%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM456+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 : n004.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 08:39:28 AM UTC 2026 % Result : Theorem 0.51s 0.74s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM456+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 % 0.16/0.34 % Computer : n004.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 11:21:22 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.74 % SZS status Theorem % 0.51/0.74 % SZS output start Proof % 0.51/0.74 ( % 0.51/0.74 (declare-sort $$unsorted 0) % 0.51/0.74 (declare-const tptp.cS2076 $$unsorted) % 0.51/0.74 (declare-const tptp.cS2200 $$unsorted) % 0.51/0.74 (declare-const tptp.isClosed0 (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.isOpen0 (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.stldt0 (-> $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.sdtslmnbsdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.cS1395 $$unsorted) % 0.51/0.74 (declare-const tptp.xp $$unsorted) % 0.51/0.74 (declare-const tptp.sdtbsmnsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.xS $$unsorted) % 0.51/0.74 (declare-const tptp.szAzrzSzezqlpdtcmdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.sbsmnsldt0 (-> $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.cS2043 $$unsorted) % 0.51/0.74 (declare-const tptp.sz10 $$unsorted) % 0.51/0.74 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.sz00 $$unsorted) % 0.51/0.74 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.74 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.74 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.51/0.74 (define @t1 () (@var "W0" $$unsorted)) % 0.51/0.74 (define @t2 () (tptp.aInteger0 @t1)) % 0.51/0.74 (define @t3 () (@list @t1)) % 0.51/0.74 (define @t4 () (tptp.smndt0 @t1)) % 0.51/0.74 (define @t5 () (@var "W1" $$unsorted)) % 0.51/0.74 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.51/0.74 (define @t7 () (tptp.aInteger0 @t5)) % 0.51/0.74 (define @t8 () (and @t2 @t7)) % 0.51/0.74 (define @t9 () (@list @t1 @t5)) % 0.51/0.74 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.51/0.74 (define @t11 () (@var "W2" $$unsorted)) % 0.51/0.74 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.51/0.74 (define @t13 () (tptp.aInteger0 @t11)) % 0.51/0.74 (define @t14 () (and @t2 @t7 @t13)) % 0.51/0.74 (define @t15 () (@list @t1 @t5 @t11)) % 0.51/0.74 (define @t16 () (tptp.sdtasdt0 @t5 @t11)) % 0.51/0.74 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.51/0.74 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.51/0.74 (define @t19 () (= @t5 tptp.sz00)) % 0.51/0.74 (define @t20 () (= @t1 tptp.sz00)) % 0.51/0.74 (define @t21 () (@list @t11)) % 0.51/0.74 (define @t22 () (not @t19)) % 0.51/0.74 (define @t23 () (tptp.aDivisorOf0 @t5 @t1)) % 0.51/0.74 (define @t24 () (@list @t5)) % 0.51/0.74 (define @t25 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11)) % 0.51/0.74 (define @t26 () (not (= @t11 tptp.sz00))) % 0.51/0.74 (define @t27 () (and @t2 @t7 @t13 @t26)) % 0.51/0.74 (define @t28 () (and @t2 @t7 @t22)) % 0.51/0.74 (define @t29 () (@var "W3" $$unsorted)) % 0.51/0.74 (define @t30 () (tptp.aInteger0 @t29)) % 0.51/0.74 (define @t31 () (@list @t1 @t5 @t11 @t29)) % 0.51/0.74 (define @t32 () (= @t1 @t18)) % 0.51/0.74 (define @t33 () (= @t1 tptp.sz10)) % 0.51/0.74 (define @t34 () (tptp.isPrime0 @t5)) % 0.51/0.74 (define @t35 () (tptp.aSet0 @t1)) % 0.51/0.74 (define @t36 () (tptp.aElementOf0 @t5 @t1)) % 0.51/0.74 (define @t37 () (tptp.aElementOf0 @t11 @t1)) % 0.51/0.74 (define @t38 () (tptp.aElementOf0 @t11 @t5)) % 0.51/0.74 (define @t39 () (tptp.aSet0 @t5)) % 0.51/0.74 (define @t40 () (tptp.isFinite0 @t1)) % 0.51/0.74 (define @t41 () (tptp.aElementOf0 @t29 @t5)) % 0.51/0.74 (define @t42 () (tptp.aElementOf0 @t29 @t1)) % 0.51/0.74 (define @t43 () (tptp.aElementOf0 @t29 @t11)) % 0.51/0.74 (define @t44 () (@list @t29)) % 0.51/0.74 (define @t45 () (tptp.aSet0 @t11)) % 0.51/0.74 (define @t46 () (tptp.sdtbsmnsldt0 @t1 @t5)) % 0.51/0.74 (define @t47 () (tptp.aSubsetOf0 @t5 tptp.cS1395)) % 0.51/0.74 (define @t48 () (tptp.aSubsetOf0 @t1 tptp.cS1395)) % 0.51/0.74 (define @t49 () (and @t48 @t47)) % 0.51/0.74 (define @t50 () (tptp.sdtslmnbsdt0 @t1 @t5)) % 0.51/0.74 (define @t51 () (tptp.sbsmnsldt0 @t1)) % 0.51/0.74 (define @t52 () (tptp.stldt0 @t1)) % 0.51/0.74 (define @t53 () (tptp.szAzrzSzezqlpdtcmdtrp0 @t1 @t5)) % 0.51/0.74 (define @t54 () (tptp.isOpen0 @t1)) % 0.51/0.74 (define @t55 () (tptp.isClosed0 @t1)) % 0.51/0.74 (define @t56 () (tptp.isOpen0 @t5)) % 0.51/0.74 (define @t57 () (tptp.isClosed0 @t5)) % 0.51/0.74 (define @t58 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.51/0.74 (define @t59 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 @t5)) % 0.51/0.74 (define @t60 () (= @t59 @t1)) % 0.51/0.74 (define @t61 () (tptp.aElementOf0 @t11 @t59)) % 0.51/0.74 (define @t62 () (tptp.sdteqdtlpzmzozddtrp0 @t11 tptp.sz00 @t5)) % 0.51/0.74 (define @t63 () (tptp.sdtpldt0 @t11 (tptp.smndt0 tptp.sz00))) % 0.51/0.74 (define @t64 () (tptp.aDivisorOf0 @t5 @t63)) % 0.51/0.74 (define @t65 () (tptp.sdtasdt0 @t5 @t29)) % 0.51/0.74 (define @t66 () (exists @t44 (and @t30 (= @t65 @t63)))) % 0.51/0.74 (define @t67 () (forall @t21 (and (=> @t61 (and @t13 @t66 @t64 @t62)) (=> (and @t13 (or @t66 @t64 @t62)) @t61)))) % 0.51/0.74 (define @t68 () (tptp.aSet0 @t59)) % 0.51/0.74 (define @t69 () (tptp.sbsmnsldt0 tptp.xS)) % 0.51/0.74 (define @t70 () (tptp.stldt0 @t69)) % 0.51/0.74 (define @t71 () (tptp.aElementOf0 @t1 @t70)) % 0.51/0.74 (define @t72 () (forall @t3 (= @t71 (or @t33 @t32)))) % 0.51/0.74 (define @t73 () (tptp.aElementOf0 @t1 @t69)) % 0.51/0.74 (define @t74 () (forall @t3 (= @t71 (and @t2 (not @t73))))) % 0.51/0.74 (define @t75 () (forall @t3 (= @t73 (and @t2 (exists @t24 (and (tptp.aElementOf0 @t5 tptp.xS) (tptp.aElementOf0 @t1 @t5))))))) % 0.51/0.74 (define @t76 () (tptp.aSet0 @t69)) % 0.51/0.74 (define @t77 () (tptp.aElementOf0 @t11 @t53)) % 0.51/0.74 (define @t78 () (tptp.sdteqdtlpzmzozddtrp0 @t11 @t1 @t5)) % 0.51/0.74 (define @t79 () (tptp.sdtpldt0 @t11 @t4)) % 0.51/0.74 (define @t80 () (tptp.aDivisorOf0 @t5 @t79)) % 0.51/0.74 (define @t81 () (exists @t44 (and @t30 (= @t65 @t79)))) % 0.51/0.74 (define @t82 () (forall @t3 (=> @t71 (exists @t24 (and @t7 @t22 (tptp.aSet0 @t53) (forall @t21 (and (=> @t77 (and @t13 @t81 @t80 @t78)) (=> (and @t13 (or @t81 @t80 @t78)) @t77))) (forall @t21 (=> @t77 (tptp.aElementOf0 @t11 @t70))) (tptp.aSubsetOf0 @t53 @t70)))))) % 0.51/0.74 (define @t83 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) % 0.51/0.74 (define @t84 () (tptp.aElementOf0 @t1 @t83)) % 0.51/0.74 (define @t85 () (forall @t3 (=> @t84 @t71))) % 0.51/0.74 (define @t86 () (tptp.sdteqdtlpzmzozddtrp0 @t1 tptp.sz10 tptp.xp)) % 0.51/0.74 (define @t87 () (tptp.sdtpldt0 @t1 @t18)) % 0.51/0.74 (define @t88 () (tptp.aDivisorOf0 tptp.xp @t87)) % 0.51/0.74 (define @t89 () (tptp.sdtasdt0 tptp.xp @t5)) % 0.51/0.74 (define @t90 () (and @t7 (= @t89 @t87))) % 0.51/0.74 (define @t91 () (exists @t24 @t90)) % 0.51/0.74 (define @t92 () (tptp.aElementOf0 @t1 tptp.cS2200)) % 0.51/0.74 (define @t93 () (or @t33 @t32 @t92)) % 0.51/0.74 (define @t94 () (not @t93)) % 0.51/0.74 (define @t95 () (and @t2 @t91 @t88 @t86 @t84 @t94)) % 0.51/0.74 (define @t96 () (exists @t3 @t95)) % 0.51/0.74 (define @t97 () (@var "BOUND_VARIABLE_8769" $$unsorted)) % 0.51/0.74 (define @t98 () (not (= @t87 (tptp.sdtasdt0 tptp.xp @t97)))) % 0.51/0.74 (define @t99 () (not (tptp.aInteger0 @t97))) % 0.51/0.74 (define @t100 () (not @t84)) % 0.51/0.74 (define @t101 () (not @t86)) % 0.51/0.74 (define @t102 () (not @t88)) % 0.51/0.74 (define @t103 () (not @t2)) % 0.51/0.74 (define @t104 () (or @t103 @t102 @t101 @t100 @t33 @t32 @t92 @t99 @t98)) % 0.51/0.74 (define @t105 () (@list @t1 @t97)) % 0.51/0.74 (define @t106 () (forall @t105 @t104)) % 0.51/0.74 (define @t107 () (@quantifiers_skolemize @t106 0)) % 0.51/0.74 (define @t108 () (@list @t107)) % 0.51/0.74 (define @t109 () (or @t99 @t98)) % 0.51/0.74 (define @t110 () (or @t103 @t109 @t102 @t101 @t100 @t33 @t32 @t92)) % 0.51/0.74 (define @t111 () (forall @t105 @t110)) % 0.51/0.74 (define @t112 () (@list @t97)) % 0.51/0.74 (define @t113 () (forall @t112 @t110)) % 0.51/0.74 (define @t114 () (forall @t112 @t109)) % 0.51/0.74 (define @t115 () (or @t103 @t114 @t102 @t101 @t100 @t33 @t32 @t92)) % 0.51/0.74 (define @t116 () (= @t87 @t89)) % 0.51/0.74 (define @t117 () (forall @t24 (or (not @t7) (not @t116)))) % 0.51/0.74 (define @t118 () (or @t103 @t117 @t102 @t101 @t100 @t33 @t32 @t92)) % 0.51/0.74 (define @t119 () (not @t94)) % 0.51/0.74 (define @t120 () (not @t117)) % 0.51/0.74 (define @t121 () (not @t120)) % 0.51/0.74 (define @t122 () (or @t103 @t121 @t102 @t101 @t100 @t119)) % 0.51/0.74 (define @t123 () (and @t2 @t120 @t88 @t86 @t84 @t94)) % 0.51/0.74 (define @t124 () (forall @t3 (not @t123))) % 0.51/0.74 (define @t125 () (not @t124)) % 0.51/0.74 (define @t126 () (and @t7 @t116)) % 0.51/0.74 (define @t127 () (forall @t24 (not @t126))) % 0.51/0.74 (define @t128 () (not @t127)) % 0.51/0.74 (define @t129 () (@quantifiers_skolemize @t106 1)) % 0.51/0.74 (define @t130 () (tptp.sdtpldt0 @t107 @t18)) % 0.51/0.74 (define @t131 () (not (= @t130 (tptp.sdtasdt0 tptp.xp @t129)))) % 0.51/0.74 (define @t132 () (not (tptp.aInteger0 @t129))) % 0.51/0.74 (define @t133 () (tptp.aElementOf0 @t107 tptp.cS2200)) % 0.51/0.74 (define @t134 () (= @t18 @t107)) % 0.51/0.74 (define @t135 () (= tptp.sz10 @t107)) % 0.51/0.74 (define @t136 () (tptp.aElementOf0 @t107 @t83)) % 0.51/0.74 (define @t137 () (not @t136)) % 0.51/0.74 (define @t138 () (not (tptp.sdteqdtlpzmzozddtrp0 @t107 tptp.sz10 tptp.xp))) % 0.51/0.74 (define @t139 () (not (tptp.aDivisorOf0 tptp.xp @t130))) % 0.51/0.74 (define @t140 () (not (tptp.aInteger0 @t107))) % 0.51/0.74 (define @t141 () (or @t140 @t139 @t138 @t137 @t135 @t134 @t133 @t132 @t131)) % 0.51/0.74 (define @t142 () (not @t141)) % 0.51/0.74 (define @t143 () (not @t106)) % 0.51/0.74 (define @t144 () (= @t107 @t18)) % 0.51/0.74 (define @t145 () (= @t107 tptp.sz10)) % 0.51/0.74 (define @t146 () (or @t140 @t139 @t138 @t137 @t145 @t144 @t133 @t132 @t131)) % 0.51/0.74 (define @t147 () (not @t146)) % 0.51/0.74 (define @t148 () (@list true)) % 0.51/0.74 (define @t149 () (@list @t141)) % 0.51/0.74 (define @t150 () (tptp.aElementOf0 @t107 @t70)) % 0.51/0.74 (define @t151 () (or @t137 @t150)) % 0.51/0.74 (define @t152 () (or @t135 @t134)) % 0.51/0.74 (define @t153 () (not @t152)) % 0.51/0.74 (define @t154 () (or @t145 @t144)) % 0.51/0.74 (define @t155 () (= @t150 @t154)) % 0.51/0.74 (define @t156 () (= @t150 @t152)) % 0.51/0.74 (assume @p1 (forall @t3 (=> @t2 true))) % 0.51/0.74 (assume @p2 (tptp.aInteger0 tptp.sz00)) % 0.51/0.74 (assume @p3 (tptp.aInteger0 tptp.sz10)) % 0.51/0.74 (assume @p4 (forall @t3 (=> @t2 (tptp.aInteger0 @t4)))) % 0.51/0.74 (assume @p5 (forall @t9 (=> @t8 (tptp.aInteger0 @t6)))) % 0.51/0.74 (assume @p6 (forall @t9 (=> @t8 (tptp.aInteger0 @t10)))) % 0.51/0.74 (assume @p7 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t1 @t12) (tptp.sdtpldt0 @t6 @t11))))) % 0.51/0.74 (assume @p8 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.51/0.74 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.51/0.74 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.51/0.74 (assume @p11 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t1 @t16) (tptp.sdtasdt0 @t10 @t11))))) % 0.51/0.74 (assume @p12 (forall @t9 (=> @t8 (= @t10 (tptp.sdtasdt0 @t5 @t1))))) % 0.51/0.74 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.51/0.74 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t6 @t11) (tptp.sdtpldt0 @t17 @t16)))))) % 0.51/0.74 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.51/0.74 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.51/0.74 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.51/0.74 (assume @p18 (forall @t3 (=> @t2 (forall @t24 (= @t23 (and @t7 @t22 (exists @t21 (and @t13 (= @t16 @t1))))))))) % 0.51/0.74 (assume @p19 (forall @t15 (=> @t27 (= @t25 (tptp.aDivisorOf0 @t11 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5))))))) % 0.51/0.74 (assume @p20 (forall @t9 (=> @t28 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t5)))) % 0.51/0.74 (assume @p21 (forall @t15 (=> @t27 (=> @t25 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t1 @t11))))) % 0.51/0.74 (assume @p22 (forall @t31 (=> (and @t2 @t7 @t13 @t26 @t30) (=> (and @t25 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t29 @t11)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t29 @t11))))) % 0.51/0.74 (assume @p23 (forall @t31 (=> (and @t2 @t7 @t13 @t26 @t30 (not (= @t29 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 (tptp.sdtasdt0 @t11 @t29)) (and @t25 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t29)))))) % 0.51/0.74 (assume @p24 (forall @t3 (=> (and @t2 (not @t20)) (=> (tptp.isPrime0 @t1) true)))) % 0.51/0.74 (assume @p25 (forall @t3 (=> @t2 (= (exists @t24 (and @t23 @t34)) (and (not @t33) (not @t32)))))) % 0.51/0.74 (assume @p26 (forall @t3 (=> @t35 true))) % 0.51/0.74 (assume @p27 (forall @t3 (=> @t35 (forall @t24 (=> @t36 true))))) % 0.51/0.74 (assume @p28 (forall @t3 (=> @t35 (forall @t24 (= (tptp.aSubsetOf0 @t5 @t1) (and @t39 (forall @t21 (=> @t38 @t37)))))))) % 0.51/0.74 (assume @p29 (forall @t3 (=> @t35 (=> @t40 true)))) % 0.51/0.74 (assume @p30 (forall @t9 (=> @t49 (forall @t21 (= (= @t11 @t46) (and @t45 (forall @t44 (= @t43 (and @t30 (or @t42 @t41)))))))))) % 0.51/0.74 (assume @p31 (forall @t9 (=> @t49 (forall @t21 (= (= @t11 @t50) (and @t45 (forall @t44 (= @t43 (and @t30 @t42 @t41))))))))) % 0.51/0.74 (assume @p32 (forall @t3 (=> (and @t35 (forall @t24 (=> @t36 @t47))) (forall @t24 (= (= @t5 @t51) (and @t39 (forall @t21 (= @t38 (and @t13 (exists @t44 (and @t42 (tptp.aElementOf0 @t11 @t29)))))))))))) % 0.51/0.74 (assume @p33 (forall @t3 (=> @t48 (forall @t24 (= (= @t5 @t52) (and @t39 (forall @t21 (= @t38 (and @t13 (not @t37)))))))))) % 0.51/0.74 (assume @p34 (forall @t9 (=> @t28 (forall @t21 (= (= @t11 @t53) (and @t45 (forall @t44 (= @t43 (and @t30 (tptp.sdteqdtlpzmzozddtrp0 @t29 @t1 @t5)))))))))) % 0.51/0.74 (assume @p35 (forall @t3 (=> @t48 (= @t54 (forall @t24 (=> @t36 (exists @t21 (and @t13 @t26 (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 @t5 @t11) @t1))))))))) % 0.51/0.74 (assume @p36 (forall @t3 (=> @t48 (= @t55 (tptp.isOpen0 @t52))))) % 0.51/0.74 (assume @p37 (forall @t3 (=> (and @t35 (forall @t24 (=> @t36 (and @t47 @t56)))) (tptp.isOpen0 @t51)))) % 0.51/0.74 (assume @p38 (forall @t9 (=> (and @t48 @t47 @t54 @t56) (tptp.isOpen0 @t50)))) % 0.51/0.74 (assume @p39 (forall @t9 (=> (and @t48 @t47 @t55 @t57) (tptp.isClosed0 @t46)))) % 0.51/0.74 (assume @p40 (forall @t3 (=> (and @t35 @t40 (forall @t24 (=> @t36 (and @t47 @t57)))) (tptp.isClosed0 @t51)))) % 0.51/0.74 (assume @p41 (forall @t9 (=> @t28 (and (tptp.aSubsetOf0 @t53 tptp.cS1395) (tptp.isClosed0 @t53))))) % 0.51/0.74 (assume @p42 (and (tptp.aSet0 tptp.xS) (forall @t3 (and (=> @t58 (exists @t24 (and @t7 @t22 @t34 @t68 @t67 @t60))) (=> (exists @t24 (and @t7 @t22 @t34 (=> (and @t68 @t67) @t60))) @t58))) (= tptp.xS tptp.cS2043))) % 0.51/0.74 (assume @p43 (and @t76 @t75 (tptp.aSet0 @t70) @t74 @t72 (= @t70 tptp.cS2076))) % 0.51/0.74 (assume @p44 (tptp.isFinite0 tptp.xS)) % 0.51/0.74 (assume @p45 (and @t76 @t75 @t74 @t82 (tptp.isOpen0 @t70) (tptp.isClosed0 @t69) @t76 @t75 @t74 @t82)) % 0.51/0.74 (assume @p46 (and (tptp.aInteger0 tptp.xp) (not (= tptp.xp tptp.sz00)) (tptp.aSet0 @t83) (forall @t3 (and (=> @t84 (and @t2 @t91 @t88 @t86)) (=> (and @t2 (or @t91 @t88 @t86)) @t84))) @t76 @t75 @t74 @t85 (tptp.aSubsetOf0 @t83 @t70))) % 0.51/0.74 (assume @p47 @t96) % 0.51/0.74 (assume @p48 (not false)) % 0.51/0.74 (assume @p49 true) % 0.51/0.74 (step @p50 :rule bool-impl-elim :args (@t84 @t71)) % 0.51/0.74 (step @p51 :rule cong :premises (@p50) :args (@t85)) % 0.51/0.74 (step @p52 :rule and_elim :premises (@p46) :args (7)) % 0.51/0.74 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 0.51/0.74 (step @p54 :rule instantiate :premises (@p53) :args (@t108)) % 0.51/0.74 (step @p55 :rule aci_norm :args ((= @t110 @t104))) % 0.51/0.74 (step @p56 :rule cong :premises (@p55) :args (@t111)) % 0.51/0.74 (step @p57 :rule quant-merge-prenex :args ((= (forall @t3 @t113) @t111))) % 0.51/0.74 (step @p58 :rule refl :args (@t92)) % 0.51/0.74 (step @p59 :rule refl :args (@t32)) % 0.51/0.74 (step @p60 :rule refl :args (@t33)) % 0.51/0.74 (step @p61 :rule refl :args (@t100)) % 0.51/0.74 (step @p62 :rule refl :args (@t101)) % 0.51/0.74 (step @p63 :rule refl :args (@t102)) % 0.51/0.74 (step @p64 :rule alpha_equiv :args (@t114 (@list @t97) (@list @t5))) % 0.51/0.74 (step @p65 :rule refl :args (@t103)) % 0.51/0.74 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63 @p62 @p61 @p60 @p59 @p58) :args (@t115)) % 0.51/0.74 (step @p67 :rule quant-miniscope-or :args ((= @t113 @t115))) % 0.51/0.74 (step @p68 :rule trans :premises (@p67 @p66)) % 0.51/0.74 (step @p69 :rule symm :premises (@p68)) % 0.51/0.74 (step @p70 :rule cong :premises (@p69) :args ((forall @t3 @t118))) % 0.51/0.74 (step @p71 :rule trans :premises (@p70 @p57)) % 0.51/0.74 (step @p72 :rule trans :premises (@p71 @p56)) % 0.51/0.74 (step @p73 :rule aci_norm :args ((= (or @t103 @t117 @t102 @t101 @t100 @t93) @t118))) % 0.51/0.74 (step @p74 :rule bool-double-not-elim :args (@t93)) % 0.51/0.74 (step @p75 :rule bool-double-not-elim :args (@t117)) % 0.51/0.74 (step @p76 :rule nary_cong :premises (@p65 @p75 @p63 @p62 @p61 @p74) :args (@t122)) % 0.51/0.74 (step @p77 :rule aci_norm :args ((= (or @t103 (or @t121 (or @t102 (or @t101 (or @t100 @t119))))) @t122))) % 0.51/0.74 (step @p78 :rule trans :premises (@p77 @p76)) % 0.51/0.74 (step @p79 :rule bool-and-de-morgan :args (@t84 @t94 true)) % 0.51/0.74 (step @p80 :rule nary_cong :premises (@p62 @p79) :args ((or @t101 (not (and @t84 @t94))))) % 0.51/0.74 (step @p81 :rule bool-and-de-morgan :args (@t86 @t84 (and @t94))) % 0.51/0.74 (step @p82 :rule trans :premises (@p81 @p80)) % 0.51/0.74 (step @p83 :rule nary_cong :premises (@p63 @p82) :args ((or @t102 (not (and @t86 @t84 @t94))))) % 0.51/0.74 (step @p84 :rule bool-and-de-morgan :args (@t88 @t86 (and @t84 @t94))) % 0.51/0.74 (step @p85 :rule trans :premises (@p84 @p83)) % 0.51/0.74 (step @p86 :rule refl :args (@t121)) % 0.51/0.74 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t121 (not (and @t88 @t86 @t84 @t94))))) % 0.51/0.74 (step @p88 :rule bool-and-de-morgan :args (@t120 @t88 (and @t86 @t84 @t94))) % 0.51/0.74 (step @p89 :rule trans :premises (@p88 @p87)) % 0.51/0.74 (step @p90 :rule nary_cong :premises (@p65 @p89) :args ((or @t103 (not (and @t120 @t88 @t86 @t84 @t94))))) % 0.51/0.74 (step @p91 :rule bool-and-de-morgan :args (@t2 @t120 (and @t88 @t86 @t84 @t94))) % 0.51/0.74 (step @p92 :rule trans :premises (@p91 @p90)) % 0.51/0.74 (step @p93 :rule trans :premises (@p92 @p78)) % 0.51/0.74 (step @p94 :rule trans :premises (@p93 @p73)) % 0.51/0.74 (step @p95 :rule cong :premises (@p94) :args (@t124)) % 0.51/0.74 (step @p96 :rule trans :premises (@p95 @p72)) % 0.51/0.74 (step @p97 :rule cong :premises (@p96) :args (@t125)) % 0.51/0.74 (step @p98 :rule exists-elim :args ((= (exists @t3 @t123) @t125))) % 0.51/0.74 (step @p99 :rule trans :premises (@p98 @p97)) % 0.51/0.74 (step @p100 :rule refl :args (@t94)) % 0.51/0.74 (step @p101 :rule refl :args (@t84)) % 0.51/0.74 (step @p102 :rule refl :args (@t86)) % 0.51/0.74 (step @p103 :rule refl :args (@t88)) % 0.51/0.74 (step @p104 :rule bool-and-de-morgan :args (@t7 @t116 true)) % 0.51/0.74 (step @p105 :rule cong :premises (@p104) :args (@t127)) % 0.51/0.74 (step @p106 :rule cong :premises (@p105) :args (@t128)) % 0.51/0.74 (step @p107 :rule exists-elim :args ((= (exists @t24 @t126) @t128))) % 0.51/0.74 (step @p108 :rule trans :premises (@p107 @p106)) % 0.51/0.74 (step @p109 :rule eq-symm :args (@t89 @t87)) % 0.51/0.74 (step @p110 :rule refl :args (@t7)) % 0.51/0.74 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t90)) % 0.51/0.74 (step @p112 :rule cong :premises (@p111) :args (@t91)) % 0.51/0.74 (step @p113 :rule trans :premises (@p112 @p108)) % 0.51/0.74 (step @p114 :rule refl :args (@t2)) % 0.51/0.74 (step @p115 :rule nary_cong :premises (@p114 @p113 @p103 @p102 @p101 @p100) :args (@t95)) % 0.51/0.74 (step @p116 :rule cong :premises (@p115) :args (@t96)) % 0.51/0.74 (step @p117 :rule trans :premises (@p116 @p99)) % 0.51/0.74 (step @p118 :rule eq_resolve :premises (@p47 @p117)) % 0.51/0.74 (step @p119 :rule refl :args (@t142)) % 0.51/0.74 (step @p120 :rule bool-double-not-elim :args (@t106)) % 0.51/0.74 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or (not @t143) @t142))) % 0.51/0.74 (step @p122 :rule refl :args (@t131)) % 0.51/0.74 (step @p123 :rule refl :args (@t132)) % 0.51/0.74 (step @p124 :rule refl :args (@t133)) % 0.51/0.74 (step @p125 :rule eq-symm :args (@t107 @t18)) % 0.51/0.74 (step @p126 :rule eq-symm :args (@t107 tptp.sz10)) % 0.51/0.74 (step @p127 :rule refl :args (@t137)) % 0.51/0.74 (step @p128 :rule refl :args (@t138)) % 0.51/0.74 (step @p129 :rule refl :args (@t139)) % 0.51/0.74 (step @p130 :rule refl :args (@t140)) % 0.51/0.74 (step @p131 :rule nary_cong :premises (@p130 @p129 @p128 @p127 @p126 @p125 @p124 @p123 @p122) :args (@t146)) % 0.51/0.74 (step @p132 :rule cong :premises (@p131) :args (@t147)) % 0.51/0.74 (step @p133 :rule refl :args (@t143)) % 0.51/0.74 (step @p134 :rule cong :premises (@p133 @p132) :args ((=> @t143 @t147))) % 0.51/0.74 (assume-push @p176 @t143) % 0.51/0.74 (step @p136 :rule skolemize :premises (@p118)) % 0.51/0.74 (step-pop @p177 :rule scope :premises (@p136)) % 0.51/0.74 (step @p137 :rule process_scope :premises (@p177) :args (@t147)) % 0.51/0.74 (step @p139 :rule eq_resolve :premises (@p137 @p134)) % 0.51/0.74 (step @p140 :rule implies_elim :premises (@p139)) % 0.51/0.74 (step @p141 :rule eq_resolve :premises (@p140 @p121)) % 0.51/0.74 (step @p142 :rule chain_m_resolution :premises (@p141 @p118) :args (@t142 @t148 (@list @t106))) % 0.51/0.74 (step @p143 :rule bool-double-not-elim :args (@t136)) % 0.51/0.74 (step @p144 :rule refl :args (@t141)) % 0.51/0.74 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((or @t141 (not @t137)))) % 0.51/0.74 (step @p146 :rule cnf_or_neg :args (@t141 3)) % 0.51/0.74 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 0.51/0.74 (step @p148 :rule reordering :premises (@p147) :args ((or @t136 @t141))) % 0.51/0.74 (step @p149 :rule chain_m_resolution :premises (@p148 @p142) :args (@t136 @t148 @t149)) % 0.51/0.74 (step @p150 :rule cnf_or_pos :args (@t151)) % 0.51/0.74 (step @p151 :rule reordering :premises (@p150) :args ((or @t137 @t150 (not @t151)))) % 0.51/0.74 (step @p152 :rule chain_m_resolution :premises (@p151 @p149 @p54) :args (@t150 (@list false false) (@list @t136 @t151))) % 0.51/0.74 (step @p153 :rule cnf_or_neg :args (@t141 5)) % 0.51/0.74 (step @p154 :rule chain_m_resolution :premises (@p153 @p142) :args ((not @t134) @t148 @t149)) % 0.51/0.74 (step @p155 :rule cnf_or_neg :args (@t141 4)) % 0.51/0.74 (step @p156 :rule chain_m_resolution :premises (@p155 @p142) :args ((not @t135) @t148 @t149)) % 0.51/0.74 (step @p157 :rule cnf_or_pos :args (@t152)) % 0.51/0.74 (step @p158 :rule reordering :premises (@p157) :args ((or @t135 @t134 @t153))) % 0.51/0.74 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p154) :args (@t153 (@list true true) (@list @t135 @t134))) % 0.51/0.74 (step @p160 :rule and_elim :premises (@p43) :args (4)) % 0.51/0.74 (step @p161 :rule nary_cong :premises (@p126 @p125) :args (@t154)) % 0.51/0.74 (step @p162 :rule refl :args (@t150)) % 0.51/0.74 (step @p163 :rule cong :premises (@p162 @p161) :args (@t155)) % 0.51/0.74 (step @p164 :rule refl :args (@t72)) % 0.51/0.74 (step @p165 :rule cong :premises (@p164 @p163) :args ((=> @t72 @t155))) % 0.51/0.74 (assume-push @p178 @t72) % 0.51/0.74 (step @p167 :rule instantiate :premises (@p160) :args (@t108)) % 0.51/0.74 (step-pop @p179 :rule scope :premises (@p167)) % 0.51/0.74 (step @p168 :rule process_scope :premises (@p179) :args (@t155)) % 0.51/0.74 (step @p170 :rule eq_resolve :premises (@p168 @p165)) % 0.51/0.74 (step @p171 :rule implies_elim :premises (@p170)) % 0.51/0.74 (step @p172 :rule chain_m_resolution :premises (@p171 @p160) :args (@t156 (@list false) (@list @t72))) % 0.51/0.74 (step @p173 :rule cnf_equiv_pos1 :args (@t156)) % 0.51/0.74 (step @p174 :rule reordering :premises (@p173) :args ((or (not @t150) @t152 (not @t156)))) % 0.51/0.74 (step @p175 false :rule chain_m_resolution :premises (@p174 @p172 @p159 @p152) :args (false (@list false true false) (@list @t156 @t152 @t150))) % 0.51/0.74 ) % 0.51/0.74 % SZS output end Proof % 0.51/0.74 % cvc5 exiting %------------------------------------------------------------------------------