%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n016.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 10:44:29 EDT 2023

% Result   : Theorem 27.66s 27.98s
% Output   : Proof 27.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.18/0.36  % Computer : n016.cluster.edu
% 0.18/0.36  % Model    : x86_64 x86_64
% 0.18/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36  % Memory   : 8042.1875MB
% 0.18/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit   : 300
% 0.18/0.36  % WCLimit    : 300
% 0.18/0.36  % DateTime   : Fri Aug 25 17:31:56 EDT 2023
% 0.18/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 27.66/27.98  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.66RqtpYxWq/cvc5---1.0.5_27087.p...
% 27.66/27.98  ------- get file name : TPTP file name is NUM498+1
% 27.66/27.98  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27087.smt2...
% 27.66/27.98  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.66/27.98  --- Run --no-e-matching --full-saturate-quant at 5...
% 27.66/27.98  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.66/27.98  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.66/27.98  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.66/27.98  % SZS status Theorem for NUM498+1
% 27.66/27.98  % SZS output start Proof for NUM498+1
% 27.66/27.98  (
% 27.66/27.98  (let ((_let_1 (tptp.doDivides0 tptp.xp tptp.xm))) (let ((_let_2 (tptp.doDivides0 tptp.xp tptp.xn))) (let ((_let_3 (or _let_2 _let_1))) (let ((_let_4 (not (=> (or (= tptp.xk tptp.sz00) (= tptp.xk tptp.sz10)) _let_3)))) (let ((_let_5 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_6 (tptp.sdtsldt0 _let_5 tptp.xp))) (let ((_let_7 (= tptp.xk _let_6))) (let ((_let_8 (= tptp.xm tptp.xp))) (let ((_let_9 (= tptp.xn tptp.xp))) (let ((_let_10 (and (not _let_9) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not _let_8) (tptp.sdtlseqdt0 tptp.xm tptp.xp)))) (let ((_let_11 (tptp.doDivides0 tptp.xp _let_5))) (let ((_let_12 (tptp.isPrime0 tptp.xp))) (let ((_let_13 (and _let_12 _let_11))) (let ((_let_14 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_15 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_16 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_17 (and _let_16 _let_15 _let_14))) (let ((_let_18 (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_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_20 (forall ((W0 $$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 ((_let_21 (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_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))) (let ((_let_23 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_24 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_28 (forall ((W0 $$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_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_30 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_31 (and _let_30 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_32 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_33 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_34 (= _let_5 _let_33))) (let ((_let_35 (= tptp.xm (tptp.sdtasdt0 tptp.xm tptp.sz10)))) (let ((_let_36 (= tptp.xp (tptp.sdtasdt0 tptp.xp tptp.sz10)))) (let ((_let_37 (tptp.sdtasdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_38 (= _let_5 _let_37))) (let ((_let_39 (= tptp.sz10 _let_6))) (let ((_let_40 (= _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_41 (tptp.sdtasdt0 tptp.xp tptp.xm))) (let ((_let_42 (tptp.sdtasdt0 tptp.xp tptp.xp))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (= (tptp.sdtasdt0 _let_41 tptp.xn) (tptp.sdtasdt0 tptp.xp _let_33)))) (let ((_let_45 (tptp.sdtsldt0 tptp.xp tptp.xp))) (let ((_let_46 (= (tptp.sdtasdt0 _let_41 _let_45) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm _let_45))))) (let ((_let_47 (= tptp.sz10 tptp.xn))) (let ((_let_48 (not _let_15))) (let ((_let_49 (not _let_16))) (let ((_let_50 (or _let_49 _let_48 _let_34))) (let ((_let_51 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (1))) (let ((_let_54 (ASSUME :args (_let_17)))) (let ((_let_55 (AND_ELIM _let_54 :args _let_53))) (let ((_let_56 (0))) (let ((_let_57 (AND_ELIM _let_54 :args _let_56))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_48 _let_34 (not _let_50)))) _let_57 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_34 false _let_16 false _let_15 false _let_50)))) (let ((_let_59 (and _let_35 (= tptp.xm (tptp.sdtasdt0 tptp.sz10 tptp.xm))))) (let ((_let_60 (or _let_48 _let_59))) (let ((_let_61 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_65 (and _let_36 (= tptp.xp (tptp.sdtasdt0 tptp.sz10 tptp.xp))))) (let ((_let_66 (not _let_14))) (let ((_let_67 (or _let_66 _let_65))) (let ((_let_68 (2))) (let ((_let_69 (AND_ELIM _let_54 :args _let_68))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 0)) :args ((or _let_36 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_65 (not _let_67)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_67 false _let_61)) :args (_let_65 false _let_14 false _let_67)) :args (_let_36 false _let_65)))) (let ((_let_71 (not _let_38))) (let ((_let_72 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 _let_71))) (let ((_let_75 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (not _let_75))) (let ((_let_78 (= _let_11 _let_77))) (let ((_let_79 (tptp.aNaturalNumber0 _let_5))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_66 _let_80 _let_78))) (let ((_let_82 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (_let_82))) (let ((_let_85 ((tptp.doDivides0 W0 W1)))) (let ((_let_86 (or _let_49 _let_48 _let_79))) (let ((_let_87 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_49 _let_48 _let_79 (not _let_86)))) _let_57 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.xn tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtasdt0 W0 W1)))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_79 false _let_16 false _let_15 false _let_86)))) (let ((_let_90 (ASSUME :args (_let_13)))) (let ((_let_91 (AND_ELIM _let_90 :args _let_53))) (let ((_let_92 (not _let_11))) (let ((_let_93 (or))) (let ((_let_94 (_let_77))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_75))) (REFL :args (_let_76)) :args _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_92 _let_77 (not _let_78)))) _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_66 _let_80 _let_78 (not _let_81)))) _let_69 _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.xp _let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_81 false _let_82)) :args (_let_78 false _let_14 false _let_79 false _let_81)) :args (_let_77 false _let_11 false _let_78)) :args (_let_76 true _let_75)))) (let ((_let_96 (REFL :args (_let_74)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_38))) :args _let_93)) :args ((or _let_38 _let_74))) _let_95 :args (_let_38 true _let_74)))) (let ((_let_98 (= tptp.sz00 _let_6))) (let ((_let_99 (tptp.sdtpldt0 tptp.sz00 tptp.sz00))) (let ((_let_100 (tptp.sdtpldt0 _let_99 tptp.sz00))) (let ((_let_101 (= _let_100 (tptp.sdtpldt0 tptp.sz00 _let_99)))) (let ((_let_102 (= tptp.sz00 _let_99))) (let ((_let_103 (= _let_6 _let_100))) (let ((_let_104 (not _let_32))) (let ((_let_105 (or _let_104 _let_104 _let_104 _let_101))) (let ((_let_106 (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_107 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (ASSUME :args (_let_32)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_105))) :args ((or _let_104 _let_101 (not _let_105)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.aNaturalNumber0 W0) false)) (not (= (tptp.aNaturalNumber0 W1) false)) (not (= (tptp.aNaturalNumber0 W2) false))))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_101 false _let_32 false _let_105)))) (let ((_let_110 (or _let_104 _let_102))) (let ((_let_111 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (_let_111))) (let ((_let_114 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_104 _let_102 (not _let_110)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_112 :args (tptp.sz00 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113))) _let_112 :args (_let_110 false _let_111)) :args (_let_102 false _let_32 false _let_110)))) (let ((_let_116 (= _let_5 (tptp.sdtasdt0 tptp.xp _let_100)))) (let ((_let_117 (and (tptp.aNaturalNumber0 _let_100) _let_116))) (let ((_let_118 (= _let_117 _let_103))) (let ((_let_119 (not _let_103))) (let ((_let_120 (= tptp.sz00 tptp.xp))) (let ((_let_121 (or _let_66 _let_80 _let_120 _let_92 _let_118))) (let ((_let_122 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1608 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1608) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1608))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1608)))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (_let_122))) (let ((_let_125 (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp))))) (let ((_let_126 (not _let_120))) (let ((_let_127 (and _let_126 (not (= tptp.sz10 tptp.xp)) _let_125))) (let ((_let_128 (= _let_12 _let_127))) (let ((_let_129 (or _let_66 _let_128))) (let ((_let_130 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= (tptp.isPrime0 W0) (and (not (= tptp.sz00 W0)) (not (= tptp.sz10 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 W0)) (= tptp.sz10 W1) (= W0 W1))))))))) (let ((_let_131 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_128)) :args ((or (not _let_12) _let_127 (not _let_128)))) (AND_ELIM _let_90 :args _let_56) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_66 _let_128 (not _let_129)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_131 :args (tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args (_let_130)))) _let_131 :args (_let_129 false _let_130)) :args (_let_128 false _let_14 false _let_129)) :args (_let_127 false _let_12 false _let_128)))) (let ((_let_133 (not _let_127))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_127 0)) :args ((or _let_126 _let_133))) _let_132 :args (_let_126 false _let_127)))) (let ((_let_135 (not _let_117))) (let ((_let_136 (tptp.sdtasdt0 tptp.xp tptp.sz00))) (let ((_let_137 (= tptp.sz00 _let_136))) (let ((_let_138 (= tptp.sz00 _let_5))) (let ((_let_139 (= tptp.xn _let_136))) (let ((_let_140 (= tptp.sz00 (tptp.sdtasdt0 tptp.xn tptp.sz00)))) (let ((_let_141 (= tptp.sz00 tptp.xn))) (let ((_let_142 (= tptp.sz00 tptp.xm))) (let ((_let_143 (not _let_138))) (let ((_let_144 (or _let_49 _let_48 _let_143 _let_141 _let_142))) (let ((_let_145 (not _let_116))) (let ((_let_146 (and _let_137 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp))))) (let ((_let_147 (or _let_66 _let_146))) (let ((_let_148 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_149 (EQ_RESOLVE 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_let_228 _let_261 _let_263 _let_191 _let_226) (SCOPE (TRANS (CONG _let_165 (TRANS _let_234 _let_232 _let_229 (SYMM _let_193)) :args _let_159) (SYMM _let_264) (CONG (REFL :args (_let_41)) (TRANS (SYMM _let_263) _let_226 (SYMM _let_235)) :args _let_159) (SYMM (SYMM _let_262)) (CONG _let_165 (TRANS (CONG (REFL :args (tptp.xm)) _let_236 :args _let_159) (SYMM _let_261)) :args _let_159)) :args (_let_44 _let_46 _let_40 _let_36 _let_38 _let_35 _let_47 _let_34 _let_39))) :args (_let_39 _let_47 _let_34 _let_35 _let_36 _let_38 _let_40 _let_44 _let_46))) :args (true _let_260)) :args ((or _let_254 (not _let_47) _let_184 (not _let_35) _let_253 _let_71 _let_43 _let_252 (not _let_44) (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_239)) :args ((or _let_9 _let_49 _let_47 _let_238 (not _let_239)))) (AND_ELIM _let_215 :args _let_56) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_243)) (CONG (REFL :args (_let_259)) (REFL :args (_let_237)) (MACRO_SR_PRED_INTRO :args ((= (not _let_242) _let_241))) :args _let_93)) :args ((or _let_237 _let_241 _let_259))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_258) :args (tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_258)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_247)) :args ((or _let_48 _let_246 _let_248))) _let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_256 _let_228 (MODUS_PONENS (AND_INTRO _let_230 _let_226 _let_233) (SCOPE (TRANS _let_234 (CONG _let_165 (TRANS (SYMM _let_227) _let_231) :args _let_159)) :args (_let_40 _let_39 _let_36))) _let_257) :args (_let_39 _let_249 _let_36 _let_38 _let_40 _let_246)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (TRANS _let_257 (TRANS (SYMM _let_257) (SYMM (SYMM (ASSUME :args (_let_255)))) _let_229)))) (FALSE_INTRO _let_256))) :args (_let_246 _let_38 _let_255 _let_249)) :args ((not (and _let_39 _let_249 _let_36 _let_38 _let_40 _let_246)) SB_LITERAL))) (CONG (REFL :args (_let_254)) (REFL :args ((not _let_249))) (REFL :args (_let_253)) (REFL :args (_let_71)) (REFL :args (_let_252)) (MACRO_SR_PRED_INTRO :args ((= (not _let_246) _let_245))) :args _let_93)) _let_205 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_250 0)) :args ((or _let_249 (not _let_250)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_251)) :args ((or _let_66 _let_250 (not _let_251)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113)) _let_112 :args (_let_251 false _let_111)) :args (_let_250 false _let_14 false _let_251)) :args (_let_249 false _let_250)) _let_70 _let_97 _let_209 :args (_let_245 false _let_39 false _let_249 false _let_36 false _let_38 false _let_40)) :args (_let_248 false _let_15 false _let_245)) :args (_let_242 true _let_247)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_244)) :args ((or _let_49 _let_66 _let_243 (not _let_244)))) _let_57 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.xn tptp.xp QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_244 false _let_82)) :args (_let_243 false _let_16 false _let_14 false _let_244)) :args (_let_237 true _let_241 false _let_243)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_240) :args (tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aNaturalNumber0 W1) false))))) :args _let_240)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_127 2)) :args ((or _let_125 _let_133))) _let_132 :args (_let_125 false _let_127)) :args (_let_239 false _let_125)) :args (_let_47 true _let_9 false _let_16 false _let_237 false _let_239)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_223)) :args ((or _let_48 _let_66 _let_222 _let_46 (not _let_223)))) _let_55 _let_69 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_224)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_225 _let_226 _let_228 _let_230 _let_233) (SCOPE (TRUE_ELIM (TRANS (CONG _let_236 :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_225))) :args (_let_30 _let_39 _let_38 _let_40 _let_36))) :args (_let_30 _let_39 _let_36 _let_38 _let_40))) :args (true _let_224)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))) :args _let_56) _let_205 _let_70 _let_97 _let_209 :args (_let_221 false _let_30 false _let_39 false _let_36 false _let_38 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_218 :args (tptp.xp tptp.xm _let_45 QUANTIFIERS_INST_E_MATCHING _let_220)) :args _let_219)) _let_218 :args (_let_223 false _let_217)) :args (_let_46 false _let_15 false _let_14 false _let_221 false _let_223)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_216)) :args ((or _let_49 _let_48 _let_66 _let_44 (not _let_216)))) _let_57 _let_55 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_218 :args (tptp.xp tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING _let_220)) :args _let_219)) _let_218 :args (_let_216 false _let_217)) :args (_let_44 false _let_16 false _let_15 false _let_14 false _let_216)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_211 0)) :args ((or _let_210 (not _let_211)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_212))) :args ((or _let_8 _let_48 _let_66 _let_120 _let_211 (not _let_212)))) (AND_ELIM _let_215 :args _let_68) _let_55 _let_69 _let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_214 :args (tptp.xp tptp.xp tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args (_let_213)))) _let_214 :args (_let_212 false _let_213)) :args (_let_211 true _let_8 false _let_15 false _let_14 true _let_120 false _let_212)) :args (_let_210 false _let_211)) _let_209 _let_205 _let_97 _let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 0)) :args ((or _let_35 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_48 _let_59 (not _let_60)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_64)) :args _let_63)) _let_62 :args (_let_60 false _let_61)) :args (_let_59 false _let_15 false _let_60)) :args (_let_35 false _let_59)) _let_58 :args (false false _let_47 false _let_46 false _let_44 true _let_43 false _let_40 false _let_39 false _let_38 false _let_36 false _let_35 false _let_34)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_32 _let_31 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_21 (forall ((W0 $$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)))) _let_20 _let_19 (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_18 (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_17 (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)))))) _let_13 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) _let_10 _let_7 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.66/27.99  )
% 27.66/27.99  % SZS output end Proof for NUM498+1
% 27.66/27.99  % cvc5---1.0.5 exiting
% 27.66/27.99  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------