%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC381+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 : n001.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 08:59:06 AM UTC 2026 % Result : Theorem 0.38s 0.74s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWC381+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n001.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 19:45:50 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.74 % SZS status Theorem % 0.38/0.74 % SZS output start Proof % 0.38/0.74 ( % 0.38/0.74 (declare-sort $$unsorted 0) % 0.38/0.74 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.nil $$unsorted) % 0.38/0.74 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (define @t1 () (@var "V" $$unsorted)) % 0.38/0.74 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.74 (define @t3 () (= @t2 @t1)) % 0.38/0.74 (define @t4 () (not @t3)) % 0.38/0.74 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.38/0.74 (define @t6 () (tptp.ssItem @t1)) % 0.38/0.74 (define @t7 () (@list @t1)) % 0.38/0.74 (define @t8 () (tptp.ssItem @t2)) % 0.38/0.74 (define @t9 () (@list @t2)) % 0.38/0.74 (define @t10 () (@var "X" $$unsorted)) % 0.38/0.74 (define @t11 () (tptp.cons @t1 @t10)) % 0.38/0.74 (define @t12 () (@var "W" $$unsorted)) % 0.38/0.74 (define @t13 () (tptp.ssList @t10)) % 0.38/0.74 (define @t14 () (@list @t10)) % 0.38/0.74 (define @t15 () (tptp.ssList @t12)) % 0.38/0.74 (define @t16 () (@list @t12)) % 0.38/0.74 (define @t17 () (tptp.ssList @t2)) % 0.38/0.74 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.38/0.74 (define @t19 () (tptp.app @t1 @t12)) % 0.38/0.74 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.38/0.74 (define @t21 () (tptp.ssList @t1)) % 0.38/0.74 (define @t22 () (tptp.app @t12 @t1)) % 0.38/0.74 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.38/0.74 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.38/0.74 (define @t25 () (tptp.leq @t12 @t1)) % 0.38/0.74 (define @t26 () (tptp.leq @t1 @t12)) % 0.38/0.74 (define @t27 () (@var "Z" $$unsorted)) % 0.38/0.74 (define @t28 () (@var "Y" $$unsorted)) % 0.38/0.74 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.38/0.74 (define @t30 () (tptp.ssList @t27)) % 0.38/0.74 (define @t31 () (@list @t27)) % 0.38/0.74 (define @t32 () (tptp.ssList @t28)) % 0.38/0.74 (define @t33 () (@list @t28)) % 0.38/0.74 (define @t34 () (tptp.ssItem @t12)) % 0.38/0.74 (define @t35 () (tptp.lt @t1 @t12)) % 0.38/0.74 (define @t36 () (= @t1 @t12)) % 0.38/0.74 (define @t37 () (tptp.cons @t1 @t2)) % 0.38/0.74 (define @t38 () (= @t1 @t2)) % 0.38/0.74 (define @t39 () (tptp.cons @t12 @t1)) % 0.38/0.74 (define @t40 () (= tptp.nil @t2)) % 0.38/0.74 (define @t41 () (tptp.hd @t2)) % 0.38/0.74 (define @t42 () (not @t40)) % 0.38/0.74 (define @t43 () (tptp.tl @t2)) % 0.38/0.74 (define @t44 () (tptp.app @t2 @t1)) % 0.38/0.74 (define @t45 () (tptp.app @t1 @t2)) % 0.38/0.74 (define @t46 () (tptp.leq @t1 @t2)) % 0.38/0.74 (define @t47 () (tptp.leq @t2 @t1)) % 0.38/0.74 (define @t48 () (tptp.geq @t2 @t1)) % 0.38/0.74 (define @t49 () (tptp.lt @t1 @t2)) % 0.38/0.74 (define @t50 () (tptp.lt @t2 @t1)) % 0.38/0.74 (define @t51 () (tptp.lt @t2 @t12)) % 0.38/0.74 (define @t52 () (tptp.gt @t2 @t1)) % 0.38/0.74 (define @t53 () (tptp.memberP @t12 @t2)) % 0.38/0.74 (define @t54 () (tptp.app @t12 @t2)) % 0.38/0.74 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.38/0.74 (define @t56 () (tptp.hd @t1)) % 0.38/0.74 (define @t57 () (= tptp.nil @t1)) % 0.38/0.74 (define @t58 () (not @t57)) % 0.38/0.74 (define @t59 () (tptp.cons @t2 @t1)) % 0.38/0.74 (define @t60 () (= @t12 @t2)) % 0.38/0.74 (define @t61 () (tptp.neq @t1 tptp.nil)) % 0.38/0.74 (define @t62 () (not @t61)) % 0.38/0.74 (define @t63 () (or @t62 (tptp.neq @t10 tptp.nil))) % 0.38/0.74 (define @t64 () (not (tptp.memberP @t10 @t27))) % 0.38/0.74 (define @t65 () (tptp.cons @t27 tptp.nil)) % 0.38/0.74 (define @t66 () (not (= @t65 @t12))) % 0.38/0.74 (define @t67 () (or @t66 @t64)) % 0.38/0.74 (define @t68 () (tptp.ssItem @t27)) % 0.38/0.74 (define @t69 () (=> @t68 @t67)) % 0.38/0.74 (define @t70 () (forall @t31 @t69)) % 0.38/0.74 (define @t71 () (tptp.memberP @t1 @t28)) % 0.38/0.74 (define @t72 () (tptp.cons @t28 tptp.nil)) % 0.38/0.74 (define @t73 () (tptp.ssItem @t28)) % 0.38/0.74 (define @t74 () (and @t73 (= @t72 @t2) @t71)) % 0.38/0.74 (define @t75 () (exists @t33 @t74)) % 0.38/0.74 (define @t76 () (or @t62 @t75 @t70)) % 0.38/0.74 (define @t77 () (and @t76 @t63)) % 0.38/0.74 (define @t78 () (not (= @t2 @t12))) % 0.38/0.74 (define @t79 () (not (= @t1 @t10))) % 0.38/0.74 (define @t80 () (or @t79 @t78 @t77)) % 0.38/0.74 (define @t81 () (=> @t13 @t80)) % 0.38/0.74 (define @t82 () (forall @t14 @t81)) % 0.38/0.74 (define @t83 () (=> @t15 @t82)) % 0.38/0.74 (define @t84 () (forall @t16 @t83)) % 0.38/0.74 (define @t85 () (=> @t21 @t84)) % 0.38/0.74 (define @t86 () (forall @t7 @t85)) % 0.38/0.74 (define @t87 () (=> @t17 @t86)) % 0.38/0.74 (define @t88 () (forall @t9 @t87)) % 0.38/0.74 (define @t89 () (not @t88)) % 0.38/0.74 (define @t90 () (@var "BOUND_VARIABLE_11066" $$unsorted)) % 0.38/0.74 (define @t91 () (@var "BOUND_VARIABLE_11064" $$unsorted)) % 0.38/0.74 (define @t92 () (not (tptp.memberP @t91 @t90))) % 0.38/0.74 (define @t93 () (not (tptp.ssItem @t90))) % 0.38/0.74 (define @t94 () (not (tptp.memberP @t91 @t28))) % 0.38/0.74 (define @t95 () (tptp.cons @t90 tptp.nil)) % 0.38/0.74 (define @t96 () (not @t73)) % 0.38/0.74 (define @t97 () (not (forall @t33 (or @t96 (not (= @t72 @t95)) @t94)))) % 0.38/0.74 (define @t98 () (not (tptp.neq @t91 tptp.nil))) % 0.38/0.74 (define @t99 () (not (tptp.ssList @t91))) % 0.38/0.74 (define @t100 () (not (tptp.ssList @t95))) % 0.38/0.74 (define @t101 () (or @t100 @t99 @t98 @t97 @t93 @t92)) % 0.38/0.74 (define @t102 () (not (= @t95 @t95))) % 0.38/0.74 (define @t103 () (not (= @t95 @t72))) % 0.38/0.74 (define @t104 () (or @t96 @t103 @t94)) % 0.38/0.74 (define @t105 () (forall @t33 @t104)) % 0.38/0.74 (define @t106 () (not @t105)) % 0.38/0.74 (define @t107 () (or @t100 @t99 @t98 @t106 @t93 @t102 @t92)) % 0.38/0.74 (define @t108 () (@list @t91 @t90)) % 0.38/0.74 (define @t109 () (not (= @t2 @t95))) % 0.38/0.74 (define @t110 () (= @t2 @t72)) % 0.38/0.74 (define @t111 () (not @t110)) % 0.38/0.74 (define @t112 () (not (forall @t33 (or @t96 @t111 @t94)))) % 0.38/0.74 (define @t113 () (not @t17)) % 0.38/0.74 (define @t114 () (or @t109 @t113 @t99 @t98 @t112 @t93 @t109 @t92)) % 0.38/0.74 (define @t115 () (or @t113 @t99 @t98 @t112 @t93 @t109 @t92)) % 0.38/0.74 (define @t116 () (forall @t9 @t115)) % 0.38/0.74 (define @t117 () (forall @t108 @t116)) % 0.38/0.74 (define @t118 () (forall (@list @t91 @t90 @t2) @t115)) % 0.38/0.74 (define @t119 () (@list @t2 @t91 @t90)) % 0.38/0.74 (define @t120 () (or @t99 @t98 @t112 @t93 @t109 @t92)) % 0.38/0.74 (define @t121 () (or @t113 @t120)) % 0.38/0.74 (define @t122 () (forall @t119 @t121)) % 0.38/0.74 (define @t123 () (forall @t108 @t121)) % 0.38/0.74 (define @t124 () (forall @t108 @t120)) % 0.38/0.74 (define @t125 () (@var "BOUND_VARIABLE_11045" $$unsorted)) % 0.38/0.74 (define @t126 () (or @t113 @t124)) % 0.38/0.74 (define @t127 () (not (tptp.memberP @t1 @t125))) % 0.38/0.74 (define @t128 () (not (= @t2 (tptp.cons @t125 tptp.nil)))) % 0.38/0.74 (define @t129 () (not (tptp.ssItem @t125))) % 0.38/0.74 (define @t130 () (not @t71)) % 0.38/0.74 (define @t131 () (or @t96 @t111 @t130)) % 0.38/0.74 (define @t132 () (not (forall @t33 @t131))) % 0.38/0.74 (define @t133 () (not @t21)) % 0.38/0.74 (define @t134 () (or @t133 @t62 @t132 @t129 @t128 @t127)) % 0.38/0.74 (define @t135 () (@list @t1 @t125)) % 0.38/0.74 (define @t136 () (or @t113 (forall @t135 @t134))) % 0.38/0.74 (define @t137 () (or @t129 @t128 @t127)) % 0.38/0.74 (define @t138 () (or @t133 @t62 @t132 @t137)) % 0.38/0.74 (define @t139 () (forall @t135 @t138)) % 0.38/0.74 (define @t140 () (@list @t125)) % 0.38/0.74 (define @t141 () (forall @t140 @t138)) % 0.38/0.74 (define @t142 () (forall @t140 @t137)) % 0.38/0.74 (define @t143 () (@var "BOUND_VARIABLE_11009" $$unsorted)) % 0.38/0.74 (define @t144 () (@list @t143)) % 0.38/0.74 (define @t145 () (or @t133 @t62 @t132 @t142)) % 0.38/0.74 (define @t146 () (not (tptp.memberP @t1 @t143))) % 0.38/0.74 (define @t147 () (tptp.cons @t143 tptp.nil)) % 0.38/0.74 (define @t148 () (not (= @t2 @t147))) % 0.38/0.74 (define @t149 () (not (tptp.ssItem @t143))) % 0.38/0.74 (define @t150 () (or @t149 @t148 @t146)) % 0.38/0.74 (define @t151 () (@list @t143)) % 0.38/0.74 (define @t152 () (forall @t151 @t150)) % 0.38/0.74 (define @t153 () (or @t133 @t62 @t132 @t152)) % 0.38/0.74 (define @t154 () (forall @t7 @t153)) % 0.38/0.74 (define @t155 () (or @t113 @t154)) % 0.38/0.74 (define @t156 () (or @t113 @t153)) % 0.38/0.74 (define @t157 () (or @t133 @t62 @t132 @t113 @t152)) % 0.38/0.74 (define @t158 () (or @t113 @t152)) % 0.38/0.74 (define @t159 () (or @t113 @t150)) % 0.38/0.74 (define @t160 () (or @t113 @t149 @t148 @t146)) % 0.38/0.74 (define @t161 () (not (= @t2 @t2))) % 0.38/0.74 (define @t162 () (or @t113 @t161 @t149 @t148 @t146)) % 0.38/0.74 (define @t163 () (not (= @t12 @t147))) % 0.38/0.74 (define @t164 () (not @t15)) % 0.38/0.74 (define @t165 () (or @t78 @t164 @t78 @t149 @t163 @t146)) % 0.38/0.74 (define @t166 () (or @t164 @t78 @t149 @t163 @t146)) % 0.38/0.74 (define @t167 () (forall @t16 @t166)) % 0.38/0.74 (define @t168 () (forall @t151 @t167)) % 0.38/0.74 (define @t169 () (forall (@list @t143 @t12) @t166)) % 0.38/0.74 (define @t170 () (@list @t12 @t143)) % 0.38/0.74 (define @t171 () (or @t149 @t163 @t146)) % 0.38/0.74 (define @t172 () (or @t164 @t78 @t171)) % 0.38/0.74 (define @t173 () (forall @t170 @t172)) % 0.38/0.74 (define @t174 () (forall @t151 @t172)) % 0.38/0.74 (define @t175 () (forall @t151 @t171)) % 0.38/0.74 (define @t176 () (@var "BOUND_VARIABLE_10961" $$unsorted)) % 0.38/0.74 (define @t177 () (@list @t176)) % 0.38/0.74 (define @t178 () (or @t164 @t78 @t175)) % 0.38/0.74 (define @t179 () (not (tptp.memberP @t1 @t176))) % 0.38/0.74 (define @t180 () (not (= @t12 (tptp.cons @t176 tptp.nil)))) % 0.38/0.74 (define @t181 () (not (tptp.ssItem @t176))) % 0.38/0.74 (define @t182 () (or @t181 @t180 @t179)) % 0.38/0.74 (define @t183 () (@list @t176)) % 0.38/0.74 (define @t184 () (forall @t183 @t182)) % 0.38/0.74 (define @t185 () (or @t164 @t78 @t184)) % 0.38/0.74 (define @t186 () (forall @t16 @t185)) % 0.38/0.74 (define @t187 () (or @t133 @t62 @t132 @t186)) % 0.38/0.74 (define @t188 () (or @t133 @t62 @t132 @t185)) % 0.38/0.74 (define @t189 () (or @t164 @t78 @t133 @t62 @t132 @t184)) % 0.38/0.74 (define @t190 () (or @t78 @t133 @t62 @t132 @t184)) % 0.38/0.74 (define @t191 () (or @t133 @t62 @t132 @t184)) % 0.38/0.74 (define @t192 () (or @t133 @t62 @t132 @t182)) % 0.38/0.74 (define @t193 () (or @t133 @t62 @t132 @t181 @t180 @t179)) % 0.38/0.74 (define @t194 () (or @t62 @t132 @t181 @t180 @t179)) % 0.38/0.74 (define @t195 () (and @t194 true)) % 0.38/0.74 (define @t196 () (or @t133 @t195)) % 0.38/0.74 (define @t197 () (and @t194 (or @t62 @t61))) % 0.38/0.74 (define @t198 () (or @t133 @t197)) % 0.38/0.74 (define @t199 () (not (= @t1 @t1))) % 0.38/0.74 (define @t200 () (or @t133 @t199 @t197)) % 0.38/0.74 (define @t201 () (not (tptp.memberP @t10 @t176))) % 0.38/0.74 (define @t202 () (or @t62 @t132 @t181 @t180 @t201)) % 0.38/0.74 (define @t203 () (and @t202 @t63)) % 0.38/0.74 (define @t204 () (not @t13)) % 0.38/0.74 (define @t205 () (or @t79 @t204 @t79 @t203)) % 0.38/0.74 (define @t206 () (or @t204 @t79 @t203)) % 0.38/0.74 (define @t207 () (forall @t14 @t206)) % 0.38/0.74 (define @t208 () (forall @t183 @t207)) % 0.38/0.74 (define @t209 () (forall (@list @t176 @t10) @t206)) % 0.38/0.74 (define @t210 () (@list @t10 @t176)) % 0.38/0.74 (define @t211 () (or @t181 @t180 @t201)) % 0.38/0.74 (define @t212 () (or @t62 @t132 @t211)) % 0.38/0.74 (define @t213 () (and @t212 @t63)) % 0.38/0.74 (define @t214 () (or @t204 @t79 @t213)) % 0.38/0.74 (define @t215 () (forall @t210 @t214)) % 0.38/0.74 (define @t216 () (forall @t183 @t214)) % 0.38/0.74 (define @t217 () (forall @t183 @t63)) % 0.38/0.74 (define @t218 () (forall @t183 @t211)) % 0.38/0.74 (define @t219 () (or @t62 @t132 @t218)) % 0.38/0.74 (define @t220 () (forall @t183 @t212)) % 0.38/0.74 (define @t221 () (and @t220 @t217)) % 0.38/0.74 (define @t222 () (forall @t183 @t213)) % 0.38/0.74 (define @t223 () (or @t204 @t79 @t222)) % 0.38/0.74 (define @t224 () (not (= @t12 @t65))) % 0.38/0.74 (define @t225 () (not @t68)) % 0.38/0.74 (define @t226 () (or @t225 @t224 @t64)) % 0.38/0.74 (define @t227 () (and (or @t62 @t132 (forall @t31 @t226)) @t63)) % 0.38/0.74 (define @t228 () (or @t204 @t79 @t227)) % 0.38/0.74 (define @t229 () (forall @t14 @t228)) % 0.38/0.74 (define @t230 () (or @t78 @t229)) % 0.38/0.74 (define @t231 () (or @t78 @t228)) % 0.38/0.74 (define @t232 () (or @t204 @t79 @t78 @t227)) % 0.38/0.74 (define @t233 () (or @t79 @t78 @t227)) % 0.38/0.74 (define @t234 () (or @t224 @t64)) % 0.38/0.74 (define @t235 () (and @t73 @t110 @t71)) % 0.38/0.74 (define @t236 () (forall @t33 (not @t235))) % 0.38/0.74 (define @t237 () (not @t236)) % 0.38/0.74 (define @t238 () (forall @t108 @t101)) % 0.38/0.74 (define @t239 () (@quantifiers_skolemize @t238 0)) % 0.38/0.74 (define @t240 () (@quantifiers_skolemize @t238 1)) % 0.38/0.74 (define @t241 () (tptp.cons @t240 tptp.nil)) % 0.38/0.74 (define @t242 () (forall @t33 (or @t96 (not (= @t72 @t241)) (not (tptp.memberP @t239 @t28))))) % 0.38/0.74 (define @t243 () (tptp.memberP @t239 @t240)) % 0.38/0.74 (define @t244 () (not @t243)) % 0.38/0.74 (define @t245 () (tptp.ssItem @t240)) % 0.38/0.74 (define @t246 () (not @t245)) % 0.38/0.74 (define @t247 () (not @t242)) % 0.38/0.74 (define @t248 () (or (not (tptp.ssList @t241)) (not (tptp.ssList @t239)) (not (tptp.neq @t239 tptp.nil)) @t247 @t246 @t244)) % 0.38/0.74 (define @t249 () (@list true)) % 0.38/0.74 (define @t250 () (@list @t248)) % 0.38/0.74 (define @t251 () (or @t246 @t244)) % 0.38/0.74 (define @t252 () (not @t251)) % 0.38/0.74 (define @t253 () (not (= @t241 @t241))) % 0.38/0.74 (define @t254 () (or @t246 @t253 @t244)) % 0.38/0.74 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.38/0.74 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.38/0.74 (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))))))))))) % 0.38/0.74 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.38/0.74 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.38/0.74 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.38/0.74 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.38/0.74 (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))))))))))))))))) % 0.38/0.74 (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)))))))))))))))) % 0.38/0.74 (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))))))))))))))))) % 0.38/0.74 (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))))))))))))))) % 0.38/0.74 (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))))))))))))))) % 0.38/0.74 (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)))))))))))))))) % 0.38/0.74 (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))))))))))))) % 0.38/0.74 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.38/0.74 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.38/0.74 (assume @p17 (tptp.ssList tptp.nil)) % 0.38/0.74 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.38/0.74 (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) @t38))))))))))) % 0.38/0.74 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.38/0.74 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.38/0.74 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.38/0.74 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.38/0.74 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.38/0.74 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.38/0.74 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.38/0.74 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.38/0.74 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.38/0.74 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.38/0.74 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.38/0.74 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.38/0.74 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.38/0.74 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.38/0.74 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.38/0.74 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.38/0.74 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.38/0.74 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.38/0.74 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.38/0.74 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.38/0.74 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.38/0.74 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.38/0.74 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.38/0.74 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.38/0.74 (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)))))))))))) % 0.38/0.74 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.38/0.74 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.38/0.74 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.38/0.74 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.38/0.74 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.38/0.74 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.38/0.74 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.38/0.74 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.38/0.74 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.38/0.74 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.38/0.74 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.38/0.74 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.38/0.74 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.38/0.74 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.38/0.74 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.38/0.74 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.38/0.74 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.38/0.74 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.38/0.74 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.38/0.74 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.38/0.74 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.38/0.74 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.38/0.74 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.38/0.74 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.38/0.74 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.38/0.74 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.38/0.74 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.38/0.74 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.38/0.74 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.38/0.74 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.38/0.74 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.38/0.74 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.38/0.74 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.38/0.74 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.38/0.74 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.38/0.74 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.38/0.74 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.38/0.74 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.38/0.74 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t57 @t40))))))) % 0.38/0.74 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.38/0.74 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.38/0.74 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.38/0.74 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.38/0.74 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.38/0.74 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.38/0.74 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.38/0.74 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.38/0.74 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.38/0.74 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.38/0.74 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.38/0.74 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.38/0.74 (assume @p96 @t89) % 0.38/0.74 (assume @p97 true) % 0.38/0.74 (step @p98 :rule aci_norm :args ((= (or @t100 @t99 @t98 @t97 @t93 false @t92) @t101))) % 0.38/0.74 (step @p99 :rule refl :args (@t92)) % 0.38/0.74 (step @p100 :rule evaluate :args ((not true))) % 0.38/0.74 (step @p101 :rule eq-refl :args (@t95)) % 0.38/0.74 (step @p102 :rule cong :premises (@p101) :args (@t102)) % 0.38/0.74 (step @p103 :rule trans :premises (@p102 @p100)) % 0.38/0.74 (step @p104 :rule refl :args (@t93)) % 0.38/0.74 (step @p105 :rule refl :args (@t94)) % 0.38/0.74 (step @p106 :rule eq-symm :args (@t95 @t72)) % 0.38/0.74 (step @p107 :rule cong :premises (@p106) :args (@t103)) % 0.38/0.74 (step @p108 :rule refl :args (@t96)) % 0.38/0.74 (step @p109 :rule nary_cong :premises (@p108 @p107 @p105) :args (@t104)) % 0.38/0.74 (step @p110 :rule cong :premises (@p109) :args (@t105)) % 0.38/0.74 (step @p111 :rule cong :premises (@p110) :args (@t106)) % 0.38/0.74 (step @p112 :rule refl :args (@t98)) % 0.38/0.74 (step @p113 :rule refl :args (@t99)) % 0.38/0.74 (step @p114 :rule refl :args (@t100)) % 0.38/0.74 (step @p115 :rule nary_cong :premises (@p114 @p113 @p112 @p111 @p104 @p103 @p99) :args (@t107)) % 0.38/0.74 (step @p116 :rule trans :premises (@p115 @p98)) % 0.38/0.74 (step @p117 :rule cong :premises (@p116) :args ((forall @t108 @t107))) % 0.38/0.74 (step @p118 :rule quant-var-elim-eq :args ((= (forall @t9 @t114) @t107))) % 0.38/0.74 (step @p119 :rule aci_norm :args ((= @t115 @t114))) % 0.38/0.74 (step @p120 :rule cong :premises (@p119) :args (@t116)) % 0.38/0.74 (step @p121 :rule trans :premises (@p120 @p118)) % 0.38/0.74 (step @p122 :rule cong :premises (@p121) :args (@t117)) % 0.38/0.74 (step @p123 :rule quant-merge-prenex :args ((= @t117 @t118))) % 0.38/0.74 (step @p124 :rule symm :premises (@p123)) % 0.38/0.74 (step @p125 :rule quant_var_reordering :args ((= (forall @t119 @t115) @t118))) % 0.38/0.74 (step @p126 :rule trans :premises (@p125 @p124 @p122)) % 0.38/0.74 (step @p127 :rule trans :premises (@p126 @p117)) % 0.38/0.74 (step @p128 :rule aci_norm :args ((= @t121 @t115))) % 0.38/0.74 (step @p129 :rule cong :premises (@p128) :args (@t122)) % 0.38/0.74 (step @p130 :rule trans :premises (@p129 @p127)) % 0.38/0.74 (step @p131 :rule quant-merge-prenex :args ((= (forall @t9 @t123) @t122))) % 0.38/0.74 (step @p132 :rule alpha_equiv :args (@t124 (@list @t91 @t90) (@list @t1 @t125))) % 0.38/0.74 (step @p133 :rule refl :args (@t113)) % 0.38/0.74 (step @p134 :rule nary_cong :premises (@p133 @p132) :args (@t126)) % 0.38/0.74 (step @p135 :rule quant-miniscope-or :args ((= 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:premises (@p382 @p364) :args (@t245 @t249 @t250)) % 0.38/0.74 (step @p384 :rule cnf_or_pos :args (@t251)) % 0.38/0.74 (step @p385 :rule reordering :premises (@p384) :args ((or @t246 @t244 @t252))) % 0.38/0.74 (step @p386 :rule chain_m_resolution :premises (@p385 @p383 @p377) :args (@t252 (@list false false) (@list @t245 @t243))) % 0.38/0.74 (step @p387 :rule aci_norm :args ((= (or @t246 false @t244) @t251))) % 0.38/0.74 (step @p388 :rule refl :args (@t244)) % 0.38/0.74 (step @p389 :rule eq-refl :args (@t241)) % 0.38/0.74 (step @p390 :rule cong :premises (@p389) :args (@t253)) % 0.38/0.74 (step @p391 :rule trans :premises (@p390 @p100)) % 0.38/0.74 (step @p392 :rule refl :args (@t246)) % 0.38/0.74 (step @p393 :rule nary_cong :premises (@p392 @p391 @p388) :args (@t254)) % 0.38/0.74 (step @p394 :rule trans :premises (@p393 @p387)) % 0.38/0.74 (step @p395 :rule refl :args (@t242)) % 0.38/0.74 (step @p396 :rule cong :premises (@p395 @p394) :args ((=> @t242 @t254))) % 0.38/0.74 (assume-push @p404 @t242) % 0.38/0.74 (step @p398 :rule instantiate :premises (@p371) :args ((@list @t240))) % 0.38/0.74 (step-pop @p405 :rule scope :premises (@p398)) % 0.38/0.74 (step @p399 :rule process_scope :premises (@p405) :args (@t254)) % 0.38/0.74 (step @p401 :rule eq_resolve :premises (@p399 @p396)) % 0.38/0.74 (step @p402 :rule implies_elim :premises (@p401)) % 0.38/0.74 (step @p403 false :rule chain_m_resolution :premises (@p402 @p386 @p371) :args (false (@list true false) (@list @t251 @t242))) % 0.38/0.74 ) % 0.38/0.74 % SZS output end Proof % 0.38/0.74 % cvc5 exiting %------------------------------------------------------------------------------