%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM473+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 10:44:15 EDT 2023

% Result   : Theorem 8.94s 9.30s
% Output   : Proof 8.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM473+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n027.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 14:23:34 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  %----Proving TF0_NAR, FOF, or CNF
% 8.94/9.30  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3yP6syZVXE/cvc5---1.0.5_15001.p...
% 8.94/9.30  ------- get file name : TPTP file name is NUM473+2
% 8.94/9.30  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15001.smt2...
% 8.94/9.30  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.94/9.30  % SZS status Theorem for NUM473+2
% 8.94/9.30  % SZS output start Proof for NUM473+2
% 8.94/9.30  (
% 8.94/9.30  (let ((_let_1 (tptp.sdtlseqdt0 tptp.xp tptp.xq))) (let ((_let_2 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xq))) _let_1)))) (let ((_let_3 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xm _let_3))) (let ((_let_5 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) (tptp.sdtpldt0 tptp.xm tptp.xn)))) _let_4))) (let ((_let_6 (= tptp.xq (tptp.sdtsldt0 _let_3 tptp.xl)))) (let ((_let_7 (tptp.sdtasdt0 tptp.xl tptp.xq))) (let ((_let_8 (= _let_3 _let_7))) (let ((_let_9 (tptp.aNaturalNumber0 tptp.xq))) (let ((_let_10 (and _let_9 _let_8 _let_6))) (let ((_let_11 (= tptp.xp (tptp.sdtsldt0 tptp.xm tptp.xl)))) (let ((_let_12 (tptp.sdtasdt0 tptp.xl tptp.xp))) (let ((_let_13 (= tptp.xm _let_12))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_15 (and _let_14 _let_13 _let_11))) (let ((_let_16 (not (= tptp.xl tptp.sz00)))) (let ((_let_17 (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.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtasdt0 tptp.xl W0)))) (tptp.doDivides0 tptp.xl _let_3)))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_21 (and _let_20 _let_19 _let_18))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W2 W0))) (let ((_let_2 (tptp.sdtasdt0 W1 W0))) (let ((_let_3 (tptp.sdtasdt0 W0 W2))) (let ((_let_4 (tptp.sdtasdt0 W0 W1))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_27 (tptp.sdtasdt0 tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (= _let_3 _let_27))) (let ((_let_29 (tptp.sdtasdt0 tptp.xp tptp.xl))) (let ((_let_30 (= _let_12 _let_29))) (let ((_let_31 (= _let_27 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xl)))) (let ((_let_32 (tptp.sdtlseqdt0 _let_3 tptp.xm))) (let ((_let_33 (tptp.sdtlseqdt0 _let_7 _let_12))) (let ((_let_34 (1))) (let ((_let_35 (ASSUME :args (_let_15)))) (let ((_let_36 (ASSUME :args (_let_10)))) (let ((_let_37 (not _let_28))) (let ((_let_38 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtasdt0 tptp.xl W0))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (2))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (_let_45))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) :args _let_43) :args (_let_42 true _let_41)))) (let ((_let_48 (REFL :args (_let_40)))) (let ((_let_49 (not _let_14))) (let ((_let_50 (not _let_20))) (let ((_let_51 (or _let_50 _let_49 _let_30))) (let ((_let_52 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_56 (0))) (let ((_let_57 (AND_ELIM _let_35 :args _let_56))) (let ((_let_58 (ASSUME :args (_let_21)))) (let ((_let_59 (AND_ELIM _let_58 :args _let_56))) (let ((_let_60 (or _let_50 _let_39 _let_31))) (let ((_let_61 (= tptp.xm _let_3))) (let ((_let_62 (not _let_32))) (let ((_let_63 (not _let_4))) (let ((_let_64 (tptp.aNaturalNumber0 _let_3))) (let ((_let_65 (not _let_64))) (let ((_let_66 (not _let_19))) (let ((_let_67 (or _let_66 _let_65 _let_63 _let_62 _let_61))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (= tptp.xp tptp.xq))) (let ((_let_71 (not _let_61))) (let ((_let_72 (tptp.sdtlseqdt0 tptp.xq tptp.xp))) (let ((_let_73 (not _let_70))) (let ((_let_74 (and _let_73 _let_72))) (let ((_let_75 (not _let_9))) (let ((_let_76 (or _let_49 _let_75 _let_1 _let_74))) (let ((_let_77 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.sdtlseqdt0 W0 W1) (and (not (= W0 W1)) (tptp.sdtlseqdt0 W1 W0)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_77))) (let ((_let_80 (AND_ELIM _let_36 :args _let_56))) (let ((_let_81 (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args _let_34))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 0)) :args ((or _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_1 _let_49 _let_75 _let_74 (not _let_76)))) _let_81 _let_57 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xp tptp.xq QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) true))))) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args (_let_74 true _let_1 false _let_14 false _let_9 false _let_76)) :args (_let_73 false _let_74)))) (let ((_let_83 (and _let_11 _let_6 _let_61))) (let ((_let_84 (ASSUME :args (_let_6)))) (let ((_let_85 (ASSUME :args (_let_61)))) (let ((_let_86 (ASSUME :args (_let_11)))) (let ((_let_87 (not _let_18))) (let ((_let_88 (or _let_66 _let_87 _let_64))) (let ((_let_89 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (AND_ELIM _let_58 :args _let_34))) (let ((_let_92 (tptp.sdtasdt0 tptp.xq tptp.xl))) (let ((_let_93 (and (not (= _let_12 _let_7)) _let_33 (not (= _let_29 _let_92)) (tptp.sdtlseqdt0 _let_92 _let_29)))) (let ((_let_94 (not _let_72))) (let ((_let_95 (= tptp.sz00 tptp.xl))) (let ((_let_96 (or _let_50 _let_75 _let_49 _let_95 _let_70 _let_94 _let_93))) (let ((_let_97 (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))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= tptp.sz00 W0) (= W1 W2) (not (tptp.sdtlseqdt0 W1 W2)) (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_98 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (and _let_73 _let_1))) (let ((_let_100 (or _let_75 _let_49 _let_72 _let_99))) (let ((_let_101 (not _let_99))) (let ((_let_102 (not _let_33))) (let ((_let_103 (not _let_31))) (let ((_let_104 (not _let_30))) (let ((_let_105 (not _let_8))) (let ((_let_106 (not _let_13))) (let ((_let_107 (ASSUME :args (_let_33)))) (let ((_let_108 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_109 (ASSUME :args (_let_30)))) (let ((_let_110 (ASSUME :args (_let_8)))) (let ((_let_111 (ASSUME :args (_let_28)))) (let ((_let_112 (ASSUME :args (_let_31)))) (let ((_let_113 (TRANS (SYMM _let_112) (SYMM _let_111)))) (let ((_let_114 (ASSUME :args (_let_13)))) (let ((_let_115 (ASSUME :args (_let_62)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_107 _let_110 _let_111 _let_112 _let_109 _let_114 _let_115) :args (_let_13 _let_8 _let_28 _let_30 _let_31 _let_62 _let_33)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_115)) (CONG (SYMM _let_113) (TRANS (SYMM (SYMM _let_114)) _let_109) :args _let_108) (CONG (TRANS _let_113 (SYMM (SYMM _let_110))) (SYMM _let_109) :args _let_108) (TRUE_INTRO _let_107))) :args (_let_33 _let_8 _let_28 _let_31 _let_30 _let_13 _let_62)) :args ((not (and _let_13 _let_8 _let_28 _let_30 _let_31 _let_62 _let_33)) SB_LITERAL))) (CONG (REFL :args (_let_106)) (REFL :args (_let_105)) (REFL :args (_let_37)) (REFL :args (_let_104)) (REFL :args (_let_103)) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_32))) (REFL :args (_let_102)) :args _let_44)) :args ((or _let_106 _let_105 _let_37 _let_32 _let_104 _let_103 _let_102))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 1)) :args ((or _let_33 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_95 _let_50 _let_49 _let_75 _let_70 _let_94 _let_93 (not _let_96)))) (SYMM (ASSUME :args (_let_16))) _let_59 _let_57 _let_80 _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_49 _let_75 _let_72 _let_99 (not _let_100)))) _let_57 _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_99 1)) :args ((or _let_1 _let_101))) _let_81 :args (_let_101 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xq tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtlseqdt0 W1 W0)))) :args _let_79))) _let_78 :args (_let_100 false _let_77)) :args (_let_72 false _let_14 false _let_9 true _let_99 false _let_100)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_98 :args (tptp.xl tptp.xq tptp.xp QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W0 W2)))) :args (_let_97)))) _let_98 :args (_let_96 false _let_97)) :args (_let_93 true _let_95 false _let_20 false _let_14 false _let_9 true _let_70 false _let_72 false _let_96)) :args (_let_33 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_63 _let_65 _let_62 _let_61 (not _let_67)))) _let_91 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args _let_34) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_66 _let_87 _let_64 (not _let_88)))) _let_91 (AND_ELIM _let_58 :args _let_43) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtpldt0 W0 W1)))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_64 false _let_19 false _let_18 false _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_83)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_84 _let_85 _let_86) (SCOPE (TRANS (SYMM (SYMM _let_86)) (CONG (SYMM (SYMM _let_85)) (REFL :args (tptp.xl)) :args (APPLY_UF tptp.sdtsldt0)) (SYMM _let_84)) :args (_let_6 _let_61 _let_11))) :args (_let_11 _let_6 _let_61))) :args (true _let_83)) :args ((or (not _let_11) (not _let_6) _let_70 _let_71))) _let_82 (AND_ELIM _let_36 :args _let_43) (AND_ELIM _let_35 :args _let_43) :args (_let_71 true _let_70 false _let_6 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xm _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_62 false _let_19 false _let_4 false _let_64 true _let_61 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_50 _let_39 _let_31 (not _let_60)))) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_44)) :args ((or _let_38 _let_40))) _let_47 :args (_let_38 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_60 false _let_52)) :args (_let_31 false _let_20 false _let_38 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_49 _let_30 (not _let_51)))) _let_59 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xl tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_51 false _let_52)) :args (_let_30 false _let_20 false _let_14 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_28))) :args _let_44)) :args ((or _let_28 _let_40))) _let_47 :args (_let_28 true _let_40)) (AND_ELIM _let_36 :args _let_34) (AND_ELIM _let_35 :args _let_34) :args (false false _let_33 true _let_32 false _let_31 false _let_30 false _let_28 false _let_8 false _let_13)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_26 (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))))) _let_25 (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))))) (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) _let_24 (forall ((W0 $$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_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) _let_22 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$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))))) _let_21 _let_17 _let_16 _let_15 _let_10 _let_5 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.94/9.32  )
% 8.94/9.32  % SZS output end Proof for NUM473+2
% 8.94/9.32  % cvc5---1.0.5 exiting
% 8.94/9.32  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------