%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM453+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 0.63s 0.81s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM453+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:20:50 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.63/0.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.63/0.81 % SZS status Theorem % 0.63/0.81 % SZS output start Proof % 0.63/0.81 ( % 0.63/0.81 (declare-sort $$unsorted 0) % 0.63/0.81 (declare-const tptp.xp $$unsorted) % 0.63/0.81 (declare-const tptp.isClosed0 (-> $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.isOpen0 (-> $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.stldt0 (-> $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.sdtslmnbsdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.cS1395 $$unsorted) % 0.63/0.81 (declare-const tptp.sdtbsmnsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.cS2043 $$unsorted) % 0.63/0.81 (declare-const tptp.szAzrzSzezqlpdtcmdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.sbsmnsldt0 (-> $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.xS $$unsorted) % 0.63/0.81 (declare-const tptp.sz10 $$unsorted) % 0.63/0.81 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.sz00 $$unsorted) % 0.63/0.81 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.63/0.81 (declare-const tptp.cS2076 $$unsorted) % 0.63/0.81 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.63/0.81 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.63/0.81 (define @t1 () (@var "W0" $$unsorted)) % 0.63/0.81 (define @t2 () (tptp.aInteger0 @t1)) % 0.63/0.81 (define @t3 () (@list @t1)) % 0.63/0.81 (define @t4 () (tptp.aInteger0 tptp.sz00)) % 0.63/0.81 (define @t5 () (tptp.aInteger0 tptp.sz10)) % 0.63/0.81 (define @t6 () (tptp.smndt0 @t1)) % 0.63/0.81 (define @t7 () (tptp.aInteger0 @t6)) % 0.63/0.81 (define @t8 () (forall @t3 (=> @t2 @t7))) % 0.63/0.81 (define @t9 () (@var "W1" $$unsorted)) % 0.63/0.81 (define @t10 () (tptp.sdtpldt0 @t1 @t9)) % 0.63/0.81 (define @t11 () (tptp.aInteger0 @t9)) % 0.63/0.81 (define @t12 () (and @t2 @t11)) % 0.63/0.81 (define @t13 () (@list @t1 @t9)) % 0.63/0.81 (define @t14 () (tptp.sdtasdt0 @t1 @t9)) % 0.63/0.81 (define @t15 () (tptp.aInteger0 @t14)) % 0.63/0.81 (define @t16 () (forall @t13 (=> @t12 @t15))) % 0.63/0.81 (define @t17 () (@var "W2" $$unsorted)) % 0.63/0.81 (define @t18 () (tptp.sdtpldt0 @t9 @t17)) % 0.63/0.81 (define @t19 () (= (tptp.sdtpldt0 @t1 @t18) (tptp.sdtpldt0 @t10 @t17))) % 0.63/0.81 (define @t20 () (tptp.aInteger0 @t17)) % 0.63/0.81 (define @t21 () (and @t2 @t11 @t20)) % 0.63/0.81 (define @t22 () (@list @t1 @t9 @t17)) % 0.63/0.81 (define @t23 () (forall @t22 (=> @t21 @t19))) % 0.63/0.81 (define @t24 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.63/0.81 (define @t25 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.63/0.81 (define @t26 () (and (= @t25 @t1) @t24)) % 0.63/0.81 (define @t27 () (=> @t2 @t26)) % 0.63/0.81 (define @t28 () (forall @t3 @t27)) % 0.63/0.81 (define @t29 () (= tptp.sz00 (tptp.sdtpldt0 @t6 @t1))) % 0.63/0.81 (define @t30 () (tptp.sdtpldt0 @t1 @t6)) % 0.63/0.81 (define @t31 () (and (= @t30 tptp.sz00) @t29)) % 0.63/0.81 (define @t32 () (=> @t2 @t31)) % 0.63/0.81 (define @t33 () (forall @t3 @t32)) % 0.63/0.81 (define @t34 () (tptp.sdtasdt0 @t9 @t17)) % 0.63/0.81 (define @t35 () (= @t14 (tptp.sdtasdt0 @t9 @t1))) % 0.63/0.81 (define @t36 () (forall @t13 (=> @t12 @t35))) % 0.63/0.81 (define @t37 () (tptp.sdtasdt0 @t1 @t17)) % 0.63/0.81 (define @t38 () (and (= (tptp.sdtasdt0 @t1 @t18) (tptp.sdtpldt0 @t14 @t37)) (= (tptp.sdtasdt0 @t10 @t17) (tptp.sdtpldt0 @t37 @t34)))) % 0.63/0.81 (define @t39 () (forall @t22 (=> @t21 @t38))) % 0.63/0.81 (define @t40 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 0.63/0.81 (define @t41 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 0.63/0.81 (define @t42 () (and (= @t41 tptp.sz00) @t40)) % 0.63/0.81 (define @t43 () (=> @t2 @t42)) % 0.63/0.81 (define @t44 () (forall @t3 @t43)) % 0.63/0.81 (define @t45 () (tptp.smndt0 tptp.sz10)) % 0.63/0.81 (define @t46 () (= @t6 (tptp.sdtasdt0 @t1 @t45))) % 0.63/0.81 (define @t47 () (tptp.sdtasdt0 @t45 @t1)) % 0.63/0.81 (define @t48 () (and (= @t47 @t6) @t46)) % 0.63/0.81 (define @t49 () (=> @t2 @t48)) % 0.63/0.81 (define @t50 () (forall @t3 @t49)) % 0.63/0.81 (define @t51 () (= @t9 tptp.sz00)) % 0.63/0.81 (define @t52 () (= @t1 tptp.sz00)) % 0.63/0.81 (define @t53 () (or @t52 @t51)) % 0.63/0.81 (define @t54 () (=> (= @t14 tptp.sz00) @t53)) % 0.63/0.81 (define @t55 () (=> @t12 @t54)) % 0.63/0.81 (define @t56 () (forall @t13 @t55)) % 0.63/0.81 (define @t57 () (@list @t17)) % 0.63/0.81 (define @t58 () (not @t51)) % 0.63/0.81 (define @t59 () (tptp.aDivisorOf0 @t9 @t1)) % 0.63/0.81 (define @t60 () (@list @t9)) % 0.63/0.81 (define @t61 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t9 @t17)) % 0.63/0.81 (define @t62 () (not (= @t17 tptp.sz00))) % 0.63/0.81 (define @t63 () (and @t2 @t11 @t20 @t62)) % 0.63/0.81 (define @t64 () (and @t2 @t11 @t58)) % 0.63/0.81 (define @t65 () (@var "W3" $$unsorted)) % 0.63/0.81 (define @t66 () (tptp.aInteger0 @t65)) % 0.63/0.81 (define @t67 () (@list @t1 @t9 @t17 @t65)) % 0.63/0.81 (define @t68 () (tptp.aSet0 @t1)) % 0.63/0.81 (define @t69 () (tptp.aElementOf0 @t9 @t1)) % 0.63/0.81 (define @t70 () (tptp.aElementOf0 @t17 @t1)) % 0.63/0.81 (define @t71 () (tptp.aElementOf0 @t17 @t9)) % 0.63/0.81 (define @t72 () (tptp.aSet0 @t9)) % 0.63/0.81 (define @t73 () (tptp.isFinite0 @t1)) % 0.63/0.81 (define @t74 () (tptp.aElementOf0 @t65 @t9)) % 0.63/0.81 (define @t75 () (tptp.aElementOf0 @t65 @t1)) % 0.63/0.81 (define @t76 () (tptp.aElementOf0 @t65 @t17)) % 0.63/0.81 (define @t77 () (@list @t65)) % 0.63/0.81 (define @t78 () (tptp.aSet0 @t17)) % 0.63/0.81 (define @t79 () (tptp.sdtbsmnsldt0 @t1 @t9)) % 0.63/0.81 (define @t80 () (tptp.aSubsetOf0 @t9 tptp.cS1395)) % 0.63/0.81 (define @t81 () (tptp.aSubsetOf0 @t1 tptp.cS1395)) % 0.63/0.81 (define @t82 () (and @t81 @t80)) % 0.63/0.81 (define @t83 () (tptp.sdtslmnbsdt0 @t1 @t9)) % 0.63/0.81 (define @t84 () (tptp.sbsmnsldt0 @t1)) % 0.63/0.81 (define @t85 () (tptp.stldt0 @t1)) % 0.63/0.81 (define @t86 () (tptp.szAzrzSzezqlpdtcmdtrp0 @t1 @t9)) % 0.63/0.81 (define @t87 () (tptp.isOpen0 @t1)) % 0.63/0.81 (define @t88 () (tptp.isClosed0 @t1)) % 0.63/0.81 (define @t89 () (tptp.isOpen0 @t9)) % 0.63/0.81 (define @t90 () (tptp.isClosed0 @t9)) % 0.63/0.81 (define @t91 () (tptp.sbsmnsldt0 tptp.xS)) % 0.63/0.81 (define @t92 () (tptp.stldt0 @t91)) % 0.63/0.81 (define @t93 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) % 0.63/0.81 (define @t94 () (= tptp.xp tptp.sz00)) % 0.63/0.81 (define @t95 () (tptp.aInteger0 tptp.xp)) % 0.63/0.81 (define @t96 () (tptp.smndt0 tptp.xp)) % 0.63/0.81 (define @t97 () (tptp.sdtpldt0 tptp.sz10 @t96)) % 0.63/0.81 (define @t98 () (tptp.sdtpldt0 tptp.sz10 tptp.xp)) % 0.63/0.81 (define @t99 () (not (= @t97 tptp.sz10))) % 0.63/0.81 (define @t100 () (not (= @t98 tptp.sz10))) % 0.63/0.81 (define @t101 () (and @t100 @t99)) % 0.63/0.81 (define @t102 () (not @t101)) % 0.63/0.81 (define @t103 () (and (= @t1 @t25) @t24)) % 0.63/0.81 (define @t104 () (@list tptp.xp)) % 0.63/0.81 (define @t105 () (tptp.sdtpldt0 tptp.xp tptp.sz00)) % 0.63/0.81 (define @t106 () (= tptp.xp @t105)) % 0.63/0.81 (define @t107 () (and @t106 (= tptp.xp (tptp.sdtpldt0 tptp.sz00 tptp.xp)))) % 0.63/0.81 (define @t108 () (not @t95)) % 0.63/0.81 (define @t109 () (or @t108 @t107)) % 0.63/0.81 (define @t110 () (@list false false)) % 0.63/0.81 (define @t111 () (@list false)) % 0.63/0.81 (define @t112 () (and (= tptp.sz00 @t30) @t29)) % 0.63/0.81 (define @t113 () (tptp.sdtpldt0 @t96 tptp.xp)) % 0.63/0.81 (define @t114 () (= tptp.sz00 @t113)) % 0.63/0.81 (define @t115 () (tptp.sdtpldt0 tptp.xp @t96)) % 0.63/0.81 (define @t116 () (= tptp.sz00 @t115)) % 0.63/0.81 (define @t117 () (and @t116 @t114)) % 0.63/0.81 (define @t118 () (or @t108 @t117)) % 0.63/0.81 (define @t119 () (not @t117)) % 0.63/0.81 (define @t120 () (@list @t117)) % 0.63/0.81 (define @t121 () (and (= tptp.sz00 @t41) @t40)) % 0.63/0.81 (define @t122 () (tptp.sdtasdt0 tptp.sz00 tptp.xp)) % 0.63/0.81 (define @t123 () (= tptp.sz00 @t122)) % 0.63/0.81 (define @t124 () (tptp.sdtasdt0 tptp.xp tptp.sz00)) % 0.63/0.81 (define @t125 () (= tptp.sz00 @t124)) % 0.63/0.81 (define @t126 () (and @t125 @t123)) % 0.63/0.81 (define @t127 () (or @t108 @t126)) % 0.63/0.81 (define @t128 () (not @t126)) % 0.63/0.81 (define @t129 () (@list @t126)) % 0.63/0.81 (define @t130 () (and (= @t6 @t47) @t46)) % 0.63/0.81 (define @t131 () (@list tptp.sz10)) % 0.63/0.81 (define @t132 () (tptp.sdtasdt0 @t45 tptp.sz10)) % 0.63/0.81 (define @t133 () (= @t45 @t132)) % 0.63/0.81 (define @t134 () (and @t133 (= @t45 (tptp.sdtasdt0 tptp.sz10 @t45)))) % 0.63/0.81 (define @t135 () (not @t5)) % 0.63/0.81 (define @t136 () (or @t135 @t134)) % 0.63/0.81 (define @t137 () (tptp.sdtasdt0 @t45 tptp.xp)) % 0.63/0.81 (define @t138 () (= @t96 @t137)) % 0.63/0.81 (define @t139 () (and @t138 (= @t96 (tptp.sdtasdt0 tptp.xp @t45)))) % 0.63/0.81 (define @t140 () (or @t108 @t139)) % 0.63/0.81 (define @t141 () (= tptp.sz10 @t97)) % 0.63/0.81 (define @t142 () (= tptp.sz10 @t98)) % 0.63/0.81 (define @t143 () (not @t141)) % 0.63/0.81 (define @t144 () (not @t142)) % 0.63/0.81 (define @t145 () (not @t20)) % 0.63/0.81 (define @t146 () (not @t11)) % 0.63/0.81 (define @t147 () (not @t2)) % 0.63/0.81 (define @t148 () (or @t147 @t146 @t145)) % 0.63/0.81 (define @t149 () (not @t21)) % 0.63/0.81 (define @t150 () (tptp.aInteger0 @t96)) % 0.63/0.81 (define @t151 () (or @t108 @t150)) % 0.63/0.81 (define @t152 () (tptp.sdtpldt0 @t97 tptp.xp)) % 0.63/0.81 (define @t153 () (= (tptp.sdtpldt0 tptp.sz10 @t113) @t152)) % 0.63/0.81 (define @t154 () (not @t150)) % 0.63/0.81 (define @t155 () (or @t135 @t154 @t108 @t153)) % 0.63/0.81 (define @t156 () (@list false false false false)) % 0.63/0.81 (define @t157 () (tptp.sdtpldt0 tptp.sz10 tptp.sz00)) % 0.63/0.81 (define @t158 () (= tptp.sz10 @t157)) % 0.63/0.81 (define @t159 () (and @t158 (= tptp.sz10 (tptp.sdtpldt0 tptp.sz00 tptp.sz10)))) % 0.63/0.81 (define @t160 () (or @t135 @t159)) % 0.63/0.81 (define @t161 () (and @t141 @t153 @t158 @t114)) % 0.63/0.81 (define @t162 () (tptp.sdtpldt0 tptp.sz00 @t96)) % 0.63/0.81 (define @t163 () (= @t96 @t162)) % 0.63/0.81 (define @t164 () (and (= @t96 (tptp.sdtpldt0 @t96 tptp.sz00)) @t163)) % 0.63/0.81 (define @t165 () (or @t154 @t164)) % 0.63/0.81 (define @t166 () (tptp.sdtasdt0 @t96 tptp.xp)) % 0.63/0.81 (define @t167 () (tptp.sdtasdt0 tptp.xp tptp.xp)) % 0.63/0.81 (define @t168 () (tptp.sdtpldt0 @t167 @t166)) % 0.63/0.81 (define @t169 () (= (tptp.sdtasdt0 @t115 tptp.xp) @t168)) % 0.63/0.81 (define @t170 () (tptp.sdtasdt0 tptp.xp @t96)) % 0.63/0.81 (define @t171 () (and (= (tptp.sdtasdt0 tptp.xp @t113) (tptp.sdtpldt0 @t170 @t167)) @t169)) % 0.63/0.81 (define @t172 () (or @t108 @t154 @t108 @t171)) % 0.63/0.81 (define @t173 () (@list false false false)) % 0.63/0.81 (define @t174 () (tptp.sdtpldt0 @t122 @t166)) % 0.63/0.81 (define @t175 () (= (tptp.sdtasdt0 @t162 tptp.xp) @t174)) % 0.63/0.81 (define @t176 () (and (= (tptp.sdtasdt0 tptp.sz00 @t113) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.sz00 @t96) @t122)) @t175)) % 0.63/0.81 (define @t177 () (not @t4)) % 0.63/0.81 (define @t178 () (or @t177 @t154 @t108 @t176)) % 0.63/0.81 (define @t179 () (tptp.sdtasdt0 tptp.xp @t105)) % 0.63/0.81 (define @t180 () (= @t179 (tptp.sdtpldt0 @t167 @t124))) % 0.63/0.81 (define @t181 () (and @t180 (= (tptp.sdtasdt0 (tptp.sdtpldt0 tptp.xp tptp.xp) tptp.sz00) (tptp.sdtpldt0 @t124 @t124)))) % 0.63/0.81 (define @t182 () (or @t108 @t108 @t177 @t181)) % 0.63/0.81 (define @t183 () (tptp.aInteger0 @t45)) % 0.63/0.81 (define @t184 () (or @t135 @t183)) % 0.63/0.81 (define @t185 () (tptp.sdtpldt0 @t137 @t166)) % 0.63/0.81 (define @t186 () (tptp.sdtpldt0 @t45 @t96)) % 0.63/0.81 (define @t187 () (tptp.sdtasdt0 @t186 tptp.xp)) % 0.63/0.81 (define @t188 () (= @t187 @t185)) % 0.63/0.81 (define @t189 () (and (= (tptp.sdtasdt0 @t45 @t113) (tptp.sdtpldt0 (tptp.sdtasdt0 @t45 @t96) @t137)) @t188)) % 0.63/0.81 (define @t190 () (not @t183)) % 0.63/0.81 (define @t191 () (or @t190 @t154 @t108 @t189)) % 0.63/0.81 (define @t192 () (tptp.sdtasdt0 @t45 @t98)) % 0.63/0.81 (define @t193 () (= @t192 (tptp.sdtpldt0 @t132 @t137))) % 0.63/0.81 (define @t194 () (and @t193 (= (tptp.sdtasdt0 (tptp.sdtpldt0 @t45 tptp.sz10) tptp.xp) (tptp.sdtpldt0 @t137 (tptp.sdtasdt0 tptp.sz10 tptp.xp))))) % 0.63/0.81 (define @t195 () (or @t190 @t135 @t108 @t194)) % 0.63/0.81 (define @t196 () (or @t147 @t146 @t35)) % 0.63/0.81 (define @t197 () (or @t147 @t146)) % 0.63/0.81 (define @t198 () (not @t12)) % 0.63/0.81 (define @t199 () (or @t108 @t154 (= @t170 @t166))) % 0.63/0.81 (define @t200 () (forall @t13 @t196)) % 0.63/0.81 (define @t201 () (= @t166 @t170)) % 0.63/0.81 (define @t202 () (or @t108 @t154 @t201)) % 0.63/0.81 (define @t203 () (= tptp.sz00 @t9)) % 0.63/0.81 (define @t204 () (= tptp.sz00 @t14)) % 0.63/0.81 (define @t205 () (not @t204)) % 0.63/0.81 (define @t206 () (or @t147 @t146 @t205 @t52 @t203)) % 0.63/0.81 (define @t207 () (or @t205 @t52 @t203)) % 0.63/0.81 (define @t208 () (or @t52 @t203)) % 0.63/0.81 (define @t209 () (=> @t204 @t208)) % 0.63/0.81 (define @t210 () (= tptp.sz00 tptp.xp)) % 0.63/0.81 (define @t211 () (= tptp.sz00 @t167)) % 0.63/0.81 (define @t212 () (not @t211)) % 0.63/0.81 (define @t213 () (or @t108 @t108 @t212 @t94 @t210)) % 0.63/0.81 (define @t214 () (forall @t13 @t206)) % 0.63/0.81 (define @t215 () (or @t108 @t108 @t212 @t210 @t210)) % 0.63/0.81 (define @t216 () (tptp.aInteger0 @t137)) % 0.63/0.81 (define @t217 () (tptp.aInteger0 @t166)) % 0.63/0.81 (define @t218 () (or @t154 @t108 @t217)) % 0.63/0.81 (define @t219 () (tptp.sdtpldt0 tptp.xp @t185)) % 0.63/0.81 (define @t220 () (= @t219 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xp @t137) @t166))) % 0.63/0.81 (define @t221 () (not @t217)) % 0.63/0.81 (define @t222 () (not @t216)) % 0.63/0.81 (define @t223 () (or @t108 @t222 @t221 @t220)) % 0.63/0.81 (define @t224 () (and @t142 @t106 @t116 @t125 @t123 @t133 @t138 @t163 @t188 @t169 @t175 @t193 @t180 @t220 @t201)) % 0.63/0.81 (assume @p1 (forall @t3 (=> @t2 true))) % 0.63/0.81 (assume @p2 @t4) % 0.63/0.81 (assume @p3 @t5) % 0.63/0.81 (assume @p4 @t8) % 0.63/0.81 (assume @p5 (forall @t13 (=> @t12 (tptp.aInteger0 @t10)))) % 0.63/0.81 (assume @p6 @t16) % 0.63/0.81 (assume @p7 @t23) % 0.63/0.81 (assume @p8 (forall @t13 (=> @t12 (= @t10 (tptp.sdtpldt0 @t9 @t1))))) % 0.63/0.81 (assume @p9 @t28) % 0.63/0.81 (assume @p10 @t33) % 0.63/0.81 (assume @p11 (forall @t22 (=> @t21 (= (tptp.sdtasdt0 @t1 @t34) (tptp.sdtasdt0 @t14 @t17))))) % 0.63/0.81 (assume @p12 @t36) % 0.63/0.81 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.63/0.81 (assume @p14 @t39) % 0.63/0.81 (assume @p15 @t44) % 0.63/0.81 (assume @p16 @t50) % 0.63/0.81 (assume @p17 @t56) % 0.63/0.81 (assume @p18 (forall @t3 (=> @t2 (forall @t60 (= @t59 (and @t11 @t58 (exists @t57 (and @t20 (= @t34 @t1))))))))) % 0.63/0.81 (assume @p19 (forall @t22 (=> @t63 (= @t61 (tptp.aDivisorOf0 @t17 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t9))))))) % 0.63/0.81 (assume @p20 (forall @t13 (=> @t64 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t9)))) % 0.63/0.81 (assume @p21 (forall @t22 (=> @t63 (=> @t61 (tptp.sdteqdtlpzmzozddtrp0 @t9 @t1 @t17))))) % 0.63/0.81 (assume @p22 (forall @t67 (=> (and @t2 @t11 @t20 @t62 @t66) (=> (and @t61 (tptp.sdteqdtlpzmzozddtrp0 @t9 @t65 @t17)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t65 @t17))))) % 0.63/0.81 (assume @p23 (forall @t67 (=> (and @t2 @t11 @t20 @t62 @t66 (not (= @t65 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 @t1 @t9 (tptp.sdtasdt0 @t17 @t65)) (and @t61 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t9 @t65)))))) % 0.63/0.81 (assume @p24 (forall @t3 (=> (and @t2 (not @t52)) (=> (tptp.isPrime0 @t1) true)))) % 0.63/0.81 (assume @p25 (forall @t3 (=> @t2 (= (exists @t60 (and @t59 (tptp.isPrime0 @t9))) (and (not (= @t1 tptp.sz10)) (not (= @t1 @t45))))))) % 0.63/0.81 (assume @p26 (forall @t3 (=> @t68 true))) % 0.63/0.81 (assume @p27 (forall @t3 (=> @t68 (forall @t60 (=> @t69 true))))) % 0.63/0.81 (assume @p28 (forall @t3 (=> @t68 (forall @t60 (= (tptp.aSubsetOf0 @t9 @t1) (and @t72 (forall @t57 (=> @t71 @t70)))))))) % 0.63/0.81 (assume @p29 (forall @t3 (=> @t68 (=> @t73 true)))) % 0.63/0.81 (assume @p30 (forall @t13 (=> @t82 (forall @t57 (= (= @t17 @t79) (and @t78 (forall @t77 (= @t76 (and @t66 (or @t75 @t74)))))))))) % 0.63/0.81 (assume @p31 (forall @t13 (=> @t82 (forall @t57 (= (= @t17 @t83) (and @t78 (forall @t77 (= @t76 (and @t66 @t75 @t74))))))))) % 0.63/0.81 (assume @p32 (forall @t3 (=> (and @t68 (forall @t60 (=> @t69 @t80))) (forall @t60 (= (= @t9 @t84) (and @t72 (forall @t57 (= @t71 (and @t20 (exists @t77 (and @t75 (tptp.aElementOf0 @t17 @t65)))))))))))) % 0.63/0.81 (assume @p33 (forall @t3 (=> @t81 (forall @t60 (= (= @t9 @t85) (and @t72 (forall @t57 (= @t71 (and @t20 (not @t70)))))))))) % 0.63/0.81 (assume @p34 (forall @t13 (=> @t64 (forall @t57 (= (= @t17 @t86) (and @t78 (forall @t77 (= @t76 (and @t66 (tptp.sdteqdtlpzmzozddtrp0 @t65 @t1 @t9)))))))))) % 0.63/0.81 (assume @p35 (forall @t3 (=> @t81 (= @t87 (forall @t60 (=> @t69 (exists @t57 (and @t20 @t62 (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 @t9 @t17) @t1))))))))) % 0.63/0.81 (assume @p36 (forall @t3 (=> @t81 (= @t88 (tptp.isOpen0 @t85))))) % 0.63/0.81 (assume @p37 (forall @t3 (=> (and @t68 (forall @t60 (=> @t69 (and @t80 @t89)))) (tptp.isOpen0 @t84)))) % 0.63/0.81 (assume @p38 (forall @t13 (=> (and @t81 @t80 @t87 @t89) (tptp.isOpen0 @t83)))) % 0.63/0.81 (assume @p39 (forall @t13 (=> (and @t81 @t80 @t88 @t90) (tptp.isClosed0 @t79)))) % 0.63/0.81 (assume @p40 (forall @t3 (=> (and @t68 @t73 (forall @t60 (=> @t69 (and @t80 @t90)))) (tptp.isClosed0 @t84)))) % 0.63/0.81 (assume @p41 (forall @t13 (=> @t64 (and (tptp.aSubsetOf0 @t86 tptp.cS1395) (tptp.isClosed0 @t86))))) % 0.63/0.81 (assume @p42 (= tptp.xS tptp.cS2043)) % 0.63/0.81 (assume @p43 (= @t92 tptp.cS2076)) % 0.63/0.81 (assume @p44 (tptp.isFinite0 tptp.xS)) % 0.63/0.81 (assume @p45 (and (tptp.isClosed0 @t91) (tptp.isOpen0 @t92))) % 0.63/0.81 (assume @p46 (and @t95 (not @t94) (tptp.aSubsetOf0 @t93 @t92))) % 0.63/0.81 (assume @p47 (and (tptp.aElementOf0 @t98 @t93) (tptp.aElementOf0 @t97 @t93))) % 0.63/0.81 (assume @p48 @t102) % 0.63/0.81 (assume @p49 true) % 0.63/0.81 (step @p50 :rule bool-impl-elim :args (@t2 @t103)) % 0.63/0.81 (step @p51 :rule cong :premises (@p50) :args ((forall @t3 (=> @t2 @t103)))) % 0.63/0.81 (step @p52 :rule refl :args (@t24)) % 0.63/0.81 (step @p53 :rule eq-symm :args (@t25 @t1)) % 0.63/0.81 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t26)) % 0.63/0.81 (step @p55 :rule refl :args (@t2)) % 0.63/0.81 (step @p56 :rule cong :premises (@p55 @p54) :args (@t27)) % 0.63/0.81 (step @p57 :rule cong :premises (@p56) :args (@t28)) % 0.63/0.81 (step @p58 :rule trans :premises (@p57 @p51)) % 0.63/0.81 (step @p59 :rule eq_resolve :premises (@p9 @p58)) % 0.63/0.81 (step @p60 :rule instantiate :premises (@p59) :args (@t104)) % 0.63/0.81 (step @p61 :rule and_elim :premises (@p46) :args (0)) % 0.63/0.81 (step @p62 :rule cnf_or_pos :args (@t109)) % 0.63/0.81 (step @p63 :rule reordering :premises (@p62) :args ((or @t108 @t107 (not @t109)))) % 0.63/0.81 (step @p64 :rule chain_m_resolution :premises (@p63 @p61 @p60) :args (@t107 @t110 (@list @t95 @t109))) % 0.63/0.81 (step @p65 :rule cnf_and_pos :args (@t107 0)) % 0.63/0.81 (step @p66 :rule reordering :premises (@p65) :args ((or @t106 (not @t107)))) % 0.63/0.81 (step @p67 :rule chain_m_resolution :premises (@p66 @p64) :args (@t106 @t111 (@list @t107))) % 0.63/0.81 (step @p68 :rule bool-impl-elim :args (@t2 @t112)) % 0.63/0.81 (step @p69 :rule cong :premises (@p68) :args ((forall @t3 (=> @t2 @t112)))) % 0.63/0.81 (step @p70 :rule refl :args (@t29)) % 0.63/0.81 (step @p71 :rule eq-symm :args (@t30 tptp.sz00)) % 0.63/0.81 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t31)) % 0.63/0.81 (step @p73 :rule cong :premises (@p55 @p72) :args (@t32)) % 0.63/0.81 (step @p74 :rule cong :premises (@p73) :args (@t33)) % 0.63/0.81 (step @p75 :rule trans :premises (@p74 @p69)) % 0.63/0.81 (step @p76 :rule eq_resolve :premises (@p10 @p75)) % 0.63/0.81 (step @p77 :rule instantiate :premises (@p76) :args (@t104)) % 0.63/0.81 (step @p78 :rule cnf_or_pos :args (@t118)) % 0.63/0.81 (step @p79 :rule reordering :premises (@p78) :args ((or @t108 @t117 (not @t118)))) % 0.63/0.81 (step @p80 :rule chain_m_resolution :premises (@p79 @p61 @p77) :args (@t117 @t110 (@list @t95 @t118))) % 0.63/0.81 (step @p81 :rule cnf_and_pos :args (@t117 0)) % 0.63/0.81 (step @p82 :rule reordering :premises (@p81) :args ((or @t116 @t119))) % 0.63/0.81 (step @p83 :rule chain_m_resolution :premises (@p82 @p80) :args (@t116 @t111 @t120)) % 0.63/0.81 (step @p84 :rule bool-impl-elim :args (@t2 @t121)) % 0.63/0.81 (step @p85 :rule cong :premises (@p84) :args ((forall @t3 (=> @t2 @t121)))) % 0.63/0.81 (step @p86 :rule refl :args (@t40)) % 0.63/0.81 (step @p87 :rule eq-symm :args (@t41 tptp.sz00)) % 0.63/0.81 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t42)) % 0.63/0.81 (step @p89 :rule cong :premises (@p55 @p88) :args (@t43)) % 0.63/0.81 (step @p90 :rule cong :premises (@p89) :args (@t44)) % 0.63/0.81 (step @p91 :rule trans :premises (@p90 @p85)) % 0.63/0.81 (step @p92 :rule eq_resolve :premises (@p15 @p91)) % 0.63/0.81 (step @p93 :rule instantiate :premises (@p92) :args (@t104)) % 0.63/0.81 (step @p94 :rule cnf_or_pos :args (@t127)) % 0.63/0.81 (step @p95 :rule reordering :premises (@p94) :args ((or @t108 @t126 (not @t127)))) % 0.63/0.81 (step @p96 :rule chain_m_resolution :premises (@p95 @p61 @p93) :args (@t126 @t110 (@list @t95 @t127))) % 0.63/0.81 (step @p97 :rule cnf_and_pos :args (@t126 0)) % 0.63/0.81 (step @p98 :rule reordering :premises (@p97) :args ((or @t125 @t128))) % 0.63/0.81 (step @p99 :rule chain_m_resolution :premises (@p98 @p96) :args (@t125 @t111 @t129)) % 0.63/0.81 (step @p100 :rule cnf_and_pos :args (@t126 1)) % 0.63/0.81 (step @p101 :rule reordering :premises (@p100) :args ((or @t123 @t128))) % 0.63/0.81 (step @p102 :rule chain_m_resolution :premises (@p101 @p96) :args (@t123 @t111 @t129)) % 0.63/0.81 (step @p103 :rule bool-impl-elim :args (@t2 @t130)) % 0.63/0.81 (step @p104 :rule cong :premises (@p103) :args ((forall @t3 (=> @t2 @t130)))) % 0.63/0.81 (step @p105 :rule refl :args (@t46)) % 0.63/0.81 (step @p106 :rule eq-symm :args (@t47 @t6)) % 0.63/0.81 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t48)) % 0.63/0.81 (step @p108 :rule cong :premises (@p55 @p107) :args (@t49)) % 0.63/0.81 (step @p109 :rule cong :premises (@p108) :args (@t50)) % 0.63/0.81 (step @p110 :rule trans :premises (@p109 @p104)) % 0.63/0.81 (step @p111 :rule eq_resolve :premises (@p16 @p110)) % 0.63/0.81 (step @p112 :rule instantiate :premises (@p111) :args (@t131)) % 0.63/0.81 (step @p113 :rule cnf_or_pos :args (@t136)) % 0.63/0.81 (step @p114 :rule reordering :premises (@p113) :args ((or @t135 @t134 (not @t136)))) % 0.63/0.81 (step @p115 :rule chain_m_resolution :premises (@p114 @p3 @p112) :args (@t134 @t110 (@list @t5 @t136))) % 0.63/0.81 (step @p116 :rule cnf_and_pos :args (@t134 0)) % 0.63/0.81 (step @p117 :rule reordering :premises (@p116) :args ((or @t133 (not @t134)))) % 0.63/0.81 (step @p118 :rule chain_m_resolution :premises (@p117 @p115) :args (@t133 @t111 (@list @t134))) % 0.63/0.81 (step @p119 :rule instantiate :premises (@p111) :args (@t104)) % 0.63/0.81 (step @p120 :rule cnf_or_pos :args (@t140)) % 0.63/0.81 (step @p121 :rule reordering :premises (@p120) :args ((or @t108 @t139 (not @t140)))) % 0.63/0.81 (step @p122 :rule chain_m_resolution :premises (@p121 @p61 @p119) :args (@t139 @t110 (@list @t95 @t140))) % 0.63/0.81 (step @p123 :rule cnf_and_pos :args (@t139 0)) % 0.63/0.81 (step @p124 :rule reordering :premises (@p123) :args ((or @t138 (not @t139)))) % 0.63/0.81 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t138 @t111 (@list @t139))) % 0.63/0.81 (step @p126 :rule bool-double-not-elim :args (@t141)) % 0.63/0.81 (step @p127 :rule bool-double-not-elim :args (@t142)) % 0.63/0.81 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or (not @t144) (not @t143)))) % 0.63/0.81 (step @p129 :rule eq-symm :args (@t97 tptp.sz10)) % 0.63/0.81 (step @p130 :rule cong :premises (@p129) :args (@t99)) % 0.63/0.81 (step @p131 :rule eq-symm :args (@t98 tptp.sz10)) % 0.63/0.81 (step @p132 :rule cong :premises (@p131) :args (@t100)) % 0.63/0.81 (step @p133 :rule nary_cong :premises (@p132 @p130) :args (@t101)) % 0.63/0.81 (step @p134 :rule cong :premises (@p133) :args (@t102)) % 0.63/0.81 (step @p135 :rule eq_resolve :premises (@p48 @p134)) % 0.63/0.81 (step @p136 :rule not_and :premises (@p135)) % 0.63/0.81 (step @p137 :rule eq_resolve :premises (@p136 @p128)) % 0.63/0.81 (step @p138 :rule aci_norm :args ((= (or @t148 @t19) (or @t147 @t146 @t145 @t19)))) % 0.63/0.81 (step @p139 :rule refl :args (@t19)) % 0.63/0.81 (step @p140 :rule aci_norm :args ((= (or @t147 (or @t146 @t145)) @t148))) % 0.63/0.81 (step @p141 :rule bool-and-de-morgan :args (@t11 @t20 true)) % 0.63/0.81 (step @p142 :rule refl :args (@t147)) % 0.63/0.81 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t147 (not (and @t11 @t20))))) % 0.63/0.81 (step @p144 :rule bool-and-de-morgan :args (@t2 @t11 (and @t20))) % 0.63/0.81 (step @p145 :rule trans :premises (@p144 @p143)) % 0.63/0.81 (step @p146 :rule trans :premises (@p145 @p140)) % 0.63/0.81 (step @p147 :rule nary_cong :premises (@p146 @p139) :args ((or @t149 @t19))) % 0.63/0.81 (step @p148 :rule trans :premises (@p147 @p138)) % 0.63/0.81 (step @p149 :rule bool-impl-elim :args (@t21 @t19)) % 0.63/0.81 (step @p150 :rule trans :premises (@p149 @p148)) % 0.63/0.81 (step @p151 :rule cong :premises (@p150) :args (@t23)) % 0.63/0.81 (step @p152 :rule eq_resolve :premises (@p7 @p151)) % 0.63/0.81 (step @p153 :rule instantiate :premises (@p152) :args ((@list tptp.sz10 @t96 tptp.xp))) % 0.63/0.81 (step @p154 :rule bool-impl-elim :args (@t2 @t7)) % 0.63/0.81 (step @p155 :rule cong :premises (@p154) :args (@t8)) % 0.63/0.81 (step @p156 :rule eq_resolve :premises (@p4 @p155)) % 0.63/0.81 (step @p157 :rule instantiate :premises (@p156) :args (@t104)) % 0.63/0.81 (step @p158 :rule cnf_or_pos :args (@t151)) % 0.63/0.81 (step @p159 :rule reordering :premises (@p158) :args ((or @t108 @t150 (not @t151)))) % 0.63/0.81 (step @p160 :rule chain_m_resolution :premises (@p159 @p61 @p157) :args (@t150 @t110 (@list @t95 @t151))) % 0.63/0.81 (step @p161 :rule cnf_or_pos :args (@t155)) % 0.63/0.81 (step @p162 :rule reordering :premises (@p161) :args ((or @t135 @t108 @t154 @t153 (not @t155)))) % 0.63/0.81 (step @p163 :rule chain_m_resolution :premises (@p162 @p3 @p61 @p160 @p153) :args (@t153 @t156 (@list @t5 @t95 @t150 @t155))) % 0.63/0.81 (step @p164 :rule instantiate :premises (@p59) :args (@t131)) % 0.63/0.81 (step @p165 :rule cnf_or_pos :args (@t160)) % 0.63/0.81 (step @p166 :rule 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:rule scope :premises (@p496)) % 0.63/0.82 (step-pop @p498 :rule scope :premises (@p497)) % 0.63/0.82 (step-pop @p499 :rule scope :premises (@p498)) % 0.63/0.82 (step-pop @p500 :rule scope :premises (@p499)) % 0.63/0.82 (step-pop @p501 :rule scope :premises (@p500)) % 0.63/0.82 (step-pop @p502 :rule scope :premises (@p501)) % 0.63/0.82 (step-pop @p503 :rule scope :premises (@p502)) % 0.63/0.82 (step-pop @p504 :rule scope :premises (@p503)) % 0.63/0.82 (step-pop @p505 :rule scope :premises (@p504)) % 0.63/0.82 (step-pop @p506 :rule scope :premises (@p505)) % 0.63/0.82 (step-pop @p507 :rule scope :premises (@p506)) % 0.63/0.82 (step-pop @p508 :rule scope :premises (@p507)) % 0.63/0.82 (step @p405 :rule process_scope :premises (@p508) :args (@t211)) % 0.63/0.82 (step @p421 :rule and_intro :premises (@p67 @p242 @p99 @p83 @p125 @p118 @p464 @p260 @p253 @p344 @p102 @p234 @p211 @p285 @p227)) % 0.63/0.82 (step @p422 :rule modus_ponens :premises (@p421 @p405)) % 0.63/0.82 (step-pop @p509 :rule scope :premises (@p422)) % 0.63/0.82 (step-pop @p510 :rule scope :premises (@p509)) % 0.63/0.82 (step-pop @p511 :rule scope :premises (@p510)) % 0.63/0.82 (step-pop @p512 :rule scope :premises (@p511)) % 0.63/0.82 (step-pop @p513 :rule scope :premises (@p512)) % 0.63/0.82 (step-pop @p514 :rule scope :premises (@p513)) % 0.63/0.82 (step-pop @p515 :rule scope :premises (@p514)) % 0.63/0.82 (step-pop @p516 :rule scope :premises (@p515)) % 0.63/0.82 (step-pop @p517 :rule scope :premises (@p516)) % 0.63/0.82 (step-pop @p518 :rule scope :premises (@p517)) % 0.63/0.82 (step-pop @p519 :rule scope :premises (@p518)) % 0.63/0.82 (step-pop @p520 :rule scope :premises (@p519)) % 0.63/0.82 (step-pop @p521 :rule scope :premises (@p520)) % 0.63/0.82 (step-pop @p522 :rule scope :premises (@p521)) % 0.63/0.82 (step-pop @p523 :rule scope :premises (@p522)) % 0.63/0.82 (step @p423 :rule process_scope :premises (@p523) :args (@t211)) % 0.63/0.82 (step @p439 :rule implies_elim :premises (@p423)) % 0.63/0.82 (step @p440 :rule cnf_and_neg :args (@t224)) % 0.63/0.82 (step @p441 :rule resolution :premises (@p440 @p439) :args (true @t224)) % 0.63/0.82 (step @p442 :rule reordering :premises (@p441) :args ((or @t144 (not @t106) (not @t116) (not @t125) (not @t123) (not @t133) (not @t138) (not @t163) (not @t188) (not @t169) (not @t175) (not @t193) (not @t180) @t211 (not @t220) (not @t201)))) % 0.63/0.82 (step @p443 false :rule chain_m_resolution :premises (@p442 @p344 @p323 @p285 @p260 @p253 @p242 @p234 @p227 @p211 @p204 @p125 @p118 @p102 @p99 @p83 @p67) :args (false (@list false true false false false false false false false false false false false false false false) (@list @t220 @t211 @t201 @t193 @t188 @t180 @t175 @t169 @t163 @t142 @t138 @t133 @t123 @t125 @t116 @t106))) % 0.63/0.82 ) % 0.63/0.82 % SZS output end Proof % 0.63/0.82 % cvc5 exiting %------------------------------------------------------------------------------