TSTP Solution File: NUM448+5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 : Thu Aug 31 10:44:00 EDT 2023
% Result : Theorem 46.08s 46.32s
% Output : Proof 46.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 09:56:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 46.08/46.32 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.AqMM4KYEwO/cvc5---1.0.5_22900.p...
% 46.08/46.32 ------- get file name : TPTP file name is NUM448+5
% 46.08/46.32 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22900.smt2...
% 46.08/46.32 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 46.08/46.32 --- Run --no-e-matching --full-saturate-quant at 5...
% 46.08/46.32 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 46.08/46.32 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 46.08/46.32 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 46.08/46.32 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 46.08/46.32 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 46.08/46.32 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.08/46.32 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 46.08/46.32 % SZS status Theorem for NUM448+5
% 46.08/46.32 % SZS output start Proof for NUM448+5
% 46.08/46.32 (
% 46.08/46.32 (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (let ((_let_2 (tptp.stldt0 _let_1))) (let ((_let_3 (and (tptp.aSet0 _let_2) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.xS))) (= (tptp.aElementOf0 W0 (tptp.stldt0 _let_1)) (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1))))))))) (let ((_let_4 (tptp.aSet0 _let_1))) (let ((_let_5 (not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)))) (=> (tptp.aInteger0 W0) (and (=> (or (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1))) _let_1) (exists ((W1 $$unsorted)) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W1 W2) W0))) (tptp.aDivisorOf0 W1 W0) (tptp.isPrime0 W1)))) (=> (exists ((W1 $$unsorted)) (and (or (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W1 W2) W0)))) (tptp.aDivisorOf0 W1 W0)) (tptp.isPrime0 W1))) (and (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1))) _let_1)))))) (=> (and _let_4 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xS) (tptp.aElementOf0 W0 W1))))))) (=> _let_3 (or (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= W0 tptp.sz10) (= W0 (tptp.smndt0 tptp.sz10))))) (= _let_2 tptp.cS2076)))))))) (let ((_let_6 (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xS))) (and (=> _let_1 (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.isPrime0 W1) (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 tptp.sz00 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1))))))) (= _let_1 W0))))) (=> (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1))) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (tptp.isPrime0 W1) (=> (and (tptp.aSet0 _let_1) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 (tptp.szAzrzSzezqlpdtcmdtrp0 tptp.sz00 W1)))) (let ((_let_2 (tptp.sdteqdtlpzmzozddtrp0 W2 tptp.sz00 W1))) (let ((_let_3 (tptp.aDivisorOf0 W1 (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) (let ((_let_4 (tptp.aInteger0 W2))) (and (=> _let_1 (and _let_4 (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) (=> (and _let_4 (or (exists ((W3 $$unsorted)) (and (tptp.aInteger0 W3) (= (tptp.sdtasdt0 W1 W3) (tptp.sdtpldt0 W2 (tptp.smndt0 tptp.sz00))))) _let_3 _let_2)) _let_1)))))))) (= _let_1 W0))))) _let_1)))) (= tptp.xS tptp.cS2043)))) (let ((_let_7 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (= (exists ((W1 $$unsorted)) (and (tptp.aDivisorOf0 W1 W0) (tptp.isPrime0 W1))) (and (not (= W0 tptp.sz10)) (not (= W0 (tptp.smndt0 tptp.sz10))))))))) (let ((_let_8 (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_9 (tptp.aInteger0 tptp.sz10))) (let ((_let_10 (tptp.isPrime0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42))) (let ((_let_11 (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (not _let_11))) (let ((_let_13 (and (or (not (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42)) (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 W2)))))) _let_12))) (let ((_let_14 (not _let_10))) (let ((_let_15 (or _let_13 _let_14))) (let ((_let_16 (or _let_12 _let_14))) (let ((_let_17 (forall ((W1 $$unsorted)) (or (not (tptp.aDivisorOf0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.isPrime0 W1)))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.smndt0 tptp.sz10))) (let ((_let_20 (= _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (not _let_20))) (let ((_let_22 (= tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (not _let_22))) (let ((_let_24 (and _let_23 _let_21))) (let ((_let_25 (not _let_17))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (= (not (forall ((W1 $$unsorted)) (or (not (tptp.aDivisorOf0 W1 W0)) (not (tptp.isPrime0 W1))))) (and (not (= tptp.sz10 W0)) (not (= (tptp.smndt0 tptp.sz10) W0)))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((not (= (tptp.aInteger0 W0) false))))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_29 false _let_30)))) (let ((_let_35 (tptp.sbsmnsldt0 tptp.cS2043))) (let ((_let_36 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_35))) (let ((_let_37 (not _let_36))) (let ((_let_38 (and _let_27 _let_37))) (let ((_let_39 (tptp.stldt0 _let_35))) (let ((_let_40 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_39))) (let ((_let_41 (= _let_40 _let_38))) (let ((_let_42 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sbsmnsldt0 tptp.cS2043))) (= (and (tptp.aInteger0 W0) (not (tptp.aElementOf0 W0 _let_1))) (tptp.aElementOf0 W0 (tptp.stldt0 _let_1))))))) (let ((_let_43 (1))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args _let_43) :args ((not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)))) (or (not (tptp.aInteger0 W0)) (and (or (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (not (tptp.aElementOf0 W0 W1)))) (not _let_1)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= W0 (tptp.sdtasdt0 W1 W2))))) (not (tptp.aDivisorOf0 W1 W0)) (not (tptp.isPrime0 W1)))))) (or (forall ((W1 $$unsorted)) (or (and (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= W0 (tptp.sdtasdt0 W1 W2)))))) (not (tptp.aDivisorOf0 W1 W0))) (not (tptp.isPrime0 W1)))) (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (not (tptp.aElementOf0 W0 W1))))) _let_1)))))) (=> (and _let_4 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.xS)) (and (tptp.aInteger0 W0) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xS)) (not (tptp.aElementOf0 W0 W1))))))))) (=> _let_3 (or (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.xS))) (or (= tptp.sz10 W0) (= (tptp.smndt0 tptp.sz10) W0)))) (= tptp.cS2076 _let_2)))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_45 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_44)))) (let ((_let_46 (AND_ELIM (NOT_IMPLIES_ELIM1 _let_45) :args _let_43))) (let ((_let_47 (_let_42))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W0 _let_39)))) :args _let_47))) _let_46 :args (_let_41 false _let_42)))) (let ((_let_50 (or _let_22 _let_20))) (let ((_let_51 (= _let_50 _let_40))) (let ((_let_52 (forall ((W0 $$unsorted)) (= (or (= tptp.sz10 W0) (= (tptp.smndt0 tptp.sz10) W0)) (tptp.aElementOf0 W0 (tptp.stldt0 (tptp.sbsmnsldt0 tptp.cS2043))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (or))) (let ((_let_55 (not _let_52))) (let ((_let_56 (_let_55))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_52))) (REFL :args (_let_53)) :args _let_54)) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 _let_45) :args (0)) :args (_let_53 true _let_52)))) (let ((_let_58 (not _let_50))) (let ((_let_59 (tptp.aInteger0 _let_19))) (let ((_let_60 (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.cS2043)) (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W1))))) _let_36))) (let ((_let_61 (forall ((W1 $$unsorted)) (or (and (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= (tptp.sdtasdt0 W1 W2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (not (tptp.aDivisorOf0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.isPrime0 W1)))))) (let ((_let_62 (or _let_61 _let_60))) (let ((_let_63 (forall ((W1 $$unsorted)) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= (tptp.sdtasdt0 W1 W2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (not (tptp.aDivisorOf0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.isPrime0 W1)))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.cS2043)) (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 W1)))) _let_37))) (let ((_let_66 (or _let_65 _let_64))) (let ((_let_67 (and _let_66 _let_62))) (let ((_let_68 (or _let_28 _let_67))) (let ((_let_69 (tptp.isPrime0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.aDivisorOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_72 (not _let_71))) (let ((_let_73 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_74 (not (tptp.aInteger0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)))) (let ((_let_75 (or _let_74 _let_73 (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 W2))))) _let_72 _let_70))) (let ((_let_76 (or _let_72 _let_70))) (let ((_let_77 (not _let_24))) (let ((_let_78 (_let_51))) (let ((_let_79 (CNF_EQUIV_NEG2 :args _let_78))) (let ((_let_80 (not _let_41))) (let ((_let_81 (not _let_38))) (let ((_let_82 (_let_41))) (let ((_let_83 (not _let_9))) (let ((_let_84 (or _let_83 _let_59))) (let ((_let_85 (forall ((W0 $$unsorted)) (or (not (tptp.aInteger0 W0)) (tptp.aInteger0 (tptp.smndt0 W0)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (ASSUME :args (_let_9)))) (let ((_let_88 (and _let_20 _let_59))) (let ((_let_89 (ASSUME :args (_let_59)))) (let ((_let_90 (ASSUME :args (_let_20)))) (let ((_let_91 (_let_38))) (let ((_let_92 (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_26 (not _let_29)))))) (let ((_let_93 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.sbsmnsldt0 tptp.cS2043)))) (or (not (tptp.aInteger0 W0)) (and (or (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.cS2043)) (not (tptp.aElementOf0 W0 W1)))) (not _let_1)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= W0 (tptp.sdtasdt0 W1 W2))))) (not (tptp.aDivisorOf0 W1 W0)) (not (tptp.isPrime0 W1)))))) (or (forall ((W1 $$unsorted)) (or (and (or (not (tptp.aInteger0 W1)) (= tptp.sz00 W1) (forall ((W2 $$unsorted)) (or (not (tptp.aInteger0 W2)) (not (= W0 (tptp.sdtasdt0 W1 W2)))))) (not (tptp.aDivisorOf0 W1 W0))) (not (tptp.isPrime0 W1)))) (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.cS2043)) (not (tptp.aElementOf0 W0 W1))))) _let_1)))))))) (let ((_let_94 (NOT_IMPLIES_ELIM1 _let_44))) (let ((_let_95 (_let_93))) (let ((_let_96 ((not (= (tptp.aInteger0 W0) false))))) (let ((_let_97 (ASSUME :args _let_95))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_95))) _let_94 :args (_let_68 false _let_93)))) (let ((_let_99 (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_28 _let_67 (not _let_68)))))) (let ((_let_100 (not _let_26))) (let ((_let_101 (_let_24))) (let ((_let_102 (REFL :args _let_101))) (let ((_let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_17))))) (let ((_let_104 (_let_26))) (let ((_let_105 (not _let_67))) (let ((_let_106 (_let_64))) (let ((_let_107 (REFL :args (_let_75)))) (let ((_let_108 (_let_17))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_108) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_108)) (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_72 _let_70 (not _let_76)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_75 4)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_69))) :args _let_54)) :args ((or _let_69 _let_75))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_75 3)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_54)) :args ((or _let_71 _let_75))) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106) (REWRITE :args ((=> _let_64 (not (or 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(=> (tptp.aInteger0 W0) (and (= (tptp.sdtasdt0 _let_1 W0) _let_2) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted)) (=> (tptp.aInteger0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aInteger0 W1) (not (= W1 tptp.sz00)) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (= (tptp.sdtasdt0 W1 W2) W0)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aDivisorOf0 W2 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (tptp.sdteqdtlpzmzozddtrp0 W0 W0 W1))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aInteger0 W3)) (=> (and (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W1 W3 W2)) (tptp.sdteqdtlpzmzozddtrp0 W0 W3 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aInteger0 W3) (not (= W3 tptp.sz00))) (=> (tptp.sdteqdtlpzmzozddtrp0 W0 W1 (tptp.sdtasdt0 W2 W3)) (and (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W3))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aInteger0 W0) (not (= W0 tptp.sz00))) (=> (tptp.isPrime0 W0) true))) _let_7 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) true)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtbsmnsldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (or (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtslmnbsdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aSubsetOf0 W1 tptp.cS1395)))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.sbsmnsldt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aInteger0 W2) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W2 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (forall ((W1 $$unsorted)) (= (= W1 (tptp.stldt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aInteger0 W2) (not (tptp.aElementOf0 W2 W0)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (forall ((W2 $$unsorted)) (= (= W2 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aInteger0 W3) (tptp.sdteqdtlpzmzozddtrp0 W3 W0 W1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (= (tptp.isOpen0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (exists ((W2 $$unsorted)) (and (tptp.aInteger0 W2) (not (= W2 tptp.sz00)) (tptp.aSubsetOf0 (tptp.szAzrzSzezqlpdtcmdtrp0 W1 W2) W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSubsetOf0 W0 tptp.cS1395) (= (tptp.isClosed0 W0) (tptp.isOpen0 (tptp.stldt0 W0))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isOpen0 W1))))) (tptp.isOpen0 (tptp.sbsmnsldt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isOpen0 W0) (tptp.isOpen0 W1)) (tptp.isOpen0 (tptp.sdtslmnbsdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.cS1395) (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W0) (tptp.isClosed0 W1)) (tptp.isClosed0 (tptp.sdtbsmnsldt0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (tptp.aSubsetOf0 W1 tptp.cS1395) (tptp.isClosed0 W1))))) (tptp.isClosed0 (tptp.sbsmnsldt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szAzrzSzezqlpdtcmdtrp0 W0 W1))) (=> (and (tptp.aInteger0 W0) (tptp.aInteger0 W1) (not (= W1 tptp.sz00))) (and (tptp.aSubsetOf0 _let_1 tptp.cS1395) (tptp.isClosed0 _let_1))))) _let_6 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 46.08/46.33 )
% 46.08/46.33 % SZS output end Proof for NUM448+5
% 46.08/46.33 % cvc5---1.0.5 exiting
% 46.08/46.33 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------