%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM455+6 : 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 : n021.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 0.77s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM455+6 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n021.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 11:22:35 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.77 % SZS status Theorem % 0.51/0.77 % SZS output start Proof % 0.51/0.77 ( % 0.51/0.77 (declare-sort $$unsorted 0) % 0.51/0.77 (declare-const tptp.cS2076 $$unsorted) % 0.51/0.77 (declare-const tptp.cS2200 $$unsorted) % 0.51/0.77 (declare-const tptp.isClosed0 (-> $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.isOpen0 (-> $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.stldt0 (-> $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.sdtslmnbsdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.cS1395 $$unsorted) % 0.51/0.77 (declare-const tptp.xp $$unsorted) % 0.51/0.77 (declare-const tptp.sdtbsmnsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.xS $$unsorted) % 0.51/0.77 (declare-const tptp.szAzrzSzezqlpdtcmdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.sbsmnsldt0 (-> $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.cS2043 $$unsorted) % 0.51/0.77 (declare-const tptp.sz10 $$unsorted) % 0.51/0.77 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.sz00 $$unsorted) % 0.51/0.77 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.77 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.77 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.51/0.77 (define @t1 () (@var "W0" $$unsorted)) % 0.51/0.77 (define @t2 () (tptp.aInteger0 @t1)) % 0.51/0.77 (define @t3 () (@list @t1)) % 0.51/0.77 (define @t4 () (tptp.smndt0 @t1)) % 0.51/0.77 (define @t5 () (@var "W1" $$unsorted)) % 0.51/0.77 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.51/0.77 (define @t7 () (tptp.aInteger0 @t5)) % 0.51/0.77 (define @t8 () (and @t2 @t7)) % 0.51/0.77 (define @t9 () (@list @t1 @t5)) % 0.51/0.77 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.51/0.77 (define @t11 () (@var "W2" $$unsorted)) % 0.51/0.77 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.51/0.77 (define @t13 () (tptp.aInteger0 @t11)) % 0.51/0.77 (define @t14 () (and @t2 @t7 @t13)) % 0.51/0.77 (define @t15 () (@list @t1 @t5 @t11)) % 0.51/0.77 (define @t16 () (tptp.sdtasdt0 @t5 @t11)) % 0.51/0.77 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.51/0.77 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.51/0.77 (define @t19 () (= @t5 tptp.sz00)) % 0.51/0.77 (define @t20 () (= @t1 tptp.sz00)) % 0.51/0.77 (define @t21 () (@list @t11)) % 0.51/0.77 (define @t22 () (not @t19)) % 0.51/0.77 (define @t23 () (tptp.aDivisorOf0 @t5 @t1)) % 0.51/0.77 (define @t24 () (@list @t5)) % 0.51/0.77 (define @t25 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11)) % 0.51/0.77 (define @t26 () (not (= @t11 tptp.sz00))) % 0.51/0.77 (define @t27 () (and @t2 @t7 @t13 @t26)) % 0.51/0.77 (define @t28 () (and @t2 @t7 @t22)) % 0.51/0.77 (define @t29 () (@var "W3" $$unsorted)) % 0.51/0.77 (define @t30 () (tptp.aInteger0 @t29)) % 0.51/0.77 (define @t31 () (@list @t1 @t5 @t11 @t29)) % 0.51/0.77 (define @t32 () (= @t1 @t18)) % 0.51/0.77 (define @t33 () (= @t1 tptp.sz10)) % 0.51/0.77 (define @t34 () (tptp.isPrime0 @t5)) % 0.51/0.77 (define @t35 () (tptp.aSet0 @t1)) % 0.51/0.77 (define @t36 () (tptp.aElementOf0 @t5 @t1)) % 0.51/0.77 (define @t37 () (tptp.aElementOf0 @t11 @t1)) % 0.51/0.77 (define @t38 () (tptp.aElementOf0 @t11 @t5)) % 0.51/0.77 (define @t39 () (tptp.aSet0 @t5)) % 0.51/0.77 (define @t40 () (tptp.isFinite0 @t1)) % 0.51/0.77 (define @t41 () (tptp.aElementOf0 @t29 @t5)) % 0.51/0.77 (define @t42 () (tptp.aElementOf0 @t29 @t1)) % 0.51/0.77 (define @t43 () (tptp.aElementOf0 @t29 @t11)) % 0.51/0.77 (define @t44 () (@list @t29)) % 0.51/0.77 (define @t45 () (tptp.aSet0 @t11)) % 0.51/0.77 (define @t46 () (tptp.sdtbsmnsldt0 @t1 @t5)) % 0.51/0.77 (define @t47 () (tptp.aSubsetOf0 @t5 tptp.cS1395)) % 0.51/0.77 (define @t48 () (tptp.aSubsetOf0 @t1 tptp.cS1395)) % 0.51/0.77 (define @t49 () (and @t48 @t47)) % 0.51/0.77 (define @t50 () (tptp.sdtslmnbsdt0 @t1 @t5)) % 0.51/0.77 (define @t51 () (tptp.sbsmnsldt0 @t1)) % 0.51/0.77 (define @t52 () (tptp.stldt0 @t1)) % 0.51/0.77 (define @t53 () (tptp.szAzrzSzezqlpdtcmdtrp0 @t1 @t5)) % 0.51/0.77 (define @t54 () (tptp.isOpen0 @t1)) % 0.51/0.77 (define @t55 () (tptp.isClosed0 @t1)) % 0.51/0.77 (define @t56 () (tptp.isOpen0 @t5)) % 0.51/0.77 (define @t57 () (tptp.isClosed0 @t5)) % 0.51/0.77 (define @t58 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.51/0.77 (define @t59 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 @t5)) % 0.51/0.77 (define @t60 () (= @t59 @t1)) % 0.51/0.77 (define @t61 () (tptp.aElementOf0 @t11 @t59)) % 0.51/0.77 (define @t62 () (tptp.sdteqdtlpzmzozddtrp0 @t11 tptp.sz00 @t5)) % 0.51/0.77 (define @t63 () (tptp.sdtpldt0 @t11 (tptp.smndt0 tptp.sz00))) % 0.51/0.77 (define @t64 () (tptp.aDivisorOf0 @t5 @t63)) % 0.51/0.77 (define @t65 () (tptp.sdtasdt0 @t5 @t29)) % 0.51/0.77 (define @t66 () (exists @t44 (and @t30 (= @t65 @t63)))) % 0.51/0.77 (define @t67 () (forall @t21 (and (=> @t61 (and @t13 @t66 @t64 @t62)) (=> (and @t13 (or @t66 @t64 @t62)) @t61)))) % 0.51/0.77 (define @t68 () (tptp.aSet0 @t59)) % 0.51/0.77 (define @t69 () (tptp.sbsmnsldt0 tptp.xS)) % 0.51/0.77 (define @t70 () (tptp.stldt0 @t69)) % 0.51/0.77 (define @t71 () (or @t33 @t32)) % 0.51/0.77 (define @t72 () (tptp.aElementOf0 @t1 @t70)) % 0.51/0.77 (define @t73 () (forall @t3 (= @t72 @t71))) % 0.51/0.77 (define @t74 () (tptp.aElementOf0 @t1 @t69)) % 0.51/0.77 (define @t75 () (forall @t3 (= @t72 (and @t2 (not @t74))))) % 0.51/0.77 (define @t76 () (forall @t3 (= @t74 (and @t2 (exists @t24 (and (tptp.aElementOf0 @t5 tptp.xS) (tptp.aElementOf0 @t1 @t5))))))) % 0.51/0.77 (define @t77 () (tptp.aSet0 @t69)) % 0.51/0.77 (define @t78 () (tptp.aElementOf0 @t11 @t53)) % 0.51/0.77 (define @t79 () (tptp.sdteqdtlpzmzozddtrp0 @t11 @t1 @t5)) % 0.51/0.77 (define @t80 () (tptp.sdtpldt0 @t11 @t4)) % 0.51/0.77 (define @t81 () (tptp.aDivisorOf0 @t5 @t80)) % 0.51/0.77 (define @t82 () (exists @t44 (and @t30 (= @t65 @t80)))) % 0.51/0.77 (define @t83 () (forall @t3 (=> @t72 (exists @t24 (and @t7 @t22 (tptp.aSet0 @t53) (forall @t21 (and (=> @t78 (and @t13 @t82 @t81 @t79)) (=> (and @t13 (or @t82 @t81 @t79)) @t78))) (forall @t21 (=> @t78 (tptp.aElementOf0 @t11 @t70))) (tptp.aSubsetOf0 @t53 @t70)))))) % 0.51/0.77 (define @t84 () (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz10 tptp.xp)) % 0.51/0.77 (define @t85 () (tptp.aElementOf0 @t1 @t84)) % 0.51/0.77 (define @t86 () (forall @t3 (=> @t85 @t72))) % 0.51/0.77 (define @t87 () (tptp.sdteqdtlpzmzozddtrp0 @t1 tptp.sz10 tptp.xp)) % 0.51/0.77 (define @t88 () (tptp.sdtpldt0 @t1 @t18)) % 0.51/0.77 (define @t89 () (tptp.aDivisorOf0 tptp.xp @t88)) % 0.51/0.77 (define @t90 () (exists @t24 (and @t7 (= (tptp.sdtasdt0 tptp.xp @t5) @t88)))) % 0.51/0.77 (define @t91 () (and @t2 (or @t90 @t89 @t87))) % 0.51/0.77 (define @t92 () (tptp.sdtpldt0 tptp.sz10 (tptp.smndt0 tptp.xp))) % 0.51/0.77 (define @t93 () (tptp.aElementOf0 @t92 @t84)) % 0.51/0.77 (define @t94 () (tptp.sdtpldt0 @t92 @t18)) % 0.51/0.77 (define @t95 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.51/0.77 (define @t96 () (tptp.sdtpldt0 tptp.sz10 tptp.xp)) % 0.51/0.77 (define @t97 () (tptp.aElementOf0 @t96 @t84)) % 0.51/0.77 (define @t98 () (tptp.sdtpldt0 @t96 @t18)) % 0.51/0.77 (define @t99 () (= @t92 tptp.sz10)) % 0.51/0.77 (define @t100 () (= @t96 tptp.sz10)) % 0.51/0.77 (define @t101 () (= @t92 @t18)) % 0.51/0.77 (define @t102 () (not @t101)) % 0.51/0.77 (define @t103 () (= @t96 @t18)) % 0.51/0.77 (define @t104 () (not @t103)) % 0.51/0.77 (define @t105 () (or @t104 @t102)) % 0.51/0.77 (define @t106 () (or @t99 @t101)) % 0.51/0.77 (define @t107 () (tptp.aElementOf0 @t92 @t70)) % 0.51/0.77 (define @t108 () (= @t107 @t106)) % 0.51/0.77 (define @t109 () (@list @t92)) % 0.51/0.77 (define @t110 () (= @t18 @t92)) % 0.51/0.77 (define @t111 () (= tptp.sz10 @t92)) % 0.51/0.77 (define @t112 () (or @t111 @t110)) % 0.51/0.77 (define @t113 () (= @t107 @t112)) % 0.51/0.77 (define @t114 () (@list false)) % 0.51/0.77 (define @t115 () (@list @t73)) % 0.51/0.77 (define @t116 () (not @t93)) % 0.51/0.77 (define @t117 () (or @t116 @t107)) % 0.51/0.77 (define @t118 () (@list false false)) % 0.51/0.77 (define @t119 () (@list true false)) % 0.51/0.77 (define @t120 () (or @t100 @t103)) % 0.51/0.77 (define @t121 () (tptp.aElementOf0 @t96 @t70)) % 0.51/0.77 (define @t122 () (= @t121 @t120)) % 0.51/0.77 (define @t123 () (@list @t96)) % 0.51/0.77 (define @t124 () (= @t18 @t96)) % 0.51/0.77 (define @t125 () (= tptp.sz10 @t96)) % 0.51/0.77 (define @t126 () (or @t125 @t124)) % 0.51/0.77 (define @t127 () (= @t121 @t126)) % 0.51/0.77 (define @t128 () (not @t97)) % 0.51/0.77 (define @t129 () (or @t128 @t121)) % 0.51/0.77 (assume @p1 (forall @t3 (=> @t2 true))) % 0.51/0.77 (assume @p2 (tptp.aInteger0 tptp.sz00)) % 0.51/0.77 (assume @p3 (tptp.aInteger0 tptp.sz10)) % 0.51/0.77 (assume @p4 (forall @t3 (=> @t2 (tptp.aInteger0 @t4)))) % 0.51/0.77 (assume @p5 (forall @t9 (=> @t8 (tptp.aInteger0 @t6)))) % 0.51/0.77 (assume @p6 (forall @t9 (=> @t8 (tptp.aInteger0 @t10)))) % 0.51/0.77 (assume @p7 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t1 @t12) (tptp.sdtpldt0 @t6 @t11))))) % 0.51/0.77 (assume @p8 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.51/0.77 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.51/0.77 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.51/0.77 (assume @p11 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t1 @t16) (tptp.sdtasdt0 @t10 @t11))))) % 0.51/0.77 (assume @p12 (forall @t9 (=> @t8 (= @t10 (tptp.sdtasdt0 @t5 @t1))))) % 0.51/0.77 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.51/0.77 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t6 @t11) (tptp.sdtpldt0 @t17 @t16)))))) % 0.51/0.77 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.51/0.77 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.51/0.77 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.51/0.77 (assume @p18 (forall @t3 (=> @t2 (forall @t24 (= @t23 (and @t7 @t22 (exists @t21 (and @t13 (= @t16 @t1))))))))) % 0.51/0.77 (assume @p19 (forall @t15 (=> @t27 (= @t25 (tptp.aDivisorOf0 @t11 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5))))))) % 0.51/0.77 (assume @p20 (forall @t9 (=> @t28 (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t5)))) % 0.51/0.77 (assume @p21 (forall @t15 (=> @t27 (=> @t25 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t1 @t11))))) % 0.51/0.77 (assume @p22 (forall @t31 (=> (and @t2 @t7 @t13 @t26 @t30) (=> (and @t25 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t29 @t11)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t29 @t11))))) % 0.51/0.77 (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)))))) % 0.51/0.77 (assume @p24 (forall @t3 (=> (and @t2 (not @t20)) (=> (tptp.isPrime0 @t1) true)))) % 0.51/0.77 (assume @p25 (forall @t3 (=> @t2 (= (exists @t24 (and @t23 @t34)) (and (not @t33) (not @t32)))))) % 0.51/0.77 (assume @p26 (forall @t3 (=> @t35 true))) % 0.51/0.77 (assume @p27 (forall @t3 (=> @t35 (forall @t24 (=> @t36 true))))) % 0.51/0.77 (assume @p28 (forall @t3 (=> @t35 (forall @t24 (= (tptp.aSubsetOf0 @t5 @t1) (and @t39 (forall @t21 (=> @t38 @t37)))))))) % 0.51/0.77 (assume @p29 (forall @t3 (=> @t35 (=> @t40 true)))) % 0.51/0.77 (assume @p30 (forall @t9 (=> @t49 (forall @t21 (= (= @t11 @t46) (and @t45 (forall @t44 (= @t43 (and @t30 (or @t42 @t41)))))))))) % 0.51/0.77 (assume @p31 (forall @t9 (=> @t49 (forall @t21 (= (= @t11 @t50) (and @t45 (forall @t44 (= @t43 (and @t30 @t42 @t41))))))))) % 0.51/0.77 (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)))))))))))) % 0.51/0.77 (assume @p33 (forall @t3 (=> @t48 (forall @t24 (= (= @t5 @t52) (and @t39 (forall @t21 (= @t38 (and @t13 (not @t37)))))))))) % 0.51/0.77 (assume @p34 (forall @t9 (=> @t28 (forall @t21 (= (= @t11 @t53) (and @t45 (forall @t44 (= @t43 (and @t30 (tptp.sdteqdtlpzmzozddtrp0 @t29 @t1 @t5)))))))))) % 0.51/0.77 (assume @p35 (forall @t3 (=> @t48 (= @t54 (forall @t24 (=> @t36 (exists @t21 (and @t13 @t26 (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 @t5 @t11) @t1))))))))) % 0.51/0.77 (assume @p36 (forall @t3 (=> @t48 (= @t55 (tptp.isOpen0 @t52))))) % 0.51/0.77 (assume @p37 (forall @t3 (=> (and @t35 (forall @t24 (=> @t36 (and @t47 @t56)))) (tptp.isOpen0 @t51)))) % 0.51/0.77 (assume @p38 (forall @t9 (=> (and @t48 @t47 @t54 @t56) (tptp.isOpen0 @t50)))) % 0.51/0.77 (assume @p39 (forall @t9 (=> (and @t48 @t47 @t55 @t57) (tptp.isClosed0 @t46)))) % 0.51/0.77 (assume @p40 (forall @t3 (=> (and @t35 @t40 (forall @t24 (=> @t36 (and @t47 @t57)))) (tptp.isClosed0 @t51)))) % 0.51/0.77 (assume @p41 (forall @t9 (=> @t28 (and (tptp.aSubsetOf0 @t53 tptp.cS1395) (tptp.isClosed0 @t53))))) % 0.51/0.77 (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))) % 0.51/0.77 (assume @p43 (and @t77 @t76 (tptp.aSet0 @t70) @t75 @t73 (= @t70 tptp.cS2076))) % 0.51/0.77 (assume @p44 (tptp.isFinite0 tptp.xS)) % 0.51/0.77 (assume @p45 (and @t77 @t76 @t75 @t83 (tptp.isOpen0 @t70) (tptp.isClosed0 @t69) @t77 @t76 @t75 @t83)) % 0.51/0.77 (assume @p46 (and (tptp.aInteger0 tptp.xp) (not (= tptp.xp tptp.sz00)) (tptp.aSet0 @t84) (forall @t3 (and (=> @t85 (and @t2 @t90 @t89 @t87)) (=> @t91 @t85))) @t77 @t76 @t75 @t86 (tptp.aSubsetOf0 @t84 @t70))) % 0.51/0.77 (assume @p47 (and (exists @t3 (and @t2 (= @t95 @t98))) (tptp.aDivisorOf0 tptp.xp @t98) (tptp.sdteqdtlpzmzozddtrp0 @t96 tptp.sz10 tptp.xp) @t97 (exists @t3 (and @t2 (= @t95 @t94))) (tptp.aDivisorOf0 tptp.xp @t94) (tptp.sdteqdtlpzmzozddtrp0 @t92 tptp.sz10 tptp.xp) @t93)) % 0.51/0.77 (assume @p48 (and (not @t100) (not @t99))) % 0.51/0.77 (assume @p49 @t105) % 0.51/0.78 (assume @p50 (not (exists @t3 (and (or @t91 @t85) (not (and @t71 (tptp.aElementOf0 @t1 tptp.cS2200))))))) % 0.51/0.78 (assume @p51 true) % 0.51/0.78 (step @p52 :rule and_elim :premises (@p43) :args (4)) % 0.51/0.78 (step @p53 :rule eq-symm :args (@t92 @t18)) % 0.51/0.78 (step @p54 :rule eq-symm :args (@t92 tptp.sz10)) % 0.51/0.78 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t106)) % 0.51/0.78 (step @p56 :rule refl :args (@t107)) % 0.51/0.78 (step @p57 :rule cong :premises (@p56 @p55) :args (@t108)) % 0.51/0.78 (step @p58 :rule refl :args (@t73)) % 0.51/0.78 (step @p59 :rule cong :premises (@p58 @p57) :args ((=> @t73 @t108))) % 0.51/0.78 (assume-push @p115 @t73) % 0.51/0.78 (step @p61 :rule instantiate :premises (@p52) :args (@t109)) % 0.51/0.78 (step-pop @p116 :rule scope :premises (@p61)) % 0.51/0.78 (step @p62 :rule process_scope :premises (@p116) :args (@t108)) % 0.51/0.78 (step @p64 :rule eq_resolve :premises (@p62 @p59)) % 0.51/0.78 (step @p65 :rule implies_elim :premises (@p64)) % 0.51/0.78 (step @p66 :rule chain_m_resolution :premises (@p65 @p52) :args (@t113 @t114 @t115)) % 0.51/0.78 (step @p67 :rule bool-impl-elim :args (@t85 @t72)) % 0.51/0.78 (step @p68 :rule cong :premises (@p67) :args (@t86)) % 0.51/0.78 (step @p69 :rule and_elim :premises (@p46) :args (7)) % 0.51/0.78 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.51/0.78 (step @p71 :rule instantiate :premises (@p70) :args (@t109)) % 0.51/0.78 (step @p72 :rule and_elim :premises (@p47) :args (7)) % 0.51/0.78 (step @p73 :rule cnf_or_pos :args (@t117)) % 0.51/0.78 (step @p74 :rule reordering :premises (@p73) :args ((or @t116 @t107 (not @t117)))) % 0.51/0.78 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p71) :args (@t107 @t118 (@list @t93 @t117))) % 0.51/0.78 (step @p76 :rule cnf_equiv_pos1 :args (@t113)) % 0.51/0.78 (step @p77 :rule reordering :premises (@p76) :args ((or (not @t107) @t112 (not @t113)))) % 0.51/0.78 (step @p78 :rule chain_m_resolution :premises (@p77 @p75 @p66) :args (@t112 @t118 (@list @t107 @t113))) % 0.51/0.78 (step @p79 :rule and_elim :premises (@p48) :args (1)) % 0.51/0.78 (step @p80 :rule symm :premises (@p79)) % 0.51/0.78 (step @p81 :rule cnf_or_pos :args (@t112)) % 0.51/0.78 (step @p82 :rule reordering :premises (@p81) :args ((or @t111 @t110 (not @t112)))) % 0.51/0.78 (step @p83 :rule chain_m_resolution :premises (@p82 @p80 @p78) :args (@t110 @t119 (@list @t111 @t112))) % 0.51/0.78 (step @p84 :rule eq-symm :args (@t96 @t18)) % 0.51/0.78 (step @p85 :rule eq-symm :args (@t96 tptp.sz10)) % 0.51/0.78 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t120)) % 0.51/0.78 (step @p87 :rule refl :args (@t121)) % 0.51/0.78 (step @p88 :rule cong :premises (@p87 @p86) :args (@t122)) % 0.51/0.78 (step @p89 :rule cong :premises (@p58 @p88) :args ((=> @t73 @t122))) % 0.51/0.78 (assume-push @p117 @t73) % 0.51/0.78 (step @p91 :rule instantiate :premises (@p52) :args (@t123)) % 0.51/0.78 (step-pop @p118 :rule scope :premises (@p91)) % 0.51/0.78 (step @p92 :rule process_scope :premises (@p118) :args (@t122)) % 0.51/0.78 (step @p94 :rule eq_resolve :premises (@p92 @p89)) % 0.51/0.78 (step @p95 :rule implies_elim :premises (@p94)) % 0.51/0.78 (step @p96 :rule chain_m_resolution :premises (@p95 @p52) :args (@t127 @t114 @t115)) % 0.51/0.78 (step @p97 :rule instantiate :premises (@p70) :args (@t123)) % 0.51/0.78 (step @p98 :rule and_elim :premises (@p47) :args (3)) % 0.51/0.78 (step @p99 :rule cnf_or_pos :args (@t129)) % 0.51/0.78 (step @p100 :rule reordering :premises (@p99) :args ((or @t128 @t121 (not @t129)))) % 0.51/0.78 (step @p101 :rule chain_m_resolution :premises (@p100 @p98 @p97) :args (@t121 @t118 (@list @t97 @t129))) % 0.51/0.78 (step @p102 :rule cnf_equiv_pos1 :args (@t127)) % 0.51/0.78 (step @p103 :rule reordering :premises (@p102) :args ((or (not @t121) @t126 (not @t127)))) % 0.51/0.78 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p96) :args (@t126 @t118 (@list @t121 @t127))) % 0.51/0.78 (step @p105 :rule and_elim :premises (@p48) :args (0)) % 0.51/0.78 (step @p106 :rule symm :premises (@p105)) % 0.51/0.78 (step @p107 :rule cnf_or_pos :args (@t126)) % 0.51/0.78 (step @p108 :rule reordering :premises (@p107) :args ((or @t125 @t124 (not @t126)))) % 0.51/0.78 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p104) :args (@t124 @t119 (@list @t125 @t126))) % 0.51/0.78 (step @p110 :rule cong :premises (@p53) :args (@t102)) % 0.51/0.78 (step @p111 :rule cong :premises (@p84) :args (@t104)) % 0.51/0.78 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t105)) % 0.51/0.78 (step @p113 :rule eq_resolve :premises (@p49 @p112)) % 0.51/0.78 (step @p114 false :rule chain_m_resolution :premises (@p113 @p109 @p83) :args (false @t118 (@list @t124 @t110))) % 0.51/0.78 ) % 0.51/0.78 % SZS output end Proof % 0.51/0.78 % cvc5 exiting %------------------------------------------------------------------------------