%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM494+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 10:44:27 EDT 2023

% Result   : Theorem 14.98s 15.18s
% Output   : Proof 14.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM494+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n018.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 12:22:28 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 14.98/15.18  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.AlfjYMlKV7/cvc5---1.0.5_2558.p...
% 14.98/15.18  ------- get file name : TPTP file name is NUM494+1
% 14.98/15.18  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2558.smt2...
% 14.98/15.18  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 14.98/15.18  --- Run --no-e-matching --full-saturate-quant at 5...
% 14.98/15.18  % SZS status Theorem for NUM494+1
% 14.98/15.18  % SZS output start Proof for NUM494+1
% 14.98/15.18  (
% 14.98/15.18  (let ((_let_1 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.sdtpldt0 _let_1 tptp.xp))) (let ((_let_3 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp))) (let ((_let_4 (tptp.sdtlseqdt0 _let_3 _let_2))) (let ((_let_5 (not (and (not (= _let_3 _let_2)) _let_4)))) (let ((_let_6 (tptp.sdtmndt0 tptp.xn tptp.xp))) (let ((_let_7 (= tptp.xr _let_6))) (let ((_let_8 (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (let ((_let_9 (tptp.isPrime0 tptp.xp))) (let ((_let_10 (and _let_9 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm))))) (let ((_let_11 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_14 (and _let_13 _let_12 _let_11))) (let ((_let_15 (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_16 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))) (let ((_let_17 (forall ((W0 $$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))))))))))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_19 (forall ((W0 $$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_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (let ((_let_21 (forall ((W0 $$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_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_29 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_30 (and _let_29 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_31 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_32 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_33 (tptp.sdtlseqdt0 tptp.sz00 tptp.xp))) (let ((_let_34 (tptp.sdtlseqdt0 tptp.sz10 tptp.xp))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.sdtlseqdt0 tptp.sz00 tptp.sz10))) (let ((_let_37 (not _let_36))) (let ((_let_38 (not _let_11))) (let ((_let_39 (not _let_29))) (let ((_let_40 (not _let_31))) (let ((_let_41 (or _let_40 _let_39 _let_38 _let_37 _let_35 _let_33))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (tptp.sdtasdt0 tptp.sz10 _let_1))) (let ((_let_45 (tptp.sdtpldt0 tptp.xp _let_44))) (let ((_let_46 (tptp.sdtpldt0 tptp.sz00 _let_44))) (let ((_let_47 (tptp.sdtlseqdt0 _let_46 _let_45))) (let ((_let_48 (not (= _let_45 _let_46)))) (let ((_let_49 (tptp.sdtpldt0 _let_44 tptp.xp))) (let ((_let_50 (tptp.sdtpldt0 _let_44 tptp.sz00))) (let ((_let_51 (= _let_49 _let_50))) (let ((_let_52 (not _let_51))) (let ((_let_53 (and _let_52 (tptp.sdtlseqdt0 _let_50 _let_49) _let_48 _let_47))) (let ((_let_54 (tptp.aNaturalNumber0 _let_44))) (let ((_let_55 (not _let_54))) (let ((_let_56 (not _let_33))) (let ((_let_57 (= tptp.sz00 tptp.xp))) (let ((_let_58 (or _let_40 _let_38 _let_57 _let_56 _let_55 _let_53))) (let ((_let_59 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1489 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1489))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1489))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1489 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1489 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1489)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (not _let_53))) (let ((_let_62 (tptp.sdtasdt0 tptp.sz10 _let_6))) (let ((_let_63 (tptp.sdtpldt0 _let_62 tptp.xm))) (let ((_let_64 (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xp _let_62) tptp.xm) (tptp.sdtpldt0 tptp.xp _let_63)))) (let ((_let_65 (= tptp.xn (tptp.sdtpldt0 tptp.xp _let_6)))) (let ((_let_66 (tptp.sdtasdt0 _let_6 tptp.sz10))) (let ((_let_67 (= _let_6 _let_66))) (let ((_let_68 (= _let_62 _let_66))) (let ((_let_69 (tptp.sdtpldt0 _let_6 tptp.xm))) (let ((_let_70 (tptp.sdtasdt0 tptp.sz10 _let_69))) (let ((_let_71 (= (tptp.sdtpldt0 tptp.xp _let_70) (tptp.sdtpldt0 _let_70 tptp.xp)))) (let ((_let_72 (tptp.sdtasdt0 _let_69 tptp.sz10))) (let ((_let_73 (= _let_69 _let_72))) (let ((_let_74 (= _let_70 _let_72))) (let ((_let_75 (= _let_49 _let_45))) (let ((_let_76 (tptp.sdtasdt0 _let_1 tptp.sz10))) (let ((_let_77 (= _let_44 _let_76))) (let ((_let_78 (= _let_1 (tptp.sdtpldt0 tptp.sz00 _let_1)))) (let ((_let_79 (= _let_1 _let_76))) (let ((_let_80 (tptp.sdtpldt0 _let_69 tptp.xp))) (let ((_let_81 (tptp.sdtlseqdt0 _let_80 _let_2))) (let ((_let_82 (not _let_47))) (let ((_let_83 (not _let_12))) (let ((_let_84 (tptp.aNaturalNumber0 _let_62))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_38 _let_85 _let_83 _let_64))) (let ((_let_87 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (tptp.aNaturalNumber0 _let_6))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_39 _let_90 _let_84))) (let ((_let_92 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_92))) (let ((_let_95 (tptp.sz10 _let_6 QUANTIFIERS_INST_ENUM))) (let ((_let_96 (and _let_89 _let_65))) (let ((_let_97 (not _let_8))) (let ((_let_98 (not _let_13))) (let ((_let_99 (or _let_38 _let_98 _let_97 _let_96))) (let ((_let_100 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1407 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1407) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1407))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1407)))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (ASSUME :args (_let_14)))) (let ((_let_103 (AND_ELIM _let_102 :args (2)))) (let ((_let_104 (0))) (let ((_let_105 (AND_ELIM _let_102 :args _let_104))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_98 _let_38 _let_97 _let_96 (not _let_99)))) _let_105 _let_103 (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args (tptp.xp tptp.xn _let_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_100)))) _let_101 :args (_let_99 false _let_100)) :args (_let_96 false _let_13 false _let_11 false _let_8 false _let_99)))) (let ((_let_107 (not _let_96))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_96 0)) :args ((or _let_89 _let_107))) _let_106 :args (_let_89 false _let_96)))) (let ((_let_109 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) :args _let_104))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_39 _let_90 _let_84 (not _let_91)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args _let_95) :args _let_94)) _let_93 :args (_let_91 false _let_92)) :args (_let_84 false _let_29 false _let_89 false _let_91)))) (let ((_let_111 (AND_ELIM _let_102 :args (1)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_83 _let_38 _let_85 _let_64 (not _let_86)))) _let_111 _let_103 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.xp _let_62 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_64 false _let_12 false _let_11 false _let_84 false _let_86)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_96 1)) :args ((or _let_65 _let_107))) _let_106 :args (_let_65 false _let_96)))) (let ((_let_114 (and _let_67 (= _let_6 _let_62)))) (let ((_let_115 (or _let_90 _let_114))) (let ((_let_116 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (_let_116))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_114 0)) :args ((or _let_67 (not _let_114)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_90 _let_114 (not _let_115)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_6 QUANTIFIERS_INST_ENUM)) :args _let_118)) _let_117 :args (_let_115 false _let_116)) :args (_let_114 false _let_89 false _let_115)) :args (_let_67 false _let_114)))) (let ((_let_120 (or _let_39 _let_90 _let_68))) (let ((_let_121 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (_let_121))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_39 _let_90 _let_68 (not _let_120)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args _let_95) :args _let_123)) _let_122 :args (_let_120 false _let_121)) :args (_let_68 false _let_29 false _let_89 false _let_120)))) (let ((_let_125 (tptp.aNaturalNumber0 _let_70))) (let ((_let_126 (not _let_125))) (let ((_let_127 (or _let_38 _let_126 _let_71))) (let ((_let_128 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (_let_128))) (let ((_let_131 (tptp.aNaturalNumber0 _let_69))) (let ((_let_132 (not _let_131))) (let ((_let_133 (or _let_39 _let_132 _let_125))) (let ((_let_134 (tptp.sz10 _let_69 QUANTIFIERS_INST_ENUM))) (let ((_let_135 (tptp.aNaturalNumber0 _let_63))) (let ((_let_136 (or _let_85 _let_83 _let_135))) (let ((_let_137 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_138 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_139 (_let_137))) (let ((_let_140 (not _let_67))) (let ((_let_141 (not _let_68))) (let ((_let_142 (and _let_68 _let_67 _let_135))) (let ((_let_143 (ASSUME :args (_let_135)))) (let ((_let_144 (APPLY_UF tptp.sdtpldt0))) (let ((_let_145 (REFL :args (tptp.xm)))) (let ((_let_146 (ASSUME :args (_let_68)))) (let ((_let_147 (SYMM (SYMM _let_146)))) (let ((_let_148 (ASSUME :args (_let_67)))) (let ((_let_149 (SYMM _let_148))) (let ((_let_150 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_142)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_143 _let_146 _let_148) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (TRANS (SYMM _let_149) (SYMM _let_147)) _let_145 :args _let_144) :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_143))) :args (_let_135 _let_68 _let_67))) :args (_let_68 _let_67 _let_135))) :args (true _let_142)) :args ((or _let_131 _let_141 _let_140 (not _let_135)))) _let_124 _let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_83 _let_85 _let_135 (not _let_136)))) _let_111 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_138 :args (_let_62 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_139)) _let_138 :args (_let_136 false 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(_let_180 _let_79 _let_78 _let_77 _let_75 _let_74 _let_73 _let_71 _let_68 _let_67 _let_65 _let_64))) :args (true _let_240)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_180) _let_81))) _let_215 (REFL :args ((not _let_78))) _let_214 (REFL :args ((not _let_75))) _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 (REFL :args (_let_82)) :args _let_206)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_7)) :args ((not (and (not (= _let_2 _let_3)) _let_4)) SB_DEFAULT SBA_FIXPOINT))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_181) _let_179))) (REFL :args _let_239) :args _let_206)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_216)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_146 _let_231 _let_148 _let_221 _let_223 _let_230 _let_234 _let_217 _let_218 _let_225 _let_227) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG _let_229 _let_220 :args _let_144) (SYMM (TRANS (SYMM (TRANS (CONG _let_220 (TRANS _let_238 _let_237 (CONG _let_236 _let_145 :args _let_144)) :args _let_144) (SYMM _let_235) (CONG (TRANS (CONG _let_220 _let_233 :args _let_144) (SYMM _let_232)) _let_145 :args _let_144) (SYMM (SYMM _let_230)) (CONG _let_229 _let_224 :args _let_144))) (SYMM (TRANS (CONG (TRANS _let_223 _let_222) _let_220 :args _let_144) (SYMM _let_219))))) :args (=)) (FALSE_INTRO _let_217))) :args (_let_68 _let_65 _let_67 _let_74 _let_73 _let_167 _let_64 _let_52 _let_71 _let_77 _let_79))) :args (_let_79 _let_167 _let_77 _let_52 _let_74 _let_73 _let_71 _let_68 _let_67 _let_65 _let_64))) :args (true _let_216)) (CONG _let_215 (REFL :args (_let_204)) _let_214 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 (REFL :args (_let_181)) :args _let_206)) :args ((or _let_181 _let_205 _let_204 _let_203 _let_51 _let_202 _let_201 _let_200 _let_141 _let_140 _let_199 _let_198))) _let_178 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_168 0)) :args ((or _let_167 _let_175))) _let_174 :args (_let_167 false _let_168)) _let_166 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_182 0)) :args ((or _let_52 (not _let_182)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_183)) :args ((or _let_40 _let_38 _let_57 _let_55 _let_182 (not _let_183)))) _let_197 _let_103 _let_196 _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_185 :args (_let_44 tptp.sz00 tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_184)))) _let_185 :args (_let_183 false _let_184)) :args (_let_182 false _let_31 false _let_11 true _let_57 false _let_54 false _let_183)) :args (_let_52 false _let_182)) _let_156 _let_154 _let_151 _let_124 _let_119 _let_113 _let_112 :args (_let_181 false _let_79 false _let_167 false _let_77 true _let_51 false _let_74 false _let_73 false _let_71 false _let_68 false _let_67 false _let_65 false _let_64)) :args (_let_180 true _let_179)) _let_178 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_168 1)) :args ((or _let_78 _let_175))) _let_174 :args (_let_78 false _let_168)) _let_166 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_157)) :args ((or _let_38 _let_55 _let_75 (not _let_157)))) _let_103 _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_129 :args (tptp.xp _let_44 QUANTIFIERS_INST_CBQI_PROP)) :args _let_130))) _let_129 :args (_let_157 false _let_128)) :args (_let_75 false _let_11 false _let_54 false _let_157)) _let_156 _let_154 _let_151 _let_124 _let_119 _let_113 _let_112 :args (_let_82 true _let_81 false _let_79 false _let_78 false _let_77 false _let_75 false _let_74 false _let_73 false _let_71 false _let_68 false _let_67 false _let_65 false _let_64)) :args (_let_61 true _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.sz00 tptp.xp _let_44 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_56 false _let_31 false _let_11 true _let_57 false _let_54 true _let_53 false _let_58)) :args (_let_43 false _let_31 false _let_29 false _let_11 false _let_36 false _let_34 true _let_33)) _let_42 :args (false true _let_41 false _let_32)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_31 _let_30 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 (forall ((W0 $$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_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$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_21 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_20 _let_19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) _let_18 (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_17 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))) _let_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_15 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_14 (forall ((W0 $$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))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) _let_10 _let_8 _let_7 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn)) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm)) _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 14.98/15.19  )
% 14.98/15.19  % SZS output end Proof for NUM494+1
% 14.98/15.19  % cvc5---1.0.5 exiting
% 14.98/15.19  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------