%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 10:44:35 EDT 2023

% Result   : Theorem 26.20s 26.42s
% Output   : Proof 26.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 10:45:32 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 26.20/26.42  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vFOreZhIiE/cvc5---1.0.5_9367.p...
% 26.20/26.42  ------- get file name : TPTP file name is NUM510+1
% 26.20/26.42  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9367.smt2...
% 26.20/26.42  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.20/26.42  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.20/26.42  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.20/26.42  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.20/26.42  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.20/26.42  % SZS status Theorem for NUM510+1
% 26.20/26.42  % SZS output start Proof for NUM510+1
% 26.20/26.42  (
% 26.20/26.42  (let ((_let_1 (tptp.sdtsldt0 tptp.xn tptp.xr))) (let ((_let_2 (tptp.sdtlseqdt0 _let_1 tptp.xn))) (let ((_let_3 (not (and (not (= _let_1 tptp.xn)) _let_2)))) (let ((_let_4 (tptp.doDivides0 tptp.xr tptp.xn))) (let ((_let_5 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_6 (tptp.isPrime0 tptp.xr))) (let ((_let_7 (tptp.aNaturalNumber0 tptp.xr))) (let ((_let_8 (and _let_7 (tptp.doDivides0 tptp.xr tptp.xk) _let_6))) (let ((_let_9 (= tptp.xk tptp.sz10))) (let ((_let_10 (= tptp.xk tptp.sz00))) (let ((_let_11 (not (or _let_10 _let_9)))) (let ((_let_12 (tptp.sdtsldt0 _let_5 tptp.xp))) (let ((_let_13 (= tptp.xk _let_12))) (let ((_let_14 (tptp.doDivides0 tptp.xp _let_5))) (let ((_let_15 (tptp.isPrime0 tptp.xp))) (let ((_let_16 (and _let_15 _let_14))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_19 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_20 (and _let_19 _let_18 _let_17))) (let ((_let_21 (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_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_23 (forall ((W0 $$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_24 (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_25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))) (let ((_let_26 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_27 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_30 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_31 (and _let_30 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_32 (= tptp.xn (tptp.sdtasdt0 tptp.xr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_33 (= _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_34 (tptp.sdtasdt0 _let_1 tptp.xr))) (let ((_let_35 (= (tptp.sdtasdt0 tptp.xr _let_1) _let_34))) (let ((_let_36 (tptp.sdtlseqdt0 _let_1 _let_34))) (let ((_let_37 (not _let_32))) (let ((_let_38 (tptp.aNaturalNumber0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= tptp.xn (tptp.sdtasdt0 tptp.xr W2))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (not _let_41))) (let ((_let_44 (= _let_4 _let_43))) (let ((_let_45 (not _let_19))) (let ((_let_46 (not _let_7))) (let ((_let_47 (or _let_46 _let_45 _let_44))) (let ((_let_48 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (0))) (let ((_let_51 (ASSUME :args (_let_13)))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO _let_51 :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (AND_ELIM _let_52 :args _let_50))) (let ((_let_54 (ASSUME :args (_let_20)))) (let ((_let_55 (AND_ELIM _let_54 :args _let_50))) (let ((_let_56 (ASSUME :args (_let_4)))) (let ((_let_57 (not _let_4))) (let ((_let_58 (or))) (let ((_let_59 (_let_43))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_41))) (REFL :args (_let_42)) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_57 _let_43 (not _let_44)))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_45 _let_46 _let_44 (not _let_47)))) _let_55 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.xr tptp.xn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.doDivides0 W0 W1)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_44 false _let_19 false _let_7 false _let_47)) :args (_let_43 false _let_4 false _let_44)) :args (_let_42 true _let_41)))) (let ((_let_61 (REFL :args (_let_40)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_32))) :args _let_58)) :args ((or _let_32 _let_40))) _let_60 :args (_let_32 true _let_40)))) (let ((_let_63 (and _let_38 _let_32))) (let ((_let_64 (= _let_63 _let_33))) (let ((_let_65 (= tptp.sz00 tptp.xr))) (let ((_let_66 (or _let_46 _let_45 _let_65 _let_57 _let_64))) (let ((_let_67 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1628 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1628) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1628))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1628)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_67))) (let ((_let_70 (= tptp.sz10 tptp.xr))) (let ((_let_71 (not _let_70))) (let ((_let_72 (not _let_65))) (let ((_let_73 (and _let_72 _let_71 (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xr)) (= tptp.sz10 W1) (= W1 tptp.xr)))))) (let ((_let_74 (= _let_6 _let_73))) (let ((_let_75 (or _let_46 _let_74))) (let ((_let_76 (forall ((W0 $$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_77 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (_let_76))) (let ((_let_79 (2))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_74)) :args ((or (not _let_6) _let_73 (not _let_74)))) (AND_ELIM _let_52 :args _let_79) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_46 _let_74 (not _let_75)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.xr QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.isPrime0 W0)))) :args _let_78))) _let_77 :args (_let_75 false _let_76)) :args (_let_74 false _let_7 false _let_75)) :args (_let_73 false _let_6 false _let_74)))) (let ((_let_81 (not _let_73))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 0)) :args ((or _let_72 _let_81))) _let_80 :args (_let_72 false _let_73)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_58)) :args ((or _let_38 _let_40))) _let_60 :args (_let_38 true _let_40)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or _let_33 (not _let_63) (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_63)) :args ((or _let_39 _let_37 _let_63))) _let_83 _let_62 :args (_let_63 false _let_38 false _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_57 _let_45 _let_46 _let_65 _let_64 (not _let_66)))) _let_56 _let_55 _let_53 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.xr tptp.xn SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_CBQI_PROP)) :args _let_69)) _let_68 :args (_let_66 false _let_67)) :args (_let_64 false _let_4 false _let_19 false _let_7 true _let_65 false _let_66)) :args (_let_33 false _let_63 false _let_64)))) (let ((_let_85 (= tptp.xn _let_1))) (let ((_let_86 (not _let_2))) (let ((_let_87 (tptp.sdtasdt0 tptp.xr tptp.xn))) (let ((_let_88 (= tptp.xn _let_87))) (let ((_let_89 (and _let_19 _let_88))) (let ((_let_90 (= _let_85 _let_89))) (let ((_let_91 (not _let_85))) (let ((_let_92 (or _let_46 _let_45 _let_65 _let_57 _let_90))) (let ((_let_93 (not _let_89))) (let ((_let_94 (tptp.sdtasdt0 tptp.sz10 tptp.xn))) (let ((_let_95 (= _let_94 _let_87))) (let ((_let_96 (= tptp.xn _let_94))) (let ((_let_97 (not _let_88))) (let ((_let_98 (not _let_95))) (let ((_let_99 (tptp.sdtasdt0 tptp.xn tptp.sz10))) (let ((_let_100 (and (not (= _let_99 (tptp.sdtasdt0 tptp.xn tptp.xr))) _let_98))) (let ((_let_101 (not _let_30))) (let ((_let_102 (= tptp.sz00 tptp.xn))) (let ((_let_103 (or _let_45 _let_102 _let_46 _let_101 _let_100 _let_70))) (let ((_let_104 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1341 $$unsorted) (BOUND_VARIABLE_1339 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1339)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1341)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1339) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1341))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1339 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1341 W0)))) (= BOUND_VARIABLE_1339 BOUND_VARIABLE_1341))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (= tptp.sz00 _let_12))) (let ((_let_107 (= tptp.xn _let_12))) (let ((_let_108 (= _let_5 (tptp.sdtasdt0 tptp.xm tptp.xn)))) (let ((_let_109 (= tptp.sz00 (tptp.sdtasdt0 tptp.xm tptp.sz00)))) (let ((_let_110 (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.sz00)))) (let ((_let_111 (= _let_5 (tptp.sdtasdt0 tptp.xp tptp.xn)))) (let ((_let_112 (and _let_19 _let_111))) (let ((_let_113 (= _let_112 _let_107))) (let ((_let_114 (not _let_102))) (let ((_let_115 (not _let_106))) (let ((_let_116 (and _let_115 _let_102))) (let ((_let_117 (_let_115 _let_102))) (let ((_let_118 (ASSUME :args (_let_115)))) (let ((_let_119 (=))) (let ((_let_120 (ASSUME :args (_let_102)))) (let ((_let_121 (SYMM _let_120))) (let ((_let_122 (not _let_18))) (let ((_let_123 (or _let_45 _let_122 _let_108))) (let ((_let_124 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (_let_124))) (let ((_let_127 (1))) (let ((_let_128 (AND_ELIM _let_54 :args _let_127))) (let ((_let_129 (and _let_109 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xm))))) (let ((_let_130 (or _let_122 _let_129))) (let ((_let_131 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= tptp.sz00 (tptp.sdtasdt0 W0 tptp.sz00)) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (_let_131))) (let ((_let_134 ((not (= (tptp.aNaturalNumber0 W0) false))))) (let ((_let_135 (and _let_110 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp))))) (let ((_let_136 (not _let_17))) (let ((_let_137 (or _let_136 _let_135))) (let ((_let_138 (AND_ELIM _let_54 :args _let_79))) (let ((_let_139 (and _let_102 _let_108 _let_109 _let_110))) (let ((_let_140 (APPLY_UF tptp.sdtasdt0))) (let ((_let_141 (ASSUME :args (_let_110)))) (let ((_let_142 (ASSUME :args (_let_109)))) (let ((_let_143 (ASSUME :args (_let_108)))) (let ((_let_144 (not _let_14))) (let ((_let_145 (= tptp.sz00 tptp.xp))) (let ((_let_146 (tptp.aNaturalNumber0 _let_5))) (let ((_let_147 (not _let_146))) (let ((_let_148 (or _let_136 _let_147 _let_145 _let_144 _let_113))) (let ((_let_149 (or _let_45 _let_122 _let_146))) (let ((_let_150 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (not _let_145))) (let ((_let_153 (and _let_152 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_154 (= _let_15 _let_153))) (let ((_let_155 (or _let_136 _let_154))) (let ((_let_156 (ASSUME :args (_let_16)))) (let ((_let_157 (and (= tptp.xn _let_99) _let_96))) (let ((_let_158 (or _let_45 _let_157))) (let ((_let_159 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_160 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_161 (and _let_96 _let_98))) (let ((_let_162 (ASSUME :args (_let_98)))) (let ((_let_163 (ASSUME :args (_let_96)))) (let ((_let_164 (_let_86))) (let ((_let_165 (tptp.aNaturalNumber0 _let_1))) (let ((_let_166 (not _let_165))) (let ((_let_167 (or _let_46 _let_166 _let_35))) (let ((_let_168 (not _let_33))) (let ((_let_169 (and _let_38 _let_33))) (let ((_let_170 (_let_38 _let_33))) (let ((_let_171 (ASSUME :args (_let_38)))) (let ((_let_172 (ASSUME :args (_let_33)))) (let ((_let_173 (SYMM _let_172))) (let ((_let_174 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_169)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_171 _let_172) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_173) :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_171))) :args _let_170)) :args _let_170)) :args (true _let_169)) :args ((or _let_165 _let_39 _let_168))) _let_83 _let_84 :args (_let_165 false _let_38 false _let_33)))) (let ((_let_175 (or _let_46 _let_166 _let_65 _let_36))) (let ((_let_176 (forall ((W0 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(tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$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))))) _let_24 (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_23 _let_22 (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_21 (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_20 (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_16 (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_13 _let_11 (and (not _let_10) (not _let_9)) _let_8 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_5)) (and (not (= tptp.xk tptp.xp)) (tptp.sdtlseqdt0 tptp.xk tptp.xp)) (or _let_4 (tptp.doDivides0 tptp.xr tptp.xm)) _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.20/26.43  )
% 26.20/26.43  % SZS output end Proof for NUM510+1
% 26.20/26.43  % cvc5---1.0.5 exiting
% 26.20/26.43  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------