%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC317+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 08:58:51 AM UTC 2026 % Result : Theorem 0.36s 0.76s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : SWC317+1 : TPTP v9.2.1. Released v2.4.0. % 0.09/0.15 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n016.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 19:41:39 EDT 2026 % 0.17/0.36 % CPUTime : % 0.26/0.54 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.76 % SZS status Theorem % 0.36/0.76 % SZS output start Proof % 0.36/0.76 ( % 0.36/0.76 (declare-sort $$unsorted 0) % 0.36/0.76 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.76 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.76 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.76 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.76 (declare-const tptp.nil $$unsorted) % 0.36/0.76 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.76 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.76 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.76 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.76 (define @t3 () (= @t2 @t1)) % 0.36/0.76 (define @t4 () (not @t3)) % 0.36/0.76 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.76 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.76 (define @t7 () (@list @t1)) % 0.36/0.76 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.76 (define @t9 () (@list @t2)) % 0.36/0.76 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.76 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.76 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.76 (define @t13 () (tptp.ssList @t10)) % 0.36/0.76 (define @t14 () (@list @t10)) % 0.36/0.76 (define @t15 () (tptp.ssList @t12)) % 0.36/0.76 (define @t16 () (@list @t12)) % 0.36/0.76 (define @t17 () (tptp.ssList @t2)) % 0.36/0.76 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.76 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.76 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.76 (define @t21 () (tptp.ssList @t1)) % 0.36/0.76 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.76 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.76 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.76 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.76 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.76 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.76 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.76 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.76 (define @t30 () (tptp.ssList @t27)) % 0.36/0.76 (define @t31 () (@list @t27)) % 0.36/0.76 (define @t32 () (tptp.ssList @t28)) % 0.36/0.76 (define @t33 () (@list @t28)) % 0.36/0.76 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.76 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.76 (define @t36 () (= @t1 @t12)) % 0.36/0.76 (define @t37 () (tptp.cons @t1 @t2)) % 0.36/0.76 (define @t38 () (= @t1 @t2)) % 0.36/0.76 (define @t39 () (tptp.cons @t12 @t1)) % 0.36/0.76 (define @t40 () (= tptp.nil @t2)) % 0.36/0.76 (define @t41 () (tptp.hd @t2)) % 0.36/0.76 (define @t42 () (not @t40)) % 0.36/0.76 (define @t43 () (tptp.tl @t2)) % 0.36/0.76 (define @t44 () (tptp.app @t2 @t1)) % 0.36/0.76 (define @t45 () (tptp.app @t1 @t2)) % 0.36/0.76 (define @t46 () (tptp.leq @t1 @t2)) % 0.36/0.76 (define @t47 () (tptp.leq @t2 @t1)) % 0.36/0.76 (define @t48 () (tptp.geq @t2 @t1)) % 0.36/0.76 (define @t49 () (tptp.lt @t1 @t2)) % 0.36/0.76 (define @t50 () (tptp.lt @t2 @t1)) % 0.36/0.76 (define @t51 () (tptp.lt @t2 @t12)) % 0.36/0.76 (define @t52 () (tptp.gt @t2 @t1)) % 0.36/0.76 (define @t53 () (tptp.memberP @t12 @t2)) % 0.36/0.76 (define @t54 () (tptp.app @t12 @t2)) % 0.36/0.76 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.36/0.76 (define @t56 () (tptp.hd @t1)) % 0.36/0.76 (define @t57 () (= tptp.nil @t1)) % 0.36/0.76 (define @t58 () (not @t57)) % 0.36/0.76 (define @t59 () (tptp.cons @t2 @t1)) % 0.36/0.76 (define @t60 () (= @t12 @t2)) % 0.36/0.76 (define @t61 () (tptp.neq @t1 tptp.nil)) % 0.36/0.76 (define @t62 () (not @t61)) % 0.36/0.76 (define @t63 () (or @t62 (tptp.neq @t10 tptp.nil))) % 0.36/0.76 (define @t64 () (@var "X1" $$unsorted)) % 0.36/0.76 (define @t65 () (tptp.cons @t64 tptp.nil)) % 0.36/0.76 (define @t66 () (@var "X2" $$unsorted)) % 0.36/0.76 (define @t67 () (tptp.app @t66 @t65)) % 0.36/0.76 (define @t68 () (not (= @t67 @t10))) % 0.36/0.76 (define @t69 () (tptp.app @t65 @t66)) % 0.36/0.76 (define @t70 () (not (= @t69 @t12))) % 0.36/0.76 (define @t71 () (or @t70 @t68)) % 0.36/0.76 (define @t72 () (tptp.ssList @t66)) % 0.36/0.76 (define @t73 () (=> @t72 @t71)) % 0.36/0.76 (define @t74 () (@list @t66)) % 0.36/0.76 (define @t75 () (forall @t74 @t73)) % 0.36/0.76 (define @t76 () (tptp.ssItem @t64)) % 0.36/0.76 (define @t77 () (=> @t76 @t75)) % 0.36/0.76 (define @t78 () (@list @t64)) % 0.36/0.76 (define @t79 () (forall @t78 @t77)) % 0.36/0.76 (define @t80 () (tptp.cons @t28 tptp.nil)) % 0.36/0.76 (define @t81 () (tptp.app @t27 @t80)) % 0.36/0.76 (define @t82 () (tptp.app @t80 @t27)) % 0.36/0.76 (define @t83 () (and @t30 (= @t82 @t2) (= @t81 @t1))) % 0.36/0.76 (define @t84 () (exists @t31 @t83)) % 0.36/0.76 (define @t85 () (tptp.ssItem @t28)) % 0.36/0.76 (define @t86 () (and @t85 @t84)) % 0.36/0.76 (define @t87 () (exists @t33 @t86)) % 0.36/0.76 (define @t88 () (or @t62 @t87 @t79)) % 0.36/0.76 (define @t89 () (and @t88 @t63)) % 0.36/0.76 (define @t90 () (not (= @t2 @t12))) % 0.36/0.76 (define @t91 () (not (= @t1 @t10))) % 0.36/0.76 (define @t92 () (or @t91 @t90 @t89)) % 0.36/0.76 (define @t93 () (=> @t13 @t92)) % 0.36/0.76 (define @t94 () (forall @t14 @t93)) % 0.36/0.76 (define @t95 () (=> @t15 @t94)) % 0.36/0.76 (define @t96 () (forall @t16 @t95)) % 0.36/0.76 (define @t97 () (=> @t21 @t96)) % 0.36/0.76 (define @t98 () (forall @t7 @t97)) % 0.36/0.76 (define @t99 () (=> @t17 @t98)) % 0.36/0.76 (define @t100 () (forall @t9 @t99)) % 0.36/0.76 (define @t101 () (not @t100)) % 0.36/0.76 (define @t102 () (@var "BOUND_VARIABLE_11167" $$unsorted)) % 0.36/0.76 (define @t103 () (not (tptp.ssList @t102))) % 0.36/0.76 (define @t104 () (@var "BOUND_VARIABLE_11165" $$unsorted)) % 0.36/0.76 (define @t105 () (not (tptp.ssItem @t104))) % 0.36/0.76 (define @t106 () (tptp.cons @t104 tptp.nil)) % 0.36/0.76 (define @t107 () (tptp.app @t102 @t106)) % 0.36/0.76 (define @t108 () (@var "BOUND_VARIABLE_10964" $$unsorted)) % 0.36/0.76 (define @t109 () (tptp.app @t108 @t80)) % 0.36/0.76 (define @t110 () (not (= @t109 @t107))) % 0.36/0.76 (define @t111 () (tptp.app @t106 @t102)) % 0.36/0.76 (define @t112 () (tptp.app @t80 @t108)) % 0.36/0.76 (define @t113 () (not (tptp.ssList @t108))) % 0.36/0.76 (define @t114 () (not @t85)) % 0.36/0.76 (define @t115 () (@list @t28 @t108)) % 0.36/0.76 (define @t116 () (not (forall @t115 (or @t114 @t113 (not (= @t112 @t111)) @t110)))) % 0.36/0.76 (define @t117 () (not (tptp.neq @t107 tptp.nil))) % 0.36/0.76 (define @t118 () (not (tptp.ssList @t107))) % 0.36/0.76 (define @t119 () (not (tptp.ssList @t111))) % 0.36/0.76 (define @t120 () (or @t119 @t118 @t117 @t116 @t105 @t103)) % 0.36/0.76 (define @t121 () (not (= @t111 @t111))) % 0.36/0.76 (define @t122 () (not (= @t111 @t112))) % 0.36/0.76 (define @t123 () (or @t114 @t113 @t122 @t110)) % 0.36/0.76 (define @t124 () (forall @t115 @t123)) % 0.36/0.76 (define @t125 () (not @t124)) % 0.36/0.76 (define @t126 () (or @t119 @t118 @t117 @t125 @t105 @t103 @t121)) % 0.36/0.76 (define @t127 () (@list @t104 @t102)) % 0.36/0.76 (define @t128 () (not (= @t2 @t111))) % 0.36/0.76 (define @t129 () (not (= @t2 @t112))) % 0.36/0.76 (define @t130 () (not (forall @t115 (or @t114 @t113 @t129 @t110)))) % 0.36/0.76 (define @t131 () (not @t17)) % 0.36/0.76 (define @t132 () (or @t128 @t131 @t118 @t117 @t130 @t105 @t103 @t128)) % 0.36/0.76 (define @t133 () (or @t131 @t118 @t117 @t130 @t105 @t103 @t128)) % 0.36/0.76 (define @t134 () (forall @t9 @t133)) % 0.36/0.76 (define @t135 () (forall @t127 @t134)) % 0.36/0.76 (define @t136 () (forall (@list @t104 @t102 @t2) @t133)) % 0.36/0.76 (define @t137 () (@list @t2 @t104 @t102)) % 0.36/0.76 (define @t138 () (or @t118 @t117 @t130 @t105 @t103 @t128)) % 0.36/0.76 (define @t139 () (or @t131 @t138)) % 0.36/0.76 (define @t140 () (forall @t137 @t139)) % 0.36/0.76 (define @t141 () (forall @t127 @t139)) % 0.36/0.76 (define @t142 () (forall @t127 @t138)) % 0.36/0.76 (define @t143 () (@var "BOUND_VARIABLE_11120" $$unsorted)) % 0.36/0.76 (define @t144 () (@var "BOUND_VARIABLE_11118" $$unsorted)) % 0.36/0.76 (define @t145 () (@list @t144 @t143)) % 0.36/0.76 (define @t146 () (or @t131 @t142)) % 0.36/0.76 (define @t147 () (tptp.cons @t144 tptp.nil)) % 0.36/0.76 (define @t148 () (not (= @t2 (tptp.app @t147 @t143)))) % 0.36/0.76 (define @t149 () (not (tptp.ssList @t143))) % 0.36/0.76 (define @t150 () (not (tptp.ssItem @t144))) % 0.36/0.76 (define @t151 () (tptp.app @t143 @t147)) % 0.36/0.76 (define @t152 () (not (forall @t115 (or @t114 @t113 @t129 (not (= @t109 @t151)))))) % 0.36/0.76 (define @t153 () (not (tptp.neq @t151 tptp.nil))) % 0.36/0.76 (define @t154 () (not (tptp.ssList @t151))) % 0.36/0.76 (define @t155 () (or @t154 @t153 @t152 @t150 @t149 @t148)) % 0.36/0.76 (define @t156 () (@list @t144 @t143)) % 0.36/0.76 (define @t157 () (or @t131 (forall @t156 @t155))) % 0.36/0.76 (define @t158 () (not (= @t151 @t151))) % 0.36/0.76 (define @t159 () (not (= @t151 @t109))) % 0.36/0.76 (define @t160 () (or @t114 @t113 @t129 @t159)) % 0.36/0.76 (define @t161 () (forall @t115 @t160)) % 0.36/0.76 (define @t162 () (not @t161)) % 0.36/0.76 (define @t163 () (or @t154 @t153 @t162 @t150 @t149 @t148 @t158)) % 0.36/0.76 (define @t164 () (not (= @t1 @t151))) % 0.36/0.76 (define @t165 () (not (= @t1 @t109))) % 0.36/0.76 (define @t166 () (or @t114 @t113 @t129 @t165)) % 0.36/0.76 (define @t167 () (not (forall @t115 @t166))) % 0.36/0.76 (define @t168 () (not @t21)) % 0.36/0.76 (define @t169 () (or @t164 @t168 @t62 @t167 @t150 @t149 @t148 @t164)) % 0.36/0.76 (define @t170 () (or @t168 @t62 @t167 @t150 @t149 @t148 @t164)) % 0.36/0.76 (define @t171 () (forall @t7 @t170)) % 0.36/0.76 (define @t172 () (forall @t156 @t171)) % 0.36/0.76 (define @t173 () (forall (@list @t144 @t143 @t1) @t170)) % 0.36/0.76 (define @t174 () (@list @t1 @t144 @t143)) % 0.36/0.76 (define @t175 () (or @t150 @t149 @t148 @t164)) % 0.36/0.76 (define @t176 () (or @t168 @t62 @t167 @t175)) % 0.36/0.76 (define @t177 () (forall @t174 @t176)) % 0.36/0.76 (define @t178 () (forall @t156 @t176)) % 0.36/0.76 (define @t179 () (forall @t156 @t175)) % 0.36/0.76 (define @t180 () (@var "BOUND_VARIABLE_11078" $$unsorted)) % 0.36/0.76 (define @t181 () (@var "BOUND_VARIABLE_11076" $$unsorted)) % 0.36/0.76 (define @t182 () (@list @t181 @t180)) % 0.36/0.76 (define @t183 () (or @t168 @t62 @t167 @t179)) % 0.36/0.76 (define @t184 () (tptp.cons @t181 tptp.nil)) % 0.36/0.76 (define @t185 () (not (= @t1 (tptp.app @t180 @t184)))) % 0.36/0.76 (define @t186 () (tptp.app @t184 @t180)) % 0.36/0.76 (define @t187 () (not (= @t2 @t186))) % 0.36/0.76 (define @t188 () (not (tptp.ssList @t180))) % 0.36/0.76 (define @t189 () (not (tptp.ssItem @t181))) % 0.36/0.76 (define @t190 () (or @t189 @t188 @t187 @t185)) % 0.36/0.76 (define @t191 () (@list @t181 @t180)) % 0.36/0.76 (define @t192 () (forall @t191 @t190)) % 0.36/0.76 (define @t193 () (or @t168 @t62 @t167 @t192)) % 0.36/0.76 (define @t194 () (forall @t7 @t193)) % 0.36/0.76 (define @t195 () (or @t131 @t194)) % 0.36/0.76 (define @t196 () (or @t131 @t193)) % 0.36/0.76 (define @t197 () (or @t168 @t62 @t167 @t131 @t192)) % 0.36/0.76 (define @t198 () (or @t131 @t192)) % 0.36/0.76 (define @t199 () (or @t131 @t190)) % 0.36/0.76 (define @t200 () (or @t131 @t189 @t188 @t187 @t185)) % 0.36/0.76 (define @t201 () (not (= @t2 @t2))) % 0.36/0.76 (define @t202 () (or @t131 @t201 @t189 @t188 @t187 @t185)) % 0.36/0.76 (define @t203 () (not (= @t12 @t186))) % 0.36/0.76 (define @t204 () (not @t15)) % 0.36/0.76 (define @t205 () (or @t90 @t204 @t90 @t189 @t188 @t203 @t185)) % 0.36/0.76 (define @t206 () (or @t204 @t90 @t189 @t188 @t203 @t185)) % 0.36/0.76 (define @t207 () (forall @t16 @t206)) % 0.36/0.76 (define @t208 () (forall @t191 @t207)) % 0.36/0.76 (define @t209 () (forall (@list @t181 @t180 @t12) @t206)) % 0.36/0.76 (define @t210 () (@list @t12 @t181 @t180)) % 0.36/0.76 (define @t211 () (or @t189 @t188 @t203 @t185)) % 0.36/0.76 (define @t212 () (or @t204 @t90 @t211)) % 0.36/0.76 (define @t213 () (forall @t210 @t212)) % 0.36/0.76 (define @t214 () (forall @t191 @t212)) % 0.36/0.76 (define @t215 () (forall @t191 @t211)) % 0.36/0.76 (define @t216 () (@var "BOUND_VARIABLE_11024" $$unsorted)) % 0.36/0.76 (define @t217 () (@var "BOUND_VARIABLE_11022" $$unsorted)) % 0.36/0.76 (define @t218 () (@list @t217 @t216)) % 0.36/0.76 (define @t219 () (or @t204 @t90 @t215)) % 0.36/0.76 (define @t220 () (tptp.cons @t217 tptp.nil)) % 0.36/0.76 (define @t221 () (tptp.app @t216 @t220)) % 0.36/0.76 (define @t222 () (not (= @t1 @t221))) % 0.36/0.76 (define @t223 () (not (= @t12 (tptp.app @t220 @t216)))) % 0.36/0.76 (define @t224 () (not (tptp.ssList @t216))) % 0.36/0.76 (define @t225 () (not (tptp.ssItem @t217))) % 0.36/0.76 (define @t226 () (or @t225 @t224 @t223 @t222)) % 0.36/0.76 (define @t227 () (@list @t217 @t216)) % 0.36/0.76 (define @t228 () (forall @t227 @t226)) % 0.36/0.76 (define @t229 () (or @t204 @t90 @t228)) % 0.36/0.76 (define @t230 () (forall @t16 @t229)) % 0.36/0.76 (define @t231 () (or @t168 @t62 @t167 @t230)) % 0.36/0.76 (define @t232 () (or @t168 @t62 @t167 @t229)) % 0.36/0.76 (define @t233 () (or @t204 @t90 @t168 @t62 @t167 @t228)) % 0.36/0.76 (define @t234 () (or @t90 @t168 @t62 @t167 @t228)) % 0.36/0.76 (define @t235 () (or @t168 @t62 @t167 @t228)) % 0.36/0.76 (define @t236 () (or @t168 @t62 @t167 @t226)) % 0.36/0.76 (define @t237 () (or @t168 @t62 @t167 @t225 @t224 @t223 @t222)) % 0.36/0.76 (define @t238 () (or @t62 @t167 @t225 @t224 @t223 @t222)) % 0.36/0.76 (define @t239 () (and @t238 true)) % 0.36/0.76 (define @t240 () (or @t168 @t239)) % 0.36/0.76 (define @t241 () (and @t238 (or @t62 @t61))) % 0.36/0.76 (define @t242 () (or @t168 @t241)) % 0.36/0.76 (define @t243 () (not (= @t1 @t1))) % 0.36/0.76 (define @t244 () (or @t168 @t243 @t241)) % 0.36/0.76 (define @t245 () (not (= @t10 @t221))) % 0.36/0.76 (define @t246 () (or @t62 @t167 @t225 @t224 @t223 @t245)) % 0.36/0.76 (define @t247 () (and @t246 @t63)) % 0.36/0.76 (define @t248 () (not @t13)) % 0.36/0.76 (define @t249 () (or @t91 @t248 @t91 @t247)) % 0.36/0.76 (define @t250 () (or @t248 @t91 @t247)) % 0.36/0.76 (define @t251 () (forall @t14 @t250)) % 0.36/0.76 (define @t252 () (forall @t227 @t251)) % 0.36/0.76 (define @t253 () (forall (@list @t217 @t216 @t10) @t250)) % 0.36/0.76 (define @t254 () (@list @t10 @t217 @t216)) % 0.36/0.76 (define @t255 () (or @t225 @t224 @t223 @t245)) % 0.36/0.76 (define @t256 () (or @t62 @t167 @t255)) % 0.36/0.76 (define @t257 () (and @t256 @t63)) % 0.36/0.76 (define @t258 () (or @t248 @t91 @t257)) % 0.36/0.76 (define @t259 () (forall @t254 @t258)) % 0.36/0.76 (define @t260 () (forall @t227 @t258)) % 0.36/0.76 (define @t261 () (forall @t227 @t63)) % 0.36/0.76 (define @t262 () (forall @t227 @t255)) % 0.36/0.76 (define @t263 () (@var "BOUND_VARIABLE_10996" $$unsorted)) % 0.36/0.76 (define @t264 () (or @t62 @t167 @t262)) % 0.36/0.76 (define @t265 () (forall @t227 @t256)) % 0.36/0.76 (define @t266 () (and @t265 @t261)) % 0.36/0.76 (define @t267 () (forall @t227 @t257)) % 0.36/0.76 (define @t268 () (or @t248 @t91 @t267)) % 0.36/0.76 (define @t269 () (not (= @t10 (tptp.app @t263 @t65)))) % 0.36/0.76 (define @t270 () (not (= @t12 (tptp.app @t65 @t263)))) % 0.36/0.76 (define @t271 () (not (tptp.ssList @t263))) % 0.36/0.76 (define @t272 () (not @t76)) % 0.36/0.76 (define @t273 () (or @t272 @t271 @t270 @t269)) % 0.36/0.76 (define @t274 () (@list @t64 @t263)) % 0.36/0.76 (define @t275 () (and (or @t62 @t167 (forall @t274 @t273)) @t63)) % 0.36/0.76 (define @t276 () (or @t248 @t91 @t275)) % 0.36/0.76 (define @t277 () (forall @t14 @t276)) % 0.36/0.76 (define @t278 () (or @t90 @t277)) % 0.36/0.76 (define @t279 () (or @t90 @t276)) % 0.36/0.76 (define @t280 () (or @t248 @t91 @t90 @t275)) % 0.36/0.76 (define @t281 () (or @t91 @t90 @t275)) % 0.36/0.76 (define @t282 () (or @t271 @t270 @t269)) % 0.36/0.76 (define @t283 () (or @t272 @t282)) % 0.36/0.76 (define @t284 () (forall @t274 @t283)) % 0.36/0.76 (define @t285 () (@list @t263)) % 0.36/0.76 (define @t286 () (forall @t285 @t283)) % 0.36/0.76 (define @t287 () (forall @t285 @t282)) % 0.36/0.76 (define @t288 () (or @t272 @t287)) % 0.36/0.76 (define @t289 () (not (= @t10 @t67))) % 0.36/0.76 (define @t290 () (not (= @t12 @t69))) % 0.36/0.76 (define @t291 () (not @t72)) % 0.36/0.76 (define @t292 () (or @t291 @t290 @t289)) % 0.36/0.76 (define @t293 () (forall @t74 @t292)) % 0.36/0.76 (define @t294 () (or @t290 @t289)) % 0.36/0.76 (define @t295 () (or @t113 @t129 @t165)) % 0.36/0.76 (define @t296 () (or @t114 @t295)) % 0.36/0.76 (define @t297 () (forall @t115 @t296)) % 0.36/0.76 (define @t298 () (@list @t108)) % 0.36/0.76 (define @t299 () (forall @t298 @t296)) % 0.36/0.76 (define @t300 () (forall @t298 @t295)) % 0.36/0.76 (define @t301 () (or @t114 @t300)) % 0.36/0.76 (define @t302 () (= @t1 @t81)) % 0.36/0.76 (define @t303 () (not @t302)) % 0.36/0.76 (define @t304 () (= @t2 @t82)) % 0.36/0.76 (define @t305 () (not @t304)) % 0.36/0.76 (define @t306 () (not @t30)) % 0.36/0.76 (define @t307 () (or @t306 @t305 @t303)) % 0.36/0.76 (define @t308 () (forall @t31 @t307)) % 0.36/0.76 (define @t309 () (not @t308)) % 0.36/0.76 (define @t310 () (and @t85 @t309)) % 0.36/0.76 (define @t311 () (forall @t33 (not @t310))) % 0.36/0.76 (define @t312 () (not @t311)) % 0.36/0.76 (define @t313 () (and @t30 @t304 @t302)) % 0.36/0.76 (define @t314 () (forall @t31 (not @t313))) % 0.36/0.76 (define @t315 () (not @t314)) % 0.36/0.76 (define @t316 () (forall @t127 @t120)) % 0.36/0.76 (define @t317 () (@quantifiers_skolemize @t316 0)) % 0.36/0.76 (define @t318 () (tptp.cons @t317 tptp.nil)) % 0.36/0.76 (define @t319 () (@quantifiers_skolemize @t316 1)) % 0.36/0.76 (define @t320 () (tptp.app @t319 @t318)) % 0.36/0.76 (define @t321 () (tptp.app @t318 @t319)) % 0.36/0.76 (define @t322 () (forall @t115 (or @t114 @t113 (not (= @t112 @t321)) (not (= @t109 @t320))))) % 0.36/0.76 (define @t323 () (tptp.ssList @t319)) % 0.36/0.76 (define @t324 () (not @t323)) % 0.36/0.76 (define @t325 () (tptp.ssItem @t317)) % 0.36/0.76 (define @t326 () (not @t325)) % 0.36/0.76 (define @t327 () (not @t322)) % 0.36/0.76 (define @t328 () (or (not (tptp.ssList @t321)) (not (tptp.ssList @t320)) (not (tptp.neq @t320 tptp.nil)) @t327 @t326 @t324)) % 0.36/0.76 (define @t329 () (@list true)) % 0.36/0.76 (define @t330 () (@list @t328)) % 0.36/0.76 (define @t331 () (or @t326 @t324)) % 0.36/0.76 (define @t332 () (not @t331)) % 0.36/0.76 (define @t333 () (not (= @t320 @t320))) % 0.36/0.76 (define @t334 () (not (= @t321 @t321))) % 0.36/0.76 (define @t335 () (or @t326 @t324 @t334 @t333)) % 0.36/0.76 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.76 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.76 (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))))))))))) % 0.36/0.76 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.76 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.76 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.76 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.76 (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))))))))))))))))) % 0.36/0.76 (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)))))))))))))))) % 0.36/0.76 (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))))))))))))))))) % 0.36/0.76 (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))))))))))))))) % 0.36/0.76 (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))))))))))))))) % 0.36/0.76 (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)))))))))))))))) % 0.36/0.76 (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))))))))))))) % 0.36/0.76 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.36/0.76 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.36/0.76 (assume @p17 (tptp.ssList tptp.nil)) % 0.36/0.76 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.36/0.76 (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))))))))))) % 0.36/0.76 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.36/0.76 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.36/0.76 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.36/0.76 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.36/0.76 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.36/0.76 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.36/0.76 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.36/0.76 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.36/0.76 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.76 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.36/0.76 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.76 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.76 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.36/0.76 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.36/0.76 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.36/0.76 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.36/0.76 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.36/0.76 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.36/0.76 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.36/0.76 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.36/0.76 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.36/0.76 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.36/0.76 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.36/0.76 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.36/0.76 (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)))))))))))) % 0.36/0.76 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.36/0.76 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.36/0.76 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.36/0.76 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.36/0.76 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.36/0.76 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.36/0.76 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.36/0.76 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.36/0.76 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.36/0.76 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.36/0.76 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.36/0.76 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.36/0.76 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.36/0.76 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.36/0.76 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.36/0.76 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.36/0.76 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.36/0.76 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.36/0.76 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.36/0.76 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.36/0.76 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.36/0.76 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.36/0.76 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.36/0.76 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.36/0.76 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.36/0.76 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.36/0.76 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.36/0.76 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.36/0.76 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.36/0.76 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.36/0.76 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.36/0.76 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.36/0.76 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.36/0.76 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.36/0.76 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.36/0.76 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.36/0.76 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.36/0.76 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.36/0.76 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t57 @t40))))))) % 0.36/0.76 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.36/0.76 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.36/0.76 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 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@t335))) % 0.36/0.76 (assume-push @p484 @t322) % 0.36/0.76 (step @p478 :rule instantiate :premises (@p448) :args ((@list @t317 @t319))) % 0.36/0.76 (step-pop @p485 :rule scope :premises (@p478)) % 0.36/0.76 (step @p479 :rule process_scope :premises (@p485) :args (@t335)) % 0.36/0.76 (step @p481 :rule eq_resolve :premises (@p479 @p476)) % 0.36/0.76 (step @p482 :rule implies_elim :premises (@p481)) % 0.36/0.76 (step @p483 false :rule chain_m_resolution :premises (@p482 @p463 @p448) :args (false (@list true false) (@list @t331 @t322))) % 0.36/0.76 ) % 0.36/0.76 % SZS output end Proof % 0.36/0.76 % cvc5 exiting %------------------------------------------------------------------------------