TSTP Solution File: NUM528+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM528+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% 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 : Thu Aug 31 10:44:48 EDT 2023
% Result : Theorem 17.52s 17.73s
% Output : Proof 17.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM528+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n004.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 15:56:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 17.52/17.73 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OIPZhoAlAo/cvc5---1.0.5_11349.p...
% 17.52/17.73 ------- get file name : TPTP file name is NUM528+3
% 17.52/17.73 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11349.smt2...
% 17.52/17.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 17.52/17.73 --- Run --no-e-matching --full-saturate-quant at 5...
% 17.52/17.73 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 17.52/17.73 % SZS status Theorem for NUM528+3
% 17.52/17.73 % SZS output start Proof for NUM528+3
% 17.52/17.73 (
% 17.52/17.73 (let ((_let_1 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_2 (not (and (not (= tptp.xm tptp.xn)) (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xn))) _let_1))))) (let ((_let_3 (tptp.sdtasdt0 tptp.xm tptp.xm))) (let ((_let_4 (tptp.sdtasdt0 tptp.xn tptp.xn))) (let ((_let_5 (tptp.sdtlseqdt0 _let_4 _let_3))) (let ((_let_6 (tptp.sdtlseqdt0 tptp.xn tptp.xm))) (let ((_let_7 (=> (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xm))) _let_6) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xn tptp.xn) W0) (tptp.sdtasdt0 tptp.xm tptp.xm)))) _let_5)))) (let ((_let_8 (tptp.sdtasdt0 tptp.xq tptp.xq))) (let ((_let_9 (tptp.sdtasdt0 tptp.xp _let_8))) (let ((_let_10 (= _let_3 _let_9))) (let ((_let_11 (tptp.sdtasdt0 tptp.xp tptp.xq))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xq))) (let ((_let_13 (and _let_12 (= tptp.xn _let_11) (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp))))) (let ((_let_14 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_15 (tptp.doDivides0 tptp.xp _let_4))) (let ((_let_16 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))) _let_15 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))) _let_14))) (let ((_let_17 (and (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp)))) (let ((_let_18 (tptp.sdtasdt0 tptp.xp _let_3))) (let ((_let_19 (= _let_18 _let_4))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_23 (and _let_22 _let_21 _let_20 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))) (let ((_let_31 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_32 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_33 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))) (let ((_let_35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (let ((_let_36 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_37 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))) (let ((_let_38 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))) (let ((_let_39 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_40 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_41 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_42 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_43 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_44 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_45 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_46 (and _let_45 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_47 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_48 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (tptp.sdtasdt0 _let_11 _let_11))) (let ((_let_50 (tptp.aNaturalNumber0 _let_49))) (let ((_let_51 (= _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (tptp.sdtlseqdt0 _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_49))) (let ((_let_55 (not _let_54))) (let ((_let_56 (not _let_50))) (let ((_let_57 (not _let_48))) (let ((_let_58 (or _let_57 _let_56 _let_55 _let_53 _let_51))) (let ((_let_59 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_60 (= _let_49 _let_59))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_57 _let_61))) (let ((_let_63 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 tptp.xp tptp.xq))) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xp W0) (tptp.sdtasdt0 _let_1 _let_1)))))))) (let ((_let_64 (not _let_62))) (let ((_let_65 (0))) (let ((_let_66 (1))) (let ((_let_67 (ASSUME :args (_let_13)))) (let ((_let_68 (AND_ELIM _let_67 :args _let_66))) (let ((_let_69 (or))) (let ((_let_70 (not _let_63))) (let ((_let_71 (_let_70))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_71)) :args _let_71) (REWRITE :args ((=> _let_70 (not (or _let_57 (not (= _let_59 _let_49))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_63))) (REFL :args (_let_64)) :args _let_69)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_68 :args ((and (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W0)))))) _let_15 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))))) _let_14) SB_DEFAULT SBA_FIXPOINT)))) :args _let_65) :args (_let_64 true _let_63)))) (let ((_let_73 (REFL :args (_let_62)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_48))) :args _let_69)) :args ((or _let_48 _let_62))) _let_72 :args (_let_48 true _let_62)))) (let ((_let_75 (tptp.aNaturalNumber0 _let_59))) (let ((_let_76 (not _let_20))) (let ((_let_77 (or _let_76 _let_57 _let_75))) (let ((_let_78 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 (= tptp.sz00 tptp.xp))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_68 :args ((and _let_22 _let_21 _let_20 (not (= tptp.sz00 tptp.xn)) (not (= tptp.sz00 tptp.xm)) (not _let_81)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_83 (AND_ELIM _let_82 :args (2)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 1)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_69)) :args ((or _let_60 _let_62))) _let_72 :args (_let_60 true _let_62)))) (let ((_let_85 (and _let_60 _let_75))) (let ((_let_86 (ASSUME :args (_let_75)))) (let ((_let_87 (APPLY_UF tptp.aNaturalNumber0))) (let ((_let_88 (ASSUME :args (_let_60)))) (let ((_let_89 (SYMM _let_88))) (let ((_let_90 (SYMM _let_89))) (let ((_let_91 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xp))) (let ((_let_92 (= _let_91 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz10)))) (let ((_let_93 (= _let_3 (tptp.sdtasdt0 tptp.sz10 _let_3)))) (let ((_let_94 (= _let_3 (tptp.sdtasdt0 _let_3 tptp.sz10)))) (let ((_let_95 (tptp.sdtasdt0 _let_3 tptp.xp))) (let ((_let_96 (= _let_18 _let_95))) (let ((_let_97 (= _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_98 (= tptp.sz10 (tptp.sdtasdt0 tptp.sz10 tptp.sz10)))) (let ((_let_99 (= _let_18 _let_49))) (let ((_let_100 (not _let_51))) (let ((_let_101 (not _let_92))) (let ((_let_102 (and _let_101 (not (= _let_59 (tptp.sdtasdt0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_103 (= tptp.sz10 tptp.xp))) (let ((_let_104 (not _let_45))) (let ((_let_105 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_106 (or _let_57 _let_105 _let_104 _let_76 _let_102 _let_103))) (let ((_let_107 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1426 $$unsorted) (BOUND_VARIABLE_1424 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1424)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1426)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1424) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1426))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1424 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1426 W0)))) (= BOUND_VARIABLE_1424 BOUND_VARIABLE_1426))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (_let_107))) (let ((_let_110 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_111 (tptp.sdtmndt0 tptp.sz00 tptp.sz00))) (let ((_let_112 (= _let_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_113 (= tptp.sz00 _let_111))) (let ((_let_114 (not _let_105))) (let ((_let_115 (tptp.sdtpldt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_116 (= _let_115 (tptp.sdtpldt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_117 (not _let_116))) (let ((_let_118 (and _let_117 (not (= (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz00) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 tptp.sz00)))))) (let ((_let_119 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_120 (not _let_119))) (let ((_let_121 (not _let_47))) (let ((_let_122 (or _let_121 _let_57 _let_120 _let_118 _let_110))) (let ((_let_123 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2))) (not (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0)))) (= W1 W2))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (not _let_118))) (let ((_let_126 (= _let_3 _let_115))) (let ((_let_127 (tptp.sdtpldt0 _let_3 tptp.sz00))) (let ((_let_128 (= _let_3 _let_127))) (let ((_let_129 (tptp.sdtpldt0 tptp.sz00 _let_3))) (let ((_let_130 (= _let_129 _let_127))) (let ((_let_131 (not _let_126))) (let ((_let_132 (or _let_120 _let_131))) (let ((_let_133 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xm tptp.xm) (tptp.sdtpldt0 tptp.sz00 W2))))))) (let ((_let_134 (not _let_132))) (let ((_let_135 (not _let_133))) (let ((_let_136 (tptp.sdtlseqdt0 tptp.sz00 _let_3))) (let ((_let_137 (= _let_136 _let_135))) (let ((_let_138 (tptp.aNaturalNumber0 _let_3))) (let ((_let_139 (not _let_138))) (let ((_let_140 (or _let_121 _let_139 _let_137))) (let ((_let_141 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtpldt0 W0 W2))))))))))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (_let_141))) (let ((_let_144 (tptp.sz00 _let_3 QUANTIFIERS_INST_ENUM))) (let ((_let_145 (tptp.aNaturalNumber0 _let_9))) (let ((_let_146 (tptp.aNaturalNumber0 _let_8))) (let ((_let_147 (not _let_146))) (let ((_let_148 (or _let_76 _let_147 _let_145))) (let ((_let_149 (not _let_12))) (let ((_let_150 (or _let_149 _let_149 _let_146))) (let ((_let_151 (ASSUME :args (_let_10)))) (let ((_let_152 (and _let_10 _let_145))) (let ((_let_153 (ASSUME :args (_let_145)))) (let ((_let_154 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_152)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO 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_let_96 false _let_94 false _let_93 true _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_86 _let_88) (SCOPE (TRUE_ELIM (TRANS (CONG _let_90 :args _let_87) (TRUE_INTRO _let_86))) :args (_let_75 _let_60))) :args (_let_60 _let_75))) :args (true _let_85)) :args ((or _let_61 _let_50 (not _let_75)))) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_76 _let_57 _let_75 (not _let_77)))) _let_83 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) _let_79 :args (_let_77 false _let_78)) :args (_let_75 false _let_20 false _let_48 false _let_77)) :args (_let_50 false _let_60 false _let_75)) _let_74 :args (false false _let_54 false _let_52 false _let_58 true _let_51 false _let_50 false _let_48)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_47 _let_46 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_44 _let_43 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) _let_42 _let_41 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) _let_40 _let_39 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) _let_38 _let_37 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) _let_29 _let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_27 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_25 _let_24 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) _let_23 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (or (and (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2))))))) _let_19 _let_17 _let_16 _let_13 _let_10 _let_7 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 17.52/17.74 )
% 17.52/17.74 % SZS output end Proof for NUM528+3
% 17.52/17.74 % cvc5---1.0.5 exiting
% 17.52/17.74 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------