TSTP Solution File: NUM512+3 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM512+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 10:44:38 EDT 2023

% Result   : Theorem 22.34s 22.72s
% Output   : Proof 22.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM512+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 09:04:28 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 22.34/22.72  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sT9p5ThF7L/cvc5---1.0.5_27400.p...
% 22.34/22.72  ------- get file name : TPTP file name is NUM512+3
% 22.34/22.72  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27400.smt2...
% 22.34/22.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 22.34/22.72  --- Run --no-e-matching --full-saturate-quant at 5...
% 22.34/22.72  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 22.34/22.72  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 22.34/22.72  % SZS status Theorem for NUM512+3
% 22.34/22.72  % SZS output start Proof for NUM512+3
% 22.34/22.72  (
% 22.34/22.72  (let ((_let_1 (tptp.sdtasdt0 tptp.xp tptp.xk))) (let ((_let_2 (tptp.sdtsldt0 _let_1 tptp.xr))) (let ((_let_3 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_4 (=> (and (tptp.aNaturalNumber0 _let_2) (= _let_1 (tptp.sdtasdt0 tptp.xr _let_2))) (= _let_3 (tptp.sdtasdt0 _let_2 tptp.xr))))) (let ((_let_5 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_6 (tptp.sdtasdt0 _let_5 tptp.xm))) (let ((_let_7 (tptp.sdtasdt0 _let_6 tptp.xr))) (let ((_let_8 (tptp.sdtasdt0 tptp.xr _let_5))) (let ((_let_9 (= tptp.xn _let_8))) (let ((_let_10 (tptp.aNaturalNumber0 _let_5))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (not (and (=> _let_11 (= _let_7 _let_3)) _let_4)))) (let ((_let_13 (and (not (=> _let_11 (= _let_5 tptp.xn))) _let_10 _let_9 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 (tptp.sdtsldt0 tptp.xn tptp.xr) W0) tptp.xn))) (tptp.sdtlseqdt0 _let_5 tptp.xn)))) (let ((_let_14 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_15 (tptp.isPrime0 tptp.xr))) (let ((_let_16 (tptp.doDivides0 tptp.xr tptp.xk))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_18 (and _let_17 (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))) _let_16 (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_15))) (let ((_let_19 (= tptp.xk tptp.sz10))) (let ((_let_20 (= tptp.xk tptp.sz00))) (let ((_let_21 (tptp.sdtsldt0 _let_3 tptp.xp))) (let ((_let_22 (and (tptp.aNaturalNumber0 tptp.xk) (= _let_3 _let_1) (= tptp.xk _let_21)))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_25 (and _let_24 _let_23 (tptp.aNaturalNumber0 tptp.xp)))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_28 (tptp.sdtasdt0 tptp.xp _let_21))) (let ((_let_29 (= _let_3 _let_28))) (let ((_let_30 (tptp.sdtsldt0 _let_28 tptp.xr))) (let ((_let_31 (tptp.sdtasdt0 _let_30 tptp.xr))) (let ((_let_32 (= _let_3 _let_31))) (let ((_let_33 (tptp.sdtasdt0 tptp.xr _let_30))) (let ((_let_34 (= _let_28 _let_33))) (let ((_let_35 (= _let_31 _let_33))) (let ((_let_36 (1))) (let ((_let_37 (ASSUME :args (_let_22)))) (let ((_let_38 (AND_ELIM _let_37 :args (2)))) (let ((_let_39 (tptp.aNaturalNumber0 _let_30))) (let ((_let_40 (and _let_39 _let_34))) (let ((_let_41 (=> _let_40 _let_32))) (let ((_let_42 (not _let_32))) (let ((_let_43 (= _let_3 _let_7))) (let ((_let_44 (=> _let_11 _let_43))) (let ((_let_45 (tptp.sdtasdt0 _let_5 tptp.xr))) (let ((_let_46 (tptp.sdtasdt0 tptp.xm _let_5))) (let ((_let_47 (= (tptp.sdtasdt0 _let_46 tptp.xr) (tptp.sdtasdt0 tptp.xm _let_45)))) (let ((_let_48 (= _let_6 _let_46))) (let ((_let_49 (= _let_3 (tptp.sdtasdt0 tptp.xm tptp.xn)))) (let ((_let_50 (= _let_8 _let_45))) (let ((_let_51 (not _let_17))) (let ((_let_52 (not _let_10))) (let ((_let_53 (not _let_23))) (let ((_let_54 (or _let_53 _let_52 _let_51 _let_47))) (let ((_let_55 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (0))) (let ((_let_58 (NOT_IMPLIES_ELIM1 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) :args _let_57)))) (let ((_let_59 (AND_ELIM _let_58 :args _let_57))) (let ((_let_60 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_38 :args ((and _let_17 (not (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (= tptp.xk (tptp.sdtasdt0 tptp.xr W0)))))) _let_16 (not (= tptp.sz00 tptp.xr)) (not (= tptp.sz10 tptp.xr)) (forall ((W0 $$unsorted) (BOUND_VARIABLE_2239 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (or (not (tptp.aNaturalNumber0 BOUND_VARIABLE_2239)) (not (= tptp.xr (tptp.sdtasdt0 W0 BOUND_VARIABLE_2239)))) (not (tptp.doDivides0 W0 tptp.xr))) (= tptp.sz10 W0) (= tptp.xr W0))) _let_15) SB_DEFAULT SBA_FIXPOINT)))) :args _let_57))) (let ((_let_61 (ASSUME :args (_let_25)))) (let ((_let_62 (AND_ELIM _let_61 :args _let_36))) (let ((_let_63 (or _let_52 _let_53 _let_48))) (let ((_let_64 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 (not _let_24))) (let ((_let_68 (or _let_67 _let_53 _let_49))) (let ((_let_69 (or _let_51 _let_52 _let_50))) (let ((_let_70 (and _let_9 _let_50 _let_49 _let_48 _let_47))) (let ((_let_71 (APPLY_UF tptp.sdtasdt0))) (let ((_let_72 (ASSUME :args (_let_48)))) (let ((_let_73 (ASSUME :args (_let_47)))) (let ((_let_74 (ASSUME :args (_let_50)))) (let ((_let_75 (ASSUME :args (_let_9)))) (let ((_let_76 (ASSUME :args (_let_49)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_38 :args ((not (and _let_44 _let_4)) SB_DEFAULT SBA_FIXPOINT))))) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73 _let_74 _let_75 _let_76) (SCOPE (TRANS (SYMM (SYMM _let_76)) (CONG (REFL :args (tptp.xm)) (TRANS (SYMM (SYMM _let_75)) (SYMM (SYMM _let_74))) :args _let_71) (SYMM _let_73) (CONG (SYMM _let_72) (REFL :args (tptp.xr)) :args _let_71)) :args (_let_48 _let_47 _let_50 _let_9 _let_49))) :args (_let_9 _let_50 _let_49 _let_48 _let_47))) :args (true _let_70)) :args ((or _let_43 (not _let_9) (not _let_50) (not _let_49) (not _let_48) (not _let_47)))) (AND_ELIM _let_58 :args _let_36) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_51 _let_52 _let_50 (not _let_69)))) _let_60 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xr _let_5 QUANTIFIERS_INST_CBQI_PROP)) :args _let_66)) _let_65 :args (_let_69 false _let_64)) :args (_let_50 false _let_17 false _let_10 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_53 _let_49 (not _let_68)))) (AND_ELIM _let_61 :args _let_57) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_66)) _let_65 :args (_let_68 false _let_64)) :args (_let_49 false _let_24 false _let_23 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_53 _let_52 _let_48 (not _let_63)))) _let_62 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_5 tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_48 false _let_23 false _let_10 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_51 _let_52 _let_47 (not _let_54)))) _let_62 _let_60 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.xm _let_5 tptp.xr QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_47 false _let_23 false _let_17 false _let_10 false _let_54)) :args (_let_43 false _let_9 false _let_50 false _let_49 false _let_48 false _let_47)) :args (_let_44 false _let_43)) :args ((not _let_41) false _let_44)))) (let ((_let_78 (_let_41))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_78) :args ((or _let_40 _let_41))) _let_77 :args (_let_40 true _let_41)))) (let ((_let_80 (not _let_40))) (let ((_let_81 (not _let_39))) (let ((_let_82 (or _let_51 _let_81 _let_35))) (let ((_let_83 (not _let_35))) (let ((_let_84 (not _let_34))) (let ((_let_85 (not _let_29))) (let ((_let_86 (ASSUME :args (_let_34)))) (let ((_let_87 (ASSUME :args (_let_35)))) (let ((_let_88 (ASSUME :args (_let_29)))) (let ((_let_89 (ASSUME :args (_let_42)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_88 _let_86 _let_87 _let_89) :args (_let_29 _let_34 _let_42 _let_35)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_89)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_88)) (SYMM (TRANS (SYMM (SYMM _let_87)) (SYMM _let_86))))))) :args (_let_29 _let_34 _let_35 _let_42)) :args ((not (and _let_29 _let_34 _let_42 _let_35)) SB_LITERAL))) (CONG (REFL :args (_let_85)) (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_32))) (REFL :args (_let_83)) :args (or))) :args ((or _let_32 _let_85 _let_84 _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_51 _let_81 _let_35 (not _let_82)))) _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 0)) :args ((or _let_39 _let_80))) _let_79 :args (_let_39 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.xr _let_30 QUANTIFIERS_INST_CBQI_PROP)) :args _let_66))) _let_65 :args (_let_82 false _let_64)) :args (_let_35 false _let_17 false _let_39 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 1)) :args ((or _let_34 _let_80))) _let_79 :args (_let_34 false _let_40)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_78) _let_77 :args (_let_42 true _let_41)) (AND_ELIM (EQ_RESOLVE _let_37 (MACRO_SR_EQ_INTRO _let_38 :args (_let_22 SB_DEFAULT SBA_FIXPOINT))) :args _let_36) :args (false false _let_35 false _let_34 true _let_32 false _let_29)) :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_27 _let_26 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))) (forall ((W0 $$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_25 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp _let_3)) (not (or (exists ((W0 $$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 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xm W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_22 (not (or _let_20 _let_19)) (and (not _let_20) (not _let_19)) _let_18 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xk))) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xr W0)))) (tptp.doDivides0 tptp.xr _let_3)) (and (not (= tptp.xk tptp.xp)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xk W0) tptp.xp))) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= tptp.xn (tptp.sdtasdt0 tptp.xr W0)))) _let_14) (and (exists ((W0 $$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_14) _let_13 _let_12 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 22.34/22.73  )
% 22.34/22.73  % SZS output end Proof for NUM512+3
% 22.34/22.73  % cvc5---1.0.5 exiting
% 22.34/22.73  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------