%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM518+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n003.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 10:44:41 EDT 2023

% Result   : Theorem 23.68s 23.95s
% Output   : Proof 23.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM518+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri Aug 25 12:10:53 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 23.68/23.95  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TTo7o08eVX/cvc5---1.0.5_29834.p...
% 23.68/23.95  ------- get file name : TPTP file name is NUM518+1
% 23.68/23.95  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29834.smt2...
% 23.68/23.95  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 23.68/23.95  --- Run --no-e-matching --full-saturate-quant at 5...
% 23.68/23.95  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 23.68/23.95  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 23.68/23.95  % SZS status Theorem for NUM518+1
% 23.68/23.95  % SZS output start Proof for NUM518+1
% 23.68/23.95  (
% 23.68/23.95  (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_3 (not (or _let_2 _let_1)))) (let ((_let_4 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_5 (tptp.doDivides0 tptp.xp _let_4))) (let ((_let_6 (or _let_5 _let_1))) (let ((_let_7 (tptp.sdtlseqdt0 _let_4 tptp.xn))) (let ((_let_8 (and (not (= _let_4 tptp.xn)) _let_7))) (let ((_let_9 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_10 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_11 (tptp.isPrime0 tptp.xr))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_13 (and _let_12 (tptp.doDivides0 tptp.xr tptp.xk) _let_11))) (let ((_let_14 (= tptp.xk tptp.sz10))) (let ((_let_15 (= tptp.xk tptp.sz00))) (let ((_let_16 (= tptp.xk (tptp.sdtsldt0 _let_10 tptp.xp)))) (let ((_let_17 (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.doDivides0 tptp.xp _let_10))) (let ((_let_20 (and (tptp.isPrime0 tptp.xp) _let_19))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_24 (and _let_23 _let_22 _let_21))) (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)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))))) (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_30 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_31 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_32 (= _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50))) (let ((_let_33 (tptp.doDivides0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50))) (let ((_let_34 (1))) (let ((_let_35 (ASSUME :args (_let_3)))) (let ((_let_36 (= tptp.xn (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50)))) (let ((_let_37 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (= _let_38 _let_32))) (let ((_let_40 (not _let_9))) (let ((_let_41 (= tptp.sz00 tptp.xr))) (let ((_let_42 (not _let_23))) (let ((_let_43 (not _let_12))) (let ((_let_44 (or _let_43 _let_42 _let_41 _let_40 _let_39))) (let ((_let_45 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1635 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1635) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1635))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1635)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (_let_45))) (let ((_let_48 (tptp.isPrime0 tptp.sz00))) (let ((_let_49 (not _let_41))) (let ((_let_50 (2))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_16)) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (not _let_48))) (let ((_let_53 (not _let_31))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (ASSUME :args (_let_52)))) (let ((_let_59 (ASSUME :args (_let_41)))) (let ((_let_60 (ASSUME :args (_let_11)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_58 _let_59 _let_60) :args (_let_11 _let_41 _let_52)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_60)) (CONG (SYMM _let_59) :args (APPLY_UF tptp.isPrime0)) (FALSE_INTRO _let_58))) :args (_let_52 _let_41 _let_11)) :args ((not (and _let_11 _let_41 _let_52)) SB_LITERAL))) (CONG (REFL :args ((not _let_11))) (REFL :args (_let_49)) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_48))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_52 (not _let_54)))) (ASSUME :args (_let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 false _let_31 false _let_54)) (AND_ELIM _let_51 :args _let_50) :args (_let_49 true _let_48 false _let_11)))) (let ((_let_62 (0))) (let ((_let_63 (AND_ELIM _let_51 :args _let_62))) (let ((_let_64 (ASSUME :args (_let_24)))) (let ((_let_65 (AND_ELIM _let_64 :args _let_62))) (let ((_let_66 (ASSUME :args (_let_9)))) (let ((_let_67 (not _let_36))) (let ((_let_68 (not _let_37))) (let ((_let_69 (or _let_68 _let_67))) (let ((_let_70 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xr W2))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (not _let_70))) (let ((_let_73 (= _let_9 _let_72))) (let ((_let_74 (or _let_43 _let_42 _let_73))) (let ((_let_75 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_72))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_77)) :args _let_77)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_70))) (REFL :args (_let_71)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or _let_40 _let_72 (not _let_73)))) _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_42 _let_43 _let_73 (not _let_74)))) _let_65 _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.xr tptp.xn QUANTIFIERS_INST_FMF_FMC_EXH)) :args (_let_75))) _let_76 :args (_let_74 false _let_75)) :args (_let_73 false _let_23 false _let_12 false _let_74)) :args (_let_72 false _let_9 false _let_73)) :args (_let_71 true _let_70)))) (let ((_let_79 (REFL :args (_let_69)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_37))) :args _let_57)) :args ((or _let_37 _let_69))) _let_78 :args (_let_37 true _let_69)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_32 (not _let_38) (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_38)) :args ((or _let_68 _let_67 _let_38))) _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_36))) :args _let_57)) :args ((or _let_36 _let_69))) _let_78 :args (_let_36 true _let_69)) :args (_let_38 false _let_37 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_40 _let_42 _let_43 _let_41 _let_39 (not _let_44)))) _let_66 _let_65 _let_63 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xr tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 QUANTIFIERS_INST_CBQI_PROP)) :args _let_47)) _let_46 :args (_let_44 false _let_45)) :args (_let_39 false _let_9 false _let_23 false _let_12 true _let_41 false _let_44)) :args (_let_32 false _let_38 false _let_39)))) (let ((_let_82 (tptp.sdtlseqdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50))) (let ((_let_83 (= tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50))) (let ((_let_84 (not _let_33))) (let ((_let_85 (not _let_21))) (let ((_let_86 (or _let_85 _let_68 _let_84 _let_83 _let_82))) (let ((_let_87 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W0 W1)) (= tptp.sz00 W1) (tptp.sdtlseqdt0 W0 W1))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 tptp.xn))) (let ((_let_90 (not _let_89))) (let ((_let_91 (not _let_82))) (let ((_let_92 (or _let_85 _let_68 _let_42 _let_91 _let_90 _let_17))) (let ((_let_93 (forall ((W0 $$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_94 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (and _let_7 _let_32))) (let ((_let_96 (_let_7 _let_32))) (let ((_let_97 (ASSUME :args (_let_7)))) (let ((_let_98 (REFL :args (tptp.xn)))) (let ((_let_99 (ASSUME :args (_let_32)))) (let ((_let_100 (SYMM (SYMM _let_99)))) (let ((_let_101 (SYMM _let_100))) (let ((_let_102 (AND_ELIM _let_64 :args _let_50))) (let ((_let_103 (= tptp.sz00 _let_4))) (let ((_let_104 (not _let_83))) (let ((_let_105 (tptp.sdtasdt0 tptp.xr tptp.sz00))) (let ((_let_106 (= tptp.xn _let_105))) (let ((_let_107 (and _let_31 _let_106))) (let ((_let_108 (= _let_103 _let_107))) (let ((_let_109 (not _let_103))) (let ((_let_110 (or _let_43 _let_42 _let_41 _let_40 _let_108))) (let ((_let_111 (not _let_107))) (let ((_let_112 (= tptp.sz00 _let_105))) (let ((_let_113 (= tptp.sz00 tptp.xn))) (let ((_let_114 (not _let_106))) (let ((_let_115 (and _let_112 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xr))))) (let ((_let_116 (or _let_43 _let_115))) (let ((_let_117 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (_let_117))) (let ((_let_120 (= tptp.sz00 _let_10))) (let ((_let_121 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xm)))) (let ((_let_122 (not _let_113))) (let ((_let_123 (not _let_120))) (let ((_let_124 (not _let_19))) (let ((_let_125 (_let_122))) (let ((_let_126 (not _let_2))) (let ((_let_127 (ASSUME :args (_let_126)))) (let ((_let_128 (APPLY_UF tptp.doDivides0))) (let ((_let_129 (ASSUME :args (_let_113)))) (let ((_let_130 (SYMM (SYMM _let_129)))) (let ((_let_131 (REFL :args (tptp.xp)))) (let ((_let_132 (ASSUME :args (_let_120)))) (let ((_let_133 (ASSUME :args (_let_19)))) (let ((_let_134 (and (= tptp.sz00 (tptp.sdtasdt0 tptp.xm tptp.sz00)) _let_121))) (let ((_let_135 (not _let_22))) (let ((_let_136 (or _let_135 _let_134))) (let ((_let_137 (and _let_113 _let_121))) (let ((_let_138 (_let_113 _let_121))) (let ((_let_139 (ASSUME :args (_let_121)))) (let ((_let_140 (and _let_122 _let_112))) (let ((_let_141 (ASSUME :args _let_125))) (let ((_let_142 (=))) (let ((_let_143 (ASSUME :args (_let_112)))) (let ((_let_144 (REFL :args ((not _let_32))))) (let ((_let_145 (and _let_109 _let_32))) (let ((_let_146 (_let_109 _let_32))) (let ((_let_147 (ASSUME :args (_let_109)))) (let ((_let_148 (ASSUME :args (_let_84)))) (let ((_let_149 (ASSUME :args (_let_5)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_148 _let_99 _let_149) :args (_let_5 _let_32 _let_84)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_149)) (CONG _let_131 _let_100 :args _let_128) (FALSE_INTRO _let_148))) :args (_let_84 _let_32 _let_5)) :args ((not (and _let_5 _let_32 _let_84)) SB_LITERAL))) (CONG (REFL :args ((not _let_5))) _let_144 (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_33))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_85 _let_68 _let_83 _let_82 _let_84 (not _let_86)))) _let_102 _let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_145)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_147 _let_99) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) _let_101 :args _let_142) (FALSE_INTRO _let_147))) :args _let_146)) :args _let_146)) :args (true _let_145)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_103))) _let_144 (REFL :args (_let_104)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_108)) :args ((or _let_109 _let_107 (not _let_108)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 1)) :args ((or _let_106 _let_111))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_140)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_143 _let_141) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (SYMM _let_143) _let_98 :args _let_142) (FALSE_INTRO _let_141)) :args ((= _let_106 false)))) :args (_let_112 _let_122))) :args (_let_122 _let_112))) :args (true _let_140)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_122) _let_113))) (REFL :args ((not _let_112))) (REFL :args (_let_114)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_137)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_129 _let_139) (SCOPE (TRANS (SYMM (SYMM _let_139)) (CONG _let_130 (REFL :args (tptp.xm)) :args (APPLY_UF tptp.sdtasdt0))) :args _let_138)) :args _let_138)) :args (true _let_137)) :args ((or _let_122 _let_120 (not _let_121)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_134 1)) :args ((or _let_121 (not _let_134)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_135 _let_134 (not _let_136)))) (AND_ELIM _let_64 :args _let_34) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_119)) _let_118 :args (_let_136 false _let_117)) :args (_let_134 false _let_22 false _let_136)) :args (_let_121 false _let_134)) (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_127 _let_129 _let_132 _let_133) :args (_let_19 _let_126 _let_113 _let_120)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_133)) (CONG _let_131 (SYMM _let_132) :args _let_128) (CONG _let_131 _let_130 :args _let_128) (FALSE_INTRO _let_127))) :args (_let_126 _let_113 _let_120 _let_19)) :args ((not (and _let_19 _let_126 _let_113 _let_120)) SB_LITERAL))) (CONG (REFL :args (_let_124)) (MACRO_SR_PRED_INTRO :args ((= (not _let_126) _let_2))) (REFL :args _let_125) (REFL :args (_let_123)) :args _let_57)) :args ((or _let_2 _let_124 _let_122 _let_123))) (NOT_OR_ELIM _let_35 :args _let_62) (AND_ELIM (ASSUME :args (_let_20)) :args _let_34) :args (_let_122 false _let_121 true _let_120 true _let_2 false _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 0)) :args ((or _let_112 (not _let_115)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_43 _let_115 (not _let_116)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (tptp.xr QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_119)) _let_118 :args (_let_116 false _let_117)) :args (_let_115 false _let_12 false _let_116)) :args (_let_112 false _let_115)) :args (_let_114 true _let_113 false _let_112)) :args (_let_111 true _let_106)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_40 _let_42 _let_43 _let_41 _let_108 (not _let_110)))) _let_66 _let_65 _let_63 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xr tptp.xn tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_47))) _let_46 :args (_let_110 false _let_45)) :args (_let_108 false _let_9 false _let_23 false _let_12 true _let_41 false _let_110)) :args (_let_109 true _let_107 false _let_108)) _let_81 :args (_let_104 true _let_103 false _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_17 _let_42 _let_85 _let_68 _let_91 _let_90 (not _let_92)))) (ASSUME :args (_let_18)) _let_65 _let_102 _let_80 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_95)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_97 _let_99) (SCOPE (TRUE_ELIM (TRANS (CONG _let_101 _let_98 :args (APPLY_UF tptp.sdtlseqdt0)) (TRUE_INTRO _let_97))) :args _let_96)) :args _let_96)) :args (true _let_95)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args _let_34) _let_81 :args (_let_89 false _let_7 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_91 true _let_17 false _let_23 false _let_21 false _let_37 false _let_89 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_84 false _let_21 false _let_37 true _let_83 true _let_82 false _let_86)) _let_81 (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_6)) (NOT_OR_ELIM _let_35 :args _let_34) :args (_let_5 true _let_1)) :args (false true _let_33 false _let_32 false _let_5)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_31 (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)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (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))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) _let_30 (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)))) _let_29 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) _let_28 _let_27 (forall ((W0 $$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)))) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_25 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_24 (forall ((W0 $$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))) (=> (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_20 _let_18 (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_16 (not (or _let_15 _let_14)) (and (not _let_15) (not _let_14)) _let_13 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_10)) (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_9 (tptp.doDivides0 tptp.xr tptp.xm)) _let_9 _let_8 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 _let_4 tptp.xm)) _let_6 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 23.79/23.96  )
% 23.79/23.96  % SZS output end Proof for NUM518+1
% 23.79/23.96  % cvc5---1.0.5 exiting
% 23.79/23.96  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------