TSTP Solution File: NUM475+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 10:44:15 EDT 2023
% Result : Theorem 11.87s 12.04s
% Output : Proof 11.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n004.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 09:29:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 11.87/12.04 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.nlQ7lplw6N/cvc5---1.0.5_9793.p...
% 11.87/12.04 ------- get file name : TPTP file name is NUM475+1
% 11.87/12.04 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9793.smt2...
% 11.87/12.04 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.87/12.04 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.87/12.04 % SZS status Theorem for NUM475+1
% 11.87/12.04 % SZS output start Proof for NUM475+1
% 11.87/12.04 (
% 11.87/12.04 (let ((_let_1 (tptp.sdtasdt0 tptp.xl tptp.xr))) (let ((_let_2 (not (= tptp.xn _let_1)))) (let ((_let_3 (tptp.sdtasdt0 tptp.xl tptp.xp))) (let ((_let_4 (= (tptp.sdtpldt0 _let_3 _let_1) (tptp.sdtpldt0 _let_3 tptp.xn)))) (let ((_let_5 (= tptp.xr (tptp.sdtmndt0 tptp.xq tptp.xp)))) (let ((_let_6 (tptp.sdtlseqdt0 tptp.xp tptp.xq))) (let ((_let_7 (tptp.sdtpldt0 tptp.xm tptp.xn))) (let ((_let_8 (tptp.sdtsldt0 _let_7 tptp.xl))) (let ((_let_9 (= tptp.xq _let_8))) (let ((_let_10 (tptp.sdtsldt0 tptp.xm tptp.xl))) (let ((_let_11 (= tptp.xp _let_10))) (let ((_let_12 (not (= tptp.xl tptp.sz00)))) (let ((_let_13 (tptp.doDivides0 tptp.xl _let_7))) (let ((_let_14 (tptp.doDivides0 tptp.xl tptp.xm))) (let ((_let_15 (and _let_14 _let_13))) (let ((_let_16 (tptp.aNaturalNumber0 tptp.xn))) (let ((_let_17 (tptp.aNaturalNumber0 tptp.xm))) (let ((_let_18 (tptp.aNaturalNumber0 tptp.xl))) (let ((_let_19 (and _let_18 _let_17 _let_16))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (let ((_let_21 (forall ((W0 $$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_22 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))) (let ((_let_23 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_27 (tptp.aNaturalNumber0 tptp.sz10))) (let ((_let_28 (and _let_27 (not (= tptp.sz10 tptp.sz00))))) (let ((_let_29 (tptp.sdtmndt0 _let_8 _let_10))) (let ((_let_30 (tptp.sdtasdt0 tptp.xl _let_29))) (let ((_let_31 (tptp.sdtasdt0 tptp.xl _let_10))) (let ((_let_32 (= (tptp.sdtpldt0 _let_31 tptp.xn) (tptp.sdtpldt0 _let_31 _let_30)))) (let ((_let_33 (= tptp.xm _let_31))) (let ((_let_34 (tptp.sdtasdt0 _let_30 tptp.sz10))) (let ((_let_35 (tptp.sdtasdt0 tptp.sz10 _let_30))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (= _let_30 _let_34))) (let ((_let_38 (= _let_7 (tptp.sdtpldt0 tptp.xm _let_35)))) (let ((_let_39 (ASSUME :args (_let_11)))) (let ((_let_40 (ASSUME :args (_let_9)))) (let ((_let_41 (AND_INTRO _let_40 _let_39))) (let ((_let_42 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO _let_41 :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) _let_40 _let_39))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO _let_42 :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.aNaturalNumber0 _let_10))) (let ((_let_45 (and _let_44 _let_33))) (let ((_let_46 (not _let_14))) (let ((_let_47 (= tptp.sz00 tptp.xl))) (let ((_let_48 (not _let_17))) (let ((_let_49 (not _let_18))) (let ((_let_50 (or _let_49 _let_48 _let_47 _let_46 _let_45))) (let ((_let_51 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1488 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= tptp.sz00 W0) (not (tptp.doDivides0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1488) (= W1 (tptp.sdtasdt0 W0 BOUND_VARIABLE_1488))) (= (tptp.sdtsldt0 W1 W0) BOUND_VARIABLE_1488)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 (0))) (let ((_let_55 (ASSUME :args (_let_15)))) (let ((_let_56 (1))) (let ((_let_57 (ASSUME :args (_let_19)))) (let ((_let_58 (AND_ELIM _let_57 :args _let_56))) (let ((_let_59 (AND_ELIM _let_57 :args _let_54))) (let ((_let_60 (SYMM (ASSUME :args (_let_12))))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_47 _let_49 _let_48 _let_46 _let_45 (not _let_50)))) _let_60 _let_59 _let_58 (AND_ELIM _let_55 :args _let_54) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xl tptp.xm _let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53))) _let_52 :args (_let_50 false _let_51)) :args (_let_45 true _let_47 false _let_18 false _let_17 false _let_14 false _let_50)))) (let ((_let_62 (not _let_45))) (let ((_let_63 (tptp.aNaturalNumber0 _let_30))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_27))) (let ((_let_66 (or _let_65 _let_64 _let_36))) (let ((_let_67 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_67))) (let ((_let_70 (tptp.sz10 _let_30 QUANTIFIERS_INST_ENUM))) (let ((_let_71 (tptp.sdtasdt0 tptp.sz10 _let_29))) (let ((_let_72 (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xl _let_71)))) (let ((_let_73 (tptp.sdtasdt0 _let_29 tptp.sz10))) (let ((_let_74 (= _let_71 _let_73))) (let ((_let_75 (= _let_29 _let_73))) (let ((_let_76 (tptp.aNaturalNumber0 _let_71))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_49 _let_77 _let_72))) (let ((_let_79 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 (tptp.aNaturalNumber0 _let_29))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_65 _let_83 _let_76))) (let ((_let_85 (tptp.sz10 _let_29 QUANTIFIERS_INST_ENUM))) (let ((_let_86 (tptp.sdtasdt0 tptp.sz10 _let_8))) (let ((_let_87 (and _let_82 (= _let_86 (tptp.sdtpldt0 _let_10 _let_29))))) (let ((_let_88 (= _let_29 (tptp.sdtmndt0 _let_86 _let_10)))) (let ((_let_89 (= _let_87 _let_88))) (let ((_let_90 (tptp.sdtlseqdt0 _let_10 _let_86))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.aNaturalNumber0 _let_86))) (let ((_let_93 (not _let_92))) (let ((_let_94 (not _let_44))) (let ((_let_95 (or _let_94 _let_93 _let_91 _let_89))) (let ((_let_96 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1292 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1292) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1292))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1292)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (tptp.sdtasdt0 _let_8 tptp.sz10))) (let ((_let_99 (= _let_86 _let_98))) (let ((_let_100 (= _let_8 _let_98))) (let ((_let_101 (tptp.sdtlseqdt0 _let_10 _let_8))) (let ((_let_102 (tptp.aNaturalNumber0 _let_8))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_65 _let_103 _let_99))) (let ((_let_105 (tptp.sz10 _let_8 QUANTIFIERS_INST_ENUM))) (let ((_let_106 (tptp.sdtasdt0 tptp.sz10 _let_7))) (let ((_let_107 (and _let_102 (= _let_106 (tptp.sdtasdt0 tptp.xl _let_8))))) (let ((_let_108 (= _let_8 (tptp.sdtsldt0 _let_106 tptp.xl)))) (let ((_let_109 (= _let_107 _let_108))) (let ((_let_110 (tptp.doDivides0 tptp.xl _let_106))) (let ((_let_111 (not _let_110))) (let ((_let_112 (tptp.aNaturalNumber0 _let_106))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_49 _let_113 _let_47 _let_111 _let_109))) (let ((_let_115 (tptp.sdtasdt0 _let_7 tptp.sz10))) (let ((_let_116 (= _let_106 _let_115))) (let ((_let_117 (= _let_7 _let_115))) (let ((_let_118 (tptp.aNaturalNumber0 _let_7))) (let ((_let_119 (not _let_118))) (let ((_let_120 (or _let_65 _let_119 _let_116))) (let ((_let_121 (tptp.sz10 _let_7 QUANTIFIERS_INST_ENUM))) (let ((_let_122 (not _let_16))) (let ((_let_123 (or _let_48 _let_122 _let_118))) (let ((_let_124 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (AND_ELIM _let_57 :args (2)))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_48 _let_122 _let_118 (not _let_123)))) _let_58 _let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (tptp.xm tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_124))) _let_125 :args (_let_123 false _let_124)) :args (_let_118 false _let_17 false _let_16 false _let_123)))) (let ((_let_128 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) :args _let_54))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_65 _let_119 _let_116 (not _let_120)))) _let_128 _let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_121) :args _let_69)) _let_68 :args (_let_120 false _let_67)) :args (_let_116 false _let_27 false _let_118 false _let_120)))) (let ((_let_130 (and _let_117 (= _let_7 _let_106)))) (let ((_let_131 (or _let_119 _let_130))) (let ((_let_132 (forall ((W0 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (and (= W0 (tptp.sdtasdt0 W0 tptp.sz10)) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (_let_132))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_130 0)) :args ((or _let_117 (not _let_130)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_119 _let_130 (not _let_131)))) _let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (_let_7 QUANTIFIERS_INST_ENUM)) :args _let_134)) _let_133 :args (_let_131 false _let_132)) :args (_let_130 false _let_118 false _let_131)) :args (_let_117 false _let_130)))) (let ((_let_136 (and _let_13 _let_117 _let_116))) (let ((_let_137 (_let_13 _let_117 _let_116))) (let ((_let_138 (ASSUME :args (_let_13)))) (let ((_let_139 (ASSUME :args (_let_117)))) (let ((_let_140 (SYMM (SYMM _let_139)))) (let ((_let_141 (ASSUME :args (_let_116)))) (let ((_let_142 (SYMM _let_141))) (let ((_let_143 (REFL :args (tptp.xl)))) (let ((_let_144 (or _let_65 _let_119 _let_112))) (let ((_let_145 (and _let_117 _let_116))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 0)) :args ((or _let_102 (not _let_107)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_109)) :args ((or _let_107 (not _let_108) (not _let_109)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_145)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_141 _let_139) (SCOPE (CONG (TRANS _let_140 _let_142) _let_143 :args (APPLY_UF tptp.sdtsldt0)) :args (_let_116 _let_117))) :args (_let_117 _let_116))) :args (true _let_145)) _let_135 _let_129 :args (_let_108 false _let_117 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_47 _let_49 _let_113 _let_111 _let_109 (not _let_114)))) _let_60 _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_65 _let_119 _let_112 (not _let_144)))) _let_128 _let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args _let_121) :args _let_81)) _let_80 :args (_let_144 false _let_79)) :args (_let_112 false _let_27 false _let_118 false _let_144)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_136)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_138 _let_139 _let_141) (SCOPE (TRUE_ELIM (TRANS (CONG _let_143 (TRANS (SYMM _let_142) (SYMM _let_140)) :args (APPLY_UF tptp.doDivides0)) (TRUE_INTRO _let_138))) :args _let_137)) :args _let_137)) :args (true _let_136)) (AND_ELIM _let_55 :args _let_56) _let_135 _let_129 :args (_let_110 false _let_13 false _let_117 false _let_116)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.xl _let_106 _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53))) _let_52 :args (_let_114 false _let_51)) :args (_let_109 true _let_47 false _let_18 false _let_112 false _let_110 false _let_114)) :args (_let_107 false _let_108 false _let_109)) :args (_let_102 false _let_107)))) (let ((_let_147 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_65 _let_103 _let_99 (not _let_104)))) _let_128 _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_105) :args _let_69)) _let_68 :args (_let_104 false _let_67)) :args (_let_99 false _let_27 false _let_102 false _let_104)))) (let ((_let_148 (and _let_100 (= _let_8 _let_86)))) (let ((_let_149 (or _let_103 _let_148))) (let ((_let_150 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 0)) :args ((or _let_100 (not _let_148)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_103 _let_148 (not _let_149)))) _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (_let_8 QUANTIFIERS_INST_ENUM)) :args _let_134)) _let_133 :args (_let_149 false _let_132)) :args (_let_148 false _let_102 false _let_149)) :args (_let_100 false _let_148)))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO _let_41 :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (and _let_101 _let_100 _let_99))) (let ((_let_153 (_let_101 _let_100 _let_99))) (let ((_let_154 (ASSUME :args (_let_100)))) (let ((_let_155 (SYMM (SYMM _let_154)))) (let ((_let_156 (ASSUME :args (_let_99)))) (let ((_let_157 (SYMM _let_156))) (let ((_let_158 (REFL :args (_let_10)))) (let ((_let_159 (or _let_65 _let_103 _let_92))) (let ((_let_160 (and _let_100 _let_99))) (let ((_let_161 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 0)) :args ((or _let_82 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_89)) :args ((or _let_87 (not _let_88) (not _let_89)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_156 _let_154) (SCOPE (CONG (TRANS _let_155 _let_157) _let_158 :args (APPLY_UF tptp.sdtmndt0)) :args (_let_99 _let_100))) :args (_let_100 _let_99))) :args (true _let_160)) _let_150 _let_147 :args (_let_88 false _let_100 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_93 _let_94 _let_91 _let_89 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_159)) :args ((or _let_65 _let_103 _let_92 (not _let_159)))) _let_128 _let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args _let_105) :args _let_81)) _let_80 :args (_let_159 false _let_79)) :args (_let_92 false _let_27 false _let_102 false _let_159)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_44 _let_62))) _let_61 :args (_let_44 false _let_45)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_152)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_151 _let_154 _let_156) (SCOPE (TRUE_ELIM (TRANS (CONG _let_158 (TRANS (SYMM _let_157) (SYMM 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_let_18 false _let_76 false _let_78)) :args (_let_63 false _let_75 false _let_74 false _let_72)))) (let ((_let_171 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_64 _let_36 (not _let_66)))) _let_128 _let_170 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_70) :args _let_69)) _let_68 :args (_let_66 false _let_67)) :args (_let_36 false _let_27 false _let_63 false _let_66)))) (let ((_let_172 (and _let_37 (= _let_30 _let_35)))) (let ((_let_173 (or _let_64 _let_172))) (let ((_let_174 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_172 0)) :args ((or _let_37 (not _let_172)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_173)) :args ((or _let_64 _let_172 (not _let_173)))) _let_170 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_133 :args (_let_30 QUANTIFIERS_INST_ENUM)) :args _let_134)) _let_133 :args (_let_173 false _let_132)) :args (_let_172 false _let_63 false _let_173)) :args (_let_37 false _let_172)))) (let ((_let_175 (not _let_38))) (let ((_let_176 (and _let_175 (not (= (tptp.sdtpldt0 tptp.xn tptp.xm) (tptp.sdtpldt0 _let_35 tptp.xm)))))) (let ((_let_177 (= tptp.xn _let_35))) (let ((_let_178 (tptp.aNaturalNumber0 _let_35))) (let ((_let_179 (not _let_178))) (let ((_let_180 (or _let_48 _let_122 _let_179 _let_176 _let_177))) (let ((_let_181 (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_182 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_183 (= tptp.xn _let_30))) (let ((_let_184 (not _let_177))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_42 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (REFL :args ((not _let_37))))) (let ((_let_187 (REFL :args ((not _let_36))))) (let ((_let_188 (not _let_183))) (let ((_let_189 (and _let_188 _let_36 _let_37))) (let ((_let_190 (ASSUME :args (_let_37)))) (let ((_let_191 (SYMM (SYMM _let_190)))) (let ((_let_192 (ASSUME :args (_let_36)))) (let ((_let_193 (SYMM _let_192))) (let ((_let_194 (REFL :args (tptp.xn)))) (let ((_let_195 (or _let_65 _let_64 _let_178))) (let ((_let_196 (ASSUME :args (_let_175)))) (let ((_let_197 (APPLY_UF tptp.sdtpldt0))) (let ((_let_198 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_198 _let_192 _let_190 _let_43) (SCOPE (TRANS (CONG _let_198 _let_194 :args _let_197) (SYMM (SYMM _let_43)) (CONG (SYMM _let_198) (TRANS _let_191 _let_193) :args _let_197)) :args (_let_33 _let_36 _let_37 _let_32))) _let_196) :args (_let_32 _let_36 _let_37 _let_33 _let_175)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME 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(MODUS_PONENS (AND_INTRO _let_185 _let_190 _let_192) (SCOPE (FALSE_ELIM (TRANS (CONG _let_194 (TRANS (SYMM _let_193) (SYMM _let_191)) :args (=)) (FALSE_INTRO _let_185))) :args (_let_188 _let_37 _let_36))) :args (_let_188 _let_36 _let_37))) :args (true _let_189)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_188) _let_183))) _let_187 _let_186 (REFL :args (_let_184)) :args _let_165)) _let_185 _let_171 _let_174 :args (_let_184 true _let_183 false _let_36 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_182 :args (tptp.xm tptp.xn _let_35 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_181))) _let_182 :args (_let_180 false _let_181)) :args (_let_176 false _let_17 false _let_16 false _let_178 true _let_177 false _let_180)) :args (_let_175 false _let_176)) _let_174 _let_171 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_33 _let_62))) _let_61 :args (_let_33 false _let_45)) _let_43 :args (false true _let_38 false _let_37 false _let_36 false _let_33 false _let_32)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (tptp.aNaturalNumber0 tptp.sz00) _let_28 _let_26 _let_25 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) _let_24 (forall ((W0 $$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_23 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) _let_22 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))) (forall ((W0 $$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)))))) _let_21 (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 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$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_20 (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_19 _let_15 _let_12 _let_11 _let_9 _let_6 _let_5 _let_4 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.87/12.05 )
% 11.87/12.05 % SZS output end Proof for NUM475+1
% 11.87/12.05 % cvc5---1.0.5 exiting
% 11.87/12.05 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------