%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM469+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 10:44:13 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : NUM469+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n024.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
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 07:58:39 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.59  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.GBvkbweYvO/cvc5---1.0.5_20131.p...
% 0.19/0.59  ------- get file name : TPTP file name is NUM469+2
% 0.19/0.59  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20131.smt2...
% 0.19/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.59  % SZS status Theorem for NUM469+2
% 0.19/0.59  % SZS output start Proof for NUM469+2
% 0.19/0.59  (
% 0.19/0.59  (let ((_let_1 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_2 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtasdt0 tptp.xl W0)))) (tptp.doDivides0 tptp.xl _let_1))))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xl))) (let ((_let_4 (tptp.sdtsldt0 tptp.xm tptp.xl))) (let ((_let_5 (tptp.sdtpldt0 _let_4 _let_3))) (let ((_let_6 (= _let_1 (tptp.sdtasdt0 tptp.xl _let_5)))) (let ((_let_7 (tptp.aNaturalNumber0 _let_3))) (let ((_let_8 (tptp.aNaturalNumber0 _let_4))) (let ((_let_9 (and _let_8 (= tptp.xm (tptp.sdtasdt0 tptp.xl _let_4)) _let_7 (= tptp.xn (tptp.sdtasdt0 tptp.xl _let_3)) _let_6))) (let ((_let_10 (=> (not (= tptp.xl tptp.sz00)) _let_9))) (let ((_let_11 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xl W0)))) (tptp.doDivides0 tptp.xl tptp.xm) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xl W0)))) (tptp.doDivides0 tptp.xl tptp.xn)))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_15 (and _let_14 _let_13 _let_12))) (let ((_let_16 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_22 (tptp.sdtasdt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (= tptp.xm _let_22))) (let ((_let_24 (tptp.sdtasdt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (= tptp.xn _let_24))) (let ((_let_26 (= _let_1 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (let ((_let_27 (= tptp.sz00 (tptp.sdtpldt0 tptp.sz00 tptp.sz00)))) (let ((_let_28 (= _let_22 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xl)))) (let ((_let_29 (= _let_24 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xl)))) (let ((_let_30 (tptp.sdtasdt0 tptp.xl tptp.sz00))) (let ((_let_31 (= _let_1 _let_30))) (let ((_let_32 (= tptp.xn (tptp.sdtpldt0 tptp.xn tptp.sz00)))) (let ((_let_33 (= tptp.sz00 _let_30))) (let ((_let_34 (= tptp.sz00 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.sz00)))) (let ((_let_35 (= tptp.sz00 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.sz00)))) (let ((_let_36 (= tptp.sz00 tptp.xl))) (let ((_let_37 (not _let_23))) (let ((_let_38 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xm (tptp.sdtasdt0 tptp.xl W0))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (0))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (or))) (let ((_let_46 (not _let_41))) (let ((_let_47 (_let_46))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_41))) (REFL :args (_let_42)) :args _let_45)) (AND_ELIM _let_44 :args _let_43) :args (_let_42 true _let_41)))) (let ((_let_49 (REFL :args (_let_40)))) (let ((_let_50 (not _let_25))) (let ((_let_51 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50))) (let ((_let_54 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xl W0))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (2))) (let ((_let_57 (not _let_54))) (let ((_let_58 (_let_57))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_54))) (REFL :args (_let_55)) :args _let_45)) (AND_ELIM _let_44 :args _let_56) :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (not _let_12))) (let ((_let_62 (not _let_13))) (let ((_let_63 (or _let_62 _let_61 _let_26))) (let ((_let_64 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_15)))) (let ((_let_67 (AND_ELIM _let_66 :args _let_56))) (let ((_let_68 (not _let_21))) (let ((_let_69 (or _let_68 _let_27))) (let ((_let_70 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_74 (ASSUME :args (_let_21)))) (let ((_let_75 (not _let_14))) (let ((_let_76 (or _let_75 _let_39 _let_28))) (let ((_let_77 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_77))) (let ((_let_80 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_45)) :args ((or _let_38 _let_40))) _let_48 :args (_let_38 true _let_40)))) (let ((_let_82 (AND_ELIM _let_66 :args _let_43))) (let ((_let_83 (or _let_75 _let_52 _let_29))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_45)) :args ((or _let_51 _let_53))) _let_59 :args (_let_51 true _let_53)))) (let ((_let_85 (not _let_31))) (let ((_let_86 (or _let_68 _let_85))) (let ((_let_87 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtasdt0 tptp.xl W0))))))) (let ((_let_88 (NOT_NOT_ELIM (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args _let_43)))) (let ((_let_89 (_let_87))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (and _let_32 (= tptp.xn (tptp.sdtpldt0 tptp.sz00 tptp.xn))))) (let ((_let_92 (or _let_61 _let_91))) (let ((_let_93 (and _let_33 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xl))))) (let ((_let_94 (or _let_75 _let_93))) (let ((_let_95 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (_let_95))) (let ((_let_98 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_99 (and _let_34 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_100 (or _let_39 _let_99))) (let ((_let_101 (and _let_35 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_102 (or _let_52 _let_101))) (let ((_let_103 (tptp.aNaturalNumber0 _let_5))) (let ((_let_104 (not _let_7))) (let ((_let_105 (not _let_8))) (let ((_let_106 (or _let_105 _let_104 _let_103))) (let ((_let_107 (not _let_6))) (let ((_let_108 (not _let_103))) (let ((_let_109 (or _let_108 _let_107))) (let ((_let_110 (not _let_9))) (let ((_let_111 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (not _let_36))) (let ((_let_114 (not _let_35))) (let ((_let_115 (not _let_34))) (let ((_let_116 (not _let_33))) (let ((_let_117 (not _let_29))) (let ((_let_118 (not _let_28))) (let ((_let_119 (not _let_32))) (let ((_let_120 (not _let_27))) (let ((_let_121 (not _let_26))) (let ((_let_122 (= tptp.sz00 _let_1))) (let ((_let_123 (ASSUME :args (_let_27)))) (let ((_let_124 (SYMM (SYMM _let_123)))) (let ((_let_125 (ASSUME :args (_let_33)))) (let ((_let_126 (ASSUME :args (_let_85)))) (let ((_let_127 (ASSUME :args (_let_26)))) (let ((_let_128 (ASSUME :args (_let_23)))) (let ((_let_129 (ASSUME :args (_let_28)))) (let ((_let_130 (APPLY_UF tptp.sdtasdt0))) (let ((_let_131 (ASSUME :args (_let_36)))) (let ((_let_132 (SYMM (SYMM _let_131)))) (let ((_let_133 (ASSUME :args (_let_34)))) (let ((_let_134 (ASSUME :args (_let_32)))) (let ((_let_135 (ASSUME :args (_let_25)))) (let ((_let_136 (ASSUME :args (_let_29)))) (let ((_let_137 (ASSUME :args (_let_35)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_123 (MODUS_PONENS (AND_INTRO _let_127 _let_128 _let_129 _let_131 _let_133 _let_134 _let_135 _let_136 _let_137) (SCOPE (TRANS (SYMM (SYMM _let_137)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_132 :args _let_130) (SYMM _let_136) (SYMM _let_135) (SYMM (SYMM _let_134)) (CONG (REFL :args (tptp.xn)) (TRANS (SYMM (SYMM _let_133)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) _let_132 :args _let_130) (SYMM _let_129) (SYMM _let_128)) :args (APPLY_UF tptp.sdtpldt0)) (SYMM _let_127)) :args (_let_26 _let_23 _let_28 _let_36 _let_34 _let_32 _let_25 _let_29 _let_35))) _let_125 _let_126) :args (_let_36 _let_23 _let_25 _let_26 _let_27 _let_32 _let_28 _let_29 _let_33 _let_34 _let_35 _let_85)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_126)) (TRUE_INTRO (TRANS (SYMM (ASSUME :args (_let_122))) _let_124 (SYMM (TRANS (SYMM _let_125) _let_124)))))) :args (_let_27 _let_122 _let_33 _let_85)) :args ((not (and _let_36 _let_23 _let_25 _let_26 _let_27 _let_32 _let_28 _let_29 _let_33 _let_34 _let_35 _let_85)) SB_LITERAL))) (CONG (REFL :args (_let_113)) (REFL :args (_let_37)) (REFL :args (_let_50)) (REFL :args (_let_121)) (REFL :args (_let_120)) (REFL :args (_let_119)) (REFL :args (_let_118)) (REFL :args (_let_117)) (REFL :args (_let_116)) (REFL :args (_let_115)) (REFL :args (_let_114)) (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_31))) :args _let_45)) :args ((or _let_113 _let_37 _let_50 _let_31 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_36))) (REFL :args (_let_9)) :args _let_45)) :args ((or _let_9 _let_36))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_107 _let_108 (not _let_109)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 tptp.xl W0)))) :args _let_89)) _let_88 :args (_let_109 false _let_87)) (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_104 _let_103 (not _let_106)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (_let_4 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_111))) _let_112 :args (_let_106 false _let_111)) (REORDERING (CNF_AND_POS :args (_let_9 4)) :args ((or _let_6 _let_110))) (REORDERING (CNF_AND_POS :args (_let_9 2)) :args ((or _let_7 _let_110))) (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_8 _let_110))) :args (_let_110 false _let_109 false _let_103 false _let_106 false _let_6 false _let_7 false _let_8)) :args (_let_36 true _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_35 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_52 _let_101 (not _let_102)))) _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_102 false _let_95)) :args (_let_101 false _let_51 false _let_102)) :args (_let_35 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_99 0)) :args ((or _let_34 (not _let_99)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_39 _let_99 (not _let_100)))) _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_100 false _let_95)) :args (_let_99 false _let_38 false _let_100)) :args (_let_34 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_33 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_75 _let_93 (not _let_94)))) _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.xl QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_97)) _let_96 :args (_let_94 false _let_95)) :args (_let_93 false _let_14 false _let_94)) :args (_let_33 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 0)) :args ((or _let_32 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_61 _let_91 (not _let_92)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72)) _let_71 :args (_let_92 false _let_70)) :args (_let_91 false _let_12 false _let_92)) :args (_let_32 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_68 _let_85 (not _let_86)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W0) false))))) :args _let_89)) _let_88 :args (_let_86 false _let_87)) :args (_let_85 false _let_21 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_75 _let_52 _let_29 (not _let_83)))) _let_82 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_80)) :args _let_79)) _let_78 :args (_let_83 false _let_77)) :args (_let_29 false _let_14 false _let_51 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_39 _let_28 (not _let_76)))) _let_82 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_80)) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args (_let_28 false _let_14 false _let_38 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_27 (not _let_69)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_72))) _let_71 :args (_let_69 false _let_70)) :args (_let_27 false _let_21 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_62 _let_61 _let_26 (not _let_63)))) (AND_ELIM _let_66 :args (1)) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_26 false _let_13 false _let_12 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_25))) :args _let_45)) :args ((or _let_25 _let_53))) _let_59 :args (_let_25 true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_23))) :args _let_45)) :args ((or _let_23 _let_40))) _let_48 :args (_let_23 true _let_40)) :args (false false _let_36 false _let_35 false _let_34 false _let_33 false _let_32 true _let_31 false _let_29 false _let_28 false _let_27 false _let_26 false _let_25 false _let_23)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_21 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) _let_19 (forall ((W0 $$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_18 _let_17 (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_16 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) (forall ((W0 $$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)))) _let_15 _let_11 _let_10 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.59  )
% 0.19/0.59  % SZS output end Proof for NUM469+2
% 0.19/0.59  % cvc5---1.0.5 exiting
% 0.19/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------