TSTP Solution File: NUM510+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM510+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 10:44:36 EDT 2023
% Result : Theorem 11.21s 11.42s
% Output : Proof 11.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM510+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n017.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 13:39:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 11.21/11.42 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sJtsOFgJ2p/cvc5---1.0.5_6088.p...
% 11.21/11.42 ------- get file name : TPTP file name is NUM510+3
% 11.21/11.42 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6088.smt2...
% 11.21/11.42 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.21/11.42 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.21/11.42 % SZS status Theorem for NUM510+3
% 11.21/11.42 % SZS output start Proof for NUM510+3
% 11.21/11.42 (
% 11.21/11.42 (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtlseqdt0 _let_1 tptp.xn))) (let ((_let_3 (tptp.sdtasdt0 tptp.xr _let_1))) (let ((_let_4 (= tptp.xn _let_3))) (let ((_let_5 (tptp.aNaturalNumber0 _let_1))) (let ((_let_6 (and _let_5 _let_4))) (let ((_let_7 (not (and (not (and _let_5 _let_4 (= _let_1 tptp.xn))) (=> _let_6 (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) _let_2)))))) (let ((_let_8 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_9 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_8))) (let ((_let_10 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_11 (tptp.doDivides0 tptp.xr _let_10))) (let ((_let_12 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xk))) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) _let_11))) (let ((_let_13 (tptp.isPrime0 tptp.xr))) (let ((_let_14 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_15 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_16 (and _let_15 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_14 (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xr (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xr))) (or (= W0 tptp.sz10) (= W0 tptp.xr)))) _let_13))) (let ((_let_17 (= tptp.xk tptp.sz10))) (let ((_let_18 (= tptp.xk tptp.sz00))) (let ((_let_19 (not (or _let_18 _let_17)))) (let ((_let_20 (tptp.sdtsldt0 _let_10 tptp.xp))) (let ((_let_21 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_10 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk _let_20)))) (let ((_let_22 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_10)))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_25 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_26 (and _let_25 _let_24 _let_23))) (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) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_30 (forall ((W0 $$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_31 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_32 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_34 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_35 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_36 (and _let_35 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_37 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_38 (= tptp.xn (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_39 (= _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_40 (tptp.sdtasdt0 _let_1 tptp.xr))) (let ((_let_41 (= _let_3 _let_40))) (let ((_let_42 (tptp.sdtlseqdt0 _let_1 _let_40))) (let ((_let_43 (not _let_38))) (let ((_let_44 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43))) (let ((_let_47 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xr W0))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (0))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (_let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_52)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_47 (= W0 W0)))) (AND_ELIM _let_51 :args _let_50) :args (_let_49 true (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xr W0))))))) :args (_let_48 true _let_47)))) (let ((_let_55 (REFL :args (_let_46)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_38))) :args _let_52)) :args ((or _let_38 _let_46))) _let_54 :args (_let_38 true _let_46)))) (let ((_let_57 (and _let_44 _let_38))) (let ((_let_58 (= _let_57 _let_39))) (let ((_let_59 (not _let_8))) (let ((_let_60 (= tptp.sz00 tptp.xr))) (let ((_let_61 (not _let_25))) (let ((_let_62 (not _let_15))) (let ((_let_63 (or _let_62 _let_61 _let_60 _let_59 _let_58))) (let ((_let_64 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1825 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1825) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1825))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1825)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (1))) (let ((_let_67 (= tptp.sz10 tptp.xr))) (let ((_let_68 (2))) (let ((_let_69 (ASSUME :args (_let_21)))) (let ((_let_70 (AND_ELIM _let_69 :args _let_68))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_70 :args ((and _let_15 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))))) _let_14 (not _let_60) (not _let_67) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2228 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_2228)) (not (= tptp.xr (tptp.sdtasdt0 W0 BOUND_VARIABLE_2228)))) (not (tptp.doDivides0 W0 tptp.xr))) (= tptp.sz10 W0) (= tptp.xr W0))) _let_13) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_72 (AND_ELIM _let_71 :args _let_50))) (let ((_let_73 (ASSUME :args (_let_26)))) (let ((_let_74 (AND_ELIM _let_73 :args _let_50))) (let ((_let_75 (AND_ELIM _let_71 :args (3)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_52)) :args ((or _let_44 _let_46))) _let_54 :args (_let_44 true _let_46)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or _let_39 (not _let_57) (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_57)) :args ((or _let_45 _let_43 _let_57))) _let_76 _let_56 :args (_let_57 false _let_44 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_60 _let_61 _let_62 _let_59 _let_58 (not _let_63)))) _let_75 _let_74 _let_72 (AND_ELIM _let_51 :args _let_66) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xr tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_58 true _let_60 false _let_25 false _let_15 false _let_8 false _let_63)) :args (_let_39 false _let_57 false _let_58)))) (let ((_let_78 (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0)))))) _let_2))) (let ((_let_79 (not _let_2))) (let ((_let_80 (=> _let_6 _let_78))) (let ((_let_81 (= tptp.xn _let_1))) (let ((_let_82 (and _let_5 _let_4 _let_81))) (let ((_let_83 (not _let_80))) (let ((_let_84 (not _let_82))) (let ((_let_85 (tptp.sdtasdt0 tptp.xn tptp.xr))) (let ((_let_86 (tptp.sdtasdt0 tptp.xr tptp.xn))) (let ((_let_87 (= _let_86 _let_85))) (let ((_let_88 (tptp.sdtasdt0 tptp.xn tptp.sz10))) (let ((_let_89 (= tptp.xn _let_88))) (let ((_let_90 (= _let_85 _let_88))) (let ((_let_91 (tptp.sdtasdt0 tptp.sz10 tptp.xn))) (let ((_let_92 (not _let_90))) (let ((_let_93 (and _let_92 (not (= _let_86 _let_91))))) (let ((_let_94 (not _let_35))) (let ((_let_95 (= tptp.sz00 tptp.xn))) (let ((_let_96 (or _let_61 _let_95 _let_94 _let_62 _let_93 _let_67))) (let ((_let_97 (tptp.sdtasdt0 tptp.xp _let_20))) (let ((_let_98 (= _let_10 _let_97))) (let ((_let_99 (= _let_10 (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_100 (= tptp.sz00 _let_97))) (let ((_let_101 (= tptp.sz00 (tptp.sdtpldt0 tptp.sz00 tptp.sz00)))) (let ((_let_102 (= _let_10 _let_85))) (let ((_let_103 (= _let_10 (tptp.sdtasdt0 tptp.xm tptp.xn)))) (let ((_let_104 (= tptp.sz00 (tptp.sdtasdt0 tptp.xm tptp.sz00)))) (let ((_let_105 (not _let_81))) (let ((_let_106 (or _let_61 _let_62 _let_87))) (let ((_let_107 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (_let_107))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_61 _let_62 _let_87 (not _let_106)))) _let_74 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xn tptp.xr QUANTIFIERS_INST_CBQI_PROP)) :args _let_109))) _let_108 :args (_let_106 false _let_107)) :args (_let_87 false _let_25 false _let_15 false _let_106)))) (let ((_let_111 (and _let_89 (= tptp.xn _let_91)))) (let ((_let_112 (or _let_61 _let_111))) (let ((_let_113 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_111 0)) :args ((or _let_89 (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_61 _let_111 (not _let_112)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.xn QUANTIFIERS_INST_ENUM)) :args (_let_113))) _let_114 :args (_let_112 false _let_113)) :args (_let_111 false _let_25 false _let_112)) :args (_let_89 false _let_111)))) (let ((_let_116 (and _let_81 _let_38 _let_39 _let_87 _let_89))) (let ((_let_117 (ASSUME :args (_let_89)))) (let ((_let_118 (SYMM _let_117))) (let ((_let_119 (ASSUME :args (_let_38)))) (let ((_let_120 (SYMM (SYMM _let_119)))) (let ((_let_121 (APPLY_UF tptp.sdtasdt0))) (let ((_let_122 (ASSUME :args (_let_39)))) (let ((_let_123 (SYMM _let_122))) (let ((_let_124 (SYMM _let_123))) (let ((_let_125 (REFL :args (tptp.xr)))) (let ((_let_126 (ASSUME :args (_let_81)))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (ASSUME :args (_let_87)))) (let ((_let_129 (SYMM (SYMM _let_128)))) (let ((_let_130 (MODUS_PONENS (AND_INTRO _let_117 _let_119 _let_122 _let_126 _let_128) (SCOPE (TRANS (SYMM _let_129) (CONG _let_125 (SYMM _let_127) :args _let_121) (CONG _let_125 _let_124 :args _let_121) (SYMM _let_120) (SYMM _let_118)) :args (_let_89 _let_38 _let_39 _let_81 _let_87))))) (let ((_let_131 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1538 $$unsorted) (BOUND_VARIABLE_1536 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1536)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1538)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1536) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1538))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1536 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1538 W0)))) (= BOUND_VARIABLE_1536 BOUND_VARIABLE_1538))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (EQ_RESOLVE _let_69 (MACRO_SR_EQ_INTRO _let_70 :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (not _let_99))) (let ((_let_135 (or (not (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_134))) (let ((_let_136 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0))))))) (let ((_let_137 (not _let_135))) (let ((_let_138 (not _let_136))) (let ((_let_139 (_let_138))) (let ((_let_140 (= tptp.sz00 _let_20))) (let ((_let_141 (= tptp.sz00 tptp.xp))) (let ((_let_142 (not _let_100))) (let ((_let_143 (tptp.aNaturalNumber0 _let_20))) (let ((_let_144 (not _let_143))) (let ((_let_145 (not _let_23))) (let ((_let_146 (or _let_145 _let_144 _let_142 _let_141 _let_140))) (let ((_let_147 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (= tptp.sz00 (tptp.sdtasdt0 W0 W1))) (= tptp.sz00 W0) (= tptp.sz00 W1))))) (let ((_let_148 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (not _let_37))) (let ((_let_150 (or _let_149 _let_101))) (let ((_let_151 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_152 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_153 (not _let_89))) (let ((_let_154 (not _let_101))) (let ((_let_155 (not _let_102))) (let ((_let_156 (not _let_87))) (let ((_let_157 (not _let_39))) (let ((_let_158 (not 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W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))) (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) _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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$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)))) (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (or (and (not (= W2 tptp.sz00)) (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)) (or (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1)))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W0 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W0)) (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))) _let_22 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm))) (and (not (= tptp.xn tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_21 _let_19 (and (not _let_18) (not _let_17)) _let_16 _let_12 (and (not (= tptp.xk tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xk W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_8) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xm))) _let_9 _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.21/11.42 )
% 11.21/11.42 % SZS output end Proof for NUM510+3
% 11.21/11.42 % cvc5---1.0.5 exiting
% 11.21/11.42 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------