%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM488+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 10:44:24 EDT 2023

% Result   : Theorem 83.34s 83.56s
% Output   : Proof 83.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUM488+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n005.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri Aug 25 15:40:53 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 83.34/83.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.VGBCUx2FTI/cvc5---1.0.5_3124.p...
% 83.34/83.56  ------- get file name : TPTP file name is NUM488+1
% 83.34/83.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3124.smt2...
% 83.34/83.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 83.34/83.56  --- Run --no-e-matching --full-saturate-quant at 5...
% 83.34/83.56  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 83.34/83.56  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 83.34/83.56  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 83.34/83.56  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 83.34/83.56  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 83.34/83.56  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 83.34/83.56  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 83.34/83.56  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 83.34/83.56  --- Run --relevant-triggers --full-saturate-quant at 5...
% 83.34/83.56  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 83.34/83.56  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 83.34/83.56  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 83.34/83.56  % SZS status Theorem for NUM488+1
% 83.34/83.56  % SZS output start Proof for NUM488+1
% 83.34/83.56  (
% 83.34/83.56  (let ((_let_1 (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm))))) (let ((_let_2 (tptp.sdtmndt0 tptp.xn tptp.xp))) (let ((_let_3 (= tptp.xr _let_2))) (let ((_let_4 (tptp.sdtlseqdt0 tptp.xp tptp.xn))) (let ((_let_5 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_6 (tptp.doDivides0 tptp.xp _let_5))) (let ((_let_7 (and (tptp.isPrime0 tptp.xp) _let_6))) (let ((_let_8 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_9 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_10 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_11 (and _let_10 _let_9 _let_8))) (let ((_let_12 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))))) (let ((_let_13 (forall ((W0 $$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_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))) (let ((_let_15 (forall ((W0 $$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)))))))) (let ((_let_16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))) (let ((_let_17 (forall ((W0 $$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 ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_20 (tptp.sdtasdt0 tptp.xp tptp.xm))) (let ((_let_21 (tptp.aNaturalNumber0 _let_20))) (let ((_let_22 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xm))) (let ((_let_23 (tptp.aNaturalNumber0 _let_22))) (let ((_let_24 (tptp.doDivides0 tptp.xp _let_20))) (let ((_let_25 (tptp.doDivides0 tptp.xp _let_22))) (let ((_let_26 (tptp.sdtpldt0 _let_20 _let_22))) (let ((_let_27 (tptp.doDivides0 tptp.xp _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_24))) (let ((_let_30 (not _let_23))) (let ((_let_31 (not _let_21))) (let ((_let_32 (not _let_8))) (let ((_let_33 (or _let_32 _let_31 _let_30 _let_29 _let_28 _let_25))) (let ((_let_34 (ASSUME :args (_let_11)))) (let ((_let_35 (AND_ELIM _let_34 :args (2)))) (let ((_let_36 (not _let_9))) (let ((_let_37 (or _let_32 _let_36 _let_21))) (let ((_let_38 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_42 (1))) (let ((_let_43 (AND_ELIM _let_34 :args _let_42))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_32 _let_21 (not _let_37)))) _let_43 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.xp tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_21 false _let_9 false _let_8 false _let_37)))) (let ((_let_45 (= _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (tptp.sdtasdt0 _let_2 tptp.xm))) (let ((_let_47 (tptp.aNaturalNumber0 _let_46))) (let ((_let_48 (tptp.sdtpldt0 tptp.xp _let_2))) (let ((_let_49 (tptp.sdtpldt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_50 (= _let_49 _let_48))) (let ((_let_51 (not _let_50))) (let ((_let_52 (and _let_51 (not (= (tptp.sdtpldt0 _let_2 tptp.xp) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xp)))))) (let ((_let_53 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.aNaturalNumber0 _let_2))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_32 _let_56 _let_54 _let_52 _let_45))) (let ((_let_58 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (and (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2))) (not (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0)))) (= W1 W2))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (not _let_52))) (let ((_let_61 (= tptp.xn _let_48))) (let ((_let_62 (= tptp.xn _let_49))) (let ((_let_63 (and _let_55 _let_61))) (let ((_let_64 (not _let_4))) (let ((_let_65 (not _let_10))) (let ((_let_66 (or _let_32 _let_65 _let_64 _let_63))) (let ((_let_67 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1401 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1401) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1401))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1401)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (ASSUME :args (_let_4)))) (let ((_let_70 (AND_ELIM _let_34 :args (0)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_32 _let_64 _let_63 (not _let_66)))) _let_70 _let_35 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.xp tptp.xn _let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_67)))) _let_68 :args (_let_66 false _let_67)) :args (_let_63 false _let_10 false _let_8 false _let_4 false _let_66)))) (let ((_let_72 (not _let_63))) (let ((_let_73 (not _let_62))) (let ((_let_74 (or _let_54 _let_73))) (let ((_let_75 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtpldt0 tptp.xp W2))))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (not _let_75))) (let ((_let_78 (= _let_4 _let_77))) (let ((_let_79 (or _let_32 _let_65 _let_78))) (let ((_let_80 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtpldt0 W0 W2))))))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (or))) (let ((_let_83 (_let_77))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_75))) (REFL :args (_let_76)) :args _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_64 _let_77 (not _let_78)))) _let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_65 _let_32 _let_78 (not _let_79)))) _let_70 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.xp tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtlseqdt0 W0 W1)))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_78 false _let_10 false _let_8 false _let_79)) :args (_let_77 false _let_4 false _let_78)) :args (_let_76 true _let_75)))) (let ((_let_85 (REFL :args (_let_74)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG _let_85 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_62))) :args _let_82)) :args ((or _let_62 _let_74))) _let_84 :args (_let_62 true _let_74)))) (let ((_let_87 (and _let_62 _let_61))) (let ((_let_88 (ASSUME :args (_let_61)))) (let ((_let_89 (ASSUME :args (_let_62)))) (let ((_let_90 (SYMM _let_89))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 0)) (CONG _let_85 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_82)) :args ((or _let_53 _let_74))) _let_84 :args (_let_53 true _let_74)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_63 0)) :args ((or _let_55 _let_72))) _let_71 :args (_let_55 false _let_63)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_32 _let_56 _let_54 _let_45 _let_52 (not _let_57)))) _let_35 _let_92 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_51 _let_60))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_89) (SCOPE (TRANS _let_90 (SYMM (SYMM _let_88))) :args (_let_61 _let_62))) :args (_let_62 _let_61))) :args (true _let_87)) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_63 1)) :args ((or _let_61 _let_72))) _let_71 :args (_let_61 false _let_63)) :args (_let_50 false _let_62 false _let_61)) :args (_let_60 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.xp _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_58)))) _let_59 :args (_let_57 false _let_58)) :args (_let_45 false _let_8 false _let_55 false _let_53 true _let_52 false _let_57)))) (let ((_let_94 (or _let_56 _let_36 _let_47))) (let ((_let_95 (and _let_47 _let_45))) (let ((_let_96 (_let_47 _let_45))) (let ((_let_97 (ASSUME :args (_let_47)))) (let ((_let_98 (APPLY_UF tptp.sdtasdt0))) (let ((_let_99 (REFL :args (tptp.xm)))) (let ((_let_100 (ASSUME :args (_let_45)))) (let ((_let_101 (SYMM _let_100))) (let ((_let_102 (SYMM _let_101))) (let ((_let_103 (CONG (SYMM _let_102) _let_99 :args _let_98))) (let ((_let_104 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xp tptp.xm) (tptp.sdtasdt0 tptp.xp W2))))))) (let ((_let_105 (not _let_104))) (let ((_let_106 (= _let_24 _let_105))) (let ((_let_107 (or _let_32 _let_31 _let_106))) (let ((_let_108 (forall ((W0 $$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_109 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (_let_104))) (let ((_let_111 (not _let_106))) (let ((_let_112 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.doDivides0 W0 W1)) (not (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (tptp.doDivides0 tptp.xp _let_46))) (let ((_let_115 (not _let_25))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (ASSUME :args (_let_3)) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (not _let_114))) (let ((_let_118 (and _let_117 _let_45))) (let ((_let_119 (_let_117 _let_45))) (let ((_let_120 (APPLY_UF tptp.doDivides0))) (let ((_let_121 (REFL :args (tptp.xp)))) (let ((_let_122 (tptp.sdtasdt0 tptp.xm tptp.xp))) (let ((_let_123 (= (tptp.sdtasdt0 tptp.xm _let_49) (tptp.sdtpldt0 _let_122 (tptp.sdtasdt0 tptp.xm SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_124 (= _let_20 _let_122))) (let ((_let_125 (= _let_46 (tptp.sdtasdt0 tptp.xm _let_2)))) (let ((_let_126 (= _let_5 (tptp.sdtasdt0 tptp.xm tptp.xn)))) (let ((_let_127 (and _let_123 (= (tptp.sdtasdt0 _let_49 tptp.xm) _let_26)))) (let ((_let_128 (or _let_36 _let_32 _let_54 _let_127))) (let ((_let_129 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (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 ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (or _let_32 _let_36 _let_124))) (let ((_let_132 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (_let_132))) (let ((_let_135 (or _let_36 _let_56 _let_125))) (let ((_let_136 ((tptp.sdtasdt0 W1 W0)))) (let ((_let_137 (or _let_36 _let_65 _let_126))) (let ((_let_138 (and _let_6 _let_126 _let_125 _let_62 _let_45 _let_124 _let_123))) (let ((_let_139 (ASSUME :args (_let_6)))) (let ((_let_140 (ASSUME :args (_let_126)))) (let ((_let_141 (ASSUME :args (_let_123)))) (let ((_let_142 (ASSUME :args (_let_125)))) (let ((_let_143 (ASSUME :args (_let_124)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_31 _let_30 _let_29 _let_28 _let_25 (not _let_33)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_138)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_139 _let_140 _let_89 _let_141 _let_143 _let_100 _let_142) (SCOPE (TRUE_ELIM (TRANS (CONG _let_121 (TRANS (CONG (SYMM (SYMM _let_143)) (TRANS (CONG _let_101 _let_99 :args _let_98) (SYMM (SYMM _let_142)) (CONG _let_99 _let_102 :args _let_98)) :args (APPLY_UF tptp.sdtpldt0)) (SYMM _let_141) (CONG _let_99 _let_90 :args _let_98) (SYMM _let_140)) :args _let_120) (TRUE_INTRO _let_139))) :args (_let_6 _let_126 _let_62 _let_123 _let_124 _let_45 _let_125))) :args (_let_6 _let_126 _let_125 _let_62 _let_45 _let_124 _let_123))) :args (true _let_138)) (AND_ELIM (ASSUME :args (_let_7)) :args _let_42) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_137)) :args ((or _let_65 _let_36 _let_126 (not _let_137)))) _let_70 _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_133 :args (tptp.xm tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_134))) _let_133 :args (_let_137 false _let_132)) :args (_let_126 false _let_10 false _let_9 false _let_137)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_36 _let_56 _let_125 (not _let_135)))) _let_43 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_133 :args (tptp.xm _let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_134))) _let_133 :args (_let_135 false _let_132)) :args (_let_125 false _let_9 false _let_55 false _let_135)) _let_86 _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_36 _let_32 _let_124 (not _let_131)))) _let_43 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (tptp.xp tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args _let_134)) _let_133 :args (_let_131 false _let_132)) :args (_let_124 false _let_9 false _let_8 false _let_131)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_127 0)) :args ((or _let_123 (not _let_127)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_36 _let_32 _let_54 _let_127 (not _let_128)))) _let_43 _let_35 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (tptp.xm tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 (tptp.sdtpldt0 W1 W2) W0)))) :args (_let_129))) _let_130 :args (_let_128 false _let_129)) :args (_let_127 false _let_9 false _let_8 false _let_53 false _let_128)) :args (_let_123 false _let_127)) :args (_let_27 false _let_6 false _let_126 false _let_125 false _let_62 false _let_45 false _let_124 false _let_123)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_118)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_116 _let_100) (SCOPE (FALSE_ELIM (TRANS (CONG _let_121 _let_103 :args _let_120) (FALSE_INTRO _let_116))) :args _let_119)) :args _let_119)) :args (true _let_118)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_117) _let_114))) (REFL :args ((not _let_45))) (REFL :args (_let_115)) :args _let_82)) _let_116 _let_93 :args (_let_115 true _let_114 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (tptp.xp _let_20 _let_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_112))) _let_113 :args (_let_33 false _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_106)) (CONG (REFL :args (_let_111)) (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_104))) :args _let_82)) :args ((or _let_24 _let_104 _let_111))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_110) :args (tptp.xm QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_110))) :args ((or _let_36 _let_105))) _let_43 :args (_let_105 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_32 _let_31 _let_106 (not _let_107)))) _let_35 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.xp _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_106 false _let_8 false _let_21 false _let_107)) :args (_let_24 true _let_104 false _let_106)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_95)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_97 _let_100) (SCOPE (TRUE_ELIM (TRANS (CONG _let_103 :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_97))) :args _let_96)) :args _let_96)) :args (true _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_36 _let_56 _let_47 (not _let_94)))) _let_43 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_2 tptp.xm QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_94 false _let_38)) :args (_let_47 false _let_9 false _let_55 false _let_94)) _let_93 :args (_let_23 false _let_47 false _let_45)) _let_44 _let_35 :args (false false _let_27 true _let_25 false _let_33 false _let_24 false _let_23 false _let_21 false _let_8)) :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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_19 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_18 (forall ((W0 $$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))))) _let_17 _let_16 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) _let_15 _let_14 (forall ((W0 $$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_13 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))) _let_12 (forall ((W0 $$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_11 (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_7 _let_4 _let_3 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 83.37/83.57  )
% 83.37/83.57  % SZS output end Proof for NUM488+1
% 83.37/83.57  % cvc5---1.0.5 exiting
% 83.37/83.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------