%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 10:44:31 EDT 2023

% Result   : Theorem 12.81s 13.06s
% Output   : Proof 12.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n024.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 09:53:24 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 12.81/13.06  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QYKeARMGMY/cvc5---1.0.5_28975.p...
% 12.81/13.06  ------- get file name : TPTP file name is NUM503+1
% 12.81/13.06  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28975.smt2...
% 12.81/13.06  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 12.81/13.06  --- Run --no-e-matching --full-saturate-quant at 5...
% 12.81/13.06  % SZS status Theorem for NUM503+1
% 12.81/13.06  % SZS output start Proof for NUM503+1
% 12.81/13.06  (
% 12.81/13.06  (let ((_let_1 (tptp.sdtasdt0 tptp.xp tptp.xk))) (let ((_let_2 (tptp.sdtasdt0 tptp.xp tptp.xm))) (let ((_let_3 (tptp.sdtlseqdt0 _let_2 _let_1))) (let ((_let_4 (tptp.sdtasdt0 tptp.xn tptp.xm))) (let ((_let_5 (tptp.sdtlseqdt0 _let_4 _let_2))) (let ((_let_6 (= _let_4 _let_2))) (let ((_let_7 (not _let_6))) (let ((_let_8 (not (and _let_7 _let_5 (not (= _let_2 _let_1)) _let_3)))) (let ((_let_9 (tptp.sdtlseqdt0 tptp.xp tptp.xk))) (let ((_let_10 (= tptp.xk tptp.sz10))) (let ((_let_11 (= tptp.xk tptp.sz00))) (let ((_let_12 (not (or _let_11 _let_10)))) (let ((_let_13 (tptp.sdtsldt0 _let_4 tptp.xp))) (let ((_let_14 (= tptp.xk _let_13))) (let ((_let_15 (tptp.sdtlseqdt0 tptp.xm tptp.xp))) (let ((_let_16 (tptp.sdtlseqdt0 tptp.xn tptp.xp))) (let ((_let_17 (= tptp.xn tptp.xp))) (let ((_let_18 (and (not _let_17) _let_16 (not (= tptp.xm tptp.xp)) _let_15))) (let ((_let_19 (tptp.doDivides0 tptp.xp _let_4))) (let ((_let_20 (tptp.isPrime0 tptp.xp))) (let ((_let_21 (and _let_20 _let_19))) (let ((_let_22 (tptp.aNaturalNumber0 tptp.xp))) (let ((_let_23 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_24 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_25 (and _let_24 _let_23 _let_22))) (let ((_let_26 (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_27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_28 (forall ((W0 $$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))))))))))) (let ((_let_29 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_30 (forall ((W0 $$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_31 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))) (let ((_let_32 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_33 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_34 (tptp.aNaturalNumber0 tptp.sz00))) (let ((_let_35 (= tptp.sz00 tptp.xp))) (let ((_let_36 (tptp.aNaturalNumber0 _let_13))) (let ((_let_37 (= tptp.xm _let_13))) (let ((_let_38 (tptp.sdtlseqdt0 tptp.xm _let_13))) (let ((_let_39 (tptp.sdtasdt0 _let_13 tptp.xp))) (let ((_let_40 (tptp.sdtasdt0 tptp.xm tptp.xp))) (let ((_let_41 (tptp.sdtasdt0 tptp.xp _let_13))) (let ((_let_42 (tptp.sdtlseqdt0 _let_2 _let_41))) (let ((_let_43 (= _let_2 _let_41))) (let ((_let_44 (not _let_43))) (let ((_let_45 (and _let_44 _let_42 (not (= _let_40 _let_39)) (tptp.sdtlseqdt0 _let_40 _let_39)))) (let ((_let_46 (not _let_38))) (let ((_let_47 (not _let_36))) (let ((_let_48 (not _let_23))) (let ((_let_49 (not _let_22))) (let ((_let_50 (or _let_49 _let_48 _let_47 _let_35 _let_37 _let_46 _let_45))) (let ((_let_51 (1))) (let ((_let_52 (ASSUME :args (_let_25)))) (let ((_let_53 (AND_ELIM _let_52 :args _let_51))) (let ((_let_54 (AND_ELIM _let_52 :args (2)))) (let ((_let_55 (not _let_35))) (let ((_let_56 (and _let_55 (not (= tptp.sz10 tptp.xp)) (forall ((W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W1)) (not (tptp.doDivides0 W1 tptp.xp)) (= tptp.sz10 W1) (= W1 tptp.xp)))))) (let ((_let_57 (= _let_20 _let_56))) (let ((_let_58 (or _let_49 _let_57))) (let ((_let_59 (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_60 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (tptp.xp QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_62 (0))) (let ((_let_63 (ASSUME :args (_let_21)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_56 0)) :args ((or _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or (not _let_20) _let_56 (not _let_57)))) (AND_ELIM _let_63 :args _let_62) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_49 _let_57 (not _let_58)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args _let_61) :args (_let_59)))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_22 false _let_58)) :args (_let_56 false _let_20 false _let_57)) :args (_let_55 false _let_56)))) (let ((_let_65 (= _let_4 _let_41))) (let ((_let_66 (and _let_36 _let_65))) (let ((_let_67 (not _let_19))) (let ((_let_68 (tptp.aNaturalNumber0 _let_4))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_49 _let_69 _let_35 _let_67 _let_66))) (let ((_let_71 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1626 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1626) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1626))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1626)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_71))) (let ((_let_74 (tptp.sdtasdt0 tptp.xm tptp.xn))) (let ((_let_75 (tptp.aNaturalNumber0 _let_74))) (let ((_let_76 (= _let_4 _let_74))) (let ((_let_77 (not _let_24))) (let ((_let_78 (or _let_48 _let_77 _let_75))) (let ((_let_79 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (AND_ELIM _let_52 :args _let_62))) (let ((_let_82 (or _let_77 _let_48 _let_76))) (let ((_let_83 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_77 _let_48 _let_76 (not _let_82)))) _let_81 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.xn tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args _let_85)) _let_84 :args (_let_82 false _let_83)) :args (_let_76 false _let_24 false _let_23 false _let_82)))) (let ((_let_87 (not _let_76))) (let ((_let_88 (and _let_76 _let_75))) (let ((_let_89 (ASSUME :args (_let_75)))) (let ((_let_90 (ASSUME :args (_let_76)))) (let ((_let_91 (SYMM (SYMM _let_90)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_88)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_90) (SCOPE (TRUE_ELIM (TRANS (CONG _let_91 :args (APPLY_UF tptp.aNaturalNumber0)) (TRUE_INTRO _let_89))) :args (_let_75 _let_76))) :args (_let_76 _let_75))) :args (true _let_88)) :args ((or _let_87 _let_68 (not _let_75)))) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_48 _let_75 (not _let_78)))) _let_81 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.xm tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_75 false _let_24 false _let_23 false _let_78)) :args (_let_68 false _let_76 false _let_75)))) (let ((_let_93 (AND_ELIM _let_63 :args _let_51))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_49 _let_67 _let_35 _let_69 _let_66 (not _let_70)))) _let_54 _let_93 _let_64 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.xp _let_4 _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_73))) _let_72 :args (_let_70 false _let_71)) :args (_let_66 false _let_22 false _let_19 true _let_35 false _let_68 false _let_70)))) (let ((_let_95 (not _let_66))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 0)) :args ((or _let_36 _let_95))) _let_94 :args (_let_36 false _let_66)))) (let ((_let_97 (and _let_23 _let_6))) (let ((_let_98 (= _let_97 _let_37))) (let ((_let_99 (not _let_37))) (let ((_let_100 (or _let_49 _let_69 _let_35 _let_67 _let_98))) (let ((_let_101 (not _let_97))) (let ((_let_102 (not (= _let_74 _let_40)))) (let ((_let_103 (and _let_102 _let_7))) (let ((_let_104 (= tptp.sz00 tptp.xm))) (let ((_let_105 (or _let_48 _let_104 _let_77 _let_49 _let_103 _let_17))) (let ((_let_106 (= tptp.sz00 (tptp.sdtasdt0 tptp.xp tptp.sz00)))) (let ((_let_107 (tptp.doDivides0 tptp.xp tptp.sz00))) (let ((_let_108 (= tptp.sz00 _let_13))) (let ((_let_109 (= tptp.sz00 (tptp.sdtsldt0 tptp.sz00 tptp.xp)))) (let ((_let_110 (and _let_34 _let_106))) (let ((_let_111 (= _let_110 _let_109))) (let ((_let_112 (not _let_107))) (let ((_let_113 (not _let_34))) (let ((_let_114 (or _let_49 _let_113 _let_35 _let_112 _let_111))) (let ((_let_115 (ASSUME :args (_let_18)))) (let ((_let_116 (AND_ELIM _let_115 :args _let_62))) (let ((_let_117 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1339 $$unsorted) (BOUND_VARIABLE_1337 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (= tptp.sz00 W0) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1337)) (not (tptp.aNaturalNumber0 BOUND_VARIABLE_1339)) (and (not (= (tptp.sdtasdt0 W0 BOUND_VARIABLE_1337) (tptp.sdtasdt0 W0 BOUND_VARIABLE_1339))) (not (= (tptp.sdtasdt0 BOUND_VARIABLE_1337 W0) (tptp.sdtasdt0 BOUND_VARIABLE_1339 W0)))) (= BOUND_VARIABLE_1337 BOUND_VARIABLE_1339))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (and _let_106 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xp))))) (let ((_let_120 (or _let_49 _let_119))) (let ((_let_121 (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_122 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (_let_121))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_119 0)) :args ((or _let_106 (not _let_119)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_49 _let_119 (not _let_120)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args _let_61) :args _let_123)) _let_122 :args (_let_120 false _let_121)) :args (_let_119 false _let_22 false _let_120)) :args (_let_106 false _let_119)))) (let ((_let_125 (not _let_106))) (let ((_let_126 (not _let_104))) (let ((_let_127 (and _let_19 _let_6 _let_104 _let_106))) (let ((_let_128 (_let_19 _let_6 _let_104 _let_106))) (let ((_let_129 (ASSUME :args (_let_19)))) (let ((_let_130 (ASSUME :args (_let_6)))) (let ((_let_131 (APPLY_UF tptp.sdtasdt0))) (let ((_let_132 (ASSUME :args (_let_104)))) (let ((_let_133 (SYMM (SYMM _let_132)))) (let ((_let_134 (REFL :args (tptp.xp)))) (let ((_let_135 (CONG _let_134 _let_133 :args _let_131))) (let ((_let_136 (ASSUME :args (_let_106)))) (let ((_let_137 (SYMM (SYMM _let_136)))) (let ((_let_138 (TRANS _let_137 _let_135 (SYMM _let_130)))) (let ((_let_139 (ASSUME :args (_let_14)))) (let ((_let_140 (or))) (let ((_let_141 (REFL :args (_let_125)))) (let ((_let_142 (REFL :args (_let_126)))) (let ((_let_143 (not _let_108))) (let ((_let_144 (_let_7))) (let ((_let_145 (and _let_6 _let_143 _let_104 _let_106))) (let ((_let_146 (ASSUME :args (_let_143)))) (let ((_let_147 (ASSUME :args (_let_34)))) (let ((_let_148 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_111)) :args ((or _let_109 (not _let_110) (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_110)) :args ((or _let_113 _let_125 _let_110))) _let_147 _let_124 :args (_let_110 false _let_34 false _let_106)) (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_113 _let_49 _let_35 _let_112 _let_111 (not _let_114)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.xp tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_73))) _let_72 :args (_let_114 false _let_71)) _let_64 _let_54 _let_147 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_145)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_146 _let_130 _let_132 _let_136) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (CONG _let_138 _let_134 :args (APPLY_UF tptp.sdtsldt0)) :args (=)) (FALSE_INTRO _let_146))) :args (_let_143 _let_6 _let_104 _let_106))) :args (_let_6 _let_143 _let_104 _let_106))) :args (true _let_145)) (CONG (REFL :args _let_144) (MACRO_SR_PRED_INTRO :args ((= (not _let_143) _let_108))) _let_142 _let_141 (REFL :args ((not _let_109))) :args _let_140)) _let_124 (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_139 :args ((not (or (= tptp.sz00 tptp.xk) (= tptp.sz10 tptp.xk))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_62) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_129 _let_130 _let_132 _let_136) (SCOPE (TRUE_ELIM (TRANS (CONG _let_134 _let_138 :args (APPLY_UF tptp.doDivides0)) (TRUE_INTRO _let_129))) :args _let_128)) :args _let_128)) :args (true _let_127)) :args ((or _let_7 _let_67 _let_126 _let_125 _let_107))) _let_124 _let_93 (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_17 _let_77 _let_48 _let_49 _let_104 _let_103 (not _let_105)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE 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(let ((_let_154 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_155 (not _let_45))) (let ((_let_156 (not _let_42))) (let ((_let_157 (and _let_102 (tptp.sdtlseqdt0 _let_74 _let_40) _let_7 _let_5))) (let ((_let_158 (not _let_16))) (let ((_let_159 (or _let_48 _let_77 _let_49 _let_104 _let_17 _let_158 _let_157))) (let ((_let_160 (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))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (= tptp.sz00 W0) (= W1 W2) (not (tptp.sdtlseqdt0 W1 W2)) (and (not (= _let_3 _let_4)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_1 _let_2)) (tptp.sdtlseqdt0 _let_2 _let_1)))))))))) (let ((_let_161 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_162 (_let_160))) (let ((_let_163 (tptp.sdtasdt0 tptp.xn tptp.sz00))) (let ((_let_164 (tptp.sdtasdt0 tptp.sz00 tptp.xn))) (let ((_let_165 (= _let_164 _let_163))) (let ((_let_166 (= tptp.sz00 _let_163))) (let ((_let_167 (or _let_113 _let_77 _let_165))) (let ((_let_168 (and _let_166 (= tptp.sz00 _let_164)))) (let ((_let_169 (or _let_77 _let_168))) (let ((_let_170 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))))) (let ((_let_171 (= tptp.sz00 _let_2))) (let ((_let_172 (= tptp.sz00 _let_4))) (let ((_let_173 (ASSUME :args (_let_166)))) (let ((_let_174 (SYMM (SYMM _let_173)))) (let ((_let_175 (ASSUME :args (_let_165)))) (let ((_let_176 (SYMM _let_175))) (let ((_let_177 (ASSUME :args _let_144))) (let ((_let_178 (SYMM (FALSE_INTRO _let_177)))) (let ((_let_179 (ASSUME :args (_let_65)))) (let ((_let_180 (ASSUME :args (_let_43)))) (let ((_let_181 (not _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_48 _let_49 _let_35 _let_47 _let_37 _let_46 _let_45 (not _let_50)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_161 :args (tptp.xp tptp.xm _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_162))) _let_161 :args (_let_50 false _let_160)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_42 _let_155))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_139 :args ((not (and _let_7 _let_5 (not (= _let_1 _let_2)) _let_3)) SB_DEFAULT SBA_FIXPOINT))))) (CONG _let_170 (REFL :args (_let_181)) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) (REFL :args (_let_156)) :args _let_140)) :args ((or _let_6 _let_43 _let_181 _let_156))) _let_148 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_90 _let_179 _let_180 _let_177) :args (_let_7 _let_43 _let_76 _let_65)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_178 (TRUE_INTRO (TRANS _let_91 (SYMM (TRANS (SYMM (SYMM _let_180)) (SYMM _let_179) _let_91)))))) :args (_let_76 _let_65 _let_43 _let_7)) :args ((not (and _let_7 _let_43 _let_76 _let_65)) SB_LITERAL))) (CONG _let_170 (REFL :args (_let_44)) (REFL :args (_let_87)) (REFL :args ((not _let_65))) :args _let_140)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_66 1)) :args ((or _let_65 _let_95))) _let_94 :args (_let_65 false _let_66)) _let_86 _let_148 :args (_let_44 false _let_65 false _let_76 true _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_157 3)) :args ((or _let_5 (not _let_157)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_159)) :args ((or _let_17 _let_77 _let_48 _let_49 _let_158 _let_104 _let_157 (not _let_159)))) _let_116 _let_81 _let_53 _let_54 (AND_ELIM _let_115 :args _let_51) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_175 _let_173 (MODUS_PONENS (AND_INTRO _let_132 _let_173) (SCOPE (TRANS _let_174 (CONG (REFL :args (tptp.xn)) _let_133 :args _let_131)) :args (_let_104 _let_166))) (MODUS_PONENS (AND_INTRO _let_132 _let_136) (SCOPE (TRANS _let_137 _let_135) :args (_let_104 _let_106))) _let_177) :args (_let_7 _let_104 _let_165 _let_166 _let_106)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_178 (TRUE_INTRO (TRANS (TRANS (SYMM (ASSUME :args (_let_172))) _let_174 _let_176) (SYMM _let_176) (SYMM (TRANS (SYMM (ASSUME :args (_let_171))) _let_174)))))) :args (_let_165 _let_166 _let_172 _let_171 _let_7)) :args ((not (and _let_7 _let_104 _let_165 _let_166 _let_106)) SB_LITERAL))) (CONG _let_170 _let_142 (REFL :args ((not _let_165))) (REFL :args ((not _let_166))) _let_141 :args _let_140)) _let_148 _let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_168 0)) :args ((or _let_166 (not _let_168)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_169)) :args ((or _let_77 _let_168 (not _let_169)))) _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args _let_123)) _let_122 :args (_let_169 false _let_121)) :args (_let_168 false _let_24 false _let_169)) :args (_let_166 false _let_168)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_113 _let_77 _let_165 (not _let_167)))) _let_147 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.sz00 tptp.xn QUANTIFIERS_INST_CBQI_PROP)) :args _let_85)) _let_84 :args (_let_167 false _let_83)) :args (_let_165 false _let_34 false _let_24 false _let_167)) :args (_let_126 true _let_6 false _let_106 false _let_166 false _let_165)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_161 :args (tptp.xm tptp.xn tptp.xp QUANTIFIERS_INST_CBQI_PROP)) :args _let_162))) _let_161 :args (_let_159 false _let_160)) :args (_let_157 true _let_17 false _let_24 false _let_23 false _let_22 false _let_16 true _let_104 false _let_159)) :args (_let_5 false _let_157)) :args (_let_156 true _let_6 true _let_43 false _let_5)) :args (_let_155 true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_152)) :args ((or _let_48 _let_49 _let_151 _let_150 _let_47 _let_38 (not _let_152)))) _let_53 _let_54 (AND_ELIM _let_115 :args (3)) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO _let_139 :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_154 :args (tptp.xm tptp.xp _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_153))) _let_154 :args (_let_152 false _let_153)) :args (_let_38 false _let_23 false _let_22 false _let_15 false _let_149 false _let_36 false _let_152)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_98)) :args ((or _let_97 _let_99 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 1)) :args ((or _let_6 _let_101))) _let_148 :args (_let_101 true _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_49 _let_67 _let_35 _let_69 _let_98 (not _let_100)))) _let_54 _let_93 _let_64 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.xp _let_4 tptp.xm QUANTIFIERS_INST_CBQI_PROP)) :args _let_73))) _let_72 :args (_let_100 false _let_71)) :args (_let_98 false _let_22 false _let_19 true _let_35 false _let_68 false _let_100)) :args (_let_99 true _let_97 false _let_98)) _let_96 _let_64 _let_54 _let_53 :args (false false _let_50 true _let_45 false _let_38 true _let_37 false _let_36 true _let_35 false _let_22 false _let_23)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) _let_34 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) _let_33 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_32 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) _let_31 (forall ((W0 $$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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))) _let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) _let_29 (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 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (let ((_let_2 (tptp.sdtpldt0 W0 W2))) (let ((_let_3 (tptp.sdtpldt0 W2 W1))) (let ((_let_4 (tptp.sdtpldt0 W2 W0))) (=> (tptp.aNaturalNumber0 W2) (and (not (= _let_4 _let_3)) (tptp.sdtlseqdt0 _let_4 _let_3) (not (= _let_2 _let_1)) (tptp.sdtlseqdt0 _let_2 _let_1))))))))))) _let_28 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))) _let_27 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))) _let_26 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))) _let_25 (forall ((W0 $$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_21 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xm)) _let_18 _let_14 _let_12 (and (not _let_11) (not _let_10)) (and (tptp.aNaturalNumber0 tptp.xr) (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr)) (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr _let_4)) _let_9 _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 12.81/13.06  )
% 12.81/13.06  % SZS output end Proof for NUM503+1
% 12.81/13.06  % cvc5---1.0.5 exiting
% 12.81/13.06  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------