%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM528+1 : 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 10:44:47 EDT 2023

% Result   : Theorem 10.71s 11.31s
% Output   : Proof 10.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM528+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.18/0.35  % Computer : n006.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit   : 300
% 0.18/0.35  % WCLimit    : 300
% 0.18/0.35  % DateTime   : Fri Aug 25 11:43:37 EDT 2023
% 0.18/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 10.71/11.31  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OCn6xkVyao/cvc5---1.0.5_24225.p...
% 10.71/11.31  ------- get file name : TPTP file name is NUM528+1
% 10.71/11.31  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24225.smt2...
% 10.71/11.31  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.71/11.31  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.71/11.31  % SZS status Theorem for NUM528+1
% 10.71/11.31  % SZS output start Proof for NUM528+1
% 10.71/11.31  (
% 10.71/11.31  (let ((_let_1 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_2 (not (and (not (= tptp.xm tptp.xn)) _let_1)))) (let ((_let_3 (tptp.sdtasdt0 tptp.xm tptp.xm))) (let ((_let_4 (tptp.sdtasdt0 tptp.xn tptp.xn))) (let ((_let_5 (tptp.sdtlseqdt0 _let_4 _let_3))) (let ((_let_6 (tptp.sdtlseqdt0 tptp.xn tptp.xm))) (let ((_let_7 (=> _let_6 _let_5))) (let ((_let_8 (tptp.isPrime0 tptp.xp))) (let ((_let_9 (tptp.sdtasdt0 tptp.xp _let_3))) (let ((_let_10 (= _let_9 _let_4))) (let ((_let_11 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_12 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_13 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_14 (and _let_13 _let_12 _let_11 (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))) (let ((_let_15 (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_16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))) (let ((_let_18 (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_19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))) (let ((_let_21 (forall ((W0 $$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))))))))) (let ((_let_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_25 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_26 (and _let_25 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_27 (= tptp.sz10 tptp.xp))) (let ((_let_28 (tptp.aNaturalNumber0 _let_3))) (let ((_let_29 (tptp.sdtasdt0 tptp.sz10 _let_3))) (let ((_let_30 (= _let_9 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.sdtasdt0 _let_3 tptp.xp))) (let ((_let_33 (tptp.sdtasdt0 _let_3 tptp.sz10))) (let ((_let_34 (and (not (= _let_33 _let_32)) _let_31))) (let ((_let_35 (not _let_11))) (let ((_let_36 (not _let_25))) (let ((_let_37 (= tptp.sz00 _let_3))) (let ((_let_38 (not _let_28))) (let ((_let_39 (or _let_38 _let_37 _let_36 _let_35 _let_34 _let_27))) (let ((_let_40 (0))) (let ((_let_41 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) :args _let_40))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (AND_ELIM _let_42 :args (2)))) (let ((_let_44 (not _let_27))) (let ((_let_45 (= tptp.sz00 tptp.xp))) (let ((_let_46 (and (not _let_45) _let_44 (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_47 (= _let_8 _let_46))) (let ((_let_48 (or _let_35 _let_47))) (let ((_let_49 (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_50 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (not _let_12))) (let ((_let_52 (or _let_51 _let_51 _let_28))) (let ((_let_53 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 (AND_ELIM _let_42 :args (1)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_52))) :args ((or _let_51 _let_28 (not _let_52)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.xm tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_28 false _let_12 false _let_52)))) (let ((_let_58 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1342 $$unsorted) (BOUND_VARIABLE_1340 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1340)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1342)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1340) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1342))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1340 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1342 W0)))) (= BOUND_VARIABLE_1340 BOUND_VARIABLE_1342))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (= _let_3 _let_4))) (let ((_let_61 (= tptp.sz00 _let_4))) (let ((_let_62 (not _let_37))) (let ((_let_63 (tptp.sdtlseqdt0 _let_3 _let_4))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_5))) (let ((_let_66 (tptp.aNaturalNumber0 _let_4))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_38 _let_65 _let_64 _let_60))) (let ((_let_69 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (tptp.sdtlseqdt0 _let_3 _let_32))) (let ((_let_72 (= _let_9 _let_32))) (let ((_let_73 (or _let_35 _let_38 _let_45 _let_71))) (let ((_let_74 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (or _let_35 _let_38 _let_72))) (let ((_let_77 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_77))) (let ((_let_80 (ASSUME :args (_let_10)))) (let ((_let_81 (and _let_10 _let_72 _let_71))) (let ((_let_82 (ASSUME :args (_let_71)))) (let ((_let_83 (APPLY_UF tptp.sdtlseqdt0))) (let ((_let_84 (ASSUME :args (_let_72)))) (let ((_let_85 (SYMM _let_80))) (let ((_let_86 (not _let_13))) (let ((_let_87 (or _let_86 _let_86 _let_66))) (let ((_let_88 (AND_ELIM _let_42 :args _let_40))) (let ((_let_89 (tptp.sdtlseqdt0 tptp.xn tptp.xn))) (let ((_let_90 (= tptp.xn tptp.xm))) (let ((_let_91 (not _let_90))) (let ((_let_92 (and _let_91 _let_1))) (let ((_let_93 (or _let_86 _let_51 _let_6 _let_92))) (let ((_let_94 (or _let_86 _let_89))) (let ((_let_95 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (not _let_89))) (let ((_let_98 (or))) (let ((_let_99 (not _let_6))) (let ((_let_100 (ASSUME :args (_let_89)))) (let ((_let_101 (ASSUME :args (_let_90)))) (let ((_let_102 (ASSUME :args (_let_99)))) (let ((_let_103 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.sdtlseqdt0 W0 W1) (and (not (= W0 W1)) (tptp.sdtlseqdt0 W1 W0)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_65 _let_60 _let_38 _let_67 _let_64 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (ASSUME :args (_let_7))) :args ((or _let_5 _let_99))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_92 1)) :args ((or _let_1 (not _let_92)))) (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) (REFL :args ((not _let_1))) :args _let_98)) (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_6 _let_92 _let_86 _let_51 (not _let_93)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_103))) _let_104 :args (_let_93 false _let_103)) _let_56 _let_88 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_100 _let_101 _let_102) :args (_let_90 _let_99 _let_89)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_102)) (CONG (REFL :args (tptp.xn)) (SYMM _let_101) :args _let_83) (TRUE_INTRO _let_100))) :args (_let_89 _let_90 _let_99)) :args ((not (and _let_90 _let_99 _let_89)) SB_LITERAL))) (CONG (REFL :args (_let_91)) (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_6))) (REFL :args (_let_97)) :args _let_98)) :args ((or _let_6 _let_91 _let_97))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_86 _let_89 (not _let_94)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_95))) _let_96 :args (_let_94 false _let_95)) :args (_let_89 false _let_13 false _let_94)) :args (_let_6 true _let_1 false _let_92 false _let_93 false _let_12 false _let_13 true _let_90 false _let_89)) :args (_let_5 false _let_6)) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_87))) :args ((or _let_86 _let_66 (not _let_87)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.xn tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_55)) _let_54 :args (_let_87 false _let_53)) :args (_let_66 false _let_13 false _let_87)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_81)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_82 _let_84 _let_80) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_3)) (TRANS _let_85 (SYMM (SYMM _let_84))) :args _let_83) (TRUE_INTRO _let_82))) :args (_let_71 _let_72 _let_10))) :args (_let_10 _let_72 _let_71))) :args (true _let_81)) _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_35 _let_38 _let_72 (not _let_76)))) _let_43 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.xp _let_3 QUANTIFIERS_INST_CBQI_PROP)) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args (_let_72 false _let_11 false _let_28 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_45 _let_35 _let_38 _let_71 (not _let_73)))) (AND_ELIM _let_42 :args (5)) _let_43 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.xp _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_71 true _let_45 false _let_11 false _let_28 false _let_73)) :args (_let_63 false _let_10 false _let_72 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_4 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_69)))) _let_70 :args (_let_68 false _let_69)) :args (_let_60 false _let_5 false _let_28 false _let_66 false _let_63 false _let_68)))) (let ((_let_106 (= tptp.sz00 tptp.xn))) (let ((_let_107 (not _let_61))) (let ((_let_108 (or _let_86 _let_86 _let_107 _let_106 _let_106))) (let ((_let_109 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (= tptp.sz00 (tptp.sdtasdt0 W0 W1))) (= tptp.sz00 W0) (= tptp.sz00 W1))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (not _let_60))) (let ((_let_112 (and _let_107 _let_60))) (let ((_let_113 (ASSUME :args (_let_107)))) (let ((_let_114 (ASSUME :args (_let_60)))) (let ((_let_115 (SYMM _let_114))) (let ((_let_116 (not _let_34))) (let ((_let_117 (= _let_29 _let_33))) (let ((_let_118 (= _let_3 _let_33))) (let ((_let_119 (or _let_36 _let_38 _let_117))) (let ((_let_120 (and _let_118 (= _let_3 _let_29)))) (let ((_let_121 (or _let_38 _let_120))) (let ((_let_122 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (and _let_10 _let_60 _let_118 _let_117))) (let ((_let_125 (ASSUME :args (_let_117)))) (let ((_let_126 (ASSUME :args (_let_118)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_36 _let_35 _let_27 _let_38 _let_37 _let_34 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_31 _let_116))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_124)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_126 _let_114 _let_80) (SCOPE (TRANS (SYMM _let_85) _let_115 (SYMM (SYMM _let_126)) (SYMM _let_125)) :args (_let_117 _let_118 _let_60 _let_10))) :args (_let_10 _let_60 _let_118 _let_117))) :args (true _let_124)) :args ((or (not _let_10) (not _let_118) (not _let_117) _let_30 _let_111))) _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_120 0)) :args ((or _let_118 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_38 _let_120 (not _let_121)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 :args (_let_3 QUANTIFIERS_INST_ENUM)) :args (_let_122))) _let_123 :args (_let_121 false _let_122)) :args (_let_120 false _let_28 false _let_121)) :args (_let_118 false _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_36 _let_38 _let_117 (not _let_119)))) _let_41 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.sz10 _let_3 QUANTIFIERS_INST_ENUM)) :args _let_79)) _let_78 :args (_let_119 false _let_77)) :args (_let_117 false _let_25 false _let_28 false _let_119)) _let_105 :args (_let_30 false _let_10 false _let_118 false _let_117 false _let_60)) :args (_let_116 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_113) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (SYMM _let_115) :args (=)) (FALSE_INTRO _let_113))) :args (_let_60 _let_107))) :args (_let_107 _let_60))) :args (true _let_112)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_61))) (REFL :args (_let_111)) (REFL :args (_let_62)) :args _let_98)) :args ((or _let_61 _let_62 _let_111))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_108))) :args ((or _let_106 _let_86 _let_107 (not _let_108)))) (AND_ELIM _let_42 :args (3)) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (tptp.xn tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args (_let_109))) _let_110 :args (_let_108 false _let_109)) :args (_let_107 true _let_106 false _let_13 false _let_108)) _let_105 :args (_let_62 true _let_61 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_3 tptp.xp tptp.sz10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_58)))) _let_59 :args (_let_39 false _let_58)) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 1)) :args ((or _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or (not _let_8) _let_46 (not _let_47)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_35 _let_47 (not _let_48)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_49)))) _let_50 :args (_let_48 false _let_49)) :args (_let_47 false _let_11 false _let_48)) :args (_let_46 false _let_8 false _let_47)) :args (_let_44 false _let_46)) _let_43 _let_41 :args (false true _let_34 true _let_37 false _let_39 false _let_28 true _let_27 false _let_11 false _let_25)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) _let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_24 (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_23 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) _let_22 (forall ((W0 $$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)))) _let_21 (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))))) _let_20 (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))))))) _let_19 _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) _let_17 (forall ((W0 $$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))))) _let_16 (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))))))) _let_15 (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))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) _let_14 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (tptp.isPrime0 W2)))))) _let_10 _let_8 (and (tptp.doDivides0 tptp.xp _let_4) (tptp.doDivides0 tptp.xp tptp.xn)) (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp)) (= _let_3 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xq tptp.xq))) _let_7 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.71/11.31  )
% 10.71/11.31  % SZS output end Proof for NUM528+1
% 10.71/11.31  % cvc5---1.0.5 exiting
% 11.09/11.31  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------