (define @t4 () (not @t3)) % 0.36/0.94 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.94 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.94 (define @t7 () (@list @t1)) % 0.36/0.94 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.94 (define @t9 () (@list @t2)) % 0.36/0.94 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.94 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.94 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.94 (define @t13 () (tptp.ssList @t10)) % 0.36/0.94 (define @t14 () (@list @t10)) % 0.36/0.94 (define @t15 () (tptp.ssList @t12)) % 0.36/0.94 (define @t16 () (@list @t12)) % 0.36/0.94 (define @t17 () (tptp.ssList @t2)) % 0.36/0.94 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.94 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.94 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.94 (define @t21 () (tptp.ssList @t1)) % 0.36/0.94 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.94 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.94 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.94 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.94 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.94 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.94 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.94 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.94 (define @t30 () (tptp.ssList @t27)) % 0.36/0.94 (define @t31 () (@list @t27)) % 0.36/0.94 (define @t32 () (tptp.ssList @t28)) % 0.36/0.94 (define @t33 () (@list @t28)) % 0.36/0.94 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.94 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.94 (define @t36 () (= @t1 @t12)) % 0.36/0.94 (define @t37 () (forall @t7 (=> @t21 @t5))) % 0.36/0.94 (define @t38 () (=> @t17 @t37)) % 0.36/0.94 (define @t39 () (forall @t9 @t38)) % 0.36/0.94 (define @t40 () (tptp.cons @t1 @t2)) % 0.36/0.94 (define @t41 () (tptp.ssList tptp.nil)) % 0.36/0.94 (define @t42 () (not (= @t40 @t2))) % 0.36/0.94 (define @t43 () (=> @t6 @t42)) % 0.36/0.94 (define @t44 () (forall @t7 @t43)) % 0.36/0.94 (define @t45 () (=> @t17 @t44)) % 0.36/0.94 (define @t46 () (forall @t9 @t45)) % 0.36/0.94 (define @t47 () (= @t1 @t2)) % 0.36/0.94 (define @t48 () (tptp.cons @t12 @t1)) % 0.36/0.94 (define @t49 () (= tptp.nil @t2)) % 0.36/0.94 (define @t50 () (tptp.hd @t2)) % 0.36/0.94 (define @t51 () (not @t49)) % 0.36/0.94 (define @t52 () (tptp.tl @t2)) % 0.36/0.94 (define @t53 () (tptp.app @t2 @t1)) % 0.36/0.94 (define @t54 () (tptp.app @t1 @t2)) % 0.36/0.94 (define @t55 () (tptp.leq @t1 @t2)) % 0.36/0.94 (define @t56 () (tptp.leq @t2 @t1)) % 0.36/0.94 (define @t57 () (tptp.geq @t2 @t1)) % 0.36/0.94 (define @t58 () (tptp.lt @t1 @t2)) % 0.36/0.94 (define @t59 () (tptp.lt @t2 @t1)) % 0.36/0.94 (define @t60 () (tptp.lt @t2 @t12)) % 0.36/0.94 (define @t61 () (tptp.gt @t2 @t1)) % 0.36/0.94 (define @t62 () (tptp.memberP @t12 @t2)) % 0.36/0.94 (define @t63 () (tptp.app @t12 @t2)) % 0.36/0.94 (define @t64 () (tptp.cons @t2 tptp.nil)) % 0.36/0.94 (define @t65 () (tptp.hd @t1)) % 0.36/0.94 (define @t66 () (= tptp.nil @t1)) % 0.36/0.94 (define @t67 () (not @t66)) % 0.36/0.94 (define @t68 () (tptp.cons @t2 @t1)) % 0.36/0.94 (define @t69 () (= @t12 @t2)) % 0.36/0.94 (define @t70 () (not (= tptp.nil @t12))) % 0.36/0.94 (define @t71 () (not (= tptp.nil @t10))) % 0.36/0.94 (define @t72 () (or @t71 @t70)) % 0.36/0.94 (define @t73 () (tptp.leq @t28 @t27)) % 0.36/0.94 (define @t74 () (tptp.memberP @t10 @t27)) % 0.36/0.94 (define @t75 () (= @t28 @t27)) % 0.36/0.94 (define @t76 () (not @t75)) % 0.36/0.94 (define @t77 () (tptp.ssItem @t27)) % 0.36/0.94 (define @t78 () (and @t77 @t76 @t74 @t73)) % 0.36/0.94 (define @t79 () (exists @t31 @t78)) % 0.36/0.94 (define @t80 () (not (tptp.memberP @t10 @t28))) % 0.36/0.94 (define @t81 () (tptp.cons @t28 tptp.nil)) % 0.36/0.94 (define @t82 () (not (= @t81 @t12))) % 0.36/0.94 (define @t83 () (or @t82 @t80 @t79)) % 0.36/0.94 (define @t84 () (tptp.ssItem @t28)) % 0.36/0.94 (define @t85 () (=> @t84 @t83)) % 0.36/0.94 (define @t86 () (forall @t33 @t85)) % 0.36/0.94 (define @t87 () (and @t86 @t72)) % 0.36/0.94 (define @t88 () (tptp.neq @t2 tptp.nil)) % 0.36/0.94 (define @t89 () (not (tptp.neq @t1 tptp.nil))) % 0.36/0.94 (define @t90 () (not (= @t2 @t12))) % 0.36/0.94 (define @t91 () (not (= @t1 @t10))) % 0.36/0.94 (define @t92 () (or @t91 @t90 @t89 @t88 @t87)) % 0.36/0.94 (define @t93 () (=> @t13 @t92)) % 0.36/0.94 (define @t94 () (forall @t14 @t93)) % 0.36/0.94 (define @t95 () (=> @t15 @t94)) % 0.36/0.94 (define @t96 () (forall @t16 @t95)) % 0.36/0.94 (define @t97 () (=> @t21 @t96)) % 0.36/0.94 (define @t98 () (forall @t7 @t97)) % 0.36/0.94 (define @t99 () (=> @t17 @t98)) % 0.36/0.94 (define @t100 () (forall @t9 @t99)) % 0.36/0.94 (define @t101 () (not @t100)) % 0.36/0.94 (define @t102 () (not (= @t2 tptp.nil))) % 0.36/0.94 (define @t103 () (@var "BOUND_VARIABLE_11134" $$unsorted)) % 0.36/0.94 (define @t104 () (not (= @t103 tptp.nil))) % 0.36/0.94 (define @t105 () (or @t104 @t102)) % 0.36/0.94 (define @t106 () (@var "BOUND_VARIABLE_11136" $$unsorted)) % 0.36/0.94 (define @t107 () (not @t77)) % 0.36/0.94 (define @t108 () (or (not (tptp.ssItem @t106)) (not (= @t2 (tptp.cons @t106 tptp.nil))) (not (tptp.memberP @t103 @t106)) (not (forall @t31 (or @t107 (= @t27 @t106) (not (tptp.memberP @t103 @t27)) (not (tptp.leq @t106 @t27))))))) % 0.36/0.94 (define @t109 () (and @t108 @t105)) % 0.36/0.94 (define @t110 () (not (tptp.neq @t103 tptp.nil))) % 0.36/0.94 (define @t111 () (not (tptp.ssList @t103))) % 0.36/0.94 (define @t112 () (not @t17)) % 0.36/0.94 (define @t113 () (or @t112 @t88 @t111 @t110 @t109)) % 0.36/0.94 (define @t114 () (or @t111 @t110 @t109)) % 0.36/0.94 (define @t115 () (or @t112 @t88 @t114)) % 0.36/0.94 (define @t116 () (@list @t2 @t103 @t106)) % 0.36/0.94 (define @t117 () (forall @t116 @t115)) % 0.36/0.94 (define @t118 () (@list @t103 @t106)) % 0.36/0.94 (define @t119 () (forall @t118 @t115)) % 0.36/0.94 (define @t120 () (forall @t118 @t114)) % 0.36/0.94 (define @t121 () (@var "BOUND_VARIABLE_11109" $$unsorted)) % 0.36/0.94 (define @t122 () (or @t112 @t88 @t120)) % 0.36/0.94 (define @t123 () (not (= @t1 tptp.nil))) % 0.36/0.94 (define @t124 () (or @t123 @t102)) % 0.36/0.94 (define @t125 () (not (tptp.memberP @t1 @t27))) % 0.36/0.94 (define @t126 () (or (not (tptp.ssItem @t121)) (not (= @t2 (tptp.cons @t121 tptp.nil))) (not (tptp.memberP @t1 @t121)) (not (forall @t31 (or @t107 (= @t27 @t121) @t125 (not (tptp.leq @t121 @t27))))))) % 0.36/0.94 (define @t127 () (and @t126 @t124)) % 0.36/0.94 (define @t128 () (not @t21)) % 0.36/0.94 (define @t129 () (or @t128 @t89 @t127)) % 0.36/0.94 (define @t130 () (forall (@list @t1 @t121) @t129)) % 0.36/0.94 (define @t131 () (or @t112 @t88 @t130)) % 0.36/0.94 (define @t132 () (or @t88 @t112 @t130)) % 0.36/0.94 (define @t133 () (@list @t121)) % 0.36/0.94 (define @t134 () (forall @t133 @t129)) % 0.36/0.94 (define @t135 () (forall @t133 @t124)) % 0.36/0.94 (define @t136 () (forall @t133 @t126)) % 0.36/0.94 (define @t137 () (@var "BOUND_VARIABLE_11078" $$unsorted)) % 0.36/0.94 (define @t138 () (@list @t137)) % 0.36/0.94 (define @t139 () (and @t136 @t135)) % 0.36/0.94 (define @t140 () (forall @t133 @t127)) % 0.36/0.94 (define @t141 () (or @t128 @t89 @t140)) % 0.36/0.94 (define @t142 () (and (forall (@list @t137) (or (not (tptp.ssItem @t137)) (not (= @t2 (tptp.cons @t137 tptp.nil))) (not (tptp.memberP @t1 @t137)) (not (forall @t31 (or @t107 (= @t27 @t137) @t125 (not (tptp.leq @t137 @t27))))))) @t124)) % 0.36/0.94 (define @t143 () (or @t128 @t89 @t142)) % 0.36/0.94 (define @t144 () (forall @t7 @t143)) % 0.36/0.94 (define @t145 () (or @t88 @t112 @t144)) % 0.36/0.94 (define @t146 () (or @t88 @t112 @t143)) % 0.36/0.94 (define @t147 () (or @t128 @t89 @t88 @t112 @t142)) % 0.36/0.94 (define @t148 () (or @t89 @t88 @t128 @t112 @t142)) % 0.36/0.94 (define @t149 () (@var "BOUND_VARIABLE_11043" $$unsorted)) % 0.36/0.94 (define @t150 () (@list @t149)) % 0.36/0.94 (define @t151 () (forall @t150 @t124)) % 0.36/0.94 (define @t152 () (not (forall @t31 (or @t107 (= @t27 @t149) @t125 (not (tptp.leq @t149 @t27)))))) % 0.36/0.94 (define @t153 () (not (tptp.memberP @t1 @t149))) % 0.36/0.94 (define @t154 () (tptp.cons @t149 tptp.nil)) % 0.36/0.94 (define @t155 () (not (tptp.ssItem @t149))) % 0.36/0.94 (define @t156 () (or @t155 (not (= @t2 @t154)) @t153 @t152)) % 0.36/0.94 (define @t157 () (forall @t150 @t156)) % 0.36/0.94 (define @t158 () (@list @t149)) % 0.36/0.94 (define @t159 () (and @t157 @t151)) % 0.36/0.94 (define @t160 () (and @t156 @t124)) % 0.36/0.94 (define @t161 () (forall @t150 @t160)) % 0.36/0.94 (define @t162 () (or @t112 @t161)) % 0.36/0.94 (define @t163 () (or @t112 @t160)) % 0.36/0.94 (define @t164 () (not (= @t2 @t2))) % 0.36/0.94 (define @t165 () (or @t112 @t164 @t160)) % 0.36/0.94 (define @t166 () (not (= @t12 tptp.nil))) % 0.36/0.94 (define @t167 () (or @t123 @t166)) % 0.36/0.94 (define @t168 () (or @t155 (not (= @t12 @t154)) @t153 @t152)) % 0.36/0.94 (define @t169 () (and @t168 @t167)) % 0.36/0.94 (define @t170 () (not @t15)) % 0.36/0.94 (define @t171 () (or @t90 @t170 @t90 @t169)) % 0.36/0.94 (define @t172 () (or @t170 @t90 @t169)) % 0.36/0.94 (define @t173 () (forall @t16 @t172)) % 0.36/0.94 (define @t174 () (forall @t150 @t173)) % 0.36/0.94 (define @t175 () (forall (@list @t149 @t12) @t172)) % 0.36/0.94 (define @t176 () (forall (@list @t12 @t149) @t172)) % 0.36/0.94 (define @t177 () (forall @t150 @t172)) % 0.36/0.94 (define @t178 () (forall @t150 @t167)) % 0.36/0.94 (define @t179 () (forall @t150 @t168)) % 0.36/0.94 (define @t180 () (@var "BOUND_VARIABLE_11012" $$unsorted)) % 0.36/0.94 (define @t181 () (@list @t180)) % 0.36/0.94 (define @t182 () (and @t179 @t178)) % 0.36/0.94 (define @t183 () (forall @t150 @t169)) % 0.36/0.94 (define @t184 () (or @t170 @t90 @t183)) % 0.36/0.94 (define @t185 () (and (forall (@list @t180) (or (not (tptp.ssItem @t180)) (not (= @t12 (tptp.cons @t180 tptp.nil))) (not (tptp.memberP @t1 @t180)) (not (forall @t31 (or @t107 (= @t27 @t180) @t125 (not (tptp.leq @t180 @t27))))))) @t167)) % 0.36/0.94 (define @t186 () (or @t170 @t90 @t185)) % 0.36/0.94 (define @t187 () (forall @t16 @t186)) % 0.36/0.94 (define @t188 () (or @t89 @t88 @t128 @t187)) % 0.36/0.94 (define @t189 () (or @t89 @t88 @t128 @t186)) % 0.36/0.94 (define @t190 () (or @t170 @t90 @t89 @t88 @t128 @t185)) % 0.36/0.94 (define @t191 () (or @t90 @t89 @t88 @t128 @t185)) % 0.36/0.94 (define @t192 () (@var "BOUND_VARIABLE_10966" $$unsorted)) % 0.36/0.94 (define @t193 () (@list @t192)) % 0.36/0.94 (define @t194 () (forall @t193 @t167)) % 0.36/0.94 (define @t195 () (not (tptp.leq @t192 @t27))) % 0.36/0.94 (define @t196 () (= @t27 @t192)) % 0.36/0.94 (define @t197 () (not (= @t12 (tptp.cons @t192 tptp.nil)))) % 0.36/0.94 (define @t198 () (not (tptp.ssItem @t192))) % 0.36/0.94 (define @t199 () (or @t198 @t197 (not (tptp.memberP @t1 @t192)) (not (forall @t31 (or @t107 @t196 @t125 @t195))))) % 0.36/0.94 (define @t200 () (forall @t193 @t199)) % 0.36/0.94 (define @t201 () (@list @t192)) % 0.36/0.94 (define @t202 () (and @t200 @t194)) % 0.36/0.94 (define @t203 () (and @t199 @t167)) % 0.36/0.94 (define @t204 () (forall @t193 @t203)) % 0.36/0.94 (define @t205 () (or @t128 @t204)) % 0.36/0.94 (define @t206 () (or @t128 @t203)) % 0.36/0.94 (define @t207 () (not (= @t1 @t1))) % 0.36/0.94 (define @t208 () (or @t128 @t207 @t203)) % 0.36/0.94 (define @t209 () (or (not (= @t10 tptp.nil)) @t166)) % 0.36/0.94 (define @t210 () (not @t74)) % 0.36/0.94 (define @t211 () (not (tptp.memberP @t10 @t192))) % 0.36/0.94 (define @t212 () (and (or @t198 @t197 @t211 (not (forall @t31 (or @t107 @t196 @t210 @t195)))) @t209)) % 0.36/0.94 (define @t213 () (not @t13)) % 0.36/0.94 (define @t214 () (or @t91 @t213 @t91 @t212)) % 0.36/0.94 (define @t215 () (or @t213 @t91 @t212)) % 0.36/0.94 (define @t216 () (forall @t14 @t215)) % 0.36/0.94 (define @t217 () (forall @t193 @t216)) % 0.36/0.94 (define @t218 () (forall (@list @t192 @t10) @t215)) % 0.36/0.94 (define @t219 () (@list @t10 @t192)) % 0.36/0.94 (define @t220 () (or @t107 (= @t192 @t27) @t210 @t195)) % 0.36/0.94 (define @t221 () (forall @t31 @t220)) % 0.36/0.94 (define @t222 () (not @t221)) % 0.36/0.94 (define @t223 () (or @t198 @t197 @t211 @t222)) % 0.36/0.94 (define @t224 () (and @t223 @t209)) % 0.36/0.94 (define @t225 () (or @t213 @t91 @t224)) % 0.36/0.94 (define @t226 () (forall @t219 @t225)) % 0.36/0.94 (define @t227 () (forall @t193 @t225)) % 0.36/0.94 (define @t228 () (forall @t193 @t209)) % 0.36/0.94 (define @t229 () (forall @t193 @t223)) % 0.36/0.94 (define @t230 () (and @t229 @t228)) % 0.36/0.94 (define @t231 () (forall @t193 @t224)) % 0.36/0.94 (define @t232 () (or @t213 @t91 @t231)) % 0.36/0.94 (define @t233 () (not @t73)) % 0.36/0.94 (define @t234 () (not (forall @t31 (or @t107 @t75 @t210 @t233)))) % 0.36/0.94 (define @t235 () (not (= @t12 @t81))) % 0.36/0.94 (define @t236 () (not @t84)) % 0.36/0.94 (define @t237 () (or @t236 @t235 @t80 @t234)) % 0.36/0.94 (define @t238 () (and (forall @t33 @t237) @t209)) % 0.36/0.94 (define @t239 () (or @t213 @t91 @t238)) % 0.36/0.94 (define @t240 () (forall @t14 @t239)) % 0.36/0.94 (define @t241 () (or @t90 @t89 @t88 @t240)) % 0.36/0.94 (define @t242 () (or @t90 @t89 @t88 @t239)) % 0.36/0.94 (define @t243 () (or @t213 @t91 @t90 @t89 @t88 @t238)) % 0.36/0.94 (define @t244 () (or @t91 @t90 @t89 @t88 @t238)) % 0.36/0.94 (define @t245 () (or @t235 @t80 @t234)) % 0.36/0.94 (define @t246 () (not @t76)) % 0.36/0.94 (define @t247 () (or @t107 @t246 @t210 @t233)) % 0.36/0.94 (define @t248 () (forall @t31 (not @t78))) % 0.36/0.94 (define @t249 () (not @t248)) % 0.36/0.94 (define @t250 () (forall @t116 (or @t112 @t88 @t111 @t110 (and @t108 (or (not (= tptp.nil @t103)) @t102))))) % 0.36/0.94 (define @t251 () (@quantifiers_skolemize @t250 0)) % 0.36/0.94 (define @t252 () (= tptp.nil @t251)) % 0.36/0.94 (define @t253 () (not @t252)) % 0.36/0.94 (define @t254 () (@quantifiers_skolemize @t250 1)) % 0.36/0.94 (define @t255 () (= tptp.nil @t254)) % 0.36/0.94 (define @t256 () (not @t255)) % 0.36/0.94 (define @t257 () (or @t256 @t253)) % 0.36/0.94 (define @t258 () (@quantifiers_skolemize @t250 2)) % 0.36/0.94 (define @t259 () (tptp.cons @t258 tptp.nil)) % 0.36/0.94 (define @t260 () (= @t251 @t259)) % 0.36/0.94 (define @t261 () (not @t260)) % 0.36/0.94 (define @t262 () (tptp.ssItem @t258)) % 0.36/0.94 (define @t263 () (not @t262)) % 0.36/0.94 (define @t264 () (or @t263 @t261 (not (tptp.memberP @t254 @t258)) (not (forall @t31 (or @t107 (= @t27 @t258) (not (tptp.memberP @t254 @t27)) (not (tptp.leq @t258 @t27))))))) % 0.36/0.94 (define @t265 () (and @t264 @t257)) % 0.36/0.94 (define @t266 () (tptp.neq @t254 tptp.nil)) % 0.36/0.94 (define @t267 () (not @t266)) % 0.36/0.94 (define @t268 () (not (tptp.ssList @t254))) % 0.36/0.94 (define @t269 () (tptp.neq @t251 tptp.nil)) % 0.36/0.94 (define @t270 () (tptp.ssList @t251)) % 0.36/0.94 (define @t271 () (not @t270)) % 0.36/0.94 (define @t272 () (or @t271 @t269 @t268 @t267 @t265)) % 0.36/0.94 (define @t273 () (not @t272)) % 0.36/0.94 (define @t274 () (not @t250)) % 0.36/0.94 (define @t275 () (not (= @t251 tptp.nil))) % 0.36/0.94 (define @t276 () (or @t256 @t275)) % 0.36/0.94 (define @t277 () (and @t264 @t276)) % 0.36/0.94 (define @t278 () (or @t271 @t269 @t268 @t267 @t277)) % 0.36/0.94 (define @t279 () (not @t278)) % 0.36/0.94 (define @t280 () (@list true)) % 0.36/0.94 (define @t281 () (@list @t272)) % 0.36/0.94 (define @t282 () (@var "BOUND_VARIABLE_9156" $$unsorted)) % 0.36/0.94 (define @t283 () (not (= @t2 (tptp.cons @t282 @t2)))) % 0.36/0.94 (define @t284 () (not (tptp.ssItem @t282))) % 0.36/0.94 (define @t285 () (or @t284 @t283)) % 0.36/0.94 (define @t286 () (or @t112 @t285)) % 0.36/0.94 (define @t287 () (forall (@list @t2 @t282) @t286)) % 0.36/0.94 (define @t288 () (@list @t282)) % 0.36/0.94 (define @t289 () (forall @t288 @t286)) % 0.36/0.94 (define @t290 () (forall @t288 @t285)) % 0.36/0.94 (define @t291 () (@list @t1)) % 0.36/0.94 (define @t292 () (or @t112 @t290)) % 0.36/0.94 (define @t293 () (not (= @t2 @t40))) % 0.36/0.94 (define @t294 () (forall @t7 (or (not @t6) @t293))) % 0.36/0.94 (define @t295 () (not @t253)) % 0.36/0.94 (define @t296 () (not @t269)) % 0.36/0.94 (define @t297 () (and @t296 @t252 @t255 @t266)) % 0.36/0.94 (define @t298 () (@list false true false false)) % 0.36/0.94 (define @t299 () (@list @t264)) % 0.36/0.94 (define @t300 () (= tptp.nil @t259)) % 0.36/0.94 (define @t301 () (not @t300)) % 0.36/0.94 (define @t302 () (not @t41)) % 0.36/0.94 (define @t303 () (or @t302 @t263 @t301)) % 0.36/0.94 (define @t304 () (and @t260 @t301)) % 0.36/0.94 (define @t305 () (= @t269 @t253)) % 0.36/0.94 (define @t306 () (not @t305)) % 0.36/0.94 (define @t307 () (@var "BOUND_VARIABLE_9112" $$unsorted)) % 0.36/0.94 (define @t308 () (= (tptp.neq @t2 @t307) (not (= @t2 @t307)))) % 0.36/0.94 (define @t309 () (not (tptp.ssList @t307))) % 0.36/0.94 (define @t310 () (or @t112 @t309 @t308)) % 0.36/0.94 (define @t311 () (or @t309 @t308)) % 0.36/0.94 (define @t312 () (or @t112 @t311)) % 0.36/0.94 (define @t313 () (@list @t2 @t307)) % 0.36/0.94 (define @t314 () (forall @t313 @t312)) % 0.36/0.94 (define @t315 () (@list @t307)) % 0.36/0.94 (define @t316 () (forall @t315 @t312)) % 0.36/0.94 (define @t317 () (forall @t315 @t311)) % 0.36/0.94 (define @t318 () (or @t112 @t317)) % 0.36/0.94 (define @t319 () (forall @t7 (or @t128 @t5))) % 0.36/0.94 (define @t320 () (= @t269 @t275)) % 0.36/0.94 (define @t321 () (or @t271 @t302 @t320)) % 0.36/0.94 (define @t322 () (forall @t313 @t310)) % 0.36/0.94 (define @t323 () (or @t271 @t302 @t305)) % 0.36/0.94 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.94 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.94 (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))))))))))) % 0.36/0.94 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.94 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.94 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.94 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.94 (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))))))))))))))))) % 0.36/0.94 (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)))))))))))))))) % 0.36/0.94 (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))))))))))))))))) % 0.36/0.94 (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))))))))))))))) % 0.36/0.94 (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))))))))))))))) % 0.36/0.94 (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)))))))))))))))) % 0.36/0.94 (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))))))))))))) % 0.36/0.94 (assume @p15 @t39) % 0.36/0.94 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t40)))))) % 0.36/0.94 (assume @p17 @t41) % 0.36/0.94 (assume @p18 @t46) % 0.36/0.94 (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) @t47))))))))))) % 0.36/0.94 (assume @p20 (forall @t9 (=> @t17 (or @t49 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t48 @t2))))))))) % 0.36/0.94 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t40))))))) % 0.36/0.94 (assume @p22 (forall @t9 (=> @t17 (=> @t51 (tptp.ssItem @t50))))) % 0.36/0.94 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t40) @t1)))))) % 0.36/0.94 (assume @p24 (forall @t9 (=> @t17 (=> @t51 (tptp.ssList @t52))))) % 0.36/0.94 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t40) @t2)))))) % 0.36/0.94 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t53)))))) % 0.36/0.94 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t54) (tptp.app @t48 @t2))))))))) % 0.36/0.94 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.94 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t56 @t55) @t3)))))) % 0.36/0.94 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t56 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.94 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.94 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t57 @t55)))))) % 0.36/0.94 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t59 (not @t58))))))) % 0.36/0.94 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t59 @t35) @t60)))))))) % 0.36/0.94 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t61 @t58)))))) % 0.36/0.94 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t62))))))))) % 0.36/0.94 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t62))))))))) % 0.36/0.94 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.36/0.94 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.36/0.94 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.36/0.94 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.36/0.94 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.36/0.94 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.36/0.94 (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)))))))))))) % 0.36/0.94 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.36/0.94 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t49)))) % 0.36/0.94 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.36/0.94 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.36/0.94 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.36/0.94 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t63 @t1))))))))) % 0.36/0.94 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.36/0.94 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t49)))) % 0.36/0.94 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.36/0.94 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.36/0.94 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.36/0.94 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t63 @t10) @t1))))))))))) % 0.36/0.94 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.36/0.94 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t49)))) % 0.36/0.94 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t64)))) % 0.36/0.94 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.36/0.94 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t64)))) % 0.36/0.94 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.36/0.94 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t64)))) % 0.36/0.94 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.36/0.94 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t64)))) % 0.36/0.94 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.36/0.94 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t68) (or @t66 (and @t67 (tptp.totalorderedP @t1) (tptp.leq @t2 @t65))))))))) % 0.36/0.94 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t64)))) % 0.36/0.94 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.36/0.94 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t68) (or @t66 (and @t67 (tptp.strictorderedP @t1) (tptp.lt @t2 @t65))))))))) % 0.36/0.94 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t64)))) % 0.36/0.94 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.36/0.94 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t64)))) % 0.36/0.94 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.36/0.94 (assume @p75 (forall @t9 (=> @t17 (=> @t51 (exists @t7 (and @t6 (= @t50 @t1))))))) % 0.36/0.94 (assume @p76 (forall @t9 (=> @t17 (=> @t51 (exists @t7 (and @t21 (= @t52 @t1))))))) % 0.36/0.94 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t67 @t51 (= @t65 @t50) (= (tptp.tl @t1) @t52)) @t47)))))) % 0.36/0.94 (assume @p78 (forall @t9 (=> @t17 (=> @t51 (= (tptp.cons @t50 @t52) @t2))))) % 0.36/0.94 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t53) @t69)))))))) % 0.36/0.94 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t54) @t69)))))))) % 0.36/0.94 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t40 (tptp.app @t18 @t2))))))) % 0.36/0.94 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t53 @t12) (tptp.app @t2 @t19))))))))) % 0.36/0.94 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t53) (and @t66 @t49))))))) % 0.36/0.94 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.36/0.94 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t51 (= (tptp.hd @t53) @t50))))))) % 0.36/0.94 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t51 (= (tptp.tl @t53) (tptp.app @t52 @t1)))))))) % 0.36/0.94 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t57 (tptp.geq @t1 @t2)) @t3)))))) % 0.36/0.94 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t57 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.36/0.94 (assume @p89 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0.36/0.94 (step @p535 :rule cong :premises (@p534) :args (@t39)) % 0.36/0.94 (step @p536 :rule trans :premises (@p535 @p531)) % 0.36/0.94 (step @p537 :rule eq_resolve :premises (@p15 @p536)) % 0.36/0.94 (step @p538 :rule cong :premises (@p363 @p356) :args (@t320)) % 0.36/0.94 (step @p539 :rule refl :args (@t302)) % 0.36/0.94 (step @p540 :rule nary_cong :premises (@p364 @p539 @p538) :args (@t321)) % 0.36/0.94 (step @p541 :rule refl :args (@t322)) % 0.36/0.94 (step @p542 :rule cong :premises (@p541 @p540) :args ((=> @t322 @t321))) % 0.36/0.94 (assume-push @p579 @t322) % 0.36/0.94 (step @p544 :rule instantiate :premises (@p537) :args ((@list @t251 tptp.nil))) % 0.36/0.94 (step-pop @p580 :rule scope :premises (@p544)) % 0.36/0.94 (step @p545 :rule process_scope :premises (@p580) :args (@t321)) % 0.36/0.94 (step @p547 :rule eq_resolve :premises (@p545 @p542)) % 0.36/0.94 (step @p548 :rule implies_elim :premises (@p547)) % 0.36/0.94 (step @p549 :rule chain_m_resolution :premises (@p548 @p537) :args (@t323 (@list false) (@list @t322))) % 0.36/0.94 (step @p550 :rule cnf_or_pos :args (@t323)) % 0.36/0.94 (step @p551 :rule reordering :premises (@p550) :args ((or @t302 @t271 @t305 (not @t323)))) % 0.36/0.94 (step @p552 false :rule chain_m_resolution :premises (@p551 @p549 @p517 @p383 @p17) :args (false @t298 (@list @t323 @t305 @t270 @t41))) % 0.36/0.94 ) % 0.36/0.94 % SZS output end Proof % 0.36/0.94 % cvc5 exiting %------------------------------------------------------------------------------