TSTP Solution File: NUM516+1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 10:44:40 EDT 2023

% Result   : Theorem 26.96s 27.26s
% Output   : Proof 26.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n017.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 15:39:25 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 26.96/27.26  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.myVw11R6rZ/cvc5---1.0.5_10095.p...
% 26.96/27.26  ------- get file name : TPTP file name is NUM516+1
% 26.96/27.26  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10095.smt2...
% 26.96/27.26  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.96/27.26  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.96/27.26  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.96/27.26  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.96/27.26  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.96/27.26  % SZS status Theorem for NUM516+1
% 26.96/27.26  % SZS output start Proof for NUM516+1
% 26.96/27.26  (
% 26.96/27.26  (let ((_let_1 (tptp.sdtpldt0 tptp.xn tptp.xm))) (let ((_let_2 (tptp.sdtpldt0 _let_1 tptp.xp))) (let ((_let_3 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_4 (tptp.sdtpldt0 _let_3 tptp.xm))) (let ((_let_5 (tptp.sdtpldt0 _let_4 tptp.xp))) (let ((_let_6 (tptp.sdtlseqdt0 _let_5 _let_2))) (let ((_let_7 (not (and (not (= _let_5 _let_2)) _let_6)))) (let ((_let_8 (tptp.sdtlseqdt0 _let_3 tptp.xn))) (let ((_let_9 (and (not (= _let_3 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.aNaturalNumber0 tptp.xr))) (let ((_let_14 (and _let_13 (tptp.doDivides0 tptp.xr tptp.xk) _let_12))) (let ((_let_15 (= tptp.xk tptp.sz10))) (let ((_let_16 (= tptp.xk tptp.sz00))) (let ((_let_17 (= tptp.xk (tptp.sdtsldt0 _let_11 tptp.xp)))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_20 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_21 (and _let_20 _let_19 _let_18))) (let ((_let_22 (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)))))))))) (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 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_24 (forall ((W0 $$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 ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_28 (tptp.sdtpldt0 tptp.xm tptp.xp))) (let ((_let_29 (tptp.sdtpldt0 tptp.xn _let_28))) (let ((_let_30 (= _let_2 _let_29))) (let ((_let_31 (tptp.sdtpldt0 _let_3 _let_28))) (let ((_let_32 (= _let_5 _let_31))) (let ((_let_33 (tptp.sdtlseqdt0 _let_31 _let_29))) (let ((_let_34 (not _let_18))) (let ((_let_35 (not _let_19))) (let ((_let_36 (not _let_20))) (let ((_let_37 (or _let_36 _let_35 _let_34 _let_30))) (let ((_let_38 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) (let ((_let_42 (2))) (let ((_let_43 (ASSUME :args (_let_21)))) (let ((_let_44 (AND_ELIM _let_43 :args _let_42))) (let ((_let_45 (1))) (let ((_let_46 (AND_ELIM _let_43 :args _let_45))) (let ((_let_47 (0))) (let ((_let_48 (AND_ELIM _let_43 :args _let_47))) (let ((_let_49 (tptp.aNaturalNumber0 _let_3))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_35 _let_34 _let_32))) (let ((_let_52 (and _let_49 (= tptp.xn (tptp.sdtasdt0 tptp.xr _let_3))))) (let ((_let_53 (not _let_10))) (let ((_let_54 (= tptp.sz00 tptp.xr))) (let ((_let_55 (not _let_13))) (let ((_let_56 (or _let_55 _let_36 _let_54 _let_53 _let_52))) (let ((_let_57 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1636 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1636) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1636))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1636)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (not _let_54))) (let ((_let_60 (and _let_59 (not (= tptp.sz10 tptp.xr)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xr)) (= tptp.sz10 W1) (= W1 tptp.xr)))))) (let ((_let_61 (= _let_12 _let_60))) (let ((_let_62 (or _let_55 _let_61))) (let ((_let_63 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_17)) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (AND_ELIM _let_65 :args _let_47))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_49 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_53 _let_36 _let_55 _let_54 _let_52 (not _let_56)))) (ASSUME :args (_let_10)) _let_48 _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_59 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or (not _let_12) _let_60 (not _let_61)))) (AND_ELIM _let_65 :args _let_42) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_55 _let_61 (not _let_62)))) _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.isPrime0 W0)))) :args (_let_63)))) _let_64 :args (_let_62 false _let_63)) :args (_let_61 false _let_13 false _let_62)) :args (_let_60 false _let_12 false _let_61)) :args (_let_59 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xr tptp.xn _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_57)))) _let_58 :args (_let_56 false _let_57)) :args (_let_52 false _let_10 false _let_20 false _let_13 true _let_54 false _let_56)) :args (_let_49 false _let_52)))) (let ((_let_68 (= _let_2 _let_5))) (let ((_let_69 (not _let_6))) (let ((_let_70 (not _let_68))) (let ((_let_71 (and (not (= (tptp.sdtpldt0 tptp.xp _let_1) (tptp.sdtpldt0 tptp.xp _let_4))) _let_70))) (let ((_let_72 (= _let_1 _let_4))) (let ((_let_73 (tptp.aNaturalNumber0 _let_4))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.aNaturalNumber0 _let_1))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_34 _let_76 _let_74 _let_71 _let_72))) (let ((_let_78 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2))) (not (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0)))) (= W1 W2))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 (not _let_72))) (let ((_let_82 (and (not (= (tptp.sdtpldt0 tptp.xm tptp.xn) (tptp.sdtpldt0 tptp.xm _let_3))) _let_81))) (let ((_let_83 (= tptp.xn _let_3))) (let ((_let_84 (or _let_35 _let_36 _let_50 _let_82 _let_83))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (AND_ELIM _let_85 :args _let_47))) (let ((_let_87 (or _let_50 _let_35 _let_73))) (let ((_let_88 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_92 (or _let_36 _let_35 _let_75))) (let ((_let_93 (or))) (let ((_let_94 (_let_69))) (let ((_let_95 (tptp.sdtpldt0 _let_28 tptp.xn))) (let ((_let_96 (tptp.sdtpldt0 _let_28 _let_3))) (let ((_let_97 (and (not (= _let_95 _let_96)) (tptp.sdtlseqdt0 _let_96 _let_95) (not (= _let_31 _let_29)) _let_33))) (let ((_let_98 (tptp.aNaturalNumber0 _let_28))) (let ((_let_99 (not _let_98))) (let ((_let_100 (not _let_8))) (let ((_let_101 (or _let_50 _let_36 _let_83 _let_100 _let_99 _let_97))) (let ((_let_102 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1522 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1522))) (let ((_let_2 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1522))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_1522 W1))) (let ((_let_4 (tptp.sdtpldt0 BOUND_VARIABLE_1522 W0))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1522)) (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_103 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (or _let_35 _let_34 _let_98))) (let ((_let_105 (and _let_69 _let_32 _let_30))) (let ((_let_106 (_let_69 _let_32 _let_30))) (let ((_let_107 (ASSUME :args _let_94))) (let ((_let_108 (ASSUME :args (_let_30)))) (let ((_let_109 (ASSUME :args (_let_32)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_107 _let_109 _let_108) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_109) (SYMM _let_108) :args (APPLY_UF tptp.sdtlseqdt0)) (FALSE_INTRO _let_107))) :args _let_106)) :args _let_106)) :args (true _let_105)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_6))) (REFL :args ((not _let_32))) (REFL :args ((not _let_30))) (REFL :args ((not _let_33))) :args _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 3)) :args ((or _let_33 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_83 _let_36 _let_100 _let_50 _let_99 _let_97 (not _let_101)))) _let_86 _let_48 (AND_ELIM _let_85 :args _let_45) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_35 _let_34 _let_98 (not _let_104)))) _let_46 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_104 false _let_88)) :args (_let_98 false _let_19 false _let_18 false _let_104)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_3 tptp.xn _let_28 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1522) (tptp.sdtpldt0 W1 BOUND_VARIABLE_1522))))) :args (_let_102)))) _let_103 :args (_let_101 false _let_102)) :args (_let_97 true _let_83 false _let_20 false _let_8 false _let_49 false _let_98 false _let_101)) :args (_let_33 false _let_97)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_68))) (REFL :args _let_94) :args _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 1)) :args ((or _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_34 _let_76 _let_74 _let_72 _let_71 (not _let_77)))) _let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_36 _let_35 _let_75 (not _let_92)))) _let_48 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_92 false _let_88)) :args (_let_75 false _let_20 false _let_19 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_35 _let_50 _let_73 (not _let_87)))) _let_46 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_3 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_87 false _let_88)) :args (_let_73 false _let_19 false _let_49 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 1)) :args ((or _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_36 _let_35 _let_50 _let_82 (not _let_84)))) _let_86 _let_48 _let_46 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.xm tptp.xn _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) _let_79 :args (_let_84 false _let_78)) :args (_let_82 true _let_83 false _let_20 false _let_19 false _let_49 false _let_84)) :args (_let_81 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.xp _let_1 _let_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) _let_79 :args (_let_77 false _let_78)) :args (_let_71 false _let_18 false _let_75 false _let_73 true _let_72 false _let_77)) :args (_let_70 false _let_71)) :args (_let_69 true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_35 _let_34 _let_50 _let_32 (not _let_51)))) _let_46 _let_44 _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_3 tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_51 false _let_38)) :args (_let_32 false _let_19 false _let_18 false _let_49 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_35 _let_34 _let_30 (not _let_37)))) _let_48 _let_46 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.xn tptp.xm tptp.xp QUANTIFIERS_INST_E_MATCHING _let_41)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_30 false _let_20 false _let_19 false _let_18 false _let_37)) :args (false false _let_33 true _let_6 false _let_32 false _let_30)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) _let_27 (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)))) _let_26 (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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$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 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) _let_25 (forall ((W0 $$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))))) _let_24 (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 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_23 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_22 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (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 (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) (and (tptp.isPrime0 tptp.xp) (tptp.doDivides0 tptp.xp _let_11)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp)) _let_17 (not (or _let_16 _let_15)) (and (not _let_16) (not _let_15)) _let_14 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_11)) (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_10 (tptp.doDivides0 tptp.xr tptp.xm)) _let_10 _let_9 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 _let_3 tptp.xm)) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.96/27.26  )
% 26.96/27.26  % SZS output end Proof for NUM516+1
% 26.96/27.26  % cvc5---1.0.5 exiting
% 26.96/27.27  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------