%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM452+6 : TPTP v9.2.1. Released v4.0.0. % 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 08:39:27 AM UTC 2026 % Result : Theorem 0.35s 0.79s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM452+6 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n001.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:21:51 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.79 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.79 % SZS status Theorem % 0.35/0.79 % SZS output start Proof % 0.35/0.79 ( % 0.35/0.79 (declare-sort $$unsorted 0) % 0.35/0.79 (declare-const tptp.cS2076 $$unsorted) % 0.35/0.79 (declare-const tptp.isClosed0 (-> $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.isOpen0 (-> $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.stldt0 (-> $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.sdtslmnbsdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.cS1395 $$unsorted) % 0.35/0.79 (declare-const tptp.xp $$unsorted) % 0.35/0.79 (declare-const tptp.sdtbsmnsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.xS $$unsorted) % 0.35/0.79 (declare-const tptp.szAzrzSzezqlpdtcmdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.sbsmnsldt0 (-> $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.cS2043 $$unsorted) % 0.35/0.79 (declare-const tptp.sz10 $$unsorted) % 0.35/0.79 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.sz00 $$unsorted) % 0.35/0.79 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.79 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.79 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.35/0.79 (define @t1 () (@var "W0" $$unsorted)) % 0.35/0.79 (define @t2 () (tptp.aInteger0 @t1)) % 0.35/0.79 (define @t3 () (@list @t1)) % 0.35/0.79 (define @t4 () (tptp.aInteger0 tptp.sz10)) % 0.35/0.79 (define @t5 () (tptp.smndt0 @t1)) % 0.35/0.79 (define @t6 () (tptp.aInteger0 @t5)) % 0.35/0.79 (define @t7 () (forall @t3 (=> @t2 @t6))) % 0.35/0.79 (define @t8 () (@var "W1" $$unsorted)) % 0.35/0.79 (define @t9 () (tptp.sdtpldt0 @t1 @t8)) % 0.35/0.79 (define @t10 () (tptp.aInteger0 @t9)) % 0.35/0.79 (define @t11 () (tptp.aInteger0 @t8)) % 0.35/0.79 (define @t12 () (and @t2 @t11)) % 0.35/0.79 (define @t13 () (@list @t1 @t8)) % 0.35/0.79 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.35/0.79 (define @t15 () (tptp.sdtasdt0 @t1 @t8)) % 0.35/0.79 (define @t16 () (@var "W2" $$unsorted)) % 0.35/0.79 (define @t17 () (tptp.sdtpldt0 @t8 @t16)) % 0.35/0.79 (define @t18 () (= (tptp.sdtpldt0 @t1 @t17) (tptp.sdtpldt0 @t9 @t16))) % 0.35/0.79 (define @t19 () (tptp.aInteger0 @t16)) % 0.35/0.79 (define @t20 () (and @t2 @t11 @t19)) % 0.35/0.79 (define @t21 () (@list @t1 @t8 @t16)) % 0.35/0.79 (define @t22 () (forall @t21 (=> @t20 @t18))) % 0.35/0.79 (define @t23 () (= @t9 (tptp.sdtpldt0 @t8 @t1))) % 0.35/0.79 (define @t24 () (forall @t13 (=> @t12 @t23))) % 0.35/0.79 (define @t25 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.35/0.79 (define @t26 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.35/0.79 (define @t27 () (and (= @t26 @t1) @t25)) % 0.35/0.79 (define @t28 () (=> @t2 @t27)) % 0.35/0.79 (define @t29 () (forall @t3 @t28)) % 0.35/0.79 (define @t30 () (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1))) % 0.35/0.79 (define @t31 () (tptp.sdtpldt0 @t1 @t5)) % 0.35/0.79 (define @t32 () (and (= @t31 tptp.sz00) @t30)) % 0.35/0.79 (define @t33 () (=> @t2 @t32)) % 0.35/0.79 (define @t34 () (forall @t3 @t33)) % 0.35/0.79 (define @t35 () (tptp.sdtasdt0 @t8 @t16)) % 0.35/0.79 (define @t36 () (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1))) % 0.35/0.79 (define @t37 () (tptp.sdtasdt0 @t1 tptp.sz10)) % 0.35/0.79 (define @t38 () (and (= @t37 @t1) @t36)) % 0.35/0.79 (define @t39 () (=> @t2 @t38)) % 0.35/0.79 (define @t40 () (forall @t3 @t39)) % 0.35/0.79 (define @t41 () (tptp.sdtasdt0 @t1 @t16)) % 0.35/0.79 (define @t42 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 0.35/0.79 (define @t43 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 0.35/0.79 (define @t44 () (and (= @t43 tptp.sz00) @t42)) % 0.35/0.79 (define @t45 () (=> @t2 @t44)) % 0.35/0.79 (define @t46 () (forall @t3 @t45)) % 0.35/0.79 (define @t47 () (tptp.smndt0 tptp.sz10)) % 0.35/0.79 (define @t48 () (= @t5 (tptp.sdtasdt0 @t1 @t47))) % 0.35/0.79 (define @t49 () (tptp.sdtasdt0 @t47 @t1)) % 0.35/0.79 (define @t50 () (and (= @t49 @t5) @t48)) % 0.35/0.79 (define @t51 () (=> @t2 @t50)) % 0.35/0.79 (define @t52 () (forall @t3 @t51)) % 0.35/0.79 (define @t53 () (= @t8 tptp.sz00)) % 0.35/0.79 (define @t54 () (= @t1 tptp.sz00)) % 0.35/0.79 (define @t55 () (@list @t16)) % 0.35/0.79 (define @t56 () (not @t53)) % 0.35/0.79 (define @t57 () (tptp.aDivisorOf0 @t8 @t1)) % 0.35/0.79 (define @t58 () (@list @t8)) % 0.35/0.79 (define @t59 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t16)) % 0.35/0.79 (define @t60 () (not (= @t16 tptp.sz00))) % 0.35/0.79 (define @t61 () (and @t2 @t11 @t19 @t60)) % 0.35/0.79 (define @t62 () (and @t2 @t11 @t56)) % 0.35/0.79 (define @t63 () (@var "W3" $$unsorted)) % 0.35/0.79 (define @t64 () (tptp.aInteger0 @t63)) % 0.35/0.79 (define @t65 () (@list @t1 @t8 @t16 @t63)) % 0.35/0.79 (define @t66 () (= @t1 @t47)) % 0.35/0.79 (define @t67 () (= @t1 tptp.sz10)) % 0.35/0.79 (define @t68 () (tptp.isPrime0 @t8)) % 0.35/0.79 (define @t69 () (tptp.aSet0 @t1)) % 0.35/0.79 (define @t70 () (tptp.aElementOf0 @t8 @t1)) % 0.35/0.79 (define @t71 () (tptp.aElementOf0 @t16 @t1)) % 0.35/0.79 (define @t72 () (tptp.aElementOf0 @t16 @t8)) % 0.35/0.79 (define @t73 () (tptp.aSet0 @t8)) % 0.35/0.79 (define @t74 () (tptp.isFinite0 @t1)) % 0.35/0.79 (define @t75 () (tptp.aElementOf0 @t63 @t8)) % 0.35/0.79 (define @t76 () (tptp.aElementOf0 @t63 @t1)) % 0.35/0.79 (define @t77 () (tptp.aElementOf0 @t63 @t16)) % 0.35/0.79 (define @t78 () (@list @t63)) % 0.35/0.79 (define @t79 () (tptp.aSet0 @t16)) % 0.35/0.79 (define @t80 () (tptp.sdtbsmnsldt0 @t1 @t8)) % 0.35/0.79 (define @t81 () (tptp.aSubsetOf0 @t8 tptp.cS1395)) % 0.35/0.79 (define @t82 () (tptp.aSubsetOf0 @t1 tptp.cS1395)) % 0.35/0.79 (define @t83 () (and @t82 @t81)) % 0.35/0.79 (define @t84 () (tptp.sdtslmnbsdt0 @t1 @t8)) % 0.35/0.79 (define @t85 () (tptp.sbsmnsldt0 @t1)) % 0.35/0.79 (define @t86 () (tptp.stldt0 @t1)) % 0.35/0.79 (define @t87 () (tptp.szAzrzSzezqlpdtcmdtrp0 @t1 @t8)) % 0.35/0.79 (define @t88 () (tptp.isOpen0 @t1)) % 0.35/0.79 (define @t89 () (tptp.isClosed0 @t1)) % 0.35/0.79 (define @t90 () (tptp.isOpen0 @t8)) % 0.35/0.79 (define @t91 () (tptp.isClosed0 @t8)) % 0.35/0.79 (define @t92 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.35/0.79 (define @t93 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 @t8)) % 0.35/0.79 (define @t94 () (= @t93 @t1)) % 0.35/0.79 (define @t95 () (tptp.aElementOf0 @t16 @t93)) % 0.35/0.79 (define @t96 () (tptp.sdteqdtlpzmzozddtrp0 @t16 tptp.sz00 @t8)) % 0.35/0.79 (define @t97 () (tptp.sdtpldt0 @t16 (tptp.smndt0 tptp.sz00))) % 0.35/0.79 (define @t98 () (tptp.aDivisorOf0 @t8 @t97)) % 0.35/0.79 (define @t99 () (tptp.sdtasdt0 @t8 @t63)) % 0.35/0.79 (define @t100 () (exists @t78 (and @t64 (= @t99 @t97)))) % 0.35/0.79 (define @t101 () (forall @t55 (and (=> @t95 (and @t19 @t100 @t98 @t96)) (=> (and @t19 (or @t100 @t98 @t96)) @t95)))) % 0.35/0.79 (define @t102 () (tptp.aSet0 @t93)) % 0.35/0.79 (define @t103 () (tptp.sbsmnsldt0 tptp.xS)) % 0.35/0.79 (define @t104 () (tptp.stldt0 @t103)) % 0.35/0.79 (define @t105 () (tptp.aElementOf0 @t1 @t104)) % 0.35/0.79 (define @t106 () (tptp.aElementOf0 @t1 @t103)) % 0.35/0.79 (define @t107 () (forall @t3 (= @t105 (and @t2 (not @t106))))) % 0.35/0.79 (define @t108 () (forall @t3 (= @t106 (and @t2 (exists @t58 (and (tptp.aElementOf0 @t8 tptp.xS) (tptp.aElementOf0 @t1 @t8))))))) % 0.35/0.79 (define @t109 () (tptp.aSet0 @t103)) % 0.35/0.79 (define @t110 () (tptp.aElementOf0 @t16 @t87)) % 0.35/0.79 (define @t111 () (tptp.sdteqdtlpzmzozddtrp0 @t16 @t1 @t8)) % 0.35/0.79 (define @t112 () (tptp.sdtpldt0 @t16 @t5)) % 0.35/0.79 (define @t113 () (tptp.aDivisorOf0 @t8 @t112)) % 0.35/0.79 (define @t114 () (exists @t78 (and @t64 (= @t99 @t112)))) % 0.35/0.79 (define @t115 () (forall @t3 (=> @t105 (exists @t58 (and @t11 @t56 (tptp.aSet0 @t87) (forall @t55 (and (=> @t110 (and @t19 @t114 @t113 @t111)) (=> (and @t19 (or @t114 @t113 @t111)) @t110))) (forall @t55 (=> @t110 (tptp.aElementOf0 @t16 @t104))) (tptp.aSubsetOf0 @t87 @t104)))))) % 0.35/0.79 (define @t116 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t117 () (tptp.aElementOf0 @t1 @t116)) % 0.35/0.79 (define @t118 () (tptp.sdteqdtlpzmzozddtrp0 @t1 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t119 () (tptp.sdtpldt0 @t1 @t47)) % 0.35/0.79 (define @t120 () (tptp.aDivisorOf0 tptp.xp @t119)) % 0.35/0.79 (define @t121 () (tptp.sdtasdt0 tptp.xp @t8)) % 0.35/0.79 (define @t122 () (and @t11 (= @t121 @t119))) % 0.35/0.79 (define @t123 () (exists @t58 @t122)) % 0.35/0.79 (define @t124 () (or @t123 @t120 @t118)) % 0.35/0.79 (define @t125 () (and @t2 @t124)) % 0.35/0.79 (define @t126 () (=> @t125 @t117)) % 0.35/0.79 (define @t127 () (and @t2 @t123 @t120 @t118)) % 0.35/0.79 (define @t128 () (=> @t117 @t127)) % 0.35/0.79 (define @t129 () (and @t128 @t126)) % 0.35/0.79 (define @t130 () (forall @t3 @t129)) % 0.35/0.79 (define @t131 () (tptp.aInteger0 tptp.xp)) % 0.35/0.79 (define @t132 () (tptp.smndt0 tptp.xp)) % 0.35/0.79 (define @t133 () (tptp.sdtpldt0 tptp.sz10 @t132)) % 0.35/0.79 (define @t134 () (tptp.aElementOf0 @t133 @t116)) % 0.35/0.79 (define @t135 () (tptp.sdteqdtlpzmzozddtrp0 @t133 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t136 () (tptp.sdtpldt0 @t133 @t47)) % 0.35/0.79 (define @t137 () (tptp.aDivisorOf0 tptp.xp @t136)) % 0.35/0.79 (define @t138 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.35/0.79 (define @t139 () (= @t138 @t136)) % 0.35/0.79 (define @t140 () (and @t2 @t139)) % 0.35/0.79 (define @t141 () (exists @t3 @t140)) % 0.35/0.79 (define @t142 () (or @t141 @t137 @t135 @t134)) % 0.35/0.79 (define @t143 () (tptp.sdtpldt0 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t144 () (tptp.aElementOf0 @t143 @t116)) % 0.35/0.79 (define @t145 () (tptp.sdteqdtlpzmzozddtrp0 @t143 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t146 () (tptp.sdtpldt0 @t143 @t47)) % 0.35/0.79 (define @t147 () (tptp.aDivisorOf0 tptp.xp @t146)) % 0.35/0.79 (define @t148 () (= @t138 @t146)) % 0.35/0.79 (define @t149 () (and @t2 @t148)) % 0.35/0.79 (define @t150 () (exists @t3 @t149)) % 0.35/0.79 (define @t151 () (or @t150 @t147 @t145 @t144)) % 0.35/0.79 (define @t152 () (and @t151 @t142)) % 0.35/0.79 (define @t153 () (not @t152)) % 0.35/0.79 (define @t154 () (and (= @t5 @t49) @t48)) % 0.35/0.79 (define @t155 () (@list tptp.xp)) % 0.35/0.79 (define @t156 () (tptp.sdtasdt0 tptp.xp @t47)) % 0.35/0.79 (define @t157 () (= @t132 @t156)) % 0.35/0.79 (define @t158 () (tptp.sdtasdt0 @t47 tptp.xp)) % 0.35/0.79 (define @t159 () (= @t132 @t158)) % 0.35/0.79 (define @t160 () (and @t159 @t157)) % 0.35/0.79 (define @t161 () (not @t131)) % 0.35/0.79 (define @t162 () (or @t161 @t160)) % 0.35/0.79 (define @t163 () (@list false false)) % 0.35/0.79 (define @t164 () (not @t160)) % 0.35/0.79 (define @t165 () (@list false)) % 0.35/0.79 (define @t166 () (@list @t160)) % 0.35/0.79 (define @t167 () (and (= @t1 @t26) @t25)) % 0.35/0.79 (define @t168 () (tptp.aInteger0 @t132)) % 0.35/0.79 (define @t169 () (or @t161 @t168)) % 0.35/0.79 (define @t170 () (= @t132 (tptp.sdtpldt0 @t132 tptp.sz00))) % 0.35/0.79 (define @t171 () (and @t170 (= @t132 (tptp.sdtpldt0 tptp.sz00 @t132)))) % 0.35/0.79 (define @t172 () (not @t168)) % 0.35/0.79 (define @t173 () (or @t172 @t171)) % 0.35/0.79 (define @t174 () (and (= tptp.sz00 @t43) @t42)) % 0.35/0.79 (define @t175 () (tptp.sdtasdt0 tptp.sz00 tptp.xp)) % 0.35/0.79 (define @t176 () (= tptp.sz00 @t175)) % 0.35/0.79 (define @t177 () (and (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.sz00)) @t176)) % 0.35/0.79 (define @t178 () (or @t161 @t177)) % 0.35/0.79 (define @t179 () (and (= tptp.sz00 @t31) @t30)) % 0.35/0.79 (define @t180 () (@list tptp.sz10)) % 0.35/0.79 (define @t181 () (tptp.sdtpldt0 @t47 tptp.sz10)) % 0.35/0.79 (define @t182 () (= tptp.sz00 @t181)) % 0.35/0.79 (define @t183 () (tptp.sdtpldt0 tptp.sz10 @t47)) % 0.35/0.79 (define @t184 () (= tptp.sz00 @t183)) % 0.35/0.79 (define @t185 () (and @t184 @t182)) % 0.35/0.79 (define @t186 () (not @t4)) % 0.35/0.79 (define @t187 () (or @t186 @t185)) % 0.35/0.79 (define @t188 () (not @t185)) % 0.35/0.79 (define @t189 () (@list @t185)) % 0.35/0.79 (define @t190 () (tptp.sdtpldt0 @t132 @t183)) % 0.35/0.79 (define @t191 () (not @t19)) % 0.35/0.79 (define @t192 () (not @t11)) % 0.35/0.79 (define @t193 () (not @t2)) % 0.35/0.79 (define @t194 () (or @t193 @t192 @t191)) % 0.35/0.79 (define @t195 () (tptp.aInteger0 @t47)) % 0.35/0.79 (define @t196 () (or @t186 @t195)) % 0.35/0.79 (define @t197 () (tptp.sdtpldt0 @t132 tptp.sz10)) % 0.35/0.79 (define @t198 () (= @t190 (tptp.sdtpldt0 @t197 @t47))) % 0.35/0.79 (define @t199 () (not @t195)) % 0.35/0.79 (define @t200 () (or @t172 @t186 @t199 @t198)) % 0.35/0.79 (define @t201 () (@list false false false false)) % 0.35/0.79 (define @t202 () (or @t193 @t192)) % 0.35/0.79 (define @t203 () (not @t12)) % 0.35/0.79 (define @t204 () (= @t133 @t197)) % 0.35/0.79 (define @t205 () (or @t186 @t172 @t204)) % 0.35/0.79 (define @t206 () (@list false false false)) % 0.35/0.79 (define @t207 () (= @t136 @t156)) % 0.35/0.79 (define @t208 () (not @t207)) % 0.35/0.79 (define @t209 () (or @t199 @t208)) % 0.35/0.79 (define @t210 () (not @t209)) % 0.35/0.79 (define @t211 () (not (= @t156 @t136))) % 0.35/0.79 (define @t212 () (or @t199 @t211)) % 0.35/0.79 (define @t213 () (forall @t3 (or @t193 (not @t139)))) % 0.35/0.79 (define @t214 () (not @t213)) % 0.35/0.79 (define @t215 () (@list true)) % 0.35/0.79 (define @t216 () (or @t214 @t137 @t135 @t134)) % 0.35/0.79 (define @t217 () (@var "BOUND_VARIABLE_8721" $$unsorted)) % 0.35/0.79 (define @t218 () (tptp.aElementOf0 @t217 @t116)) % 0.35/0.79 (define @t219 () (not (tptp.sdteqdtlpzmzozddtrp0 @t217 tptp.sz10 tptp.xp))) % 0.35/0.79 (define @t220 () (tptp.sdtpldt0 @t217 @t47)) % 0.35/0.79 (define @t221 () (not (tptp.aDivisorOf0 tptp.xp @t220))) % 0.35/0.79 (define @t222 () (@var "BOUND_VARIABLE_8755" $$unsorted)) % 0.35/0.79 (define @t223 () (tptp.sdtasdt0 tptp.xp @t222)) % 0.35/0.79 (define @t224 () (not (= @t223 @t220))) % 0.35/0.79 (define @t225 () (not (tptp.aInteger0 @t222))) % 0.35/0.79 (define @t226 () (or @t225 @t224)) % 0.35/0.79 (define @t227 () (and @t226 @t221 @t219)) % 0.35/0.79 (define @t228 () (not (tptp.aInteger0 @t217))) % 0.35/0.79 (define @t229 () (or @t228 @t227 @t218)) % 0.35/0.79 (define @t230 () (forall (@list @t217 @t222) @t229)) % 0.35/0.79 (define @t231 () (@list @t222)) % 0.35/0.79 (define @t232 () (forall @t231 @t229)) % 0.35/0.79 (define @t233 () (@list @t217)) % 0.35/0.79 (define @t234 () (forall @t231 @t219)) % 0.35/0.79 (define @t235 () (forall @t231 @t221)) % 0.35/0.79 (define @t236 () (forall @t231 @t226)) % 0.35/0.79 (define @t237 () (and @t236 @t235 @t234)) % 0.35/0.79 (define @t238 () (forall @t231 @t227)) % 0.35/0.79 (define @t239 () (or @t228 @t238 @t218)) % 0.35/0.79 (define @t240 () (not (= @t220 @t121))) % 0.35/0.79 (define @t241 () (or @t192 @t240)) % 0.35/0.79 (define @t242 () (forall @t58 @t241)) % 0.35/0.79 (define @t243 () (and @t242 @t221 @t219)) % 0.35/0.79 (define @t244 () (or @t228 @t243 @t218)) % 0.35/0.79 (define @t245 () (forall @t233 @t244)) % 0.35/0.79 (define @t246 () (@var "BOUND_VARIABLE_8704" $$unsorted)) % 0.35/0.79 (define @t247 () (tptp.sdteqdtlpzmzozddtrp0 @t246 tptp.sz10 tptp.xp)) % 0.35/0.79 (define @t248 () (tptp.sdtpldt0 @t246 @t47)) % 0.35/0.79 (define @t249 () (tptp.aDivisorOf0 tptp.xp @t248)) % 0.35/0.79 (define @t250 () (not (= @t248 @t121))) % 0.35/0.79 (define @t251 () (or @t192 @t250)) % 0.35/0.79 (define @t252 () (forall @t58 @t251)) % 0.35/0.79 (define @t253 () (not @t252)) % 0.35/0.79 (define @t254 () (tptp.aInteger0 @t246)) % 0.35/0.79 (define @t255 () (and @t254 @t253 @t249 @t247)) % 0.35/0.79 (define @t256 () (not (tptp.aElementOf0 @t246 @t116))) % 0.35/0.79 (define @t257 () (or @t256 @t255)) % 0.35/0.79 (define @t258 () (forall (@list @t246) @t257)) % 0.35/0.79 (define @t259 () (not @t118)) % 0.35/0.79 (define @t260 () (not @t120)) % 0.35/0.79 (define @t261 () (= @t119 @t121)) % 0.35/0.79 (define @t262 () (forall @t58 (or @t192 (not @t261)))) % 0.35/0.79 (define @t263 () (and @t262 @t260 @t259)) % 0.35/0.79 (define @t264 () (or @t193 @t263 @t117)) % 0.35/0.79 (define @t265 () (forall @t3 @t264)) % 0.35/0.79 (define @t266 () (@list @t1)) % 0.35/0.79 (define @t267 () (not @t262)) % 0.35/0.79 (define @t268 () (and @t2 @t267 @t120 @t118)) % 0.35/0.79 (define @t269 () (or (not @t117) @t268)) % 0.35/0.79 (define @t270 () (forall @t3 @t269)) % 0.35/0.79 (define @t271 () (and @t270 @t265)) % 0.35/0.79 (define @t272 () (not @t267)) % 0.35/0.79 (define @t273 () (and @t272 @t260 @t259)) % 0.35/0.79 (define @t274 () (or @t267 @t120 @t118)) % 0.35/0.79 (define @t275 () (and @t2 @t274)) % 0.35/0.79 (define @t276 () (and (=> @t117 @t268) (=> @t275 @t117))) % 0.35/0.79 (define @t277 () (and @t11 @t261)) % 0.35/0.79 (define @t278 () (forall @t58 (not @t277))) % 0.35/0.79 (define @t279 () (not @t278)) % 0.35/0.79 (define @t280 () (and (= @t1 @t37) @t36)) % 0.35/0.79 (define @t281 () (tptp.sdtasdt0 tptp.xp tptp.sz10)) % 0.35/0.79 (define @t282 () (= tptp.xp @t281)) % 0.35/0.79 (define @t283 () (and @t282 (= tptp.xp (tptp.sdtasdt0 tptp.sz10 tptp.xp)))) % 0.35/0.79 (define @t284 () (or @t161 @t283)) % 0.35/0.79 (define @t285 () (= tptp.xp (tptp.sdtpldt0 tptp.sz00 tptp.xp))) % 0.35/0.79 (define @t286 () (and (= tptp.xp (tptp.sdtpldt0 tptp.xp tptp.sz00)) @t285)) % 0.35/0.79 (define @t287 () (or @t161 @t286)) % 0.35/0.79 (define @t288 () (tptp.sdtpldt0 @t181 tptp.xp)) % 0.35/0.79 (define @t289 () (tptp.sdtpldt0 @t47 @t143)) % 0.35/0.79 (define @t290 () (= @t289 @t288)) % 0.35/0.79 (define @t291 () (or @t199 @t186 @t161 @t290)) % 0.35/0.79 (define @t292 () (tptp.aInteger0 @t143)) % 0.35/0.79 (define @t293 () (or @t186 @t161 @t292)) % 0.35/0.79 (define @t294 () (= @t146 @t289)) % 0.35/0.79 (define @t295 () (not @t292)) % 0.35/0.79 (define @t296 () (or @t295 @t199 @t294)) % 0.35/0.79 (define @t297 () (= @t146 @t281)) % 0.35/0.79 (define @t298 () (not @t297)) % 0.35/0.79 (define @t299 () (or @t186 @t298)) % 0.35/0.79 (define @t300 () (not @t299)) % 0.35/0.79 (define @t301 () (and @t299 (not @t147) (not @t145))) % 0.35/0.79 (define @t302 () (not @t301)) % 0.35/0.79 (define @t303 () (or @t295 @t301 @t144)) % 0.35/0.79 (define @t304 () (or (not (forall @t3 (or @t193 (not @t148)))) @t147 @t145 @t144)) % 0.35/0.79 (define @t305 () (forall @t3 (not @t140))) % 0.35/0.79 (define @t306 () (not @t305)) % 0.35/0.79 (define @t307 () (forall @t3 (not @t149))) % 0.35/0.79 (define @t308 () (not @t307)) % 0.35/0.79 (assume @p1 (forall @t3 (=> @t2 true))) % 0.35/0.79 (assume @p2 (tptp.aInteger0 tptp.sz00)) % 0.35/0.79 (assume @p3 @t4) % 0.35/0.79 (assume @p4 @t7) % 0.35/0.79 (assume @p5 @t14) % 0.35/0.79 (assume @p6 (forall @t13 (=> @t12 (tptp.aInteger0 @t15)))) % 0.35/0.79 (assume @p7 @t22) % 0.35/0.79 (assume @p8 @t24) % 0.35/0.79 (assume @p9 @t29) % 0.35/0.79 (assume @p10 @t34) % 0.35/0.79 (assume @p11 (forall @t21 (=> @t20 (= (tptp.sdtasdt0 @t1 @t35) (tptp.sdtasdt0 @t15 @t16))))) % 0.35/0.79 (assume @p12 (forall @t13 (=> @t12 (= @t15 (tptp.sdtasdt0 @t8 @t1))))) % 0.35/0.79 (assume @p13 @t40) % 0.35/0.79 (assume @p14 (forall @t21 (=> @t20 (and (= (tptp.sdtasdt0 @t1 @t17) (tptp.sdtpldt0 @t15 @t41)) (= (tptp.sdtasdt0 @t9 @t16) (tptp.sdtpldt0 @t41 @t35)))))) % 0.35/0.79 (assume @p15 @t46) % 0.35/0.79 (assume @p16 @t52) % 0.35/0.79 (assume @p17 (forall @t13 (=> @t12 (=> (= @t15 tptp.sz00) (or @t54 @t53))))) % 0.35/0.79 (assume @p18 (forall @t3 (=> @t2 (forall @t58 (= @t57 (and @t11 @t56 (exists @t55 (and @t19 (= @t35 @t1))))))))) % 0.35/0.79 (assume @p19 (forall @t21 (=> @t61 (= @t59 (tptp.aDivisorOf0 @t16 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t8))))))) % 0.35/0.79 (assume @p20 (forall @t13 (=> @t62 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t8)))) % 0.35/0.79 (assume @p21 (forall @t21 (=> @t61 (=> @t59 (tptp.sdteqdtlpzmzozddtrp0 @t8 @t1 @t16))))) % 0.35/0.79 (assume @p22 (forall @t65 (=> (and @t2 @t11 @t19 @t60 @t64) (=> (and @t59 (tptp.sdteqdtlpzmzozddtrp0 @t8 @t63 @t16)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t63 @t16))))) % 0.35/0.79 (assume @p23 (forall @t65 (=> (and @t2 @t11 @t19 @t60 @t64 (not (= @t63 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 (tptp.sdtasdt0 @t16 @t63)) (and @t59 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t63)))))) % 0.35/0.79 (assume @p24 (forall @t3 (=> (and @t2 (not @t54)) (=> (tptp.isPrime0 @t1) true)))) % 0.35/0.79 (assume @p25 (forall @t3 (=> @t2 (= (exists @t58 (and @t57 @t68)) (and (not @t67) (not @t66)))))) % 0.35/0.79 (assume @p26 (forall @t3 (=> @t69 true))) % 0.35/0.79 (assume @p27 (forall @t3 (=> @t69 (forall @t58 (=> @t70 true))))) % 0.35/0.79 (assume @p28 (forall @t3 (=> @t69 (forall @t58 (= (tptp.aSubsetOf0 @t8 @t1) (and @t73 (forall @t55 (=> @t72 @t71)))))))) % 0.35/0.79 (assume @p29 (forall @t3 (=> @t69 (=> @t74 true)))) % 0.35/0.79 (assume @p30 (forall @t13 (=> @t83 (forall @t55 (= (= @t16 @t80) (and @t79 (forall @t78 (= @t77 (and @t64 (or @t76 @t75)))))))))) % 0.35/0.79 (assume @p31 (forall @t13 (=> @t83 (forall @t55 (= (= @t16 @t84) (and @t79 (forall @t78 (= @t77 (and @t64 @t76 @t75))))))))) % 0.35/0.79 (assume @p32 (forall @t3 (=> (and @t69 (forall @t58 (=> @t70 @t81))) (forall @t58 (= (= @t8 @t85) (and @t73 (forall @t55 (= @t72 (and @t19 (exists @t78 (and @t76 (tptp.aElementOf0 @t16 @t63)))))))))))) % 0.35/0.79 (assume @p33 (forall @t3 (=> @t82 (forall @t58 (= (= @t8 @t86) (and @t73 (forall @t55 (= @t72 (and @t19 (not @t71)))))))))) % 0.35/0.79 (assume @p34 (forall @t13 (=> @t62 (forall @t55 (= (= @t16 @t87) (and @t79 (forall @t78 (= @t77 (and @t64 (tptp.sdteqdtlpzmzozddtrp0 @t63 @t1 @t8)))))))))) % 0.35/0.79 (assume @p35 (forall @t3 (=> @t82 (= @t88 (forall @t58 (=> @t70 (exists @t55 (and @t19 @t60 (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 @t8 @t16) @t1))))))))) % 0.35/0.79 (assume @p36 (forall @t3 (=> @t82 (= @t89 (tptp.isOpen0 @t86))))) % 0.35/0.79 (assume @p37 (forall @t3 (=> (and @t69 (forall @t58 (=> @t70 (and @t81 @t90)))) (tptp.isOpen0 @t85)))) % 0.35/0.79 (assume @p38 (forall @t13 (=> (and @t82 @t81 @t88 @t90) (tptp.isOpen0 @t84)))) % 0.35/0.79 (assume @p39 (forall @t13 (=> (and @t82 @t81 @t89 @t91) (tptp.isClosed0 @t80)))) % 0.35/0.79 (assume @p40 (forall @t3 (=> (and @t69 @t74 (forall @t58 (=> @t70 (and @t81 @t91)))) (tptp.isClosed0 @t85)))) % 0.35/0.79 (assume @p41 (forall @t13 (=> @t62 (and (tptp.aSubsetOf0 @t87 tptp.cS1395) (tptp.isClosed0 @t87))))) % 0.35/0.79 (assume @p42 (and (tptp.aSet0 tptp.xS) (forall @t3 (and (=> @t92 (exists @t58 (and @t11 @t56 @t68 @t102 @t101 @t94))) (=> (exists @t58 (and @t11 @t56 @t68 (=> (and @t102 @t101) @t94))) @t92))) (= tptp.xS tptp.cS2043))) % 0.35/0.79 (assume @p43 (and @t109 @t108 (tptp.aSet0 @t104) @t107 (forall @t3 (= @t105 (or @t67 @t66))) (= @t104 tptp.cS2076))) % 0.35/0.79 (assume @p44 (tptp.isFinite0 tptp.xS)) % 0.35/0.79 (assume @p45 (and @t109 @t108 @t107 @t115 (tptp.isOpen0 @t104) (tptp.isClosed0 @t103) @t109 @t108 @t107 @t115)) % 0.35/0.79 (assume @p46 (and @t131 (not (= tptp.xp tptp.sz00)) (tptp.aSet0 @t116) @t130 @t109 @t108 @t107 (forall @t3 (=> @t117 @t105)) (tptp.aSubsetOf0 @t116 @t104))) % 0.35/0.79 (assume @p47 @t153) % 0.35/0.79 (assume @p48 true) % 0.35/0.79 (step @p49 :rule bool-impl-elim :args (@t2 @t154)) % 0.35/0.79 (step @p50 :rule cong :premises (@p49) :args ((forall @t3 (=> @t2 @t154)))) % 0.35/0.79 (step @p51 :rule refl :args (@t48)) % 0.35/0.79 (step @p52 :rule eq-symm :args (@t49 @t5)) % 0.35/0.79 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t50)) % 0.35/0.79 (step @p54 :rule refl :args (@t2)) % 0.35/0.79 (step @p55 :rule cong :premises (@p54 @p53) :args (@t51)) % 0.35/0.79 (step @p56 :rule cong :premises (@p55) :args (@t52)) % 0.35/0.79 (step @p57 :rule trans :premises (@p56 @p50)) % 0.35/0.79 (step @p58 :rule eq_resolve :premises (@p16 @p57)) % 0.35/0.79 (step @p59 :rule instantiate :premises (@p58) :args (@t155)) % 0.35/0.79 (step @p60 :rule and_elim :premises (@p46) :args (0)) % 0.35/0.79 (step @p61 :rule cnf_or_pos :args (@t162)) % 0.35/0.79 (step @p62 :rule reordering :premises (@p61) :args ((or @t161 @t160 (not @t162)))) % 0.35/0.79 (step @p63 :rule chain_m_resolution :premises (@p62 @p60 @p59) :args (@t160 @t163 (@list @t131 @t162))) % 0.35/0.79 (step @p64 :rule cnf_and_pos :args (@t160 1)) % 0.35/0.79 (step @p65 :rule reordering :premises (@p64) :args ((or @t157 @t164))) % 0.35/0.79 (step @p66 :rule chain_m_resolution :premises (@p65 @p63) :args (@t157 @t165 @t166)) % 0.35/0.79 (step @p67 :rule bool-impl-elim :args (@t2 @t167)) % 0.35/0.79 (step @p68 :rule cong :premises (@p67) :args ((forall @t3 (=> @t2 @t167)))) % 0.35/0.79 (step @p69 :rule refl :args (@t25)) % 0.35/0.79 (step @p70 :rule eq-symm :args (@t26 @t1)) % 0.35/0.79 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t27)) % 0.35/0.79 (step @p72 :rule cong :premises (@p54 @p71) :args (@t28)) % 0.35/0.79 (step @p73 :rule cong :premises (@p72) :args (@t29)) % 0.35/0.79 (step @p74 :rule trans :premises (@p73 @p68)) % 0.35/0.79 (step @p75 :rule eq_resolve :premises (@p9 @p74)) % 0.35/0.79 (step @p76 :rule instantiate :premises (@p75) :args ((@list @t132))) % 0.35/0.79 (step @p77 :rule bool-impl-elim :args (@t2 @t6)) % 0.35/0.79 (step @p78 :rule cong :premises (@p77) :args (@t7)) % 0.35/0.79 (step @p79 :rule eq_resolve :premises (@p4 @p78)) % 0.35/0.79 (step @p80 :rule instantiate :premises (@p79) :args (@t155)) % 0.35/0.79 (step @p81 :rule cnf_or_pos :args (@t169)) % 0.35/0.79 (step @p82 :rule reordering :premises (@p81) :args ((or @t161 @t168 (not @t169)))) % 0.35/0.79 (step @p83 :rule chain_m_resolution :premises (@p82 @p60 @p80) :args (@t168 @t163 (@list @t131 @t169))) % 0.35/0.79 (step @p84 :rule cnf_or_pos :args (@t173)) % 0.35/0.79 (step @p85 :rule reordering :premises (@p84) :args ((or @t172 @t171 (not @t173)))) % 0.35/0.79 (step @p86 :rule chain_m_resolution :premises (@p85 @p83 @p76) :args (@t171 @t163 (@list @t168 @t173))) % 0.35/0.79 (step @p87 :rule 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(step @p333 :rule chain_m_resolution :premises (@p332 @p3 @p60 @p151 @p330) :args (@t290 @t201 (@list @t4 @t131 @t195 @t291))) % 0.35/0.79 (step @p334 :rule instantiate :premises (@p165) :args ((@list @t143 @t47))) % 0.35/0.79 (step @p335 :rule aci_norm :args ((= (or @t202 @t10) (or @t193 @t192 @t10)))) % 0.35/0.79 (step @p336 :rule refl :args (@t10)) % 0.35/0.79 (step @p337 :rule nary_cong :premises (@p159 @p336) :args ((or @t203 @t10))) % 0.35/0.79 (step @p338 :rule trans :premises (@p337 @p335)) % 0.35/0.79 (step @p339 :rule bool-impl-elim :args (@t12 @t10)) % 0.35/0.79 (step @p340 :rule trans :premises (@p339 @p338)) % 0.35/0.79 (step @p341 :rule cong :premises (@p340) :args (@t14)) % 0.35/0.79 (step @p342 :rule eq_resolve :premises (@p5 @p341)) % 0.35/0.79 (step @p343 :rule instantiate :premises (@p342) :args ((@list tptp.sz10 tptp.xp))) % 0.35/0.79 (step @p344 :rule cnf_or_pos :args (@t293)) % 0.35/0.79 (step @p345 :rule reordering :premises (@p344) :args ((or @t186 @t161 @t292 (not @t293)))) % 0.35/0.79 (step @p346 :rule chain_m_resolution :premises (@p345 @p3 @p60 @p343) :args (@t292 @t206 (@list @t4 @t131 @t293))) % 0.35/0.79 (step @p347 :rule cnf_or_pos :args (@t296)) % 0.35/0.79 (step @p348 :rule reordering :premises (@p347) :args ((or @t199 @t295 @t294 (not @t296)))) % 0.35/0.79 (step @p349 :rule chain_m_resolution :premises (@p348 @p151 @p346 @p334) :args (@t294 @t206 (@list @t195 @t292 @t296))) % 0.35/0.79 (step @p350 :rule trans :premises (@p349 @p333 @p329 @p323 @p315)) % 0.35/0.79 (step @p351 :rule cnf_or_pos :args (@t299)) % 0.35/0.79 (step @p352 :rule reordering :premises (@p351) :args ((or @t186 @t298 @t300))) % 0.35/0.79 (step @p353 :rule chain_m_resolution :premises (@p352 @p3 @p350) :args (@t300 @t163 (@list @t4 @t297))) % 0.35/0.79 (step @p354 :rule cnf_and_pos :args (@t301 0)) % 0.35/0.79 (step @p355 :rule reordering :premises (@p354) :args ((or @t299 @t302))) % 0.35/0.79 (step @p356 :rule chain_m_resolution :premises (@p355 @p353) :args (@t302 @t215 (@list @t299))) % 0.35/0.79 (step @p357 :rule cnf_or_pos :args (@t303)) % 0.35/0.79 (step @p358 :rule reordering :premises (@p357) :args ((or @t144 @t295 @t301 (not @t303)))) % 0.35/0.79 (step @p359 :rule chain_m_resolution :premises (@p358 @p346 @p356 @p299) :args (@t144 (@list false true false) (@list @t292 @t301 @t303))) % 0.35/0.79 (step @p360 :rule cnf_or_neg :args (@t304 3)) % 0.35/0.79 (step @p361 :rule chain_m_resolution :premises (@p360 @p359) :args (@t304 @t165 (@list @t144))) % 0.35/0.79 (step @p362 :rule refl :args (@t134)) % 0.35/0.79 (step @p363 :rule refl :args (@t135)) % 0.35/0.79 (step @p364 :rule refl :args (@t137)) % 0.35/0.79 (step @p365 :rule bool-and-de-morgan :args (@t2 @t139 true)) % 0.35/0.79 (step @p366 :rule cong :premises (@p365) :args (@t305)) % 0.35/0.79 (step @p367 :rule cong :premises (@p366) :args (@t306)) % 0.35/0.79 (step @p368 :rule exists-elim :args ((= @t141 @t306))) % 0.35/0.79 (step @p369 :rule trans :premises (@p368 @p367)) % 0.35/0.79 (step @p370 :rule nary_cong :premises (@p369 @p364 @p363 @p362) :args (@t142)) % 0.35/0.79 (step @p371 :rule refl :args (@t144)) % 0.35/0.79 (step @p372 :rule refl :args (@t145)) % 0.35/0.79 (step @p373 :rule refl :args (@t147)) % 0.35/0.79 (step @p374 :rule bool-and-de-morgan :args (@t2 @t148 true)) % 0.35/0.79 (step @p375 :rule cong :premises (@p374) :args (@t307)) % 0.35/0.79 (step @p376 :rule cong :premises (@p375) :args (@t308)) % 0.35/0.79 (step @p377 :rule exists-elim :args ((= @t150 @t308))) % 0.35/0.79 (step @p378 :rule trans :premises (@p377 @p376)) % 0.35/0.79 (step @p379 :rule nary_cong :premises (@p378 @p373 @p372 @p371) :args (@t151)) % 0.35/0.79 (step @p380 :rule nary_cong :premises (@p379 @p370) :args (@t152)) % 0.35/0.79 (step @p381 :rule cong :premises (@p380) :args (@t153)) % 0.35/0.79 (step @p382 :rule eq_resolve :premises (@p47 @p381)) % 0.35/0.79 (step @p383 :rule not_and :premises (@p382)) % 0.35/0.79 (step @p384 false :rule chain_m_resolution :premises (@p383 @p361 @p194) :args (false @t163 (@list @t304 @t216))) % 0.35/0.79 ) % 0.35/0.79 % SZS output end Proof % 0.35/0.79 % cvc5 exiting %------------------------------------------------------------------------------