%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM512+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 10:44:37 EDT 2023

% Result   : Theorem 21.53s 22.06s
% Output   : Proof 21.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM512+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 14:58:08 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  %----Proving TF0_NAR, FOF, or CNF
% 21.53/22.06  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8pBtfwjj00/cvc5---1.0.5_22757.p...
% 21.53/22.06  ------- get file name : TPTP file name is NUM512+1
% 21.53/22.06  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22757.smt2...
% 21.53/22.06  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 21.53/22.06  --- Run --no-e-matching --full-saturate-quant at 5...
% 21.53/22.06  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.53/22.06  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 21.53/22.06  % SZS status Theorem for NUM512+1
% 21.53/22.06  % SZS output start Proof for NUM512+1
% 21.53/22.06  (
% 21.53/22.06  (let ((_let_1 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_2 (= _let_1 (tptp.sdtasdt0 (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xp tptp.xk) tptp.xr) tptp.xr)))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_4 (tptp.sdtasdt0 (tptp.sdtasdt0 _let_3 tptp.xm) tptp.xr))) (let ((_let_5 (not (and (= _let_4 _let_1) _let_2)))) (let ((_let_6 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_7 (tptp.doDivides0 tptp.xr _let_1))) (let ((_let_8 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) _let_7))) (let ((_let_9 (tptp.isPrime0 tptp.xr))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_11 (and _let_10 (tptp.doDivides0 tptp.xr tptp.xk) _let_9))) (let ((_let_12 (= tptp.xk tptp.sz10))) (let ((_let_13 (= tptp.xk tptp.sz00))) (let ((_let_14 (tptp.sdtsldt0 _let_1 tptp.xp))) (let ((_let_15 (= tptp.xk _let_14))) (let ((_let_16 (tptp.doDivides0 tptp.xp _let_1))) (let ((_let_17 (tptp.isPrime0 tptp.xp))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_22 (and _let_21 _let_20 _let_19))) (let ((_let_23 (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_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_29 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_30 (tptp.sdtasdt0 tptp.xn tptp.sz10))) (let ((_let_31 (tptp.sdtsldt0 _let_30 tptp.xr))) (let ((_let_32 (tptp.sdtasdt0 tptp.xr _let_31))) (let ((_let_33 (= tptp.xn _let_32))) (let ((_let_34 (tptp.sdtasdt0 _let_31 tptp.xm))) (let ((_let_35 (tptp.sdtasdt0 tptp.xr _let_34))) (let ((_let_36 (= (tptp.sdtasdt0 _let_32 tptp.xm) _let_35))) (let ((_let_37 (= _let_35 (tptp.sdtasdt0 _let_34 tptp.xr)))) (let ((_let_38 (tptp.sdtasdt0 tptp.xp _let_14))) (let ((_let_39 (= _let_1 (tptp.sdtasdt0 (tptp.sdtsldt0 _let_38 tptp.xr) tptp.xr)))) (let ((_let_40 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_41 (= _let_38 _let_40))) (let ((_let_42 (= _let_34 (tptp.sdtsldt0 _let_40 tptp.xr)))) (let ((_let_43 (tptp.aNaturalNumber0 _let_31))) (let ((_let_44 (and _let_43 _let_33))) (let ((_let_45 (= _let_3 _let_31))) (let ((_let_46 (= _let_44 _let_45))) (let ((_let_47 (not _let_6))) (let ((_let_48 (= tptp.sz00 tptp.xr))) (let ((_let_49 (not _let_21))) (let ((_let_50 (not _let_10))) (let ((_let_51 (or _let_50 _let_49 _let_48 _let_47 _let_46))) (let ((_let_52 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1636 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1636) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1636))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1636)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (tptp.isPrime0 tptp.sz00))) (let ((_let_56 (not _let_48))) (let ((_let_57 (2))) (let ((_let_58 (ASSUME :args (_let_15)))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_58 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (not _let_55))) (let ((_let_61 (not _let_29))) (let ((_let_62 (or _let_61 _let_60))) (let ((_let_63 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 (ASSUME :args (_let_60)))) (let ((_let_67 (ASSUME :args (_let_48)))) (let ((_let_68 (ASSUME :args (_let_9)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_66 _let_67 _let_68) :args (_let_9 _let_48 _let_60)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_68)) (CONG (SYMM _let_67) :args (APPLY_UF tptp.isPrime0)) (FALSE_INTRO _let_66))) :args (_let_60 _let_48 _let_9)) :args ((not (and _let_9 _let_48 _let_60)) SB_LITERAL))) (CONG (REFL :args ((not _let_9))) (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_55))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_60 (not _let_62)))) (ASSUME :args (_let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_65))) _let_64 :args (_let_62 false _let_63)) :args (_let_60 false _let_29 false _let_62)) (AND_ELIM _let_59 :args _let_57) :args (_let_56 true _let_55 false _let_9)))) (let ((_let_70 (0))) (let ((_let_71 (AND_ELIM _let_59 :args _let_70))) (let ((_let_72 (ASSUME :args (_let_22)))) (let ((_let_73 (AND_ELIM _let_72 :args _let_70))) (let ((_let_74 (= tptp.xn _let_30))) (let ((_let_75 (and _let_74 (= tptp.xn (tptp.sdtasdt0 tptp.sz10 tptp.xn))))) (let ((_let_76 (or _let_49 _let_75))) (let ((_let_77 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_49 _let_75 (not _let_76)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_75 false _let_21 false _let_76)) :args (_let_74 false _let_75)))) (let ((_let_80 (_let_74))) (let ((_let_81 (APPLY_UF tptp.sdtsldt0))) (let ((_let_82 (REFL :args (tptp.xr)))) (let ((_let_83 (ASSUME :args _let_80))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_46)) :args ((or _let_44 (not _let_45) (not _let_46)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_83 (SCOPE (CONG (SYMM _let_84) _let_82 :args _let_81) :args _let_80)) :args _let_80)) _let_79 :args (_let_45 false _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_47 _let_49 _let_50 _let_48 _let_46 (not _let_51)))) (ASSUME :args (_let_6)) _let_73 _let_71 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xr tptp.xn _let_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_54)) _let_53 :args (_let_51 false _let_52)) :args (_let_46 false _let_6 false _let_21 false _let_10 true _let_48 false _let_51)) :args (_let_44 false _let_45 false _let_46)))) (let ((_let_86 (not _let_44))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 1)) :args ((or _let_33 _let_86))) _let_85 :args (_let_33 false _let_44)))) (let ((_let_88 (not _let_20))) (let ((_let_89 (not _let_43))) (let ((_let_90 (or _let_50 _let_89 _let_88 _let_36))) (let ((_let_91 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_43 _let_86))) _let_85 :args (_let_43 false _let_44)))) (let ((_let_94 (1))) (let ((_let_95 (AND_ELIM _let_72 :args _let_94))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_88 _let_50 _let_89 _let_36 (not _let_90)))) _let_95 _let_71 _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (tptp.xr _let_31 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_36 false _let_20 false _let_10 false _let_43 false _let_90)))) (let ((_let_97 (tptp.aNaturalNumber0 _let_34))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_50 _let_98 _let_37))) (let ((_let_100 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (_let_100))) (let ((_let_103 (or _let_89 _let_88 _let_97))) (let ((_let_104 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (_let_104))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_88 _let_89 _let_97 (not _let_103)))) _let_95 _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (_let_31 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) _let_105 :args (_let_103 false _let_104)) :args (_let_97 false _let_20 false _let_43 false _let_103)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_50 _let_98 _let_37 (not _let_99)))) _let_71 _let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (tptp.xr _let_34 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_102)) _let_101 :args (_let_99 false _let_100)) :args (_let_37 false _let_10 false _let_97 false _let_99)))) (let ((_let_109 (= _let_1 _let_4))) (let ((_let_110 (not _let_37))) (let ((_let_111 (not _let_36))) (let ((_let_112 (not _let_33))) (let ((_let_113 (and _let_74 _let_33 _let_36 _let_37))) (let ((_let_114 (APPLY_UF tptp.sdtasdt0))) (let ((_let_115 (REFL :args (tptp.xm)))) (let ((_let_116 (ASSUME :args (_let_37)))) (let ((_let_117 (SYMM (SYMM _let_116)))) (let ((_let_118 (ASSUME :args (_let_36)))) (let ((_let_119 (SYMM (SYMM _let_118)))) (let ((_let_120 (ASSUME :args (_let_33)))) (let ((_let_121 (CONG (SYMM (SYMM _let_120)) _let_115 :args _let_114))) (let ((_let_122 (and (tptp.aNaturalNumber0 _let_14) _let_41))) (let ((_let_123 (= _let_14 (tptp.sdtsldt0 _let_40 tptp.xp)))) (let ((_let_124 (= _let_123 _let_122))) (let ((_let_125 (tptp.doDivides0 tptp.xp _let_40))) (let ((_let_126 (not _let_125))) (let ((_let_127 (= tptp.sz00 tptp.xp))) (let ((_let_128 (tptp.aNaturalNumber0 _let_40))) (let ((_let_129 (not _let_128))) (let ((_let_130 (not _let_19))) (let ((_let_131 (or _let_130 _let_129 _let_127 _let_126 _let_124))) (let ((_let_132 (= _let_1 _let_40))) (let ((_let_133 (or _let_49 _let_88 _let_132))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_49 _let_88 _let_132 (not _let_133)))) _let_73 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_102)) _let_101 :args (_let_133 false _let_100)) :args (_let_132 false _let_21 false _let_20 false _let_133)))) (let ((_let_135 (ASSUME :args (_let_18)))) (let ((_let_136 (and _let_16 _let_132))) (let ((_let_137 (_let_16 _let_132))) (let ((_let_138 (ASSUME :args (_let_16)))) (let ((_let_139 (APPLY_UF tptp.doDivides0))) (let ((_let_140 (_let_132))) (let ((_let_141 (ASSUME :args _let_140))) (let ((_let_142 (SYMM _let_141))) (let ((_let_143 (REFL :args (tptp.xp)))) (let ((_let_144 (or _let_88 _let_49 _let_128))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_49 _let_88 _let_128 (not _let_144)))) _let_73 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.xm tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) _let_105 :args (_let_144 false _let_104)) :args (_let_128 false _let_21 false _let_20 false _let_144)))) (let ((_let_146 (not _let_127))) (let ((_let_147 (and _let_146 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_148 (= _let_17 _let_147))) (let ((_let_149 (or _let_130 _let_148))) (let ((_let_150 (AND_ELIM _let_72 :args _let_57))) (let ((_let_151 (= _let_40 _let_35))) (let ((_let_152 (and _let_97 _let_151))) (let ((_let_153 (= _let_152 _let_42))) (let ((_let_154 (tptp.doDivides0 tptp.xr _let_40))) (let ((_let_155 (not _let_154))) (let ((_let_156 (or _let_50 _let_129 _let_48 _let_155 _let_153))) (let ((_let_157 (and _let_7 _let_132))) (let ((_let_158 (_let_7 _let_132))) (let ((_let_159 (ASSUME :args (_let_7)))) (let ((_let_160 (and _let_132 _let_33 _let_36))) (let ((_let_161 (and _let_33 _let_36 _let_37 _let_41 _let_42))) (let ((_let_162 (ASSUME :args (_let_41)))) (let ((_let_163 (ASSUME :args (_let_42)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_161)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_162 _let_116 _let_163 _let_118 _let_120) (SCOPE (TRANS _let_121 _let_119 _let_117 (CONG (TRANS (SYMM (SYMM _let_163)) (CONG (SYMM _let_162) _let_82 :args _let_81)) _let_82 :args _let_114)) :args (_let_41 _let_37 _let_42 _let_36 _let_33))) :args (_let_33 _let_36 _let_37 _let_41 _let_42))) :args (true _let_161)) :args ((or _let_39 _let_112 _let_111 _let_110 (not _let_41) (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_153)) :args ((or _let_42 (not _let_152) (not _let_153)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_152)) :args ((or _let_98 _let_152 (not _let_151)))) _let_107 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_120 _let_141) (SCOPE (TRANS _let_142 _let_121 _let_119) :args (_let_36 _let_33 _let_132))) :args (_let_132 _let_33 _let_36))) :args (true _let_160)) _let_134 _let_87 _let_96 :args (_let_151 false _let_132 false _let_33 false _let_36)) :args (_let_152 false _let_97 false _let_151)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_156)) :args ((or _let_50 _let_48 _let_129 _let_155 _let_153 (not _let_156)))) _let_71 _let_69 _let_145 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_157)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_159 _let_141) (SCOPE (TRUE_ELIM (TRANS (CONG _let_82 _let_142 :args _let_139) (TRUE_INTRO _let_159))) :args _let_158)) :args _let_158)) :args (true _let_157)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_58 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args _let_94) _let_134 :args (_let_154 false _let_7 false _let_132)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xr _let_40 _let_34 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_54))) _let_53 :args (_let_156 false _let_52)) :args (_let_153 false _let_10 true _let_48 false _let_128 false _let_154 false _let_156)) :args (_let_42 false _let_152 false _let_153)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_122 1)) :args ((or _let_41 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_124)) :args ((or _let_122 (not _let_123) (not _let_124)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_141 (SCOPE (CONG (SYMM _let_142) _let_143 :args _let_81) :args _let_140)) :args _let_140)) _let_134 :args (_let_123 false _let_132)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_130 _let_127 _let_129 _let_126 _let_124 (not _let_131)))) _let_150 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_147 0)) :args ((or _let_146 (not _let_147)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_148)) :args ((or (not _let_17) _let_147 (not _let_148)))) (AND_ELIM _let_135 :args _let_70) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_130 _let_148 (not _let_149)))) _let_150 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args _let_65))) _let_64 :args (_let_149 false _let_63)) :args (_let_148 false _let_19 false _let_149)) :args (_let_147 false _let_17 false _let_148)) :args (_let_146 false _let_147)) _let_145 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_136)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_138 _let_141) (SCOPE (TRUE_ELIM (TRANS (CONG _let_143 _let_142 :args _let_139) (TRUE_INTRO _let_138))) :args _let_137)) :args _let_137)) :args (true _let_136)) (AND_ELIM _let_135 :args _let_94) _let_134 :args (_let_125 false _let_16 false _let_132)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xp _let_40 _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_54))) _let_53 :args (_let_131 false _let_52)) :args (_let_124 false _let_19 true _let_127 false _let_128 false _let_125 false _let_131)) :args (_let_122 false _let_123 false _let_124)) :args (_let_41 false _let_122)) (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_58 :args ((not (and _let_109 _let_2)) SB_DEFAULT SBA_FIXPOINT))))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_113)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_83 _let_116 _let_118 _let_120) (SCOPE (TRANS _let_121 _let_119 _let_117 (CONG (CONG (CONG _let_84 _let_82 :args _let_81) _let_115 :args _let_114) _let_82 :args _let_114)) :args (_let_74 _let_37 _let_36 _let_33))) :args (_let_74 _let_33 _let_36 _let_37))) :args (true _let_113)) :args ((or _let_109 (not _let_74) _let_112 _let_111 _let_110))) _let_79 _let_87 _let_96 _let_108 :args (_let_109 false _let_74 false _let_33 false _let_36 false _let_37)) :args ((not _let_39) false _let_109)) _let_108 _let_96 _let_87 :args (false false _let_42 false _let_41 true _let_39 false _let_37 false _let_36 false _let_33)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_29 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_27 _let_26 _let_25 (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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) (forall ((W0 $$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))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$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))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$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))))))) _let_24 (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_23 (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_22 (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_18 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_15 (not (or _let_13 _let_12)) (and (not _let_13) (not _let_12)) _let_11 _let_8 (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_6 (tptp.doDivides0 tptp.xr tptp.xm)) _let_6 (and (not (= _let_3 tptp.xn)) (tptp.sdtlseqdt0 _let_3 tptp.xn)) _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 21.67/22.07  )
% 21.67/22.07  % SZS output end Proof for NUM512+1
% 21.67/22.07  % cvc5---1.0.5 exiting
% 21.67/22.07  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------