%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC097+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:58:02 AM UTC 2026 % Result : Theorem 0.45s 0.69s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC097+1 : TPTP v9.2.1. Released v2.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n022.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 19:15:08 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.69 % SZS status Theorem % 0.45/0.69 % SZS output start Proof % 0.45/0.69 ( % 0.45/0.69 (declare-sort $$unsorted 0) % 0.45/0.69 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.45/0.69 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.45/0.69 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.69 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.69 (declare-const tptp.nil $$unsorted) % 0.45/0.69 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.45/0.69 (define @t1 () (@var "V" $$unsorted)) % 0.45/0.69 (define @t2 () (@var "U" $$unsorted)) % 0.45/0.69 (define @t3 () (= @t2 @t1)) % 0.45/0.69 (define @t4 () (not @t3)) % 0.45/0.69 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.45/0.69 (define @t6 () (tptp.ssItem @t1)) % 0.45/0.69 (define @t7 () (@list @t1)) % 0.45/0.69 (define @t8 () (tptp.ssItem @t2)) % 0.45/0.69 (define @t9 () (@list @t2)) % 0.45/0.69 (define @t10 () (@var "X" $$unsorted)) % 0.45/0.69 (define @t11 () (tptp.cons @t1 @t10)) % 0.45/0.69 (define @t12 () (@var "W" $$unsorted)) % 0.45/0.69 (define @t13 () (tptp.ssList @t10)) % 0.45/0.69 (define @t14 () (@list @t10)) % 0.45/0.69 (define @t15 () (tptp.ssList @t12)) % 0.45/0.69 (define @t16 () (@list @t12)) % 0.45/0.69 (define @t17 () (tptp.ssList @t2)) % 0.45/0.69 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.45/0.69 (define @t19 () (tptp.app @t1 @t12)) % 0.45/0.69 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.45/0.69 (define @t21 () (tptp.ssList @t1)) % 0.45/0.69 (define @t22 () (tptp.app @t12 @t1)) % 0.45/0.69 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.45/0.69 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.45/0.69 (define @t25 () (tptp.leq @t12 @t1)) % 0.45/0.69 (define @t26 () (tptp.leq @t1 @t12)) % 0.45/0.69 (define @t27 () (@var "Z" $$unsorted)) % 0.45/0.69 (define @t28 () (@var "Y" $$unsorted)) % 0.45/0.69 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.45/0.69 (define @t30 () (tptp.ssList @t27)) % 0.45/0.69 (define @t31 () (@list @t27)) % 0.45/0.69 (define @t32 () (tptp.ssList @t28)) % 0.45/0.69 (define @t33 () (@list @t28)) % 0.45/0.69 (define @t34 () (tptp.ssItem @t12)) % 0.45/0.69 (define @t35 () (tptp.lt @t1 @t12)) % 0.45/0.69 (define @t36 () (= @t1 @t12)) % 0.45/0.69 (define @t37 () (tptp.cons @t1 @t2)) % 0.45/0.69 (define @t38 () (= @t1 @t2)) % 0.45/0.69 (define @t39 () (tptp.cons @t12 @t1)) % 0.45/0.69 (define @t40 () (= tptp.nil @t2)) % 0.45/0.69 (define @t41 () (tptp.hd @t2)) % 0.45/0.69 (define @t42 () (not @t40)) % 0.45/0.69 (define @t43 () (tptp.tl @t2)) % 0.45/0.70 (define @t44 () (tptp.app @t2 @t1)) % 0.45/0.70 (define @t45 () (tptp.app @t1 @t2)) % 0.45/0.70 (define @t46 () (tptp.leq @t1 @t2)) % 0.45/0.70 (define @t47 () (tptp.leq @t2 @t1)) % 0.45/0.70 (define @t48 () (tptp.geq @t2 @t1)) % 0.45/0.70 (define @t49 () (tptp.lt @t1 @t2)) % 0.45/0.70 (define @t50 () (tptp.lt @t2 @t1)) % 0.45/0.70 (define @t51 () (tptp.lt @t2 @t12)) % 0.45/0.70 (define @t52 () (tptp.gt @t2 @t1)) % 0.45/0.70 (define @t53 () (tptp.memberP @t12 @t2)) % 0.45/0.70 (define @t54 () (tptp.app @t12 @t2)) % 0.45/0.70 (define @t55 () (tptp.cons @t2 tptp.nil)) % 0.45/0.70 (define @t56 () (tptp.hd @t1)) % 0.45/0.70 (define @t57 () (= tptp.nil @t1)) % 0.45/0.70 (define @t58 () (not @t57)) % 0.45/0.70 (define @t59 () (tptp.cons @t2 @t1)) % 0.45/0.70 (define @t60 () (= @t12 @t2)) % 0.45/0.70 (define @t61 () (tptp.neq @t1 tptp.nil)) % 0.45/0.70 (define @t62 () (not @t61)) % 0.45/0.70 (define @t63 () (or @t62 (tptp.neq @t10 tptp.nil))) % 0.45/0.70 (define @t64 () (tptp.app @t12 (tptp.cons @t27 tptp.nil))) % 0.45/0.70 (define @t65 () (not (= @t64 @t10))) % 0.45/0.70 (define @t66 () (tptp.ssItem @t27)) % 0.45/0.70 (define @t67 () (=> @t66 @t65)) % 0.45/0.70 (define @t68 () (forall @t31 @t67)) % 0.45/0.70 (define @t69 () (tptp.cons @t28 tptp.nil)) % 0.45/0.70 (define @t70 () (tptp.app @t2 @t69)) % 0.45/0.70 (define @t71 () (tptp.ssItem @t28)) % 0.45/0.70 (define @t72 () (and @t71 (= @t70 @t1))) % 0.45/0.70 (define @t73 () (exists @t33 @t72)) % 0.45/0.70 (define @t74 () (or @t62 @t73 @t68)) % 0.45/0.70 (define @t75 () (and @t74 @t63)) % 0.45/0.70 (define @t76 () (not (= @t2 @t12))) % 0.45/0.70 (define @t77 () (not (= @t1 @t10))) % 0.45/0.70 (define @t78 () (or @t77 @t76 @t75)) % 0.45/0.70 (define @t79 () (=> @t13 @t78)) % 0.45/0.70 (define @t80 () (forall @t14 @t79)) % 0.45/0.70 (define @t81 () (=> @t15 @t80)) % 0.45/0.70 (define @t82 () (forall @t16 @t81)) % 0.45/0.70 (define @t83 () (=> @t21 @t82)) % 0.45/0.70 (define @t84 () (forall @t7 @t83)) % 0.45/0.70 (define @t85 () (=> @t17 @t84)) % 0.45/0.70 (define @t86 () (forall @t9 @t85)) % 0.45/0.70 (define @t87 () (not @t86)) % 0.45/0.70 (define @t88 () (@var "BOUND_VARIABLE_11080" $$unsorted)) % 0.45/0.70 (define @t89 () (not (tptp.ssItem @t88))) % 0.45/0.70 (define @t90 () (tptp.app @t2 (tptp.cons @t88 tptp.nil))) % 0.45/0.70 (define @t91 () (not @t71)) % 0.45/0.70 (define @t92 () (not (forall @t33 (or @t91 (not (= @t70 @t90)))))) % 0.45/0.70 (define @t93 () (not (tptp.neq @t90 tptp.nil))) % 0.45/0.70 (define @t94 () (not (tptp.ssList @t90))) % 0.45/0.70 (define @t95 () (not @t17)) % 0.45/0.70 (define @t96 () (or @t95 @t94 @t93 @t92 @t89)) % 0.45/0.70 (define @t97 () (or @t94 @t93 @t92 @t89)) % 0.45/0.70 (define @t98 () (or @t95 @t97)) % 0.45/0.70 (define @t99 () (@list @t2 @t88)) % 0.45/0.70 (define @t100 () (forall @t99 @t98)) % 0.45/0.70 (define @t101 () (@list @t88)) % 0.45/0.70 (define @t102 () (forall @t101 @t98)) % 0.45/0.70 (define @t103 () (forall @t101 @t97)) % 0.45/0.70 (define @t104 () (@var "BOUND_VARIABLE_11040" $$unsorted)) % 0.45/0.70 (define @t105 () (@list @t104)) % 0.45/0.70 (define @t106 () (or @t95 @t103)) % 0.45/0.70 (define @t107 () (not (tptp.ssItem @t104))) % 0.45/0.70 (define @t108 () (tptp.app @t2 (tptp.cons @t104 tptp.nil))) % 0.45/0.70 (define @t109 () (not (forall @t33 (or @t91 (not (= @t70 @t108)))))) % 0.45/0.70 (define @t110 () (not (tptp.neq @t108 tptp.nil))) % 0.45/0.70 (define @t111 () (not (tptp.ssList @t108))) % 0.45/0.70 (define @t112 () (or @t111 @t110 @t109 @t107)) % 0.45/0.70 (define @t113 () (@list @t104)) % 0.45/0.70 (define @t114 () (or @t95 (forall @t113 @t112))) % 0.45/0.70 (define @t115 () (not (= @t108 @t108))) % 0.45/0.70 (define @t116 () (not (= @t108 @t70))) % 0.45/0.70 (define @t117 () (or @t91 @t116)) % 0.45/0.70 (define @t118 () (forall @t33 @t117)) % 0.45/0.70 (define @t119 () (not @t118)) % 0.45/0.70 (define @t120 () (or @t111 @t110 @t119 @t107 @t115)) % 0.45/0.70 (define @t121 () (not (= @t1 @t108))) % 0.45/0.70 (define @t122 () (= @t1 @t70)) % 0.45/0.70 (define @t123 () (not (forall @t33 (or @t91 (not @t122))))) % 0.45/0.70 (define @t124 () (not @t21)) % 0.45/0.70 (define @t125 () (or @t121 @t124 @t62 @t123 @t107 @t121)) % 0.45/0.70 (define @t126 () (or @t124 @t62 @t123 @t107 @t121)) % 0.45/0.70 (define @t127 () (forall @t7 @t126)) % 0.45/0.70 (define @t128 () (forall @t113 @t127)) % 0.45/0.70 (define @t129 () (forall (@list @t104 @t1) @t126)) % 0.45/0.70 (define @t130 () (@list @t1 @t104)) % 0.45/0.70 (define @t131 () (or @t107 @t121)) % 0.45/0.70 (define @t132 () (or @t124 @t62 @t123 @t131)) % 0.45/0.70 (define @t133 () (forall @t130 @t132)) % 0.45/0.70 (define @t134 () (forall @t113 @t132)) % 0.45/0.70 (define @t135 () (forall @t113 @t131)) % 0.45/0.70 (define @t136 () (@var "BOUND_VARIABLE_11004" $$unsorted)) % 0.45/0.70 (define @t137 () (@list @t136)) % 0.45/0.70 (define @t138 () (or @t124 @t62 @t123 @t135)) % 0.45/0.70 (define @t139 () (tptp.cons @t136 tptp.nil)) % 0.45/0.70 (define @t140 () (not (= @t1 (tptp.app @t2 @t139)))) % 0.45/0.70 (define @t141 () (not (tptp.ssItem @t136))) % 0.45/0.70 (define @t142 () (or @t141 @t140)) % 0.45/0.70 (define @t143 () (@list @t136)) % 0.45/0.70 (define @t144 () (forall @t143 @t142)) % 0.45/0.70 (define @t145 () (or @t124 @t62 @t123 @t144)) % 0.45/0.70 (define @t146 () (forall @t7 @t145)) % 0.45/0.70 (define @t147 () (or @t95 @t146)) % 0.45/0.70 (define @t148 () (or @t95 @t145)) % 0.45/0.70 (define @t149 () (or @t124 @t62 @t123 @t95 @t144)) % 0.45/0.70 (define @t150 () (or @t95 @t144)) % 0.45/0.70 (define @t151 () (or @t95 @t142)) % 0.45/0.70 (define @t152 () (or @t95 @t141 @t140)) % 0.45/0.70 (define @t153 () (not (= @t2 @t2))) % 0.45/0.70 (define @t154 () (or @t95 @t153 @t141 @t140)) % 0.45/0.70 (define @t155 () (not (= @t1 (tptp.app @t12 @t139)))) % 0.45/0.70 (define @t156 () (not @t15)) % 0.45/0.70 (define @t157 () (or @t76 @t156 @t76 @t141 @t155)) % 0.45/0.70 (define @t158 () (or @t156 @t76 @t141 @t155)) % 0.45/0.70 (define @t159 () (forall @t16 @t158)) % 0.45/0.70 (define @t160 () (forall @t143 @t159)) % 0.45/0.70 (define @t161 () (forall (@list @t136 @t12) @t158)) % 0.45/0.70 (define @t162 () (@list @t12 @t136)) % 0.45/0.70 (define @t163 () (or @t141 @t155)) % 0.45/0.70 (define @t164 () (or @t156 @t76 @t163)) % 0.45/0.70 (define @t165 () (forall @t162 @t164)) % 0.45/0.70 (define @t166 () (forall @t143 @t164)) % 0.45/0.70 (define @t167 () (forall @t143 @t163)) % 0.45/0.70 (define @t168 () (@var "BOUND_VARIABLE_10957" $$unsorted)) % 0.45/0.70 (define @t169 () (@list @t168)) % 0.45/0.70 (define @t170 () (or @t156 @t76 @t167)) % 0.45/0.70 (define @t171 () (tptp.app @t12 (tptp.cons @t168 tptp.nil))) % 0.45/0.70 (define @t172 () (not (= @t1 @t171))) % 0.45/0.70 (define @t173 () (not (tptp.ssItem @t168))) % 0.45/0.70 (define @t174 () (or @t173 @t172)) % 0.45/0.70 (define @t175 () (@list @t168)) % 0.45/0.70 (define @t176 () (forall @t175 @t174)) % 0.45/0.70 (define @t177 () (or @t156 @t76 @t176)) % 0.45/0.70 (define @t178 () (forall @t16 @t177)) % 0.45/0.70 (define @t179 () (or @t124 @t62 @t123 @t178)) % 0.45/0.70 (define @t180 () (or @t124 @t62 @t123 @t177)) % 0.45/0.70 (define @t181 () (or @t156 @t76 @t124 @t62 @t123 @t176)) % 0.45/0.70 (define @t182 () (or @t76 @t124 @t62 @t123 @t176)) % 0.45/0.70 (define @t183 () (or @t124 @t62 @t123 @t176)) % 0.45/0.70 (define @t184 () (or @t124 @t62 @t123 @t174)) % 0.45/0.70 (define @t185 () (or @t124 @t62 @t123 @t173 @t172)) % 0.45/0.70 (define @t186 () (or @t62 @t123 @t173 @t172)) % 0.45/0.70 (define @t187 () (and @t186 true)) % 0.45/0.70 (define @t188 () (or @t124 @t187)) % 0.45/0.70 (define @t189 () (and @t186 (or @t62 @t61))) % 0.45/0.70 (define @t190 () (or @t124 @t189)) % 0.45/0.70 (define @t191 () (not (= @t1 @t1))) % 0.45/0.70 (define @t192 () (or @t124 @t191 @t189)) % 0.45/0.70 (define @t193 () (not (= @t10 @t171))) % 0.45/0.70 (define @t194 () (or @t62 @t123 @t173 @t193)) % 0.45/0.70 (define @t195 () (and @t194 @t63)) % 0.45/0.70 (define @t196 () (not @t13)) % 0.45/0.70 (define @t197 () (or @t77 @t196 @t77 @t195)) % 0.45/0.70 (define @t198 () (or @t196 @t77 @t195)) % 0.45/0.70 (define @t199 () (forall @t14 @t198)) % 0.45/0.70 (define @t200 () (forall @t175 @t199)) % 0.45/0.70 (define @t201 () (forall (@list @t168 @t10) @t198)) % 0.45/0.70 (define @t202 () (@list @t10 @t168)) % 0.45/0.70 (define @t203 () (or @t173 @t193)) % 0.45/0.70 (define @t204 () (or @t62 @t123 @t203)) % 0.45/0.70 (define @t205 () (and @t204 @t63)) % 0.45/0.70 (define @t206 () (or @t196 @t77 @t205)) % 0.45/0.70 (define @t207 () (forall @t202 @t206)) % 0.45/0.70 (define @t208 () (forall @t175 @t206)) % 0.45/0.70 (define @t209 () (forall @t175 @t63)) % 0.45/0.70 (define @t210 () (forall @t175 @t203)) % 0.45/0.70 (define @t211 () (or @t62 @t123 @t210)) % 0.45/0.70 (define @t212 () (forall @t175 @t204)) % 0.45/0.70 (define @t213 () (and @t212 @t209)) % 0.45/0.70 (define @t214 () (forall @t175 @t205)) % 0.45/0.70 (define @t215 () (or @t196 @t77 @t214)) % 0.45/0.70 (define @t216 () (not (= @t10 @t64))) % 0.45/0.70 (define @t217 () (and (or @t62 @t123 (forall @t31 (or (not @t66) @t216))) @t63)) % 0.45/0.70 (define @t218 () (or @t196 @t77 @t217)) % 0.45/0.70 (define @t219 () (forall @t14 @t218)) % 0.45/0.70 (define @t220 () (or @t76 @t219)) % 0.45/0.70 (define @t221 () (or @t76 @t218)) % 0.45/0.70 (define @t222 () (or @t196 @t77 @t76 @t217)) % 0.45/0.70 (define @t223 () (or @t77 @t76 @t217)) % 0.45/0.70 (define @t224 () (and @t71 @t122)) % 0.45/0.70 (define @t225 () (forall @t33 (not @t224))) % 0.45/0.70 (define @t226 () (not @t225)) % 0.45/0.70 (define @t227 () (forall @t99 @t96)) % 0.45/0.70 (define @t228 () (@quantifiers_skolemize @t227 1)) % 0.45/0.70 (define @t229 () (tptp.ssItem @t228)) % 0.45/0.70 (define @t230 () (not @t229)) % 0.45/0.70 (define @t231 () (@quantifiers_skolemize @t227 0)) % 0.45/0.70 (define @t232 () (tptp.app @t231 @t69)) % 0.45/0.70 (define @t233 () (tptp.app @t231 (tptp.cons @t228 tptp.nil))) % 0.45/0.70 (define @t234 () (forall @t33 (or @t91 (not (= @t233 @t232))))) % 0.45/0.70 (define @t235 () (not @t234)) % 0.45/0.70 (define @t236 () (not (tptp.neq @t233 tptp.nil))) % 0.45/0.70 (define @t237 () (not (tptp.ssList @t233))) % 0.45/0.70 (define @t238 () (not (tptp.ssList @t231))) % 0.45/0.70 (define @t239 () (or @t238 @t237 @t236 @t235 @t230)) % 0.45/0.70 (define @t240 () (not @t239)) % 0.45/0.70 (define @t241 () (not @t227)) % 0.45/0.70 (define @t242 () (not (= @t232 @t233))) % 0.45/0.70 (define @t243 () (or @t91 @t242)) % 0.45/0.70 (define @t244 () (forall @t33 @t243)) % 0.45/0.70 (define @t245 () (not @t244)) % 0.45/0.70 (define @t246 () (or @t238 @t237 @t236 @t245 @t230)) % 0.45/0.70 (define @t247 () (not @t246)) % 0.45/0.70 (define @t248 () (@list true)) % 0.45/0.70 (define @t249 () (@list @t239)) % 0.45/0.70 (define @t250 () (not (= @t233 @t233))) % 0.45/0.70 (define @t251 () (or @t230 @t250)) % 0.45/0.70 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.45/0.70 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.45/0.70 (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))))))))))) % 0.45/0.70 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.45/0.70 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.45/0.70 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.45/0.70 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.45/0.70 (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))))))))))))))))) % 0.45/0.70 (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)))))))))))))))) % 0.45/0.70 (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))))))))))))))))) % 0.45/0.70 (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))))))))))))))) % 0.45/0.70 (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))))))))))))))) % 0.45/0.70 (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)))))))))))))))) % 0.45/0.70 (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))))))))))))) % 0.45/0.70 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.45/0.70 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.45/0.70 (assume @p17 (tptp.ssList tptp.nil)) % 0.45/0.70 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.45/0.70 (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))))))))))) % 0.45/0.70 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.45/0.70 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.45/0.70 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.45/0.70 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.45/0.70 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.45/0.70 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.45/0.70 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.45/0.70 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.45/0.70 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.45/0.70 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.45/0.70 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.45/0.70 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.45/0.70 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.45/0.70 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 0.45/0.70 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 @t35) @t51)))))))) % 0.45/0.70 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t49)))))) % 0.45/0.70 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t53))))))))) % 0.45/0.70 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t53))))))))) % 0.45/0.70 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.45/0.70 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.45/0.70 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.45/0.70 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.45/0.70 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.45/0.70 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.45/0.70 (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)))))))))))) % 0.45/0.70 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.45/0.70 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t40)))) % 0.45/0.70 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.45/0.70 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.45/0.70 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.45/0.70 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t54 @t1))))))))) % 0.45/0.70 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.45/0.70 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t40)))) % 0.45/0.70 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.45/0.70 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.45/0.70 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.45/0.70 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t54 @t10) @t1))))))))))) % 0.45/0.70 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.45/0.70 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t40)))) % 0.45/0.70 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t55)))) % 0.45/0.70 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.45/0.70 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t55)))) % 0.45/0.70 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.45/0.70 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t55)))) % 0.45/0.70 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.45/0.70 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t55)))) % 0.45/0.70 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.45/0.70 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t59) (or @t57 (and @t58 (tptp.totalorderedP @t1) (tptp.leq @t2 @t56))))))))) % 0.45/0.70 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t55)))) % 0.45/0.70 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.45/0.70 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t59) (or @t57 (and @t58 (tptp.strictorderedP @t1) (tptp.lt @t2 @t56))))))))) % 0.45/0.70 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t55)))) % 0.45/0.70 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.45/0.70 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t55)))) % 0.45/0.70 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.45/0.70 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.45/0.70 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.45/0.70 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t58 @t42 (= @t56 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.45/0.70 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.45/0.70 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t60)))))))) % 0.45/0.70 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t60)))))))) % 0.45/0.70 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.45/0.70 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.45/0.70 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t57 @t40))))))) % 0.45/0.70 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.45/0.70 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.45/0.70 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.45/0.70 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.45/0.70 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.45/0.70 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.45/0.70 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.45/0.70 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.45/0.70 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.45/0.70 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.45/0.70 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.45/0.70 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.45/0.70 (assume @p96 @t87) % 0.45/0.70 (assume @p97 true) % 0.45/0.70 (step @p98 :rule aci_norm :args ((= @t98 @t96))) % 0.45/0.70 (step @p99 :rule cong :premises (@p98) :args (@t100)) % 0.45/0.70 (step @p100 :rule quant-merge-prenex :args ((= (forall @t9 @t102) @t100))) % 0.45/0.70 (step @p101 :rule alpha_equiv :args (@t103 (@list @t88) @t105)) % 0.45/0.70 (step @p102 :rule refl :args (@t95)) % 0.45/0.70 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t106)) % 0.45/0.70 (step @p104 :rule quant-miniscope-or :args ((= @t102 @t106))) % 0.45/0.70 (step @p105 :rule trans :premises (@p104 @p103)) % 0.45/0.70 (step @p106 :rule symm :premises (@p105)) % 0.45/0.70 (step @p107 :rule cong :premises (@p106) :args ((forall @t9 @t114))) % 0.45/0.70 (step @p108 :rule trans :premises (@p107 @p100)) % 0.45/0.70 (step @p109 :rule trans :premises (@p108 @p99)) % 0.45/0.70 (step @p110 :rule aci_norm :args ((= (or @t95 @t114) @t114))) % 0.45/0.70 (step @p111 :rule bool-impl-elim :args (@t17 @t114)) % 0.45/0.70 (step @p112 :rule trans :premises (@p111 @p110)) % 0.45/0.70 (step @p113 :rule cong :premises (@p112) :args ((forall @t9 (=> @t17 @t114)))) % 0.45/0.70 (step @p114 :rule trans :premises (@p113 @p109)) % 0.45/0.70 (step @p115 :rule aci_norm :args ((= (or @t111 @t110 @t109 @t107 false) @t112))) % 0.45/0.70 (step @p116 :rule evaluate :args ((not true))) % 0.45/0.70 (step @p117 :rule eq-refl :args (@t108)) % 0.45/0.70 (step @p118 :rule cong :premises (@p117) :args (@t115)) % 0.45/0.70 (step @p119 :rule trans :premises (@p118 @p116)) % 0.45/0.70 (step @p120 :rule refl :args (@t107)) % 0.45/0.70 (step @p121 :rule eq-symm :args (@t108 @t70)) % 0.45/0.70 (step @p122 :rule cong :premises (@p121) :args (@t116)) % 0.45/0.70 (step @p123 :rule refl :args (@t91)) % 0.45/0.70 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t117)) % 0.45/0.70 (step @p125 :rule cong :premises 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0.36/0.70 (step @p389 :rule nary_cong :premises (@p351 @p388) :args (@t251)) % 0.36/0.70 (step @p390 :rule trans :premises (@p389 @p385)) % 0.36/0.70 (step @p391 :rule refl :args (@t234)) % 0.36/0.70 (step @p392 :rule cong :premises (@p391 @p390) :args ((=> @t234 @t251))) % 0.36/0.70 (assume-push @p403 @t234) % 0.36/0.70 (step @p394 :rule instantiate :premises (@p378) :args ((@list @t228))) % 0.36/0.70 (step-pop @p404 :rule scope :premises (@p394)) % 0.36/0.70 (step @p395 :rule process_scope :premises (@p404) :args (@t251)) % 0.36/0.70 (step @p397 :rule eq_resolve :premises (@p395 @p392)) % 0.36/0.70 (step @p398 :rule implies_elim :premises (@p397)) % 0.36/0.70 (step @p399 :rule reordering :premises (@p398) :args ((or @t230 @t235))) % 0.36/0.70 (step @p400 false :rule chain_m_resolution :premises (@p399 @p384 @p378) :args (false (@list false false) (@list @t229 @t234))) % 0.36/0.70 ) % 0.36/0.70 % SZS output end Proof % 0.36/0.70 % cvc5 exiting %------------------------------------------------------------------------------