%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM511+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n019.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 48.17s 48.39s
% Output   : Proof 48.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM511+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 09:37:43 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 48.17/48.39  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8Ehl5oLhKl/cvc5---1.0.5_1454.p...
% 48.17/48.39  ------- get file name : TPTP file name is NUM511+3
% 48.17/48.39  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1454.smt2...
% 48.17/48.39  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 48.17/48.39  --- Run --no-e-matching --full-saturate-quant at 5...
% 48.17/48.39  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 48.17/48.39  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 48.17/48.39  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 48.17/48.39  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 48.17/48.39  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 48.17/48.39  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 48.17/48.39  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 48.17/48.39  % SZS status Theorem for NUM511+3
% 48.17/48.39  % SZS output start Proof for NUM511+3
% 48.17/48.39  (
% 48.17/48.39  (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtasdt0 _let_1 tptp.xm))) (let ((_let_3 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_1)))) (let ((_let_4 (tptp.aNaturalNumber0 _let_1))) (let ((_let_5 (and _let_4 _let_3))) (let ((_let_6 (not (=> _let_5 (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_2)))))) (let ((_let_7 (and (not (=> _let_5 (= _let_1 tptp.xn))) _let_4 _let_3 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) (tptp.sdtlseqdt0 _let_1 tptp.xn)))) (let ((_let_8 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_9 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_8))) (let ((_let_10 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_11 (tptp.isPrime0 tptp.xr))) (let ((_let_12 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_14 (and _let_13 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_12 (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xr (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xr))) (or (= W0 tptp.sz10) (= W0 tptp.xr)))) _let_11))) (let ((_let_15 (= tptp.xk tptp.sz10))) (let ((_let_16 (= tptp.xk tptp.sz00))) (let ((_let_17 (tptp.sdtsldt0 _let_10 tptp.xp))) (let ((_let_18 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_10 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk _let_17)))) (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 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))))) (let ((_let_24 (forall ((W0 $$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 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_26 (tptp.sdtasdt0 tptp.xp _let_17))) (let ((_let_27 (= _let_10 _let_26))) (let ((_let_28 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_29 (= _let_10 _let_28))) (let ((_let_30 (tptp.sdtasdt0 tptp.xm _let_1))) (let ((_let_31 (= _let_2 _let_30))) (let ((_let_32 (= _let_30 (tptp.sdtsldt0 _let_28 tptp.xr)))) (let ((_let_33 (= _let_2 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_34 (tptp.sdtsldt0 _let_17 tptp.xr))) (let ((_let_35 (= (tptp.sdtasdt0 tptp.xp _let_34) (tptp.sdtsldt0 _let_26 tptp.xr)))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_34))) (let ((_let_37 (1))) (let ((_let_38 (2))) (let ((_let_39 (ASSUME :args (_let_18)))) (let ((_let_40 (AND_ELIM _let_39 :args _let_38))) (let ((_let_41 (EQ_RESOLVE _let_39 (MACRO_SR_EQ_INTRO _let_40 :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (not _let_20))) (let ((_let_43 (not _let_21))) (let ((_let_44 (or _let_43 _let_42 _let_29))) (let ((_let_45 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (_let_45))) (let ((_let_48 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_49 (ASSUME :args (_let_22)))) (let ((_let_50 (AND_ELIM _let_49 :args _let_37))) (let ((_let_51 (0))) (let ((_let_52 (AND_ELIM _let_49 :args _let_51))) (let ((_let_53 (not _let_4))) (let ((_let_54 (or _let_53 _let_42 _let_31))) (let ((_let_55 (or _let_42 _let_32))) (let ((_let_56 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 tptp.xn tptp.xr)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 tptp.xn) tptp.xr)))))) (let ((_let_57 (not _let_8))) (let ((_let_58 (= tptp.sz00 tptp.xr))) (let ((_let_59 (not _let_13))) (let ((_let_60 (or _let_59 _let_43 _let_58 _let_57 _let_56))) (let ((_let_61 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0)))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_40 :args ((and _let_13 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))))) _let_12 (not _let_58) (not (= tptp.sz10 tptp.xr)) (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (= tptp.xr (tptp.sdtasdt0 W0 W1))))) (not (tptp.doDivides0 W0 tptp.xr))) (= tptp.sz10 W0) (= tptp.xr W0))) _let_11) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_65 (AND_ELIM _let_64 :args _let_51))) (let ((_let_66 (AND_ELIM _let_64 :args (3)))) (let ((_let_67 (_let_56))) (let ((_let_68 ((not (= (tptp.aNaturalNumber0 W2) false))))) (let ((_let_69 (not _let_33))) (let ((_let_70 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_69))) (let ((_let_73 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtasdt0 (tptp.sdtsldt0 tptp.xn tptp.xr) tptp.xm) (tptp.sdtasdt0 tptp.xp W0))))))) (let ((_let_74 (_let_73))) (let ((_let_75 (= _let_17 (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_71 _let_76))) (let ((_let_78 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtasdt0 tptp.xr W0))))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (or))) (let ((_let_81 (not _let_78))) (let ((_let_82 (_let_81))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_78))) (REFL :args (_let_79)) :args _let_80)) (AND_ELIM _let_64 :args _let_37) :args (_let_79 true _let_78)))) (let ((_let_84 (REFL :args (_let_77)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_80)) :args ((or _let_70 _let_77))) _let_83 :args (_let_70 true _let_77)))) (let ((_let_86 (not _let_19))) (let ((_let_87 (or _let_86 _let_35))) (let ((_let_88 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp))) (or (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 _let_1 tptp.xr)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 _let_1) tptp.xr))))))) (let ((_let_89 (tptp.doDivides0 tptp.xr _let_17))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.aNaturalNumber0 _let_17))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_59 _let_92 _let_58 _let_90 _let_88))) (let ((_let_94 (AND_ELIM _let_64 :args _let_38))) (let ((_let_95 (AND_ELIM _let_41 :args _let_51))) (let ((_let_96 (_let_88))) (let ((_let_97 (and _let_70 _let_75))) (let ((_let_98 (= _let_36 _let_97))) (let ((_let_99 (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtsldt0 (tptp.sdtasdt0 tptp.xn tptp.xm) tptp.xp))) (= (= W2 (tptp.sdtsldt0 _let_1 tptp.xr)) (and (tptp.aNaturalNumber0 W2) (= _let_1 (tptp.sdtasdt0 tptp.xr W2)))))))) (let ((_let_100 (or _let_59 _let_92 _let_58 _let_90 _let_99))) (let ((_let_101 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_99))) (let ((_let_104 (and _let_27 _let_29 _let_31 _let_32 _let_35 _let_36))) (let ((_let_105 (ASSUME :args (_let_36)))) (let ((_let_106 (ASSUME :args (_let_35)))) (let ((_let_107 (ASSUME :args (_let_27)))) (let ((_let_108 (ASSUME :args (_let_29)))) (let ((_let_109 (ASSUME :args (_let_32)))) (let ((_let_110 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_104)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_105 _let_106 _let_107 _let_108 _let_109 _let_110) (SCOPE (TRANS (SYMM (SYMM _let_110)) (SYMM (SYMM _let_109)) (CONG (TRANS (SYMM _let_108) (SYMM (SYMM _let_107))) (REFL :args (tptp.xr)) :args (APPLY_UF tptp.sdtsldt0)) (SYMM _let_106) (CONG (REFL :args (tptp.xp)) (SYMM _let_105) :args (APPLY_UF tptp.sdtasdt0))) :args (_let_36 _let_35 _let_27 _let_29 _let_32 _let_31))) :args (_let_27 _let_29 _let_31 _let_32 _let_35 _let_36))) :args (true _let_104)) :args ((or (not _let_27) (not _let_29) (not _let_31) (not _let_32) _let_33 (not _let_35) (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_98)) :args ((or _let_36 (not _let_97) (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_97)) :args ((or _let_71 _let_76 _let_97))) _let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_80)) :args ((or _let_75 _let_77))) _let_83 :args (_let_75 true _let_77)) :args (_let_97 false _let_70 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_103) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aNaturalNumber0 W2)))) :args _let_103)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_58 _let_92 _let_59 _let_90 _let_99 (not _let_100)))) _let_66 _let_95 _let_65 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.xr _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.doDivides0 W0 W1) false))))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_99 true _let_58 false _let_91 false _let_13 false _let_89 false _let_100)) :args (_let_98 false _let_99)) :args (_let_36 false _let_97 false _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_86 _let_35 (not _let_87)))) (AND_ELIM _let_49 :args _let_38) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_58 _let_92 _let_59 _let_90 _let_88 (not _let_93)))) _let_66 _let_95 _let_65 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xr _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.doDivides0 W0 W1) false))))) :args _let_63)) _let_62 :args (_let_93 false _let_61)) :args (_let_88 true _let_58 false _let_91 false _let_13 false _let_89 false _let_93)) :args (_let_87 false _let_88)) :args (_let_35 false _let_19 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_71 _let_69 (not _let_72)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W0) false))))) :args _let_74)) (NOT_NOT_ELIM (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)))) :args _let_51)) :args (_let_72 false _let_73)) :args (_let_69 false _let_70 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_42 _let_32 (not _let_55)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_58 _let_43 _let_59 _let_57 _let_56 (not _let_60)))) _let_66 _let_52 _let_65 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args _let_37) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xr tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_56 true _let_58 false _let_21 false _let_13 false _let_8 false _let_60)) :args (_let_55 false _let_56)) :args (_let_32 false _let_20 false _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_42 _let_53 _let_31 (not _let_54)))) _let_50 (AND_ELIM (NOT_IMPLIES_ELIM1 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args _let_51)) :args _let_51) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_1 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47)) _let_46 :args (_let_54 false _let_45)) :args (_let_31 false _let_20 false _let_4 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_42 _let_29 (not _let_44)))) _let_52 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47)) _let_46 :args (_let_44 false _let_45)) :args (_let_29 false _let_21 false _let_20 false _let_44)) (AND_ELIM _let_41 :args _let_37) :args (false false _let_36 false _let_35 true _let_33 false _let_32 false _let_31 false _let_29 false _let_27)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_25 (forall ((W0 $$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))) (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)))) _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)))))))) (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (or (and (not (= W2 tptp.sz00)) (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2)) (or (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W2 W3)))) (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 (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W0 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W0)) (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))) (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_10)) (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm))) (and (not (= tptp.xn tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_18 (not (or _let_16 _let_15)) (and (not _let_16) (not _let_15)) _let_14 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xk))) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr _let_10)) (and (not (= tptp.xk tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xk W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_8) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xm))) _let_9 _let_7 _let_6 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 48.17/48.40  )
% 48.17/48.40  % SZS output end Proof for NUM511+3
% 48.17/48.40  % cvc5---1.0.5 exiting
% 48.17/48.40  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------