%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 10:44:42 EDT 2023

% Result   : Theorem 27.28s 27.47s
% Output   : Proof 27.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n006.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 14:26:07 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 27.28/27.47  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.y4gN9IL3yK/cvc5---1.0.5_4276.p...
% 27.28/27.47  ------- get file name : TPTP file name is NUM518+3
% 27.28/27.47  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4276.smt2...
% 27.28/27.47  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.28/27.47  --- Run --no-e-matching --full-saturate-quant at 5...
% 27.28/27.47  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.28/27.47  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.28/27.47  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.28/27.47  % SZS status Theorem for NUM518+3
% 27.28/27.47  % SZS output start Proof for NUM518+3
% 27.28/27.47  (
% 27.28/27.47  (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (not (or (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp tptp.xn) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xp W0)))) _let_1)))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_4 (tptp.doDivides0 tptp.xp _let_3))) (let ((_let_5 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_3)))) (let ((_let_6 (tptp.aNaturalNumber0 _let_3))) (let ((_let_7 (or (and _let_6 _let_5 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtsldt0 tptp.xn tptp.xr) (tptp.sdtasdt0 tptp.xp W0)))) _let_4) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xp W0)))) _let_1)))) (let ((_let_8 (tptp.sdtlseqdt0 _let_3 tptp.xn))) (let ((_let_9 (and (not (=> (and _let_6 _let_5) (= _let_3 tptp.xn))) _let_6 _let_5 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) _let_8))) (let ((_let_10 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_11 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_12 (tptp.isPrime0 tptp.xr))) (let ((_let_13 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_15 (and _let_14 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_13 (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_12))) (let ((_let_16 (= tptp.xk tptp.sz10))) (let ((_let_17 (= tptp.xk tptp.sz00))) (let ((_let_18 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_11 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 _let_11 tptp.xp))))) (let ((_let_19 (tptp.sdtlseqdt0 tptp.xn tptp.xp))) (let ((_let_20 (and (not (= tptp.xn tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xn W0) tptp.xp))) _let_19 (not (= tptp.xm tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)))) (let ((_let_21 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_23 (and _let_22 (tptp.aNaturalNumber0 tptp.xm) _let_21))) (let ((_let_24 (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_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_28 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_29 (tptp.sdtasdt0 tptp.xp tptp.sz00))) (let ((_let_30 (= tptp.xn _let_29))) (let ((_let_31 (= tptp.sz00 _let_29))) (let ((_let_32 (= tptp.sz00 (tptp.sdtasdt0 tptp.xr tptp.sz00)))) (let ((_let_33 (= tptp.sz00 _let_3))) (let ((_let_34 (0))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (AND_ELIM _let_35 :args _let_34))) (let ((_let_37 (NOT_IMPLIES_ELIM1 _let_36))) (let ((_let_38 (not _let_30))) (let ((_let_39 (not _let_28))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xp W0))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 (and _let_31 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp))))) (let ((_let_45 (not _let_21))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_51 (2))) (let ((_let_52 (ASSUME :args (_let_23)))) (let ((_let_53 (AND_ELIM _let_52 :args _let_51))) (let ((_let_54 (and _let_32 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xr))))) (let ((_let_55 (not _let_14))) (let ((_let_56 (or _let_55 _let_54))) (let ((_let_57 (tptp.sdtlseqdt0 tptp.xp _let_3))) (let ((_let_58 (not _let_4))) (let ((_let_59 (not _let_6))) (let ((_let_60 (or _let_45 _let_59 _let_58 _let_33 _let_57))) (let ((_let_61 (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_62 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.sdtlseqdt0 tptp.xn _let_3))) (let ((_let_64 (not _let_57))) (let ((_let_65 (not _let_19))) (let ((_let_66 (not _let_22))) (let ((_let_67 (or _let_66 _let_45 _let_59 _let_65 _let_64 _let_63))) (let ((_let_68 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (= tptp.xn _let_3))) (let ((_let_71 (not _let_63))) (let ((_let_72 (not _let_8))) (let ((_let_73 (or _let_59 _let_66 _let_72 _let_71 _let_70))) (let ((_let_74 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (AND_ELIM _let_37 :args _let_34))) (let ((_let_77 (AND_ELIM _let_52 :args _let_34))) (let ((_let_78 (and _let_6 _let_5 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= (tptp.sdtsldt0 tptp.xn tptp.xr) (tptp.sdtasdt0 tptp.xp W0)))))) _let_4))) (let ((_let_79 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xm (tptp.sdtasdt0 tptp.xp W0))))))) (let ((_let_80 (not _let_79))) (let ((_let_81 (and _let_80 _let_1))) (let ((_let_82 (not _let_81))) (let ((_let_83 (and _let_5 _let_33 _let_31 _let_32))) (let ((_let_84 (ASSUME :args (_let_31)))) (let ((_let_85 (ASSUME :args (_let_32)))) (let ((_let_86 (ASSUME :args (_let_33)))) (let ((_let_87 (ASSUME :args (_let_5)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_83)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_84 _let_85 _let_86 _let_87) (SCOPE (TRANS (SYMM (SYMM _let_87)) (CONG (REFL :args (tptp.xr)) (SYMM _let_86) :args (APPLY_UF tptp.sdtasdt0)) (SYMM _let_85) (SYMM (SYMM _let_84))) :args (_let_31 _let_32 _let_33 _let_5))) :args (_let_5 _let_33 _let_31 _let_32))) :args (true _let_83)) :args ((or (not _let_5) (not _let_33) _let_30 (not _let_31) (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_45 _let_59 _let_58 _let_33 _let_57 (not _let_60)))) _let_53 _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 3)) :args ((or _let_4 (not _let_78)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 0)) :args ((or _let_80 _let_82))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_79 (= W0 W0)))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_42 :args _let_51)) :args (_let_79 false (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xm (tptp.sdtasdt0 tptp.xp W0))))))) :args (_let_82 false _let_79)) :args (_let_78 true _let_81)) :args (_let_4 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_45 _let_65 _let_59 _let_63 _let_64 (not _let_67)))) _let_77 _let_53 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) :args _let_51) _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_70 _let_66 _let_59 _let_72 _let_71 (not _let_73)))) (NOT_IMPLIES_ELIM2 _let_36) _let_77 _let_76 (AND_ELIM _let_35 :args (4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_3 tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.sdtlseqdt0 W0 W1) false))))) :args (_let_74)))) _let_75 :args (_let_73 false _let_74)) :args (_let_71 true _let_70 false _let_22 false _let_6 false _let_8 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.xn tptp.xp _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_64 false _let_22 false _let_21 false _let_19 false _let_6 true _let_63 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xp _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.doDivides0 W0 W1) false))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_33 false _let_21 false _let_6 false _let_4 true _let_57 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_32 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_54 (not _let_56)))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_ELIM (ASSUME :args (_let_18)) :args _let_51) :args ((and _let_14 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))))) _let_13 (not (= tptp.sz00 tptp.xr)) (not (= tptp.sz10 tptp.xr)) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2271 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_2271)) (not (= tptp.xr (tptp.sdtasdt0 W0 BOUND_VARIABLE_2271)))) (not (tptp.doDivides0 W0 tptp.xr))) (= tptp.sz10 W0) (= tptp.xr W0))) _let_12) SB_DEFAULT SBA_FIXPOINT)))) :args _let_34) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_56 false _let_47)) :args (_let_54 false _let_14 false _let_56)) :args (_let_32 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_31 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_44 (not _let_46)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_46 false _let_47)) :args (_let_44 false _let_21 false _let_46)) :args (_let_31 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_38 (not _let_40)))) (ASSUME :args (_let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W0) false))))) :args _let_43)) (NOT_NOT_ELIM (NOT_OR_ELIM _let_42 :args _let_34)) :args (_let_40 false _let_41)) :args (_let_38 false _let_28 false _let_40)) (AND_ELIM _let_37 :args (1)) :args (false false _let_33 false _let_32 false _let_31 true _let_30 false _let_5)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_28 (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_27 (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_26 _let_25 (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)))) (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_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) (forall ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_23 (forall ((W0 $$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_11)) (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))) _let_20 _let_18 (not (or _let_17 _let_16)) (and (not _let_17) (not _let_16)) _let_15 (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_11)) (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_10) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xm (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr tptp.xm))) (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_10) _let_9 (and _let_6 _let_5 (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 (tptp.sdtasdt0 _let_3 tptp.xm))) _let_7 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.28/27.48  )
% 27.28/27.48  % SZS output end Proof for NUM518+3
% 27.28/27.48  % cvc5---1.0.5 exiting
% 27.28/27.48  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------