%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC406+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 : n008.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 08:59:12 AM UTC 2026 % Result : Theorem 0.38s 0.96s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC406+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n008.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 19:46:18 EDT 2026 % 0.18/0.34 % CPUTime : % 0.29/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.96 % SZS status Theorem % 0.38/0.96 % SZS output start Proof % 0.38/0.96 ( % 0.38/0.96 (declare-sort $$unsorted 0) % 0.38/0.96 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.38/0.96 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.38/0.96 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.96 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.96 (declare-const tptp.nil $$unsorted) % 0.38/0.96 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.38/0.96 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.38/0.96 (define @t1 () (@var "V" $$unsorted)) % 0.38/0.96 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.96 (define @t3 () (= @t2 @t1)) % 0.38/0.96 (define @t4 () (not @t3)) % 0.38/0.96 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.38/0.96 (define @t6 () (tptp.ssItem @t1)) % 0.38/0.96 (define @t7 () (@list @t1)) % 0.38/0.96 (define @t8 () (tptp.ssItem @t2)) % 0.38/0.96 (define @t9 () (@list @t2)) % 0.38/0.96 (define @t10 () (@var "X" $$unsorted)) % 0.38/0.96 (define @t11 () (tptp.cons @t1 @t10)) % 0.38/0.96 (define @t12 () (@var "W" $$unsorted)) % 0.38/0.96 (define @t13 () (tptp.ssList @t10)) % 0.38/0.96 (define @t14 () (@list @t10)) % 0.38/0.96 (define @t15 () (tptp.ssList @t12)) % 0.38/0.96 (define @t16 () (@list @t12)) % 0.38/0.96 (define @t17 () (tptp.ssList @t2)) % 0.38/0.96 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.38/0.96 (define @t19 () (tptp.app @t1 @t12)) % 0.38/0.96 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.38/0.96 (define @t21 () (tptp.ssList @t1)) % 0.38/0.96 (define @t22 () (tptp.app @t12 @t1)) % 0.38/0.96 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.38/0.96 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.38/0.96 (define @t25 () (tptp.leq @t12 @t1)) % 0.38/0.96 (define @t26 () (tptp.leq @t1 @t12)) % 0.38/0.96 (define @t27 () (@var "Z" $$unsorted)) % 0.38/0.96 (define @t28 () (@var "Y" $$unsorted)) % 0.38/0.96 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.38/0.96 (define @t30 () (tptp.ssList @t27)) % 0.38/0.96 (define @t31 () (@list @t27)) % 0.38/0.96 (define @t32 () (tptp.ssList @t28)) % 0.38/0.96 (define @t33 () (@list @t28)) % 0.38/0.96 (define @t34 () (tptp.ssItem @t12)) % 0.38/0.96 (define @t35 () (tptp.lt @t1 @t12)) % 0.38/0.96 (define @t36 () (= @t1 @t12)) % 0.38/0.96 (define @t37 () (tptp.cons @t1 @t2)) % 0.38/0.96 (define @t38 () (= @t1 @t2)) % 0.38/0.96 (define @t39 () (tptp.cons @t12 @t1)) % 0.38/0.96 (define @t40 () (= tptp.nil @t2)) % 0.38/0.96 (define @t41 () (tptp.hd @t2)) % 0.38/0.96 (define @t42 () (not @t40)) % 0.38/0.96 (define @t43 () (tptp.tl @t2)) % 0.38/0.96 (define @t44 () (tptp.app @t2 @t1)) % 0.38/0.96 (define @t45 () (tptp.app @t1 @t2)) % 0.38/0.96 (define @t46 () (tptp.leq @t1 @t2)) % 0.38/0.96 (define @t47 () (tptp.leq @t2 @t1)) % 0.38/0.96 (define @t48 () (tptp.geq @t2 @t1)) % 0.38/0.96 (define @t49 () (tptp.lt @t1 @t2)) % 0.38/0.96 (define @t50 () (tptp.lt @t2 @t1)) % 0.38/0.96 (define @t51 () (tptp.lt @t2 @t12)) % 0.38/0.96 (define @t52 () (tptp.gt @t2 @t1)) % 0.38/0.96 (define @t53 () (tptp.memberP @t12 @t2)) % 0.38/0.96 (define @t54 () (tptp.app @t12 @t2)) % 0.38/0.96 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.38/0.96 (define @t56 () (tptp.hd @t1)) % 0.38/0.96 (define @t57 () (= tptp.nil @t1)) % 0.38/0.96 (define @t58 () (not @t57)) % 0.38/0.96 (define @t59 () (tptp.cons @t2 @t1)) % 0.38/0.96 (define @t60 () (= @t12 @t2)) % 0.38/0.96 (define @t61 () (@var "X1" $$unsorted)) % 0.38/0.96 (define @t62 () (tptp.memberP @t1 @t61)) % 0.38/0.96 (define @t63 () (not (tptp.memberP @t2 @t61))) % 0.38/0.96 (define @t64 () (or @t63 @t62)) % 0.38/0.96 (define @t65 () (tptp.ssItem @t61)) % 0.38/0.96 (define @t66 () (@list @t61)) % 0.38/0.96 (define @t67 () (forall @t66 (=> @t65 @t64))) % 0.38/0.96 (define @t68 () (tptp.leq @t27 @t28)) % 0.38/0.96 (define @t69 () (tptp.memberP @t10 @t27)) % 0.38/0.96 (define @t70 () (= @t28 @t27)) % 0.38/0.96 (define @t71 () (not @t70)) % 0.38/0.96 (define @t72 () (tptp.ssItem @t27)) % 0.38/0.96 (define @t73 () (and @t72 @t71 @t69 @t68)) % 0.38/0.96 (define @t74 () (exists @t31 @t73)) % 0.38/0.96 (define @t75 () (tptp.memberP @t10 @t28)) % 0.38/0.96 (define @t76 () (not @t75)) % 0.38/0.96 (define @t77 () (or @t76 @t74)) % 0.38/0.96 (define @t78 () (tptp.memberP @t12 @t28)) % 0.38/0.96 (define @t79 () (and @t78 @t77)) % 0.38/0.96 (define @t80 () (not @t68)) % 0.38/0.96 (define @t81 () (not @t69)) % 0.38/0.96 (define @t82 () (or @t81 @t80 @t70)) % 0.38/0.96 (define @t83 () (forall @t31 (=> @t72 @t82))) % 0.38/0.96 (define @t84 () (not @t78)) % 0.38/0.96 (define @t85 () (and @t84 @t83 @t75)) % 0.38/0.96 (define @t86 () (or @t85 @t79)) % 0.38/0.96 (define @t87 () (tptp.ssItem @t28)) % 0.38/0.96 (define @t88 () (and @t87 @t86)) % 0.38/0.96 (define @t89 () (exists @t33 @t88)) % 0.38/0.96 (define @t90 () (not (= @t2 @t12))) % 0.38/0.96 (define @t91 () (not (= @t1 @t10))) % 0.38/0.96 (define @t92 () (or @t91 @t90 @t89 @t67)) % 0.38/0.96 (define @t93 () (=> @t13 @t92)) % 0.38/0.96 (define @t94 () (forall @t14 @t93)) % 0.38/0.96 (define @t95 () (=> @t15 @t94)) % 0.38/0.96 (define @t96 () (forall @t16 @t95)) % 0.38/0.96 (define @t97 () (=> @t21 @t96)) % 0.38/0.96 (define @t98 () (forall @t7 @t97)) % 0.38/0.96 (define @t99 () (=> @t17 @t98)) % 0.38/0.96 (define @t100 () (forall @t9 @t99)) % 0.38/0.96 (define @t101 () (not @t100)) % 0.38/0.96 (define @t102 () (@var "BOUND_VARIABLE_11070" $$unsorted)) % 0.38/0.96 (define @t103 () (@var "BOUND_VARIABLE_11068" $$unsorted)) % 0.38/0.96 (define @t104 () (tptp.memberP @t103 @t102)) % 0.38/0.96 (define @t105 () (not (tptp.memberP @t2 @t102))) % 0.38/0.96 (define @t106 () (not (tptp.ssItem @t102))) % 0.38/0.96 (define @t107 () (@var "BOUND_VARIABLE_10972" $$unsorted)) % 0.38/0.96 (define @t108 () (not (tptp.leq @t107 @t28))) % 0.38/0.96 (define @t109 () (= @t28 @t107)) % 0.38/0.96 (define @t110 () (not (tptp.ssItem @t107))) % 0.38/0.96 (define @t111 () (tptp.memberP @t103 @t28)) % 0.38/0.96 (define @t112 () (tptp.memberP @t2 @t28)) % 0.38/0.96 (define @t113 () (not @t112)) % 0.38/0.96 (define @t114 () (not @t72)) % 0.38/0.96 (define @t115 () (not @t87)) % 0.38/0.96 (define @t116 () (@list @t28 @t107)) % 0.38/0.96 (define @t117 () (not (forall @t116 (or @t115 (and (or @t112 (not (forall @t31 (or @t114 (not (tptp.memberP @t103 @t27)) @t80 @t70))) (not @t111)) (or @t113 (and @t111 (or @t110 @t109 (not (tptp.memberP @t103 @t107)) @t108)))))))) % 0.38/0.96 (define @t118 () (not (tptp.ssList @t103))) % 0.38/0.96 (define @t119 () (not @t17)) % 0.38/0.96 (define @t120 () (or @t119 @t118 @t117 @t106 @t105 @t104)) % 0.38/0.96 (define @t121 () (or @t118 @t117 @t106 @t105 @t104)) % 0.38/0.96 (define @t122 () (or @t119 @t121)) % 0.38/0.96 (define @t123 () (@list @t2 @t103 @t102)) % 0.38/0.96 (define @t124 () (forall @t123 @t122)) % 0.38/0.96 (define @t125 () (@list @t103 @t102)) % 0.38/0.96 (define @t126 () (forall @t125 @t122)) % 0.38/0.96 (define @t127 () (forall @t125 @t121)) % 0.38/0.96 (define @t128 () (@var "BOUND_VARIABLE_11051" $$unsorted)) % 0.38/0.96 (define @t129 () (or @t119 @t127)) % 0.38/0.96 (define @t130 () (tptp.memberP @t1 @t128)) % 0.38/0.96 (define @t131 () (not (tptp.memberP @t2 @t128))) % 0.38/0.96 (define @t132 () (not (tptp.ssItem @t128))) % 0.38/0.96 (define @t133 () (tptp.memberP @t1 @t28)) % 0.38/0.96 (define @t134 () (and @t133 (or @t110 @t109 (not (tptp.memberP @t1 @t107)) @t108))) % 0.38/0.96 (define @t135 () (not @t133)) % 0.38/0.96 (define @t136 () (not (forall @t31 (or @t114 (not (tptp.memberP @t1 @t27)) @t80 @t70)))) % 0.38/0.96 (define @t137 () (not (forall @t116 (or @t115 (and (or @t112 @t136 @t135) (or @t113 @t134)))))) % 0.38/0.96 (define @t138 () (not @t21)) % 0.38/0.96 (define @t139 () (or @t138 @t137 @t132 @t131 @t130)) % 0.38/0.96 (define @t140 () (@list @t1 @t128)) % 0.38/0.96 (define @t141 () (or @t119 (forall @t140 @t139))) % 0.38/0.96 (define @t142 () (or @t132 @t131 @t130)) % 0.38/0.96 (define @t143 () (or @t138 @t142 @t137)) % 0.38/0.96 (define @t144 () (forall @t140 @t143)) % 0.38/0.96 (define @t145 () (@list @t128)) % 0.38/0.96 (define @t146 () (forall @t145 @t143)) % 0.38/0.96 (define @t147 () (forall @t145 @t142)) % 0.38/0.96 (define @t148 () (or @t138 @t147 @t137)) % 0.38/0.96 (define @t149 () (not @t65)) % 0.38/0.96 (define @t150 () (or @t149 @t63 @t62)) % 0.38/0.96 (define @t151 () (forall @t66 @t150)) % 0.38/0.96 (define @t152 () (or @t138 @t151 @t137)) % 0.38/0.96 (define @t153 () (forall @t7 @t152)) % 0.38/0.96 (define @t154 () (or @t119 @t153)) % 0.38/0.96 (define @t155 () (or @t119 @t152)) % 0.38/0.96 (define @t156 () (or @t138 @t151 @t119 @t137)) % 0.38/0.96 (define @t157 () (or @t151 @t138 @t119 @t137)) % 0.38/0.96 (define @t158 () (or @t119 @t137)) % 0.38/0.96 (define @t159 () (not (= @t2 @t2))) % 0.38/0.96 (define @t160 () (or @t119 @t159 @t137)) % 0.38/0.96 (define @t161 () (not (forall @t116 (or @t115 (and (or @t78 @t136 @t135) (or @t84 @t134)))))) % 0.38/0.96 (define @t162 () (not @t15)) % 0.38/0.96 (define @t163 () (or @t90 @t162 @t90 @t161)) % 0.38/0.96 (define @t164 () (or @t162 @t90 @t161)) % 0.38/0.96 (define @t165 () (forall @t16 @t164)) % 0.38/0.96 (define @t166 () (or @t151 @t138 @t165)) % 0.38/0.96 (define @t167 () (or @t151 @t138 @t164)) % 0.38/0.96 (define @t168 () (or @t162 @t90 @t151 @t138 @t161)) % 0.38/0.96 (define @t169 () (or @t90 @t151 @t138 @t161)) % 0.38/0.96 (define @t170 () (or @t138 @t161)) % 0.38/0.96 (define @t171 () (not (= @t1 @t1))) % 0.38/0.96 (define @t172 () (or @t138 @t171 @t161)) % 0.38/0.96 (define @t173 () (or @t110 @t109 (not (tptp.memberP @t10 @t107)) @t108)) % 0.38/0.96 (define @t174 () (and @t75 @t173)) % 0.38/0.96 (define @t175 () (or @t84 @t174)) % 0.38/0.96 (define @t176 () (or @t114 @t81 @t80 @t70)) % 0.38/0.96 (define @t177 () (forall @t31 @t176)) % 0.38/0.96 (define @t178 () (not @t177)) % 0.38/0.96 (define @t179 () (or @t78 @t178 @t76)) % 0.38/0.96 (define @t180 () (and @t179 @t175)) % 0.38/0.96 (define @t181 () (or @t115 @t180)) % 0.38/0.96 (define @t182 () (forall @t116 @t181)) % 0.38/0.96 (define @t183 () (not @t182)) % 0.38/0.96 (define @t184 () (not @t13)) % 0.38/0.96 (define @t185 () (or @t91 @t184 @t91 @t183)) % 0.38/0.96 (define @t186 () (or @t184 @t91 @t183)) % 0.38/0.96 (define @t187 () (forall @t14 @t186)) % 0.38/0.96 (define @t188 () (or @t90 @t151 @t187)) % 0.38/0.96 (define @t189 () (or @t90 @t151 @t186)) % 0.38/0.96 (define @t190 () (or @t184 @t91 @t90 @t183 @t151)) % 0.38/0.96 (define @t191 () (or @t91 @t90 @t183 @t151)) % 0.38/0.96 (define @t192 () (@list @t107)) % 0.38/0.96 (define @t193 () (forall @t192 @t181)) % 0.38/0.96 (define @t194 () (forall @t192 @t173)) % 0.38/0.96 (define @t195 () (forall @t192 @t75)) % 0.38/0.96 (define @t196 () (and @t195 @t194)) % 0.38/0.96 (define @t197 () (forall @t192 @t174)) % 0.38/0.96 (define @t198 () (or @t84 @t197)) % 0.38/0.96 (define @t199 () (forall @t192 @t175)) % 0.38/0.96 (define @t200 () (forall @t192 @t179)) % 0.38/0.96 (define @t201 () (and @t200 @t199)) % 0.38/0.96 (define @t202 () (forall @t192 @t180)) % 0.38/0.96 (define @t203 () (or @t115 @t202)) % 0.38/0.96 (define @t204 () (forall @t31 (or @t114 @t70 @t81 @t80))) % 0.38/0.96 (define @t205 () (not @t204)) % 0.38/0.96 (define @t206 () (or @t76 @t205)) % 0.38/0.96 (define @t207 () (not @t84)) % 0.38/0.96 (define @t208 () (or @t207 @t178 @t76)) % 0.38/0.96 (define @t209 () (and @t78 @t206)) % 0.38/0.96 (define @t210 () (and @t84 @t177 @t75)) % 0.38/0.96 (define @t211 () (or @t210 @t209)) % 0.38/0.96 (define @t212 () (and @t87 @t211)) % 0.38/0.96 (define @t213 () (forall @t33 (not @t212))) % 0.38/0.96 (define @t214 () (not @t213)) % 0.38/0.96 (define @t215 () (not @t71)) % 0.38/0.96 (define @t216 () (or @t114 @t215 @t81 @t80)) % 0.38/0.96 (define @t217 () (forall @t31 (not @t73))) % 0.38/0.96 (define @t218 () (not @t217)) % 0.38/0.96 (define @t219 () (forall @t123 @t120)) % 0.38/0.96 (define @t220 () (@quantifiers_skolemize @t219 2)) % 0.38/0.96 (define @t221 () (tptp.ssItem @t220)) % 0.38/0.96 (define @t222 () (@quantifiers_skolemize @t219 1)) % 0.38/0.96 (define @t223 () (tptp.memberP @t222 @t220)) % 0.38/0.96 (define @t224 () (@quantifiers_skolemize @t219 0)) % 0.38/0.96 (define @t225 () (tptp.memberP @t224 @t220)) % 0.38/0.96 (define @t226 () (not @t225)) % 0.38/0.96 (define @t227 () (not @t221)) % 0.38/0.96 (define @t228 () (tptp.memberP @t222 @t28)) % 0.38/0.96 (define @t229 () (tptp.memberP @t224 @t28)) % 0.38/0.96 (define @t230 () (not (tptp.memberP @t222 @t27))) % 0.38/0.96 (define @t231 () (forall @t116 (or @t115 (and (or @t229 (not (forall @t31 (or @t114 @t230 @t80 @t70))) (not @t228)) (or (not @t229) (and @t228 (or @t110 @t109 (not (tptp.memberP @t222 @t107)) @t108))))))) % 0.38/0.96 (define @t232 () (not @t231)) % 0.38/0.96 (define @t233 () (or (not (tptp.ssList @t224)) (not (tptp.ssList @t222)) @t232 @t227 @t226 @t223)) % 0.38/0.96 (define @t234 () (@list true)) % 0.38/0.96 (define @t235 () (@list @t233)) % 0.38/0.96 (define @t236 () (not (tptp.leq @t220 @t220))) % 0.38/0.96 (define @t237 () (not @t223)) % 0.38/0.96 (define @t238 () (or @t227 (= @t220 @t220) @t237 @t236)) % 0.38/0.96 (define @t239 () (and @t223 @t238)) % 0.38/0.96 (define @t240 () (or @t226 @t239)) % 0.38/0.96 (define @t241 () (not (tptp.leq @t27 @t220))) % 0.38/0.96 (define @t242 () (or @t114 @t230 @t241 (= @t220 @t27))) % 0.38/0.96 (define @t243 () (forall @t31 @t242)) % 0.38/0.96 (define @t244 () (not @t243)) % 0.38/0.96 (define @t245 () (or @t225 @t244 @t237)) % 0.38/0.96 (define @t246 () (and @t245 @t240)) % 0.38/0.96 (define @t247 () (or @t227 @t246)) % 0.38/0.96 (define @t248 () (or @t226 @t223)) % 0.38/0.96 (define @t249 () (and (or @t225 (not (forall @t31 (or @t114 @t230 @t241 (= @t27 @t220)))) @t237) @t248)) % 0.38/0.96 (define @t250 () (or @t227 @t249)) % 0.38/0.96 (define @t251 () (not @t248)) % 0.38/0.96 (define @t252 () (not @t249)) % 0.38/0.96 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.38/0.96 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.38/0.96 (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))))))))))) % 0.38/0.96 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.38/0.96 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.38/0.96 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.38/0.96 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.38/0.96 (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))))))))))))))))) % 0.38/0.96 (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)))))))))))))))) % 0.38/0.96 (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))))))))))))))))) % 0.38/0.96 (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))))))))))))))) % 0.38/0.96 (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))))))))))))))) % 0.38/0.96 (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)))))))))))))))) % 0.38/0.96 (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))))))))))))) % 0.38/0.96 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.38/0.96 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.38/0.96 (assume @p17 (tptp.ssList tptp.nil)) % 0.38/0.96 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.38/0.96 (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))))))))))) % 0.38/0.96 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.38/0.96 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.38/0.96 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.38/0.96 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.38/0.96 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.38/0.96 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.38/0.96 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.38/0.96 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.38/0.96 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.38/0.96 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.38/0.96 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.38/0.96 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.38/0.96 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.38/0.96 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.38/0.96 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.38/0.96 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.38/0.96 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.38/0.96 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.38/0.96 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.38/0.96 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.38/0.96 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.38/0.96 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.38/0.96 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.38/0.96 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.38/0.96 (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)))))))))))) % 0.38/0.96 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.38/0.96 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.38/0.96 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.38/0.96 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.38/0.96 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.38/0.96 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.38/0.96 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.38/0.96 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.38/0.96 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.38/0.96 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.38/0.96 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.38/0.96 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.38/0.96 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.38/0.96 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.38/0.96 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.38/0.96 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.38/0.96 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.38/0.96 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.38/0.96 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.38/0.96 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.38/0.96 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.38/0.96 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.38/0.96 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.38/0.96 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.38/0.96 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.38/0.96 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.38/0.96 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.38/0.96 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.38/0.96 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.38/0.96 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.38/0.96 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.38/0.96 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.38/0.96 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.38/0.96 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.38/0.96 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.38/0.96 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.38/0.96 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.38/0.96 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.38/0.96 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t57 @t40))))))) % 0.38/0.96 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.38/0.96 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.38/0.96 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.38/0.96 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.38/0.96 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.38/0.96 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.38/0.96 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.38/0.96 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.38/0.96 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.38/0.96 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.38/0.96 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.38/0.96 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.38/0.96 (assume @p96 @t101) % 0.38/0.96 (assume @p97 true) % 0.38/0.96 (step @p98 :rule aci_norm :args ((= @t122 @t120))) % 0.38/0.96 (step @p99 :rule cong :premises (@p98) :args (@t124)) % 0.38/0.96 (step @p100 :rule quant-merge-prenex :args ((= (forall @t9 @t126) @t124))) % 0.38/0.96 (step @p101 :rule alpha_equiv :args (@t127 (@list @t103 @t102) (@list @t1 @t128))) % 0.38/0.96 (step @p102 :rule refl :args (@t119)) % 0.38/0.96 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t129)) % 0.38/0.96 (step @p104 :rule quant-miniscope-or :args ((= @t126 @t129))) % 0.38/0.96 (step @p105 :rule trans :premises (@p104 @p103)) % 0.38/0.96 (step @p106 :rule symm :premises (@p105)) % 0.38/0.96 (step @p107 :rule cong :premises (@p106) :args ((forall @t9 @t141))) % 0.38/0.96 (step @p108 :rule trans :premises (@p107 @p100)) % 0.38/0.96 (step @p109 :rule trans :premises (@p108 @p99)) % 0.38/0.96 (step @p110 :rule aci_norm :args ((= (or @t119 @t141) @t141))) % 0.38/0.96 (step @p111 :rule bool-impl-elim :args (@t17 @t141)) % 0.38/0.96 (step @p112 :rule trans :premises (@p111 @p110)) % 0.38/0.96 (step @p113 :rule cong :premises (@p112) :args ((forall @t9 (=> @t17 @t141)))) % 0.38/0.96 (step @p114 :rule trans :premises (@p113 @p109)) % 0.38/0.96 (step @p115 :rule aci_norm :args ((= @t143 @t139))) % 0.38/0.96 (step @p116 :rule cong :premises (@p115) :args (@t144)) % 0.38/0.96 (step @p117 :rule quant-merge-prenex :args ((= (forall @t7 @t146) @t144))) % 0.38/0.96 (step @p118 :rule refl :args (@t137)) % 0.38/0.96 (step @p119 :rule alpha_equiv 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:rule reordering :premises (@p378) :args ((or @t248 @t252))) % 0.38/0.97 (step @p380 :rule chain_m_resolution :premises (@p379 @p377) :args (@t252 @t234 (@list @t248))) % 0.38/0.97 (step @p381 :rule cnf_or_pos :args (@t250)) % 0.38/0.97 (step @p382 :rule reordering :premises (@p381) :args ((or @t227 @t249 (not @t250)))) % 0.38/0.97 (step @p383 false :rule chain_m_resolution :premises (@p382 @p380 @p366 @p327) :args (false (@list true false false) (@list @t249 @t250 @t221))) % 0.38/0.97 ) % 0.38/0.97 % SZS output end Proof % 0.38/0.97 % cvc5 exiting %------------------------------------------------------------------------------