%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KLE128+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n031.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 05:27:20 EDT 2023

% Result   : Theorem 0.69s 0.88s
% Output   : Proof 0.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : KLE128+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n031.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Aug 29 12:25:11 EDT 2023
% 0.21/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.69/0.88  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.4molmqtyhl/cvc5---1.0.5_11662.p...
% 0.69/0.88  ------- get file name : TPTP file name is KLE128+1
% 0.69/0.88  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11662.smt2...
% 0.69/0.88  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.69/0.88  % SZS status Theorem for KLE128+1
% 0.69/0.88  % SZS output start Proof for KLE128+1
% 0.69/0.88  (
% 0.69/0.88  (let ((_let_1 (not (forall ((X0 $$unsorted)) (=> (= (tptp.divergence X0) tptp.zero) (forall ((X1 $$unsorted)) (let ((_let_1 (tptp.domain X1))) (let ((_let_2 (tptp.forward_diamond X0 _let_1))) (=> (= (tptp.addition _let_1 _let_2) _let_2) (= _let_1 tptp.zero)))))))))) (let ((_let_2 (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.domain X2))) (let ((_let_2 (tptp.addition (tptp.divergence X1) (tptp.forward_diamond (tptp.star X1) _let_1)))) (let ((_let_3 (tptp.domain X0))) (let ((_let_4 (tptp.addition (tptp.forward_diamond X1 _let_3) _let_1))) (=> (= (tptp.addition _let_3 _let_4) _let_4) (= (tptp.addition _let_3 _let_2) _let_2))))))))) (let ((_let_3 (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.divergence X0))) (= (tptp.forward_diamond X0 _let_1) _let_1))))) (let ((_let_4 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.forward_diamond X0 X1) (tptp.domain (tptp.multiplication X0 (tptp.domain X1))))))) (let ((_let_5 (forall ((X0 $$unsorted)) (= (tptp.domain X0) (tptp.antidomain (tptp.antidomain X0)))))) (let ((_let_6 (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.antidomain X0))) (= (tptp.addition (tptp.antidomain _let_1) _let_1) tptp.one))))) (let ((_let_7 (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.antidomain (tptp.multiplication X0 (tptp.antidomain (tptp.antidomain X1)))))) (= (tptp.addition (tptp.antidomain (tptp.multiplication X0 X1)) _let_1) _let_1))))) (let ((_let_8 (forall ((X0 $$unsorted)) (= (tptp.multiplication (tptp.antidomain X0) X0) tptp.zero)))) (let ((_let_9 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.zero) tptp.zero)))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.multiplication B C)) (tptp.multiplication (tptp.multiplication A B) C))))) (let ((_let_11 (forall ((A $$unsorted)) (= (tptp.addition A tptp.zero) A)))) (let ((_let_12 (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (tptp.addition A (tptp.addition B C)) (tptp.addition (tptp.addition A B) C))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.addition A B) (tptp.addition B A))))) (let ((_let_14 (tptp.divergence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.domain _let_14))) (let ((_let_16 (tptp.star SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (tptp.addition _let_14 (tptp.forward_diamond _let_16 _let_15)))) (let ((_let_18 (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (= _let_17 (tptp.addition _let_18 _let_17)))) (let ((_let_20 (tptp.forward_diamond SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18))) (let ((_let_21 (tptp.addition _let_20 _let_15))) (let ((_let_22 (= _let_21 (tptp.addition _let_18 _let_21)))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_19))) (let ((_let_25 (forall ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.domain X2))) (let ((_let_2 (tptp.addition (tptp.divergence X1) (tptp.forward_diamond (tptp.star X1) _let_1)))) (let ((_let_3 (tptp.domain X0))) (let ((_let_4 (tptp.addition (tptp.forward_diamond X1 _let_3) _let_1))) (or (not (= _let_4 (tptp.addition _let_3 _let_4))) (= _let_2 (tptp.addition _let_3 _let_2)))))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_28 (tptp.domain _let_27))) (let ((_let_29 (tptp.forward_diamond SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_28))) (let ((_let_30 (tptp.addition _let_18 _let_20))) (let ((_let_31 (tptp.addition _let_29 _let_30))) (let ((_let_32 (= _let_31 (tptp.addition _let_30 _let_29)))) (let ((_let_33 (= tptp.zero (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.zero)))) (let ((_let_34 (tptp.antidomain _let_27))) (let ((_let_35 (tptp.antidomain _let_34))) (let ((_let_36 (tptp.antidomain _let_35))) (let ((_let_37 (= _let_36 (tptp.addition _let_36 tptp.zero)))) (let ((_let_38 (tptp.antidomain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_39 (tptp.addition _let_29 _let_18))) (let ((_let_40 (= (tptp.addition _let_29 (tptp.addition _let_18 _let_38)) (tptp.addition _let_39 _let_38)))) (let ((_let_41 (= _let_31 (tptp.addition _let_39 _let_20)))) (let ((_let_42 (tptp.antidomain (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.antidomain (tptp.antidomain _let_28)))))) (let ((_let_43 (tptp.antidomain (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_28)))) (let ((_let_44 (tptp.addition _let_43 _let_42))) (let ((_let_45 (= (tptp.addition _let_35 _let_44) (tptp.addition (tptp.addition _let_35 _let_43) _let_42)))) (let ((_let_46 (= tptp.one (tptp.addition _let_35 _let_34)))) (let ((_let_47 (= tptp.one (tptp.addition _let_36 _let_35)))) (let ((_let_48 (= _let_42 _let_44))) (let ((_let_49 (= _let_18 (tptp.addition _let_18 tptp.zero)))) (let ((_let_50 (= (tptp.addition _let_18 _let_14) (tptp.addition _let_14 _let_18)))) (let ((_let_51 (= _let_28 _let_35))) (let ((_let_52 (= _let_15 (tptp.antidomain (tptp.antidomain _let_14))))) (let ((_let_53 (tptp.antidomain _let_38))) (let ((_let_54 (tptp.antidomain _let_53))) (let ((_let_55 (tptp.addition _let_54 _let_53))) (let ((_let_56 (= _let_55 (tptp.addition _let_53 _let_54)))) (let ((_let_57 (tptp.forward_diamond SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_58 (= _let_57 _let_28))) (let ((_let_59 (= tptp.one _let_55))) (let ((_let_60 (= tptp.one (tptp.addition _let_53 _let_38)))) (let ((_let_61 (= _let_14 _let_57))) (let ((_let_62 (= _let_18 _let_53))) (let ((_let_63 (= _let_20 _let_30))) (let ((_let_64 (= tptp.zero _let_14))) (let ((_let_65 (_let_13))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 ((tptp.addition B A)))) (let ((_let_68 (forall ((A $$unsorted)) (= tptp.zero (tptp.multiplication A tptp.zero))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((not (= (tptp.multiplication A tptp.zero) tptp.zero))))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_33 false _let_68)))) (let ((_let_73 (forall ((A $$unsorted)) (= A (tptp.addition A tptp.zero))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_73))) (let ((_let_76 ((tptp.addition A tptp.zero)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_75)) _let_74 :args (_let_37 false _let_73)))) (let ((_let_78 (_let_12))) (let ((_let_79 (ASSUME :args _let_78))) (let ((_let_80 ((tptp.addition (tptp.addition A B) C)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_38 _let_18 _let_29 QUANTIFIERS_INST_E_MATCHING _let_80)) :args _let_78)) _let_79 :args (_let_40 false _let_12)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_42 _let_43 _let_35 QUANTIFIERS_INST_E_MATCHING ((tptp.addition A (tptp.addition B C))))) :args _let_78)) _let_79 :args (_let_45 false _let_12)))) (let ((_let_83 (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.antidomain X0))) (= tptp.one (tptp.addition (tptp.antidomain _let_1) _let_1)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 ((tptp.antidomain (tptp.antidomain X0))))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_27 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_46 false _let_83)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_34 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_47 false _let_83)))) (let ((_let_89 (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.antidomain (tptp.multiplication X0 (tptp.antidomain (tptp.antidomain X1)))))) (= _let_1 (tptp.addition (tptp.antidomain (tptp.multiplication X0 X1)) _let_1)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_28 QUANTIFIERS_INST_E_MATCHING ((tptp.multiplication X0 (tptp.antidomain (tptp.antidomain X1)))))) :args (_let_89))) _let_90 :args (_let_48 false _let_89)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_75)) _let_74 :args (_let_49 false _let_73)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_14 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_65))) _let_66 :args (_let_50 false _let_13)))) (let ((_let_94 (_let_5))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 ((tptp.domain X0)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_51 false _let_5)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_52 false _let_5)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_53 _let_54 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_65))) _let_66 :args (_let_56 false _let_13)))) (let ((_let_100 (_let_4))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 ((tptp.forward_diamond X0 X1)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_100)) _let_101 :args (_let_58 false _let_4)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_38 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_59 false _let_83)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_60 false _let_83)))) (let ((_let_106 (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.divergence X0))) (= _let_1 (tptp.forward_diamond X0 _let_1)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.divergence X0)))) :args (_let_106))) _let_107 :args (_let_61 false _let_106)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_62 false _let_5)))) (let ((_let_110 (= tptp.zero _let_18))) (let ((_let_111 (not _let_63))) (let ((_let_112 (not _let_64))) (let ((_let_113 (or _let_112 _let_111 _let_110))) (let ((_let_114 (forall ((X0 $$unsorted) (BOUND_VARIABLE_900 $$unsorted)) (let ((_let_1 (tptp.domain BOUND_VARIABLE_900))) (let ((_let_2 (tptp.forward_diamond X0 _let_1))) (or (not (= tptp.zero (tptp.divergence X0))) (not (= _let_2 (tptp.addition _let_1 _let_2))) (= tptp.zero _let_1))))))) (let ((_let_115 (not _let_113))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (or))) (let ((_let_118 (not _let_114))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_116) :args (_let_118))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_114))) (REFL :args (_let_115)) :args _let_117)) _let_116 :args (_let_115 true _let_114)))) (let ((_let_120 (REFL :args (_let_113)))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 0)) (CONG _let_120 (MACRO_SR_PRED_INTRO :args ((= (not _let_112) _let_64))) :args _let_117)) :args ((or _let_64 _let_113))) _let_119 :args (_let_64 true _let_113)))) (let ((_let_122 (not _let_33))) (let ((_let_123 (not _let_37))) (let ((_let_124 (not _let_40))) (let ((_let_125 (not _let_45))) (let ((_let_126 (not _let_46))) (let ((_let_127 (not _let_47))) (let ((_let_128 (not _let_48))) (let ((_let_129 (not _let_49))) (let ((_let_130 (not _let_50))) (let ((_let_131 (not _let_51))) (let ((_let_132 (not _let_52))) (let ((_let_133 (not _let_56))) (let ((_let_134 (not _let_58))) (let ((_let_135 (not _let_59))) (let ((_let_136 (not _let_60))) (let ((_let_137 (not _let_61))) (let ((_let_138 (not _let_62))) (let ((_let_139 (and _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_56 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_41 _let_40 _let_37 _let_33 _let_32))) (let ((_let_140 (APPLY_UF tptp.addition))) (let ((_let_141 (ASSUME :args (_let_52)))) (let ((_let_142 (SYMM _let_141))) (let ((_let_143 (APPLY_UF tptp.antidomain))) (let ((_let_144 (ASSUME :args (_let_61)))) (let ((_let_145 (SYMM _let_144))) (let ((_let_146 (ASSUME :args (_let_58)))) (let ((_let_147 (SYMM _let_146))) (let ((_let_148 (TRANS _let_147 _let_145))) (let ((_let_149 (CONG _let_148 :args _let_143))) (let ((_let_150 (ASSUME :args (_let_51)))) (let ((_let_151 (SYMM _let_150))) (let ((_let_152 (CONG _let_151 :args _let_143))) (let ((_let_153 (ASSUME :args (_let_37)))) (let ((_let_154 (SYMM _let_153))) (let ((_let_155 (ASSUME :args (_let_64)))) (let ((_let_156 (SYMM _let_155))) (let ((_let_157 (CONG (REFL :args (_let_36)) (TRANS _let_151 _let_147 _let_145 _let_156) :args _let_140))) (let ((_let_158 (ASSUME :args (_let_47)))) (let ((_let_159 (SYMM _let_158))) (let ((_let_160 (SYMM _let_159))) (let ((_let_161 (ASSUME :args (_let_46)))) (let ((_let_162 (APPLY_UF tptp.multiplication))) (let ((_let_163 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_164 (CONG (CONG _let_163 (TRANS (CONG _let_149 :args _let_143) _let_142) :args _let_162) :args _let_143))) (let ((_let_165 (ASSUME :args (_let_48)))) (let ((_let_166 (SYMM _let_165))) (let ((_let_167 (ASSUME :args (_let_45)))) (let ((_let_168 (CONG _let_163 _let_151 :args _let_162))) (let ((_let_169 (CONG _let_168 :args _let_143))) (let ((_let_170 (ASSUME :args (_let_33)))) (let ((_let_171 (CONG (TRANS _let_147 _let_145 _let_156 (SYMM (SYMM _let_170)) (CONG _let_163 (TRANS _let_155 _let_144 _let_146) :args _let_162) (SYMM _let_168)) :args _let_143))) (let ((_let_172 (ASSUME :args (_let_59)))) (let ((_let_173 (SYMM _let_172))) (let ((_let_174 (ASSUME :args (_let_56)))) (let ((_let_175 (REFL :args (_let_54)))) (let ((_let_176 (ASSUME :args (_let_62)))) (let ((_let_177 (SYMM _let_176))) (let ((_let_178 (SYMM _let_177))) (let ((_let_179 (CONG _let_178 _let_175 :args _let_140))) (let ((_let_180 (APPLY_UF tptp.forward_diamond))) (let ((_let_181 (CONG _let_163 _let_148 :args _let_180))) (let ((_let_182 (TRANS _let_181 _let_145))) (let ((_let_183 (ASSUME :args (_let_60)))) (let ((_let_184 (REFL :args (_let_38)))) (let ((_let_185 (REFL :args (_let_29)))) (let ((_let_186 (ASSUME :args (_let_40)))) (let ((_let_187 (REFL :args (_let_18)))) (let ((_let_188 (ASSUME :args (_let_50)))) (let ((_let_189 (TRANS (SYMM (SYMM _let_188)) (CONG (SYMM _let_182) _let_187 :args _let_140)))) (let ((_let_190 (ASSUME :args (_let_49)))) (let ((_let_191 (SYMM (TRANS (CONG _let_187 _let_156 :args _let_140) (SYMM _let_190))))) (let ((_let_192 (CONG _let_175 _let_178 :args _let_140))) (let ((_let_193 (CONG (TRANS (SYMM _let_164) _let_165 (CONG (REFL :args (_let_43)) _let_165 :args _let_140) (CONG (TRANS (TRANS (SYMM _let_169) (SYMM _let_171) (SYMM _let_152) _let_153 (SYMM _let_157) _let_159 _let_172 (SYMM _let_192)) (TRANS _let_192 _let_173 _let_183 (CONG (TRANS _let_177 _let_191 _let_189) _let_184 :args _let_140) (SYMM _let_186) (CONG _let_185 (TRANS (CONG _let_178 _let_184 :args _let_140) (SYMM _let_183) _let_172 _let_174 (SYMM _let_179)) :args _let_140) (CONG (TRANS _let_182 (TRANS _let_144 _let_146 _let_150)) (TRANS _let_179 (SYMM _let_174) _let_173 _let_160 _let_157 _let_154 _let_152 _let_171 _let_169) :args _let_140))) _let_166 :args _let_140) (SYMM _let_167) (CONG (REFL :args (_let_35)) (TRANS _let_166 _let_164) :args _let_140) (SYMM _let_161) _let_160 _let_157 _let_154 _let_152 _let_149) :args _let_143))) (let ((_let_194 (REFL :args (_let_20)))) (let ((_let_195 (CONG _let_194 (TRANS _let_181 _let_146 _let_150 _let_193 _let_142) :args _let_140))) (let ((_let_196 (ASSUME :args (_let_63)))) (let ((_let_197 (CONG (SYMM _let_196) _let_185 :args _let_140))) (let ((_let_198 (ASSUME :args (_let_32)))) (let ((_let_199 (SYMM _let_198))) (let ((_let_200 (ASSUME :args (_let_41)))) (let ((_let_201 (CONG (TRANS _let_191 _let_189) _let_194 :args _let_140))) (let ((_let_202 (= tptp.zero (tptp.multiplication _let_16 tptp.zero)))) (let ((_let_203 (tptp.forward_diamond _let_16 _let_28))) (let ((_let_204 (= _let_203 (tptp.addition _let_203 tptp.zero)))) (let ((_let_205 (tptp.domain _let_18))) (let ((_let_206 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_205))) (let ((_let_207 (tptp.antidomain _let_206))) (let ((_let_208 (tptp.multiplication _let_207 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_209 (= (tptp.forward_diamond _let_208 _let_18) (tptp.domain (tptp.multiplication _let_208 _let_205))))) (let ((_let_210 (= _let_203 (tptp.domain (tptp.multiplication _let_16 (tptp.domain _let_28)))))) (let ((_let_211 (= (tptp.addition _let_14 _let_203) (tptp.addition _let_203 _let_14)))) (let ((_let_212 (tptp.antidomain (tptp.antidomain _let_18)))) (let ((_let_213 (= (tptp.multiplication _let_207 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_212)) (tptp.multiplication _let_208 _let_212)))) (let ((_let_214 (= tptp.zero (tptp.multiplication _let_207 _let_206)))) (let ((_let_215 (= _let_205 _let_212))) (let ((_let_216 (not _let_19))) (let ((_let_217 (_let_10))) (let ((_let_218 (ASSUME :args _let_217))) (let ((_let_219 (forall ((X0 $$unsorted)) (= tptp.zero (tptp.multiplication (tptp.antidomain X0) X0))))) (let ((_let_220 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_221 (not _let_110))) (let ((_let_222 (and _let_64 _let_221 _let_62 _let_61 _let_60 _let_59 _let_215 _let_58 _let_56 _let_214 _let_52 _let_51 _let_50 _let_49 _let_213 _let_48 _let_47 _let_46 _let_211 _let_45 _let_40 _let_37 _let_33 _let_210 _let_209 _let_204 _let_202))) (let ((_let_223 (ASSUME :args (_let_221)))) (let ((_let_224 (ASSUME :args (_let_210)))) (let ((_let_225 (SYMM (SYMM _let_224)))) (let ((_let_226 (ASSUME :args (_let_209)))) (let ((_let_227 (APPLY_UF tptp.domain))) (let ((_let_228 (ASSUME :args (_let_215)))) (let ((_let_229 (ASSUME :args (_let_213)))) (let ((_let_230 (CONG _let_163 _let_228 :args _let_162))) (let ((_let_231 (CONG (SYMM _let_230) :args _let_143))) (let ((_let_232 (ASSUME :args (_let_214)))) (let ((_let_233 (CONG (TRANS _let_144 _let_146 _let_150 _let_193 _let_142 (CONG (TRANS _let_156 (SYMM (SYMM _let_232)) (CONG (SYMM _let_231) (REFL :args (_let_206)) :args _let_162) (CONG _let_231 _let_230 :args _let_162) (SYMM (SYMM _let_229)) (CONG (REFL :args (_let_208)) (SYMM _let_228) :args _let_162)) :args _let_227) (SYMM _let_226)) _let_225 :args _let_140))) (let ((_let_234 (SYMM _let_193))) (let ((_let_235 (REFL :args (_let_16)))) (let ((_let_236 (TRANS (CONG (REFL :args (_let_14)) (CONG _let_235 (TRANS _let_141 _let_234 _let_151) :args _let_180) :args _let_140) _let_233))) (let ((_let_237 (ASSUME :args (_let_202)))) (let ((_let_238 (ASSUME :args (_let_204)))) (let ((_let_239 (ASSUME :args (_let_211)))) (let ((_let_240 (TRANS (SYMM _let_233) (SYMM (SYMM _let_239)) (CONG (REFL :args (_let_203)) _let_156 :args _let_140) (SYMM _let_238) _let_225 (CONG (TRANS (CONG _let_235 (TRANS (CONG _let_148 :args _let_227) _let_141 _let_234 _let_151 _let_147 _let_145 _let_156) :args _let_162) (SYMM _let_237) _let_155) :args _let_227) _let_141 _let_234 _let_151 _let_147 _let_145))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_19 (not _let_24)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_222)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_223 _let_155 _let_190 _let_144 _let_146 _let_150 _let_141 _let_165 _let_170 _let_153 _let_158 _let_172 _let_176 _let_183 _let_188 _let_186 _let_174 _let_167 _let_161 _let_237 _let_224 _let_238 _let_239 _let_232 _let_228 _let_229 _let_226) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (TRANS _let_155 (SYMM _let_240) (SYMM _let_236))) (SYMM (TRANS _let_191 (SYMM (CONG _let_187 _let_240 :args _let_140)) (SYMM (CONG _let_187 _let_236 :args _let_140)))) :args (=)) (FALSE_INTRO _let_223))) :args (_let_221 _let_64 _let_49 _let_61 _let_58 _let_51 _let_52 _let_48 _let_33 _let_37 _let_47 _let_59 _let_62 _let_60 _let_50 _let_40 _let_56 _let_45 _let_46 _let_202 _let_210 _let_204 _let_211 _let_214 _let_215 _let_213 _let_209))) :args (_let_64 _let_221 _let_62 _let_61 _let_60 _let_59 _let_215 _let_58 _let_56 _let_214 _let_52 _let_51 _let_50 _let_49 _let_213 _let_48 _let_47 _let_46 _let_211 _let_45 _let_40 _let_37 _let_33 _let_210 _let_209 _let_204 _let_202))) :args (true _let_222)) (CONG (REFL :args (_let_112)) (MACRO_SR_PRED_INTRO :args ((= (not _let_221) _let_110))) (REFL :args (_let_138)) (REFL :args (_let_137)) (REFL :args (_let_136)) (REFL :args (_let_135)) (REFL :args ((not _let_215))) (REFL :args (_let_134)) (REFL :args (_let_133)) (REFL :args ((not _let_214))) (REFL :args (_let_132)) (REFL :args (_let_131)) (REFL :args (_let_130)) (REFL :args (_let_129)) (REFL :args ((not _let_213))) (REFL :args (_let_128)) (REFL :args (_let_127)) (REFL :args (_let_126)) (REFL :args ((not _let_211))) (REFL :args (_let_125)) (REFL :args (_let_124)) (REFL :args (_let_123)) (REFL :args (_let_122)) (REFL :args ((not _let_210))) (REFL :args ((not _let_209))) (REFL :args ((not _let_204))) (REFL :args ((not _let_202))) (REFL :args (_let_216)) :args _let_117)) _let_121 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_113 2)) _let_119 :args (_let_221 true _let_113)) _let_109 _let_108 _let_105 _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_96)) :args _let_94)) _let_95 :args (_let_215 false _let_5)) _let_103 _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_220 :args (_let_206 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.antidomain X0)))) :args (_let_219))) _let_220 :args (_let_214 false _let_219)) _let_98 _let_97 _let_93 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_218 :args (_let_207 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_212 QUANTIFIERS_INST_E_MATCHING ((tptp.multiplication A (tptp.multiplication B C))))) :args _let_217)) _let_218 :args (_let_213 false _let_10)) _let_91 _let_88 _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_203 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_65))) _let_66 :args (_let_211 false _let_13)) _let_82 _let_81 _let_77 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_16 _let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_100)) _let_101 :args (_let_210 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_208 _let_18 QUANTIFIERS_INST_E_MATCHING ((tptp.multiplication X0 (tptp.domain X1))))) :args _let_100)) _let_101 :args (_let_209 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_203 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_75)) _let_74 :args (_let_204 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_202 false _let_68)) :args (_let_216 false _let_64 true _let_110 false _let_62 false _let_61 false _let_60 false _let_59 false _let_215 false _let_58 false _let_56 false _let_214 false _let_52 false _let_51 false _let_50 false _let_49 false _let_213 false _let_48 false _let_47 false _let_46 false _let_211 false _let_45 false _let_40 false _let_37 false _let_33 false _let_210 false _let_209 false _let_204 false _let_202)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_139)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_190 _let_155 _let_141 _let_144 _let_146 _let_150 _let_153 _let_158 _let_161 _let_165 _let_167 _let_170 _let_172 _let_174 _let_176 _let_183 _let_186 _let_188 _let_196 _let_198 _let_200) (SCOPE (TRANS (SYMM _let_195) (SYMM _let_197) _let_199 _let_200 (SYMM _let_201) (CONG _let_187 (TRANS _let_196 _let_201 (SYMM _let_200) (SYMM _let_199) _let_197 _let_195) :args _let_140)) :args (_let_49 _let_64 _let_52 _let_61 _let_58 _let_51 _let_37 _let_47 _let_46 _let_48 _let_45 _let_33 _let_59 _let_56 _let_62 _let_60 _let_40 _let_50 _let_63 _let_32 _let_41))) :args (_let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_56 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_41 _let_40 _let_37 _let_33 _let_32))) :args (true _let_139)) :args ((or _let_112 _let_111 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 (not _let_41) _let_124 _let_123 _let_122 _let_22 (not _let_32)))) _let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 1)) (CONG _let_120 (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_63))) :args _let_117)) :args ((or _let_63 _let_113))) _let_119 :args (_let_63 true _let_113)) _let_109 _let_108 _let_105 _let_104 _let_103 _let_99 _let_98 _let_97 _let_93 _let_92 _let_91 _let_88 _let_87 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_20 _let_18 _let_29 QUANTIFIERS_INST_E_MATCHING _let_80)) :args _let_78)) _let_79 :args (_let_41 false _let_12)) _let_81 _let_77 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_30 _let_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_65))) _let_66 :args (_let_32 false _let_13)) :args (_let_22 false _let_64 false _let_63 false _let_62 false _let_61 false _let_60 false _let_59 false _let_58 false _let_56 false _let_52 false _let_51 false _let_50 false _let_49 false _let_48 false _let_47 false _let_46 false _let_45 false _let_41 false _let_40 false _let_37 false _let_33 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING ((tptp.addition (tptp.forward_diamond X1 (tptp.domain X0)) (tptp.domain X2))))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (false true _let_19 false _let_22 false _let_24)) :args (_let_13 _let_12 _let_11 (forall ((A $$unsorted)) (= (tptp.addition A A) A)) _let_10 (forall ((A $$unsorted)) (= (tptp.multiplication A tptp.one) A)) (forall ((A $$unsorted)) (= (tptp.multiplication tptp.one A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication A (tptp.addition B C)) (tptp.addition (tptp.multiplication A B) (tptp.multiplication A C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.multiplication (tptp.addition A B) C) (tptp.addition (tptp.multiplication A C) (tptp.multiplication B C)))) _let_9 (forall ((A $$unsorted)) (= (tptp.multiplication tptp.zero A) tptp.zero)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.leq A B) (= (tptp.addition A B) B))) _let_8 _let_7 _let_6 _let_5 (forall ((X0 $$unsorted)) (= (tptp.multiplication X0 (tptp.coantidomain X0)) tptp.zero)) (forall ((X0 $$unsorted) (X1 $$unsorted)) (let ((_let_1 (tptp.coantidomain (tptp.multiplication (tptp.coantidomain (tptp.coantidomain X0)) X1)))) (= (tptp.addition (tptp.coantidomain (tptp.multiplication X0 X1)) _let_1) _let_1))) (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.coantidomain X0))) (= (tptp.addition (tptp.coantidomain _let_1) _let_1) tptp.one))) (forall ((X0 $$unsorted)) (= (tptp.codomain X0) (tptp.coantidomain (tptp.coantidomain X0)))) (forall ((X0 $$unsorted)) (= (tptp.c X0) (tptp.antidomain (tptp.domain X0)))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.domain_difference X0 X1) (tptp.multiplication (tptp.domain X0) (tptp.antidomain X1)))) _let_4 (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.backward_diamond X0 X1) (tptp.codomain (tptp.multiplication (tptp.codomain X1) X0)))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.forward_box X0 X1) (tptp.c (tptp.forward_diamond X0 (tptp.c X1))))) (forall ((X0 $$unsorted) (X1 $$unsorted)) (= (tptp.backward_box X0 X1) (tptp.c (tptp.backward_diamond X0 (tptp.c X1))))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.69/0.89  )
% 0.69/0.89  % SZS output end Proof for KLE128+1
% 0.69/0.89  % cvc5---1.0.5 exiting
% 0.69/0.89  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------