%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC398+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 : n009.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 08:59:10 AM UTC 2026 % Result : Theorem 0.37s 0.73s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC398+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 19:45:29 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.73 % SZS status Theorem % 0.37/0.73 % SZS output start Proof % 0.37/0.73 ( % 0.37/0.73 (declare-sort $$unsorted 0) % 0.37/0.73 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.73 (declare-const tptp.nil $$unsorted) % 0.37/0.73 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.73 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.73 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.73 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.73 (define @t3 () (= @t2 @t1)) % 0.37/0.73 (define @t4 () (not @t3)) % 0.37/0.73 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.73 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.73 (define @t7 () (@list @t1)) % 0.37/0.73 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.73 (define @t9 () (@list @t2)) % 0.37/0.73 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.73 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.73 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.73 (define @t13 () (tptp.ssList @t10)) % 0.37/0.73 (define @t14 () (@list @t10)) % 0.37/0.73 (define @t15 () (tptp.ssList @t12)) % 0.37/0.73 (define @t16 () (@list @t12)) % 0.37/0.73 (define @t17 () (tptp.ssList @t2)) % 0.37/0.73 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.73 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.73 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.73 (define @t21 () (tptp.ssList @t1)) % 0.37/0.73 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.73 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.73 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.73 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.73 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.73 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.73 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.73 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.73 (define @t30 () (tptp.ssList @t27)) % 0.37/0.73 (define @t31 () (@list @t27)) % 0.37/0.73 (define @t32 () (tptp.ssList @t28)) % 0.37/0.73 (define @t33 () (@list @t28)) % 0.37/0.73 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.73 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.73 (define @t36 () (= @t1 @t12)) % 0.37/0.73 (define @t37 () (tptp.equalelemsP @t2)) % 0.37/0.73 (define @t38 () (tptp.cons @t1 @t2)) % 0.37/0.73 (define @t39 () (= @t1 @t2)) % 0.37/0.73 (define @t40 () (tptp.cons @t12 @t1)) % 0.37/0.73 (define @t41 () (= tptp.nil @t2)) % 0.37/0.73 (define @t42 () (tptp.hd @t2)) % 0.37/0.73 (define @t43 () (not @t41)) % 0.37/0.73 (define @t44 () (tptp.tl @t2)) % 0.37/0.73 (define @t45 () (tptp.app @t2 @t1)) % 0.37/0.73 (define @t46 () (tptp.app @t1 @t2)) % 0.37/0.73 (define @t47 () (tptp.leq @t1 @t2)) % 0.37/0.73 (define @t48 () (tptp.leq @t2 @t1)) % 0.37/0.73 (define @t49 () (tptp.geq @t2 @t1)) % 0.37/0.73 (define @t50 () (tptp.lt @t1 @t2)) % 0.37/0.73 (define @t51 () (tptp.lt @t2 @t1)) % 0.37/0.73 (define @t52 () (tptp.lt @t2 @t12)) % 0.37/0.73 (define @t53 () (tptp.gt @t2 @t1)) % 0.37/0.73 (define @t54 () (tptp.memberP @t12 @t2)) % 0.37/0.73 (define @t55 () (tptp.memberP @t1 @t2)) % 0.37/0.73 (define @t56 () (= (tptp.memberP @t19 @t2) (or @t55 @t54))) % 0.37/0.73 (define @t57 () (forall @t16 (=> @t15 @t56))) % 0.37/0.73 (define @t58 () (=> @t21 @t57)) % 0.37/0.73 (define @t59 () (forall @t7 @t58)) % 0.37/0.73 (define @t60 () (=> @t8 @t59)) % 0.37/0.73 (define @t61 () (forall @t9 @t60)) % 0.37/0.73 (define @t62 () (tptp.app @t12 @t2)) % 0.37/0.73 (define @t63 () (tptp.cons @t2 tptp.nil)) % 0.37/0.73 (define @t64 () (tptp.hd @t1)) % 0.37/0.73 (define @t65 () (= tptp.nil @t1)) % 0.37/0.73 (define @t66 () (not @t65)) % 0.37/0.73 (define @t67 () (tptp.cons @t2 @t1)) % 0.37/0.73 (define @t68 () (= @t12 @t2)) % 0.37/0.73 (define @t69 () (not (= tptp.nil @t10))) % 0.37/0.73 (define @t70 () (and @t69 (= tptp.nil @t12))) % 0.37/0.73 (define @t71 () (@var "X3" $$unsorted)) % 0.37/0.73 (define @t72 () (tptp.memberP @t1 @t71)) % 0.37/0.73 (define @t73 () (not (tptp.memberP @t2 @t71))) % 0.37/0.73 (define @t74 () (or @t73 @t72)) % 0.37/0.73 (define @t75 () (tptp.ssItem @t71)) % 0.37/0.73 (define @t76 () (@list @t71)) % 0.37/0.73 (define @t77 () (forall @t76 (=> @t75 @t74))) % 0.37/0.73 (define @t78 () (tptp.cons @t27 tptp.nil)) % 0.37/0.73 (define @t79 () (@var "X2" $$unsorted)) % 0.37/0.73 (define @t80 () (tptp.app @t79 @t78)) % 0.37/0.73 (define @t81 () (tptp.ssList @t79)) % 0.37/0.73 (define @t82 () (and @t81 (= @t80 @t12))) % 0.37/0.73 (define @t83 () (@list @t79)) % 0.37/0.73 (define @t84 () (exists @t83 @t82)) % 0.37/0.73 (define @t85 () (@var "X1" $$unsorted)) % 0.37/0.73 (define @t86 () (tptp.app @t78 @t85)) % 0.37/0.73 (define @t87 () (tptp.ssList @t85)) % 0.37/0.73 (define @t88 () (and @t87 (= @t86 @t28) @t84)) % 0.37/0.73 (define @t89 () (@list @t85)) % 0.37/0.73 (define @t90 () (exists @t89 @t88)) % 0.37/0.73 (define @t91 () (tptp.ssItem @t27)) % 0.37/0.73 (define @t92 () (and @t91 @t90)) % 0.37/0.73 (define @t93 () (exists @t31 @t92)) % 0.37/0.73 (define @t94 () (not (tptp.equalelemsP @t12))) % 0.37/0.73 (define @t95 () (tptp.app @t12 @t28)) % 0.37/0.73 (define @t96 () (not (= @t95 @t10))) % 0.37/0.73 (define @t97 () (or @t96 @t94 @t93)) % 0.37/0.73 (define @t98 () (=> @t32 @t97)) % 0.37/0.73 (define @t99 () (forall @t33 @t98)) % 0.37/0.73 (define @t100 () (not (= @t2 @t12))) % 0.37/0.73 (define @t101 () (not (= @t1 @t10))) % 0.37/0.73 (define @t102 () (or @t101 @t100 @t99 @t77 @t70)) % 0.37/0.73 (define @t103 () (=> @t13 @t102)) % 0.37/0.73 (define @t104 () (forall @t14 @t103)) % 0.37/0.73 (define @t105 () (=> @t15 @t104)) % 0.37/0.73 (define @t106 () (forall @t16 @t105)) % 0.37/0.73 (define @t107 () (=> @t21 @t106)) % 0.37/0.73 (define @t108 () (forall @t7 @t107)) % 0.37/0.73 (define @t109 () (=> @t17 @t108)) % 0.37/0.73 (define @t110 () (forall @t9 @t109)) % 0.37/0.73 (define @t111 () (not @t110)) % 0.37/0.73 (define @t112 () (@var "BOUND_VARIABLE_11172" $$unsorted)) % 0.37/0.73 (define @t113 () (@var "BOUND_VARIABLE_10992" $$unsorted)) % 0.37/0.73 (define @t114 () (tptp.app @t78 @t113)) % 0.37/0.73 (define @t115 () (not (tptp.ssList @t113))) % 0.37/0.73 (define @t116 () (@var "BOUND_VARIABLE_10984" $$unsorted)) % 0.37/0.73 (define @t117 () (tptp.app @t116 @t78)) % 0.37/0.73 (define @t118 () (not (= @t2 @t117))) % 0.37/0.73 (define @t119 () (not (tptp.ssList @t116))) % 0.37/0.73 (define @t120 () (not @t91)) % 0.37/0.73 (define @t121 () (@list @t27 @t116 @t113)) % 0.37/0.73 (define @t122 () (not (forall @t121 (or @t120 @t119 @t118 @t115 (not (= @t114 @t112)))))) % 0.37/0.73 (define @t123 () (not (tptp.ssList @t112))) % 0.37/0.73 (define @t124 () (@var "BOUND_VARIABLE_11170" $$unsorted)) % 0.37/0.73 (define @t125 () (tptp.app @t2 @t112)) % 0.37/0.73 (define @t126 () (tptp.memberP @t125 @t124)) % 0.37/0.73 (define @t127 () (not (tptp.memberP @t2 @t124))) % 0.37/0.73 (define @t128 () (not (tptp.ssItem @t124))) % 0.37/0.73 (define @t129 () (= @t2 tptp.nil)) % 0.37/0.73 (define @t130 () (and (not (= tptp.nil @t125)) @t129)) % 0.37/0.73 (define @t131 () (not (tptp.ssList @t125))) % 0.37/0.73 (define @t132 () (not @t37)) % 0.37/0.73 (define @t133 () (not @t17)) % 0.37/0.73 (define @t134 () (or @t133 @t132 @t131 @t130 @t128 @t127 @t126 @t123 @t122)) % 0.37/0.73 (define @t135 () (or @t131 @t130 @t128 @t127 @t126 @t123 @t122)) % 0.37/0.73 (define @t136 () (or @t133 @t132 @t135)) % 0.37/0.73 (define @t137 () (@list @t2 @t124 @t112)) % 0.37/0.73 (define @t138 () (forall @t137 @t136)) % 0.37/0.73 (define @t139 () (@list @t124 @t112)) % 0.37/0.73 (define @t140 () (forall @t139 @t136)) % 0.37/0.73 (define @t141 () (forall @t139 @t135)) % 0.37/0.73 (define @t142 () (@var "BOUND_VARIABLE_11131" $$unsorted)) % 0.37/0.73 (define @t143 () (@var "BOUND_VARIABLE_11123" $$unsorted)) % 0.37/0.73 (define @t144 () (or @t133 @t132 @t141)) % 0.37/0.73 (define @t145 () (not (forall @t121 (or @t120 @t119 @t118 @t115 (not (= @t114 @t142)))))) % 0.37/0.73 (define @t146 () (not (tptp.ssList @t142))) % 0.37/0.73 (define @t147 () (tptp.app @t2 @t142)) % 0.37/0.73 (define @t148 () (tptp.memberP @t147 @t143)) % 0.37/0.73 (define @t149 () (not (tptp.memberP @t2 @t143))) % 0.37/0.73 (define @t150 () (not (tptp.ssItem @t143))) % 0.37/0.73 (define @t151 () (and (not (= tptp.nil @t147)) @t129)) % 0.37/0.73 (define @t152 () (not (tptp.ssList @t147))) % 0.37/0.73 (define @t153 () (or @t152 @t151 @t150 @t149 @t148 @t146 @t145)) % 0.37/0.73 (define @t154 () (@list @t143 @t142)) % 0.37/0.73 (define @t155 () (or @t133 @t132 (forall @t154 @t153))) % 0.37/0.73 (define @t156 () (not (= @t147 @t147))) % 0.37/0.73 (define @t157 () (not (= @t147 tptp.nil))) % 0.37/0.73 (define @t158 () (and @t157 @t129)) % 0.37/0.73 (define @t159 () (or @t152 @t158 @t150 @t149 @t148 @t146 @t156 @t145)) % 0.37/0.73 (define @t160 () (not (= @t1 @t147))) % 0.37/0.73 (define @t161 () (tptp.memberP @t1 @t143)) % 0.37/0.73 (define @t162 () (not (= @t1 tptp.nil))) % 0.37/0.73 (define @t163 () (and @t162 @t129)) % 0.37/0.73 (define @t164 () (not @t21)) % 0.37/0.73 (define @t165 () (or @t160 @t164 @t163 @t150 @t149 @t161 @t146 @t160 @t145)) % 0.37/0.73 (define @t166 () (or @t164 @t163 @t150 @t149 @t161 @t146 @t160 @t145)) % 0.37/0.73 (define @t167 () (forall @t7 @t166)) % 0.37/0.73 (define @t168 () (forall @t154 @t167)) % 0.37/0.73 (define @t169 () (forall (@list @t143 @t142 @t1) @t166)) % 0.37/0.73 (define @t170 () (@list @t1 @t143 @t142)) % 0.37/0.73 (define @t171 () (or @t146 @t160 @t145)) % 0.37/0.73 (define @t172 () (or @t150 @t149 @t161)) % 0.37/0.73 (define @t173 () (or @t164 @t172 @t163 @t171)) % 0.37/0.73 (define @t174 () (forall @t170 @t173)) % 0.37/0.73 (define @t175 () (forall @t154 @t173)) % 0.37/0.73 (define @t176 () (forall (@list @t142) @t171)) % 0.37/0.73 (define @t177 () (@var "BOUND_VARIABLE_11075" $$unsorted)) % 0.37/0.73 (define @t178 () (@list @t177)) % 0.37/0.73 (define @t179 () (forall (@list @t143) @t172)) % 0.37/0.73 (define @t180 () (or @t164 @t179 @t163 @t176)) % 0.37/0.73 (define @t181 () (not (= @t114 @t177))) % 0.37/0.73 (define @t182 () (not (forall @t121 (or @t120 @t119 @t118 @t115 @t181)))) % 0.37/0.73 (define @t183 () (not (= @t1 (tptp.app @t2 @t177)))) % 0.37/0.73 (define @t184 () (not (tptp.ssList @t177))) % 0.37/0.73 (define @t185 () (or @t184 @t183 @t182)) % 0.37/0.73 (define @t186 () (@list @t177)) % 0.37/0.73 (define @t187 () (forall @t186 @t185)) % 0.37/0.73 (define @t188 () (not @t75)) % 0.37/0.73 (define @t189 () (or @t188 @t73 @t72)) % 0.37/0.73 (define @t190 () (forall @t76 @t189)) % 0.37/0.73 (define @t191 () (or @t164 @t190 @t163 @t187)) % 0.37/0.73 (define @t192 () (forall @t7 @t191)) % 0.37/0.73 (define @t193 () (or @t133 @t132 @t192)) % 0.37/0.73 (define @t194 () (or @t133 @t132 @t191)) % 0.37/0.73 (define @t195 () (or @t164 @t190 @t133 @t132 @t163 @t187)) % 0.37/0.73 (define @t196 () (or @t190 @t164 @t133 @t132 @t163 @t187)) % 0.37/0.73 (define @t197 () (or @t133 @t132 @t163 @t187)) % 0.37/0.73 (define @t198 () (or @t133 @t132 @t163 @t185)) % 0.37/0.73 (define @t199 () (or @t133 @t132 @t163 @t184 @t183 @t182)) % 0.37/0.73 (define @t200 () (not (= @t2 @t2))) % 0.37/0.73 (define @t201 () (or @t133 @t200 @t132 @t163 @t184 @t183 @t182)) % 0.37/0.73 (define @t202 () (not (= @t12 @t117))) % 0.37/0.73 (define @t203 () (not (forall @t121 (or @t120 @t119 @t202 @t115 @t181)))) % 0.37/0.73 (define @t204 () (not (= @t1 (tptp.app @t12 @t177)))) % 0.37/0.73 (define @t205 () (= @t12 tptp.nil)) % 0.37/0.73 (define @t206 () (and @t162 @t205)) % 0.37/0.73 (define @t207 () (not @t15)) % 0.37/0.73 (define @t208 () (or @t100 @t207 @t100 @t94 @t206 @t184 @t204 @t203)) % 0.37/0.73 (define @t209 () (or @t207 @t100 @t94 @t206 @t184 @t204 @t203)) % 0.37/0.73 (define @t210 () (forall @t16 @t209)) % 0.37/0.73 (define @t211 () (forall @t186 @t210)) % 0.37/0.73 (define @t212 () (forall (@list @t177 @t12) @t209)) % 0.37/0.73 (define @t213 () (@list @t12 @t177)) % 0.37/0.73 (define @t214 () (or @t184 @t204 @t203)) % 0.37/0.73 (define @t215 () (or @t207 @t100 @t94 @t206 @t214)) % 0.37/0.73 (define @t216 () (forall @t213 @t215)) % 0.37/0.73 (define @t217 () (forall @t186 @t215)) % 0.37/0.73 (define @t218 () (forall @t186 @t214)) % 0.37/0.73 (define @t219 () (@var "BOUND_VARIABLE_11030" $$unsorted)) % 0.37/0.73 (define @t220 () (@list @t219)) % 0.37/0.73 (define @t221 () (or @t207 @t100 @t94 @t206 @t218)) % 0.37/0.73 (define @t222 () (not (forall @t121 (or @t120 @t119 @t202 @t115 (not (= @t114 @t219)))))) % 0.37/0.73 (define @t223 () (tptp.app @t12 @t219)) % 0.37/0.73 (define @t224 () (not (= @t1 @t223))) % 0.37/0.73 (define @t225 () (not (tptp.ssList @t219))) % 0.37/0.73 (define @t226 () (or @t225 @t224 @t222)) % 0.37/0.73 (define @t227 () (@list @t219)) % 0.37/0.73 (define @t228 () (forall @t227 @t226)) % 0.37/0.73 (define @t229 () (or @t207 @t100 @t94 @t206 @t228)) % 0.37/0.73 (define @t230 () (forall @t16 @t229)) % 0.37/0.73 (define @t231 () (or @t190 @t164 @t230)) % 0.37/0.73 (define @t232 () (or @t190 @t164 @t229)) % 0.37/0.73 (define @t233 () (or @t207 @t100 @t190 @t94 @t164 @t206 @t228)) % 0.37/0.73 (define @t234 () (or @t100 @t190 @t94 @t164 @t206 @t228)) % 0.37/0.73 (define @t235 () (or @t164 @t206 @t228)) % 0.37/0.73 (define @t236 () (or @t164 @t206 @t226)) % 0.37/0.73 (define @t237 () (or @t164 @t206 @t225 @t224 @t222)) % 0.37/0.73 (define @t238 () (not (= @t1 @t1))) % 0.37/0.73 (define @t239 () (or @t164 @t238 @t206 @t225 @t224 @t222)) % 0.37/0.73 (define @t240 () (not (= @t10 @t223))) % 0.37/0.73 (define @t241 () (and (not (= @t10 tptp.nil)) @t205)) % 0.37/0.73 (define @t242 () (not @t13)) % 0.37/0.73 (define @t243 () (or @t101 @t242 @t101 @t241 @t225 @t240 @t222)) % 0.37/0.73 (define @t244 () (or @t242 @t101 @t241 @t225 @t240 @t222)) % 0.37/0.73 (define @t245 () (forall @t14 @t244)) % 0.37/0.73 (define @t246 () (forall @t227 @t245)) % 0.37/0.73 (define @t247 () (forall (@list @t219 @t10) @t244)) % 0.37/0.73 (define @t248 () (@list @t10 @t219)) % 0.37/0.73 (define @t249 () (not (= @t219 @t114))) % 0.37/0.73 (define @t250 () (or @t120 @t119 @t202 @t115 @t249)) % 0.37/0.73 (define @t251 () (forall @t121 @t250)) % 0.37/0.73 (define @t252 () (not @t251)) % 0.37/0.73 (define @t253 () (or @t242 @t101 @t241 @t225 @t240 @t252)) % 0.37/0.73 (define @t254 () (or @t225 @t240 @t252)) % 0.37/0.73 (define @t255 () (or @t242 @t101 @t241 @t254)) % 0.37/0.73 (define @t256 () (forall @t248 @t255)) % 0.37/0.73 (define @t257 () (forall @t227 @t255)) % 0.37/0.73 (define @t258 () (forall @t227 @t254)) % 0.37/0.73 (define @t259 () (or @t242 @t101 @t241 @t258)) % 0.37/0.73 (define @t260 () (not (= @t28 @t114))) % 0.37/0.73 (define @t261 () (or @t120 @t119 @t202 @t115 @t260)) % 0.37/0.73 (define @t262 () (not (forall @t121 @t261))) % 0.37/0.73 (define @t263 () (not (= @t10 @t95))) % 0.37/0.73 (define @t264 () (not @t32)) % 0.37/0.73 (define @t265 () (or @t264 @t263 @t262)) % 0.37/0.73 (define @t266 () (forall @t33 @t265)) % 0.37/0.73 (define @t267 () (or @t242 @t101 @t241 @t266)) % 0.37/0.73 (define @t268 () (forall @t14 @t267)) % 0.37/0.73 (define @t269 () (or @t100 @t190 @t94 @t268)) % 0.37/0.73 (define @t270 () (or @t100 @t190 @t94 @t267)) % 0.37/0.73 (define @t271 () (or @t242 @t101 @t100 @t190 @t241 @t94 @t266)) % 0.37/0.73 (define @t272 () (or @t101 @t100 @t190 @t241 @t94 @t266)) % 0.37/0.73 (define @t273 () (or @t94 @t266)) % 0.37/0.73 (define @t274 () (or @t94 @t265)) % 0.37/0.73 (define @t275 () (or @t264 @t263 @t94 @t262)) % 0.37/0.73 (define @t276 () (or @t263 @t94 @t262)) % 0.37/0.73 (define @t277 () (or @t115 @t260)) % 0.37/0.73 (define @t278 () (or @t119 @t202)) % 0.37/0.73 (define @t279 () (or @t120 @t278 @t277)) % 0.37/0.73 (define @t280 () (forall @t121 @t279)) % 0.37/0.73 (define @t281 () (forall (@list @t116 @t113) @t279)) % 0.37/0.73 (define @t282 () (forall (@list @t113) @t277)) % 0.37/0.73 (define @t283 () (forall (@list @t116) @t278)) % 0.37/0.73 (define @t284 () (or @t120 @t283 @t282)) % 0.37/0.73 (define @t285 () (= @t28 @t86)) % 0.37/0.73 (define @t286 () (not @t285)) % 0.37/0.73 (define @t287 () (not @t87)) % 0.37/0.73 (define @t288 () (or @t287 @t286)) % 0.37/0.73 (define @t289 () (forall @t89 @t288)) % 0.37/0.73 (define @t290 () (= @t12 @t80)) % 0.37/0.73 (define @t291 () (forall @t83 (or (not @t81) (not @t290)))) % 0.37/0.73 (define @t292 () (or @t120 @t291 @t289)) % 0.37/0.73 (define @t293 () (or @t291 @t289)) % 0.37/0.73 (define @t294 () (not @t293)) % 0.37/0.73 (define @t295 () (and @t91 @t294)) % 0.37/0.73 (define @t296 () (forall @t31 (not @t295))) % 0.37/0.73 (define @t297 () (not @t296)) % 0.37/0.73 (define @t298 () (or @t291 @t288)) % 0.37/0.73 (define @t299 () (or @t287 @t286 @t291)) % 0.37/0.73 (define @t300 () (not @t291)) % 0.37/0.73 (define @t301 () (not @t300)) % 0.37/0.73 (define @t302 () (or @t287 @t286 @t301)) % 0.37/0.73 (define @t303 () (and @t87 @t285 @t300)) % 0.37/0.73 (define @t304 () (forall @t89 (not @t303))) % 0.37/0.73 (define @t305 () (not @t304)) % 0.37/0.73 (define @t306 () (and @t81 @t290)) % 0.37/0.73 (define @t307 () (forall @t83 (not @t306))) % 0.37/0.73 (define @t308 () (not @t307)) % 0.37/0.73 (define @t309 () (forall @t137 @t134)) % 0.37/0.73 (define @t310 () (@quantifiers_skolemize @t309 2)) % 0.37/0.73 (define @t311 () (not (= @t114 @t310))) % 0.37/0.73 (define @t312 () (@quantifiers_skolemize @t309 0)) % 0.37/0.73 (define @t313 () (tptp.ssList @t310)) % 0.37/0.73 (define @t314 () (not @t313)) % 0.37/0.73 (define @t315 () (@quantifiers_skolemize @t309 1)) % 0.37/0.73 (define @t316 () (tptp.app @t312 @t310)) % 0.37/0.73 (define @t317 () (tptp.memberP @t316 @t315)) % 0.37/0.73 (define @t318 () (tptp.memberP @t312 @t315)) % 0.37/0.73 (define @t319 () (not @t318)) % 0.37/0.73 (define @t320 () (tptp.ssItem @t315)) % 0.37/0.73 (define @t321 () (not @t320)) % 0.37/0.73 (define @t322 () (not (= tptp.nil @t316))) % 0.37/0.73 (define @t323 () (not (tptp.ssList @t316))) % 0.37/0.73 (define @t324 () (not (tptp.equalelemsP @t312))) % 0.37/0.73 (define @t325 () (tptp.ssList @t312)) % 0.37/0.73 (define @t326 () (not @t325)) % 0.37/0.73 (define @t327 () (or @t326 @t324 @t323 (and @t322 (= tptp.nil @t312)) @t321 @t319 @t317 @t314 (not (forall @t121 (or @t120 @t119 (not (= @t117 @t312)) @t115 @t311))))) % 0.37/0.73 (define @t328 () (not @t327)) % 0.37/0.73 (define @t329 () (not @t309)) % 0.37/0.73 (define @t330 () (not (= @t312 @t117))) % 0.37/0.73 (define @t331 () (or @t120 @t119 @t330 @t115 @t311)) % 0.37/0.73 (define @t332 () (forall @t121 @t331)) % 0.37/0.73 (define @t333 () (not @t332)) % 0.37/0.73 (define @t334 () (and @t322 (= @t312 tptp.nil))) % 0.37/0.73 (define @t335 () (or @t326 @t324 @t323 @t334 @t321 @t319 @t317 @t314 @t333)) % 0.37/0.73 (define @t336 () (not @t335)) % 0.37/0.73 (define @t337 () (@list true)) % 0.37/0.73 (define @t338 () (@list @t327)) % 0.37/0.73 (define @t339 () (@var "BOUND_VARIABLE_9679" $$unsorted)) % 0.37/0.73 (define @t340 () (@var "BOUND_VARIABLE_9677" $$unsorted)) % 0.37/0.73 (define @t341 () (= (tptp.memberP (tptp.app @t340 @t339) @t2) (or (tptp.memberP @t340 @t2) (tptp.memberP @t339 @t2)))) % 0.37/0.73 (define @t342 () (not (tptp.ssList @t339))) % 0.37/0.73 (define @t343 () (not (tptp.ssList @t340))) % 0.37/0.73 (define @t344 () (not @t8)) % 0.37/0.73 (define @t345 () (or @t343 @t342 @t341)) % 0.37/0.73 (define @t346 () (or @t344 @t345)) % 0.37/0.73 (define @t347 () (forall (@list @t2 @t340 @t339) @t346)) % 0.37/0.73 (define @t348 () (@list @t340 @t339)) % 0.37/0.73 (define @t349 () (forall @t348 @t346)) % 0.37/0.73 (define @t350 () (forall @t348 @t345)) % 0.37/0.73 (define @t351 () (@var "BOUND_VARIABLE_9658" $$unsorted)) % 0.37/0.73 (define @t352 () (or @t344 @t350)) % 0.37/0.73 (define @t353 () (= (tptp.memberP (tptp.app @t1 @t351) @t2) (or @t55 (tptp.memberP @t351 @t2)))) % 0.37/0.73 (define @t354 () (not (tptp.ssList @t351))) % 0.37/0.73 (define @t355 () (or @t164 @t354 @t353)) % 0.37/0.73 (define @t356 () (@list @t1 @t351)) % 0.37/0.73 (define @t357 () (forall @t356 @t355)) % 0.37/0.73 (define @t358 () (or @t354 @t353)) % 0.37/0.73 (define @t359 () (or @t164 @t358)) % 0.37/0.73 (define @t360 () (forall @t356 @t359)) % 0.37/0.73 (define @t361 () (@list @t351)) % 0.37/0.73 (define @t362 () (forall @t361 @t359)) % 0.37/0.73 (define @t363 () (forall @t361 @t358)) % 0.37/0.73 (define @t364 () (or @t164 @t363)) % 0.37/0.73 (define @t365 () (forall @t16 (or @t207 @t56))) % 0.37/0.73 (define @t366 () (or @t318 (tptp.memberP @t310 @t315))) % 0.37/0.73 (define @t367 () (= @t317 @t366)) % 0.37/0.73 (define @t368 () (not @t367)) % 0.37/0.73 (define @t369 () (or @t321 @t326 @t314 @t367)) % 0.37/0.73 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.73 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.73 (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))))))))))) % 0.37/0.73 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.73 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.73 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.73 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.73 (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))))))))))))))))) % 0.37/0.73 (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)))))))))))))))) % 0.37/0.73 (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))))))))))))))))) % 0.37/0.73 (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))))))))))))))) % 0.37/0.73 (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))))))))))))))) % 0.37/0.73 (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)))))))))))))))) % 0.37/0.73 (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))))))))))))) % 0.37/0.73 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.73 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.37/0.73 (assume @p17 (tptp.ssList tptp.nil)) % 0.37/0.73 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.37/0.73 (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) @t39))))))))))) % 0.37/0.73 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.37/0.73 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.37/0.73 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.37/0.73 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.37/0.73 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.37/0.73 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.37/0.73 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.37/0.73 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.37/0.73 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.73 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.37/0.73 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.73 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.73 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.37/0.73 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.37/0.73 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.37/0.73 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.37/0.73 (assume @p36 @t61) % 0.37/0.73 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54))))))))) % 0.37/0.73 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.73 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.73 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.73 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.73 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.73 (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)))))))))))) % 0.37/0.73 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.37/0.73 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41)))) % 0.37/0.73 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.73 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.73 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t62 @t1))))))))) % 0.37/0.73 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.73 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41)))) % 0.37/0.73 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.73 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.73 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.73 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t62 @t10) @t1))))))))))) % 0.37/0.73 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.73 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41)))) % 0.37/0.73 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t63)))) % 0.37/0.73 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.73 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t63)))) % 0.37/0.73 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.73 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t63)))) % 0.37/0.73 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.73 (assume @p65 (forall @t9 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:premises (@p503) :args (@t59)) % 0.37/0.73 (step @p505 :rule trans :premises (@p504 @p500)) % 0.37/0.73 (step @p506 :rule refl :args (@t8)) % 0.37/0.73 (step @p507 :rule cong :premises (@p506 @p505) :args (@t60)) % 0.37/0.73 (step @p508 :rule cong :premises (@p507) :args (@t61)) % 0.37/0.73 (step @p509 :rule trans :premises (@p508 @p486)) % 0.37/0.73 (step @p510 :rule eq_resolve :premises (@p36 @p509)) % 0.37/0.73 (step @p511 :rule instantiate :premises (@p510) :args ((@list @t315 @t312 @t310))) % 0.37/0.73 (step @p512 :rule bool-double-not-elim :args (@t318)) % 0.37/0.73 (step @p513 :rule nary_cong :premises (@p454 @p512) :args ((or @t327 (not @t319)))) % 0.37/0.73 (step @p514 :rule cnf_or_neg :args (@t327 5)) % 0.37/0.73 (step @p515 :rule eq_resolve :premises (@p514 @p513)) % 0.37/0.73 (step @p516 :rule reordering :premises (@p515) :args ((or @t318 @t327))) % 0.37/0.73 (step @p517 :rule chain_m_resolution :premises (@p516 @p452) :args (@t318 @t337 @t338)) % 0.37/0.73 (step @p518 :rule cnf_or_neg :args (@t366 0)) % 0.37/0.73 (step @p519 :rule reordering :premises (@p518) :args ((or @t319 @t366))) % 0.37/0.73 (step @p520 :rule chain_m_resolution :premises (@p519 @p517) :args (@t366 (@list false) (@list @t318))) % 0.37/0.73 (step @p521 :rule cnf_or_neg :args (@t327 6)) % 0.37/0.73 (step @p522 :rule chain_m_resolution :premises (@p521 @p452) :args ((not @t317) @t337 @t338)) % 0.37/0.73 (step @p523 :rule cnf_equiv_pos2 :args (@t367)) % 0.37/0.73 (step @p524 :rule reordering :premises (@p523) :args ((or @t317 (not @t366) @t368))) % 0.37/0.73 (step @p525 :rule chain_m_resolution :premises (@p524 @p522 @p520) :args (@t368 (@list true false) (@list @t317 @t366))) % 0.37/0.73 (step @p526 :rule cnf_or_pos :args (@t369)) % 0.37/0.73 (step @p527 :rule reordering :premises (@p526) :args ((or @t326 @t321 @t314 @t367 (not @t369)))) % 0.37/0.73 (step @p528 false :rule chain_m_resolution :premises (@p527 @p525 @p511 @p471 @p465 @p459) :args (false (@list true false false false false) (@list @t367 @t369 @t313 @t320 @t325))) % 0.37/0.73 ) % 0.37/0.73 % SZS output end Proof % 0.37/0.73 % cvc5 exiting %------------------------------------------------------------------------------