%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC327+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 : n021.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 08:58:53 AM UTC 2026 % Result : Theorem 0.36s 0.74s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC327+1 : TPTP v9.2.1. Released v2.4.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n021.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 19:42:35 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.74 % SZS status Theorem % 0.36/0.74 % SZS output start Proof % 0.36/0.74 ( % 0.36/0.74 (declare-sort $$unsorted 0) % 0.36/0.74 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.74 (declare-const tptp.nil $$unsorted) % 0.36/0.74 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.36/0.74 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.74 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.74 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.74 (define @t3 () (= @t2 @t1)) % 0.36/0.74 (define @t4 () (not @t3)) % 0.36/0.74 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.36/0.74 (define @t6 () (tptp.ssItem @t1)) % 0.36/0.74 (define @t7 () (@list @t1)) % 0.36/0.74 (define @t8 () (tptp.ssItem @t2)) % 0.36/0.74 (define @t9 () (@list @t2)) % 0.36/0.74 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.74 (define @t11 () (tptp.cons @t1 @t10)) % 0.36/0.74 (define @t12 () (@var "W" $$unsorted)) % 0.36/0.74 (define @t13 () (tptp.ssList @t10)) % 0.36/0.74 (define @t14 () (@list @t10)) % 0.36/0.74 (define @t15 () (tptp.ssList @t12)) % 0.36/0.74 (define @t16 () (@list @t12)) % 0.36/0.74 (define @t17 () (tptp.ssList @t2)) % 0.36/0.74 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.36/0.74 (define @t19 () (tptp.app @t1 @t12)) % 0.36/0.74 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.36/0.74 (define @t21 () (tptp.ssList @t1)) % 0.36/0.74 (define @t22 () (tptp.app @t12 @t1)) % 0.36/0.74 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.36/0.74 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.36/0.74 (define @t25 () (tptp.leq @t12 @t1)) % 0.36/0.74 (define @t26 () (tptp.leq @t1 @t12)) % 0.36/0.74 (define @t27 () (@var "Z" $$unsorted)) % 0.36/0.74 (define @t28 () (@var "Y" $$unsorted)) % 0.36/0.74 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.36/0.74 (define @t30 () (tptp.ssList @t27)) % 0.36/0.74 (define @t31 () (@list @t27)) % 0.36/0.74 (define @t32 () (tptp.ssList @t28)) % 0.36/0.74 (define @t33 () (@list @t28)) % 0.36/0.74 (define @t34 () (tptp.ssItem @t12)) % 0.36/0.74 (define @t35 () (tptp.lt @t1 @t12)) % 0.36/0.74 (define @t36 () (= @t1 @t12)) % 0.36/0.74 (define @t37 () (tptp.equalelemsP @t2)) % 0.36/0.74 (define @t38 () (tptp.cons @t1 @t2)) % 0.36/0.74 (define @t39 () (= @t1 @t2)) % 0.36/0.74 (define @t40 () (tptp.cons @t12 @t1)) % 0.36/0.74 (define @t41 () (= tptp.nil @t2)) % 0.36/0.74 (define @t42 () (tptp.hd @t2)) % 0.36/0.74 (define @t43 () (not @t41)) % 0.36/0.74 (define @t44 () (tptp.tl @t2)) % 0.36/0.74 (define @t45 () (tptp.app @t2 @t1)) % 0.36/0.74 (define @t46 () (tptp.app @t1 @t2)) % 0.36/0.74 (define @t47 () (tptp.leq @t1 @t2)) % 0.36/0.74 (define @t48 () (tptp.leq @t2 @t1)) % 0.36/0.74 (define @t49 () (tptp.geq @t2 @t1)) % 0.36/0.74 (define @t50 () (tptp.lt @t1 @t2)) % 0.36/0.74 (define @t51 () (tptp.lt @t2 @t1)) % 0.36/0.74 (define @t52 () (tptp.lt @t2 @t12)) % 0.36/0.74 (define @t53 () (tptp.gt @t2 @t1)) % 0.36/0.74 (define @t54 () (tptp.memberP @t12 @t2)) % 0.36/0.74 (define @t55 () (tptp.app @t12 @t2)) % 0.36/0.74 (define @t56 () (tptp.cons @t2 tptp.nil)) % 0.36/0.74 (define @t57 () (tptp.hd @t1)) % 0.36/0.74 (define @t58 () (= tptp.nil @t1)) % 0.36/0.74 (define @t59 () (not @t58)) % 0.36/0.74 (define @t60 () (tptp.cons @t2 @t1)) % 0.36/0.74 (define @t61 () (= @t12 @t2)) % 0.36/0.74 (define @t62 () (or @t43 @t58)) % 0.36/0.74 (define @t63 () (@var "X4" $$unsorted)) % 0.36/0.74 (define @t64 () (tptp.cons @t63 tptp.nil)) % 0.36/0.74 (define @t65 () (@var "X6" $$unsorted)) % 0.36/0.74 (define @t66 () (tptp.app @t65 @t64)) % 0.36/0.74 (define @t67 () (not (= @t66 @t2))) % 0.36/0.74 (define @t68 () (tptp.ssList @t65)) % 0.36/0.74 (define @t69 () (=> @t68 @t67)) % 0.36/0.74 (define @t70 () (@list @t65)) % 0.36/0.74 (define @t71 () (forall @t70 @t69)) % 0.36/0.74 (define @t72 () (@var "X3" $$unsorted)) % 0.36/0.74 (define @t73 () (@var "X5" $$unsorted)) % 0.36/0.74 (define @t74 () (tptp.app @t64 @t73)) % 0.36/0.74 (define @t75 () (not (= @t74 @t72))) % 0.36/0.74 (define @t76 () (or @t75 @t71)) % 0.36/0.74 (define @t77 () (tptp.ssList @t73)) % 0.36/0.74 (define @t78 () (=> @t77 @t76)) % 0.36/0.74 (define @t79 () (@list @t73)) % 0.36/0.74 (define @t80 () (forall @t79 @t78)) % 0.36/0.74 (define @t81 () (tptp.ssItem @t63)) % 0.36/0.74 (define @t82 () (=> @t81 @t80)) % 0.36/0.74 (define @t83 () (@list @t63)) % 0.36/0.74 (define @t84 () (forall @t83 @t82)) % 0.36/0.74 (define @t85 () (tptp.app @t2 @t72)) % 0.36/0.74 (define @t86 () (tptp.ssList @t72)) % 0.36/0.74 (define @t87 () (and @t86 (= @t85 @t1) @t84 @t37)) % 0.36/0.74 (define @t88 () (@list @t72)) % 0.36/0.74 (define @t89 () (exists @t88 @t87)) % 0.36/0.74 (define @t90 () (and @t89 @t62)) % 0.36/0.74 (define @t91 () (not (= tptp.nil @t10))) % 0.36/0.74 (define @t92 () (and @t91 (= tptp.nil @t12))) % 0.36/0.74 (define @t93 () (tptp.cons @t27 tptp.nil)) % 0.36/0.74 (define @t94 () (@var "X2" $$unsorted)) % 0.36/0.74 (define @t95 () (tptp.app @t94 @t93)) % 0.36/0.74 (define @t96 () (tptp.ssList @t94)) % 0.36/0.74 (define @t97 () (and @t96 (= @t95 @t12))) % 0.36/0.74 (define @t98 () (@list @t94)) % 0.36/0.74 (define @t99 () (exists @t98 @t97)) % 0.36/0.74 (define @t100 () (@var "X1" $$unsorted)) % 0.36/0.74 (define @t101 () (tptp.app @t93 @t100)) % 0.36/0.74 (define @t102 () (tptp.ssList @t100)) % 0.36/0.74 (define @t103 () (and @t102 (= @t101 @t28) @t99)) % 0.36/0.74 (define @t104 () (@list @t100)) % 0.36/0.74 (define @t105 () (exists @t104 @t103)) % 0.36/0.74 (define @t106 () (tptp.ssItem @t27)) % 0.36/0.74 (define @t107 () (and @t106 @t105)) % 0.36/0.74 (define @t108 () (exists @t31 @t107)) % 0.36/0.74 (define @t109 () (not (tptp.equalelemsP @t12))) % 0.36/0.74 (define @t110 () (tptp.app @t12 @t28)) % 0.36/0.74 (define @t111 () (not (= @t110 @t10))) % 0.36/0.74 (define @t112 () (or @t111 @t109 @t108)) % 0.36/0.74 (define @t113 () (=> @t32 @t112)) % 0.36/0.74 (define @t114 () (forall @t33 @t113)) % 0.36/0.74 (define @t115 () (not (= @t2 @t12))) % 0.36/0.74 (define @t116 () (not (= @t1 @t10))) % 0.36/0.74 (define @t117 () (or @t116 @t115 @t114 @t92 @t90)) % 0.36/0.74 (define @t118 () (=> @t13 @t117)) % 0.36/0.74 (define @t119 () (forall @t14 @t118)) % 0.36/0.74 (define @t120 () (=> @t15 @t119)) % 0.36/0.74 (define @t121 () (forall @t16 @t120)) % 0.36/0.74 (define @t122 () (=> @t21 @t121)) % 0.36/0.74 (define @t123 () (forall @t7 @t122)) % 0.36/0.74 (define @t124 () (=> @t17 @t123)) % 0.36/0.74 (define @t125 () (forall @t9 @t124)) % 0.36/0.74 (define @t126 () (not @t125)) % 0.36/0.74 (define @t127 () (@var "BOUND_VARIABLE_11260" $$unsorted)) % 0.36/0.74 (define @t128 () (@var "BOUND_VARIABLE_11015" $$unsorted)) % 0.36/0.74 (define @t129 () (tptp.app @t93 @t128)) % 0.36/0.74 (define @t130 () (not (tptp.ssList @t128))) % 0.36/0.74 (define @t131 () (@var "BOUND_VARIABLE_11007" $$unsorted)) % 0.36/0.74 (define @t132 () (tptp.app @t131 @t93)) % 0.36/0.74 (define @t133 () (not (= @t2 @t132))) % 0.36/0.74 (define @t134 () (not (tptp.ssList @t131))) % 0.36/0.74 (define @t135 () (not @t106)) % 0.36/0.74 (define @t136 () (@list @t27 @t131 @t128)) % 0.36/0.74 (define @t137 () (not (forall @t136 (or @t135 @t134 @t133 @t130 (not (= @t129 @t127)))))) % 0.36/0.74 (define @t138 () (not (tptp.ssList @t127))) % 0.36/0.74 (define @t139 () (= @t2 tptp.nil)) % 0.36/0.74 (define @t140 () (tptp.app @t2 @t127)) % 0.36/0.74 (define @t141 () (= tptp.nil @t140)) % 0.36/0.74 (define @t142 () (and (not @t141) @t139)) % 0.36/0.74 (define @t143 () (not @t139)) % 0.36/0.74 (define @t144 () (@var "BOUND_VARIABLE_11073" $$unsorted)) % 0.36/0.74 (define @t145 () (tptp.app @t64 @t144)) % 0.36/0.74 (define @t146 () (not (= @t72 @t145))) % 0.36/0.74 (define @t147 () (not (tptp.ssList @t144))) % 0.36/0.74 (define @t148 () (@var "BOUND_VARIABLE_11065" $$unsorted)) % 0.36/0.74 (define @t149 () (tptp.app @t148 @t64)) % 0.36/0.74 (define @t150 () (not (= @t2 @t149))) % 0.36/0.74 (define @t151 () (not (tptp.ssList @t148))) % 0.36/0.74 (define @t152 () (not @t81)) % 0.36/0.74 (define @t153 () (or @t152 @t151 @t150 @t147 @t146)) % 0.36/0.74 (define @t154 () (@list @t63 @t148 @t144)) % 0.36/0.74 (define @t155 () (forall @t154 @t153)) % 0.36/0.74 (define @t156 () (not @t155)) % 0.36/0.74 (define @t157 () (not @t86)) % 0.36/0.74 (define @t158 () (and @t37 (not (forall @t88 (or @t157 (not (= @t85 @t140)) @t156))) (or @t143 @t141))) % 0.36/0.74 (define @t159 () (not (tptp.ssList @t140))) % 0.36/0.74 (define @t160 () (not @t37)) % 0.36/0.74 (define @t161 () (not @t17)) % 0.36/0.74 (define @t162 () (or @t161 @t160 @t159 @t158 @t142 @t138 @t137)) % 0.36/0.74 (define @t163 () (or @t159 @t158 @t142 @t138 @t137)) % 0.36/0.74 (define @t164 () (or @t161 @t160 @t163)) % 0.36/0.74 (define @t165 () (@list @t2 @t127)) % 0.36/0.74 (define @t166 () (forall @t165 @t164)) % 0.36/0.74 (define @t167 () (@list @t127)) % 0.36/0.74 (define @t168 () (forall @t167 @t164)) % 0.36/0.74 (define @t169 () (forall @t167 @t163)) % 0.36/0.74 (define @t170 () (@var "BOUND_VARIABLE_11208" $$unsorted)) % 0.36/0.74 (define @t171 () (@list @t170)) % 0.36/0.74 (define @t172 () (or @t161 @t160 @t169)) % 0.36/0.74 (define @t173 () (not (forall @t136 (or @t135 @t134 @t133 @t130 (not (= @t129 @t170)))))) % 0.36/0.74 (define @t174 () (not (tptp.ssList @t170))) % 0.36/0.74 (define @t175 () (tptp.app @t2 @t170)) % 0.36/0.74 (define @t176 () (= tptp.nil @t175)) % 0.36/0.74 (define @t177 () (and (not @t176) @t139)) % 0.36/0.74 (define @t178 () (and @t37 (not (forall @t88 (or @t157 (not (= @t85 @t175)) @t156))) (or @t143 @t176))) % 0.36/0.74 (define @t179 () (not (tptp.ssList @t175))) % 0.36/0.74 (define @t180 () (or @t179 @t178 @t177 @t174 @t173)) % 0.36/0.74 (define @t181 () (@list @t170)) % 0.36/0.74 (define @t182 () (or @t161 @t160 (forall @t181 @t180))) % 0.36/0.74 (define @t183 () (not (= @t175 @t175))) % 0.36/0.74 (define @t184 () (= @t175 tptp.nil)) % 0.36/0.74 (define @t185 () (not @t184)) % 0.36/0.74 (define @t186 () (and @t185 @t139)) % 0.36/0.74 (define @t187 () (or @t143 @t184)) % 0.36/0.74 (define @t188 () (not (= @t175 @t85))) % 0.36/0.74 (define @t189 () (or @t157 @t188 @t156)) % 0.36/0.74 (define @t190 () (forall @t88 @t189)) % 0.36/0.74 (define @t191 () (not @t190)) % 0.36/0.74 (define @t192 () (and @t37 @t191 @t187)) % 0.36/0.74 (define @t193 () (or @t179 @t192 @t186 @t174 @t183 @t173)) % 0.36/0.74 (define @t194 () (not (= @t1 @t175))) % 0.36/0.74 (define @t195 () (= @t1 tptp.nil)) % 0.36/0.74 (define @t196 () (not @t195)) % 0.36/0.74 (define @t197 () (and @t196 @t139)) % 0.36/0.74 (define @t198 () (or @t143 @t195)) % 0.36/0.74 (define @t199 () (= @t1 @t85)) % 0.36/0.74 (define @t200 () (not @t199)) % 0.36/0.74 (define @t201 () (or @t157 @t200 @t156)) % 0.36/0.74 (define @t202 () (forall @t88 @t201)) % 0.36/0.74 (define @t203 () (not @t202)) % 0.36/0.74 (define @t204 () (and @t37 @t203 @t198)) % 0.36/0.74 (define @t205 () (not @t21)) % 0.36/0.74 (define @t206 () (or @t194 @t205 @t204 @t197 @t174 @t194 @t173)) % 0.36/0.74 (define @t207 () (or @t205 @t204 @t197 @t174 @t194 @t173)) % 0.36/0.74 (define @t208 () (forall @t7 @t207)) % 0.36/0.74 (define @t209 () (forall @t181 @t208)) % 0.36/0.74 (define @t210 () (forall (@list @t170 @t1) @t207)) % 0.36/0.74 (define @t211 () (@list @t1 @t170)) % 0.36/0.74 (define @t212 () (or @t174 @t194 @t173)) % 0.36/0.74 (define @t213 () (or @t205 @t204 @t197 @t212)) % 0.36/0.74 (define @t214 () (forall @t211 @t213)) % 0.36/0.74 (define @t215 () (forall @t181 @t213)) % 0.36/0.74 (define @t216 () (forall @t181 @t212)) % 0.36/0.74 (define @t217 () (@var "BOUND_VARIABLE_11161" $$unsorted)) % 0.36/0.74 (define @t218 () (@list @t217)) % 0.36/0.74 (define @t219 () (or @t205 @t204 @t197 @t216)) % 0.36/0.74 (define @t220 () (not (= @t129 @t217))) % 0.36/0.74 (define @t221 () (not (forall @t136 (or @t135 @t134 @t133 @t130 @t220)))) % 0.36/0.74 (define @t222 () (not (= @t1 (tptp.app @t2 @t217)))) % 0.36/0.74 (define @t223 () (not (tptp.ssList @t217))) % 0.36/0.74 (define @t224 () (or @t223 @t222 @t221)) % 0.36/0.74 (define @t225 () (@list @t217)) % 0.36/0.74 (define @t226 () (forall @t225 @t224)) % 0.36/0.74 (define @t227 () (or @t205 @t204 @t197 @t226)) % 0.36/0.74 (define @t228 () (forall @t7 @t227)) % 0.36/0.74 (define @t229 () (or @t161 @t160 @t228)) % 0.36/0.74 (define @t230 () (or @t161 @t160 @t227)) % 0.36/0.74 (define @t231 () (or @t205 @t204 @t161 @t160 @t197 @t226)) % 0.36/0.74 (define @t232 () (or @t204 @t205 @t161 @t160 @t197 @t226)) % 0.36/0.74 (define @t233 () (or @t161 @t160 @t197 @t226)) % 0.36/0.74 (define @t234 () (or @t161 @t160 @t197 @t224)) % 0.36/0.74 (define @t235 () (or @t161 @t160 @t197 @t223 @t222 @t221)) % 0.36/0.74 (define @t236 () (not (= @t2 @t2))) % 0.36/0.74 (define @t237 () (or @t161 @t236 @t160 @t197 @t223 @t222 @t221)) % 0.36/0.74 (define @t238 () (not (= @t12 @t132))) % 0.36/0.74 (define @t239 () (not (forall @t136 (or @t135 @t134 @t238 @t130 @t220)))) % 0.36/0.74 (define @t240 () (not (= @t1 (tptp.app @t12 @t217)))) % 0.36/0.74 (define @t241 () (= @t12 tptp.nil)) % 0.36/0.74 (define @t242 () (and @t196 @t241)) % 0.36/0.74 (define @t243 () (not @t15)) % 0.36/0.74 (define @t244 () (or @t115 @t243 @t115 @t109 @t242 @t223 @t240 @t239)) % 0.36/0.74 (define @t245 () (or @t243 @t115 @t109 @t242 @t223 @t240 @t239)) % 0.36/0.74 (define @t246 () (forall @t16 @t245)) % 0.36/0.74 (define @t247 () (forall @t225 @t246)) % 0.36/0.74 (define @t248 () (forall (@list @t217 @t12) @t245)) % 0.36/0.74 (define @t249 () (@list @t12 @t217)) % 0.36/0.74 (define @t250 () (or @t223 @t240 @t239)) % 0.36/0.74 (define @t251 () (or @t243 @t115 @t109 @t242 @t250)) % 0.36/0.74 (define @t252 () (forall @t249 @t251)) % 0.36/0.74 (define @t253 () (forall @t225 @t251)) % 0.36/0.74 (define @t254 () (forall @t225 @t250)) % 0.36/0.74 (define @t255 () (@var "BOUND_VARIABLE_11116" $$unsorted)) % 0.36/0.74 (define @t256 () (@list @t255)) % 0.36/0.74 (define @t257 () (or @t243 @t115 @t109 @t242 @t254)) % 0.36/0.74 (define @t258 () (not (forall @t136 (or @t135 @t134 @t238 @t130 (not (= @t129 @t255)))))) % 0.36/0.74 (define @t259 () (tptp.app @t12 @t255)) % 0.36/0.74 (define @t260 () (not (= @t1 @t259))) % 0.36/0.74 (define @t261 () (not (tptp.ssList @t255))) % 0.36/0.74 (define @t262 () (or @t261 @t260 @t258)) % 0.36/0.74 (define @t263 () (@list @t255)) % 0.36/0.74 (define @t264 () (forall @t263 @t262)) % 0.36/0.74 (define @t265 () (or @t243 @t115 @t109 @t242 @t264)) % 0.36/0.74 (define @t266 () (forall @t16 @t265)) % 0.36/0.74 (define @t267 () (or @t204 @t205 @t266)) % 0.36/0.74 (define @t268 () (or @t204 @t205 @t265)) % 0.36/0.74 (define @t269 () (or @t243 @t115 @t204 @t109 @t205 @t242 @t264)) % 0.36/0.74 (define @t270 () (or @t115 @t204 @t109 @t205 @t242 @t264)) % 0.36/0.74 (define @t271 () (or @t205 @t242 @t264)) % 0.36/0.74 (define @t272 () (or @t205 @t242 @t262)) % 0.36/0.74 (define @t273 () (or @t205 @t242 @t261 @t260 @t258)) % 0.36/0.74 (define @t274 () (not (= @t1 @t1))) % 0.36/0.74 (define @t275 () (or @t205 @t274 @t242 @t261 @t260 @t258)) % 0.36/0.74 (define @t276 () (not (= @t10 @t259))) % 0.36/0.74 (define @t277 () (and (not (= @t10 tptp.nil)) @t241)) % 0.36/0.74 (define @t278 () (not @t13)) % 0.36/0.74 (define @t279 () (or @t116 @t278 @t116 @t277 @t261 @t276 @t258)) % 0.36/0.74 (define @t280 () (or @t278 @t116 @t277 @t261 @t276 @t258)) % 0.36/0.74 (define @t281 () (forall @t14 @t280)) % 0.36/0.74 (define @t282 () (forall @t263 @t281)) % 0.36/0.74 (define @t283 () (forall (@list @t255 @t10) @t280)) % 0.36/0.74 (define @t284 () (@list @t10 @t255)) % 0.36/0.74 (define @t285 () (not (= @t255 @t129))) % 0.36/0.74 (define @t286 () (or @t135 @t134 @t238 @t130 @t285)) % 0.36/0.74 (define @t287 () (forall @t136 @t286)) % 0.36/0.74 (define @t288 () (not @t287)) % 0.36/0.74 (define @t289 () (or @t278 @t116 @t277 @t261 @t276 @t288)) % 0.36/0.74 (define @t290 () (or @t261 @t276 @t288)) % 0.36/0.74 (define @t291 () (or @t278 @t116 @t277 @t290)) % 0.36/0.74 (define @t292 () (forall @t284 @t291)) % 0.36/0.74 (define @t293 () (forall @t263 @t291)) % 0.36/0.74 (define @t294 () (forall @t263 @t290)) % 0.36/0.74 (define @t295 () (or @t278 @t116 @t277 @t294)) % 0.36/0.74 (define @t296 () (not (= @t28 @t129))) % 0.36/0.74 (define @t297 () (or @t135 @t134 @t238 @t130 @t296)) % 0.36/0.74 (define @t298 () (not (forall @t136 @t297))) % 0.36/0.74 (define @t299 () (not (= @t10 @t110))) % 0.36/0.74 (define @t300 () (not @t32)) % 0.36/0.74 (define @t301 () (or @t300 @t299 @t298)) % 0.36/0.74 (define @t302 () (forall @t33 @t301)) % 0.36/0.74 (define @t303 () (or @t278 @t116 @t277 @t302)) % 0.36/0.74 (define @t304 () (forall @t14 @t303)) % 0.36/0.74 (define @t305 () (or @t115 @t204 @t109 @t304)) % 0.36/0.74 (define @t306 () (or @t115 @t204 @t109 @t303)) % 0.36/0.74 (define @t307 () (or @t278 @t116 @t115 @t277 @t204 @t109 @t302)) % 0.36/0.74 (define @t308 () (or @t160 @t202)) % 0.36/0.74 (define @t309 () (and (not @t308) @t198)) % 0.36/0.74 (define @t310 () (or @t116 @t115 @t277 @t309 @t109 @t302)) % 0.36/0.74 (define @t311 () (or @t109 @t302)) % 0.36/0.74 (define @t312 () (or @t160 @t201)) % 0.36/0.74 (define @t313 () (or @t157 @t200 @t156 @t160)) % 0.36/0.74 (define @t314 () (and @t86 @t199 @t155 @t37)) % 0.36/0.74 (define @t315 () (forall @t88 (not @t314))) % 0.36/0.74 (define @t316 () (not @t315)) % 0.36/0.74 (define @t317 () (or @t147 @t146)) % 0.36/0.74 (define @t318 () (or @t151 @t150)) % 0.36/0.74 (define @t319 () (or @t152 @t318 @t317)) % 0.36/0.74 (define @t320 () (forall @t154 @t319)) % 0.36/0.74 (define @t321 () (forall (@list @t148 @t144) @t319)) % 0.36/0.74 (define @t322 () (forall (@list @t144) @t317)) % 0.36/0.74 (define @t323 () (forall (@list @t148) @t318)) % 0.36/0.74 (define @t324 () (or @t152 @t323 @t322)) % 0.36/0.74 (define @t325 () (not (= @t72 @t74))) % 0.36/0.74 (define @t326 () (not @t77)) % 0.36/0.74 (define @t327 () (or @t326 @t325)) % 0.36/0.74 (define @t328 () (forall @t79 @t327)) % 0.36/0.74 (define @t329 () (not (= @t2 @t66))) % 0.36/0.74 (define @t330 () (forall @t70 (or (not @t68) @t329))) % 0.36/0.74 (define @t331 () (or @t152 @t330 @t328)) % 0.36/0.74 (define @t332 () (or @t330 @t328)) % 0.36/0.74 (define @t333 () (or @t330 @t327)) % 0.36/0.74 (define @t334 () (or @t326 @t325 @t330)) % 0.36/0.74 (define @t335 () (or @t325 @t330)) % 0.36/0.74 (define @t336 () (or @t109 @t301)) % 0.36/0.74 (define @t337 () (or @t300 @t299 @t109 @t298)) % 0.36/0.74 (define @t338 () (or @t299 @t109 @t298)) % 0.36/0.74 (define @t339 () (or @t130 @t296)) % 0.36/0.74 (define @t340 () (or @t134 @t238)) % 0.36/0.74 (define @t341 () (or @t135 @t340 @t339)) % 0.36/0.74 (define @t342 () (forall @t136 @t341)) % 0.36/0.74 (define @t343 () (forall (@list @t131 @t128) @t341)) % 0.36/0.74 (define @t344 () (forall (@list @t128) @t339)) % 0.36/0.74 (define @t345 () (forall (@list @t131) @t340)) % 0.36/0.74 (define @t346 () (or @t135 @t345 @t344)) % 0.36/0.74 (define @t347 () (= @t28 @t101)) % 0.36/0.74 (define @t348 () (not @t347)) % 0.36/0.74 (define @t349 () (not @t102)) % 0.36/0.74 (define @t350 () (or @t349 @t348)) % 0.36/0.74 (define @t351 () (forall @t104 @t350)) % 0.36/0.74 (define @t352 () (= @t12 @t95)) % 0.36/0.74 (define @t353 () (forall @t98 (or (not @t96) (not @t352)))) % 0.36/0.74 (define @t354 () (or @t135 @t353 @t351)) % 0.36/0.74 (define @t355 () (or @t353 @t351)) % 0.36/0.74 (define @t356 () (not @t355)) % 0.36/0.74 (define @t357 () (and @t106 @t356)) % 0.36/0.74 (define @t358 () (forall @t31 (not @t357))) % 0.36/0.74 (define @t359 () (not @t358)) % 0.36/0.74 (define @t360 () (or @t353 @t350)) % 0.36/0.74 (define @t361 () (or @t349 @t348 @t353)) % 0.36/0.74 (define @t362 () (not @t353)) % 0.36/0.74 (define @t363 () (not @t362)) % 0.36/0.74 (define @t364 () (or @t349 @t348 @t363)) % 0.36/0.74 (define @t365 () (and @t102 @t347 @t362)) % 0.36/0.74 (define @t366 () (forall @t104 (not @t365))) % 0.36/0.74 (define @t367 () (not @t366)) % 0.36/0.74 (define @t368 () (and @t96 @t352)) % 0.36/0.74 (define @t369 () (forall @t98 (not @t368))) % 0.36/0.74 (define @t370 () (not @t369)) % 0.36/0.74 (define @t371 () (forall @t165 @t162)) % 0.36/0.74 (define @t372 () (@quantifiers_skolemize @t371 1)) % 0.36/0.74 (define @t373 () (not (= @t129 @t372))) % 0.36/0.74 (define @t374 () (@quantifiers_skolemize @t371 0)) % 0.36/0.74 (define @t375 () (forall @t136 (or @t135 @t134 (not (= @t132 @t374)) @t130 @t373))) % 0.36/0.74 (define @t376 () (not @t375)) % 0.36/0.74 (define @t377 () (tptp.ssList @t372)) % 0.36/0.74 (define @t378 () (not @t377)) % 0.36/0.74 (define @t379 () (= tptp.nil @t374)) % 0.36/0.74 (define @t380 () (tptp.app @t374 @t372)) % 0.36/0.74 (define @t381 () (= tptp.nil @t380)) % 0.36/0.74 (define @t382 () (not @t381)) % 0.36/0.74 (define @t383 () (and @t382 @t379)) % 0.36/0.74 (define @t384 () (not @t379)) % 0.36/0.74 (define @t385 () (or @t384 @t381)) % 0.36/0.74 (define @t386 () (not (= @t149 @t374))) % 0.36/0.74 (define @t387 () (tptp.app @t374 @t72)) % 0.36/0.74 (define @t388 () (forall @t88 (or @t157 (not (= @t380 @t387)) (not (forall @t154 (or @t152 @t151 @t386 @t147 @t146)))))) % 0.36/0.74 (define @t389 () (not @t388)) % 0.36/0.74 (define @t390 () (tptp.equalelemsP @t374)) % 0.36/0.74 (define @t391 () (and @t390 @t389 @t385)) % 0.36/0.74 (define @t392 () (not (tptp.ssList @t380))) % 0.36/0.74 (define @t393 () (not @t390)) % 0.36/0.74 (define @t394 () (not (tptp.ssList @t374))) % 0.36/0.74 (define @t395 () (or @t394 @t393 @t392 @t391 @t383 @t378 @t376)) % 0.36/0.74 (define @t396 () (not @t395)) % 0.36/0.74 (define @t397 () (not @t371)) % 0.36/0.74 (define @t398 () (not (= @t374 @t132))) % 0.36/0.74 (define @t399 () (or @t135 @t134 @t398 @t130 @t373)) % 0.36/0.74 (define @t400 () (forall @t136 @t399)) % 0.36/0.74 (define @t401 () (not @t400)) % 0.36/0.74 (define @t402 () (= @t374 tptp.nil)) % 0.36/0.74 (define @t403 () (and @t382 @t402)) % 0.36/0.74 (define @t404 () (not @t402)) % 0.36/0.74 (define @t405 () (or @t404 @t381)) % 0.36/0.74 (define @t406 () (not (= @t374 @t149))) % 0.36/0.74 (define @t407 () (or @t152 @t151 @t406 @t147 @t146)) % 0.36/0.74 (define @t408 () (forall @t154 @t407)) % 0.36/0.74 (define @t409 () (not @t408)) % 0.36/0.74 (define @t410 () (not (= @t387 @t380))) % 0.36/0.74 (define @t411 () (or @t157 @t410 @t409)) % 0.36/0.74 (define @t412 () (forall @t88 @t411)) % 0.36/0.74 (define @t413 () (not @t412)) % 0.36/0.74 (define @t414 () (and @t390 @t413 @t405)) % 0.36/0.74 (define @t415 () (or @t394 @t393 @t392 @t414 @t403 @t378 @t401)) % 0.36/0.74 (define @t416 () (not @t415)) % 0.36/0.74 (define @t417 () (@list true)) % 0.36/0.74 (define @t418 () (@list @t395)) % 0.36/0.74 (define @t419 () (forall @t154 (or @t152 @t151 @t386 @t147 (not (= @t145 @t372))))) % 0.36/0.74 (define @t420 () (@list false)) % 0.36/0.74 (define @t421 () (not @t385)) % 0.36/0.74 (define @t422 () (not @t419)) % 0.36/0.74 (define @t423 () (or @t378 @t422)) % 0.36/0.74 (define @t424 () (not (= @t372 @t145))) % 0.36/0.74 (define @t425 () (or @t152 @t151 @t386 @t147 @t424)) % 0.36/0.74 (define @t426 () (forall @t154 @t425)) % 0.36/0.74 (define @t427 () (not @t426)) % 0.36/0.74 (define @t428 () (not (= @t380 @t380))) % 0.36/0.74 (define @t429 () (or @t378 @t428 @t427)) % 0.36/0.74 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.36/0.74 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.36/0.74 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 0.36/0.74 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.36/0.74 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.36/0.74 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.36/0.74 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.36/0.74 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not (and @t26 @t25))))))))))))))))) % 0.36/0.74 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t26 @t25)))))))))))))))) % 0.36/0.74 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t35 (tptp.lt @t12 @t1))))))))))))))))) % 0.36/0.74 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t26))))))))))))))) % 0.36/0.74 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.36/0.74 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not @t36)))))))))))))))) % 0.36/0.74 (assume @p14 (forall @t9 (=> @t17 (= @t37 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t28))) @t2) @t36))))))))))))) % 0.36/0.74 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.36/0.74 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.36/0.74 (assume @p17 (tptp.ssList tptp.nil)) % 0.36/0.74 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.36/0.74 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t39))))))))))) % 0.36/0.74 (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t40 @t2))))))))) % 0.36/0.74 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.36/0.74 (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42))))) % 0.36/0.74 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.36/0.74 (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44))))) % 0.36/0.74 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.36/0.74 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t45)))))) % 0.36/0.74 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2))))))))) % 0.36/0.74 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.36/0.74 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3)))))) % 0.36/0.74 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 @t26) (tptp.leq @t2 @t12))))))))) % 0.36/0.74 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.36/0.74 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47)))))) % 0.36/0.74 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50))))))) % 0.36/0.74 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t52)))))))) % 0.36/0.74 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50)))))) % 0.36/0.74 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t54))))))))) % 0.36/0.74 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 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% 0.36/0.75 (step @p607 :rule nary_cong :premises (@p606 @p548 @p605 @p604) :args ((or @t391 @t393 (not @t389) @t421))) % 0.36/0.75 (step @p608 :rule cnf_and_neg :args (@t391)) % 0.36/0.75 (step @p609 :rule eq_resolve :premises (@p608 @p607)) % 0.36/0.75 (step @p610 :rule reordering :premises (@p609) :args ((or @t393 @t388 @t391 @t421))) % 0.36/0.75 (step @p611 :rule chain_m_resolution :premises (@p610 @p603 @p597 @p595) :args (@t388 (@list false true false) (@list @t390 @t391 @t385))) % 0.36/0.75 (step @p612 :rule aci_norm :args ((= (or @t378 false @t422) @t423))) % 0.36/0.75 (step @p613 :rule eq-symm :args (@t372 @t145)) % 0.36/0.75 (step @p614 :rule cong :premises (@p613) :args (@t424)) % 0.36/0.75 (step @p615 :rule refl :args (@t386)) % 0.36/0.75 (step @p616 :rule nary_cong :premises (@p536 @p535 @p615 @p532 @p614) :args (@t425)) % 0.36/0.75 (step @p617 :rule cong :premises (@p616) :args (@t426)) % 0.36/0.75 (step @p618 :rule cong :premises (@p617) :args (@t427)) % 0.36/0.75 (step @p619 :rule eq-refl :args (@t380)) % 0.36/0.75 (step @p620 :rule cong :premises (@p619) :args (@t428)) % 0.36/0.75 (step @p621 :rule trans :premises (@p620 @p118)) % 0.36/0.75 (step @p622 :rule nary_cong :premises (@p524 @p621 @p618) :args (@t429)) % 0.36/0.75 (step @p623 :rule trans :premises (@p622 @p612)) % 0.36/0.75 (step @p624 :rule refl :args (@t388)) % 0.36/0.75 (step @p625 :rule cong :premises (@p624 @p623) :args ((=> @t388 @t429))) % 0.36/0.75 (assume-push @p638 @t388) % 0.36/0.75 (step @p627 :rule instantiate :premises (@p611) :args ((@list @t372))) % 0.36/0.75 (step-pop @p639 :rule scope :premises (@p627)) % 0.36/0.75 (step @p628 :rule process_scope :premises (@p639) :args (@t429)) % 0.36/0.75 (step @p630 :rule eq_resolve :premises (@p628 @p625)) % 0.36/0.75 (step @p631 :rule implies_elim :premises (@p630)) % 0.36/0.75 (step @p632 :rule chain_m_resolution :premises (@p631 @p611) :args (@t423 @t420 (@list @t388))) % 0.36/0.75 (step @p633 :rule cnf_or_pos :args (@t423)) % 0.36/0.75 (step @p634 :rule reordering :premises (@p633) :args ((or @t378 @t422 (not @t423)))) % 0.36/0.75 (step @p635 false :rule chain_m_resolution :premises (@p634 @p632 @p577 @p568) :args (false (@list false false false) (@list @t423 @t419 @t377))) % 0.36/0.75 ) % 0.36/0.75 % SZS output end Proof % 0.36/0.75 % cvc5 exiting %------------------------------------------------------------------------------