TSTP Solution File: SWV091+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV091+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 21:49:16 EDT 2023
% Result : Theorem 0.37s 0.86s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV091+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 10:11:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.37/0.86 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.pwf9MVFhlw/cvc5---1.0.5_10715.p...
% 0.37/0.86 ------- get file name : TPTP file name is SWV091+1
% 0.37/0.86 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10715.smt2...
% 0.37/0.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.37/0.86 % SZS status Theorem for SWV091+1
% 0.37/0.86 % SZS output start Proof for SWV091+1
% 0.37/0.86 (
% 0.37/0.86 (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (= _let_3 tptp.n3))) (let ((_let_5 (= _let_2 tptp.n2))) (let ((_let_6 (= _let_1 tptp.n1))) (let ((_let_7 (tptp.succ _let_3))) (let ((_let_8 (tptp.succ _let_7))) (let ((_let_9 (= _let_8 tptp.n5))) (let ((_let_10 (= _let_7 tptp.n4))) (let ((_let_11 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))))) (let ((_let_12 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_13 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))))) (let ((_let_14 (tptp.gt tptp.n5 tptp.n3))) (let ((_let_15 (tptp.gt tptp.n4 tptp.n3))) (let ((_let_16 (tptp.gt tptp.n3 tptp.n2))) (let ((_let_17 (tptp.gt tptp.n3 tptp.n1))) (let ((_let_18 (tptp.gt tptp.n5 tptp.n1))) (let ((_let_19 (tptp.gt tptp.n3 tptp.n0))) (let ((_let_20 (tptp.gt tptp.n2 tptp.n0))) (let ((_let_21 (tptp.gt tptp.n1 tptp.n0))) (let ((_let_22 (tptp.tptp_update2 tptp.xinit_noise_defuse tptp.n0 tptp.use))) (let ((_let_23 (tptp.tptp_update2 _let_22 tptp.n1 tptp.use))) (let ((_let_24 (tptp.tptp_update2 _let_23 tptp.n2 tptp.use))) (let ((_let_25 (tptp.tptp_update2 _let_24 tptp.n3 tptp.use))) (let ((_let_26 (tptp.tptp_update2 _let_25 tptp.n4 tptp.use))) (let ((_let_27 (tptp.tptp_update2 _let_26 tptp.n5 tptp.use))) (let ((_let_28 (tptp.a_select2 _let_27 tptp.n5))) (let ((_let_29 (tptp.a_select2 _let_27 tptp.n4))) (let ((_let_30 (tptp.a_select2 _let_27 tptp.n3))) (let ((_let_31 (tptp.a_select2 _let_27 tptp.n2))) (let ((_let_32 (tptp.a_select2 _let_27 tptp.n1))) (let ((_let_33 (tptp.a_select2 _let_27 tptp.n0))) (let ((_let_34 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n5))) (let ((_let_35 (= _let_34 tptp.use))) (let ((_let_36 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n4))) (let ((_let_37 (= _let_36 tptp.use))) (let ((_let_38 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n3))) (let ((_let_39 (= _let_38 tptp.use))) (let ((_let_40 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n2))) (let ((_let_41 (= _let_40 tptp.use))) (let ((_let_42 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n1))) (let ((_let_43 (= _let_42 tptp.use))) (let ((_let_44 (tptp.a_select2 tptp.xinit_mean_defuse tptp.n0))) (let ((_let_45 (= _let_44 tptp.use))) (let ((_let_46 (tptp.a_select2 tptp.xinit_defuse tptp.n5))) (let ((_let_47 (= _let_46 tptp.use))) (let ((_let_48 (tptp.a_select2 tptp.xinit_defuse tptp.n4))) (let ((_let_49 (= _let_48 tptp.use))) (let ((_let_50 (tptp.a_select2 tptp.xinit_defuse tptp.n3))) (let ((_let_51 (= _let_50 tptp.use))) (let ((_let_52 (tptp.a_select3 tptp.u_defuse tptp.n2 tptp.n0))) (let ((_let_53 (= _let_52 tptp.use))) (let ((_let_54 (tptp.a_select3 tptp.u_defuse tptp.n1 tptp.n0))) (let ((_let_55 (= _let_54 tptp.use))) (let ((_let_56 (tptp.a_select3 tptp.u_defuse tptp.n0 tptp.n0))) (let ((_let_57 (= _let_56 tptp.use))) (let ((_let_58 (tptp.a_select2 tptp.sigma_defuse tptp.n5))) (let ((_let_59 (= _let_58 tptp.use))) (let ((_let_60 (tptp.a_select2 tptp.sigma_defuse tptp.n4))) (let ((_let_61 (= _let_60 tptp.use))) (let ((_let_62 (tptp.a_select2 tptp.sigma_defuse tptp.n3))) (let ((_let_63 (= _let_62 tptp.use))) (let ((_let_64 (tptp.a_select2 tptp.sigma_defuse tptp.n2))) (let ((_let_65 (= _let_64 tptp.use))) (let ((_let_66 (tptp.a_select2 tptp.sigma_defuse tptp.n1))) (let ((_let_67 (= _let_66 tptp.use))) (let ((_let_68 (tptp.a_select2 tptp.sigma_defuse tptp.n0))) (let ((_let_69 (= _let_68 tptp.use))) (let ((_let_70 (tptp.a_select2 tptp.rho_defuse tptp.n2))) (let ((_let_71 (= _let_70 tptp.use))) (let ((_let_72 (tptp.a_select2 tptp.rho_defuse tptp.n1))) (let ((_let_73 (= _let_72 tptp.use))) (let ((_let_74 (tptp.a_select2 tptp.rho_defuse tptp.n0))) (let ((_let_75 (= _let_74 tptp.use))) (let ((_let_76 (not (=> (and _let_75 _let_73 _let_71 _let_69 _let_67 _let_65 _let_63 _let_61 _let_59 _let_57 _let_55 _let_53 _let_51 _let_49 _let_47 _let_45 _let_43 _let_41 _let_39 _let_37 _let_35) (and _let_75 _let_73 _let_71 _let_69 _let_67 _let_65 _let_63 _let_61 _let_59 _let_57 _let_55 _let_53 _let_51 _let_49 _let_47 _let_45 _let_43 _let_41 _let_39 _let_37 _let_35 (= _let_33 tptp.use) (= _let_32 tptp.use) (= _let_31 tptp.use) (= _let_30 tptp.use) (= _let_29 tptp.use) (= _let_28 tptp.use)))))) (let ((_let_77 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))))) (let ((_let_78 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))) (let ((_let_79 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))) (let ((_let_80 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))))) (let ((_let_81 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))))) (let ((_let_82 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)))) (let ((_let_83 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_84 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_85 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_86 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_87 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))))) (let ((_let_88 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_89 (tptp.succ tptp.tptp_minus_1))) (let ((_let_90 (= _let_89 tptp.n0))) (let ((_let_91 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_92 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_93 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))))) (let ((_let_94 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_95 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))))) (let ((_let_96 (= tptp.n0 _let_89))) (let ((_let_97 (= tptp.n1 _let_1))) (let ((_let_98 (= tptp.n1 _let_2))) (let ((_let_99 (tptp.pred tptp.tptp_minus_1))) (let ((_let_100 (tptp.succ _let_99))) (let ((_let_101 (= tptp.tptp_minus_1 _let_100))) (let ((_let_102 (tptp.succ (tptp.succ _let_100)))) (let ((_let_103 (= (tptp.plus _let_99 tptp.n3) _let_102))) (let ((_let_104 (= (tptp.plus _let_99 tptp.n4) (tptp.succ _let_102)))) (let ((_let_105 (= tptp.n3 tptp.n4))) (let ((_let_106 (SYMM (ASSUME :args (_let_90))))) (let ((_let_107 (SYMM (ASSUME :args (_let_6))))) (let ((_let_108 (= tptp.n1 tptp.n2))) (let ((_let_109 (= tptp.n2 _let_2))) (let ((_let_110 (not _let_98))) (let ((_let_111 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_112 (tptp.pred _let_2))) (let ((_let_113 (= _let_1 _let_112))) (let ((_let_114 (= tptp.n0 tptp.n2))) (let ((_let_115 (not _let_108))) (let ((_let_116 (SYMM (ASSUME :args (_let_5))))) (let ((_let_117 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (_let_117))) (let ((_let_120 ((tptp.succ X)))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_120)) :args _let_119)) _let_118 :args (_let_111 false _let_117)))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_120)) :args _let_119)) _let_118 :args (_let_113 false _let_117)))) (let ((_let_123 (= tptp.n5 _let_8))) (let ((_let_124 (= tptp.n3 _let_3))) (let ((_let_125 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_126 (= _let_3 (tptp.plus tptp.n1 _let_2)))) (let ((_let_127 (= _let_8 (tptp.plus _let_3 tptp.n2)))) (let ((_let_128 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_129 (= tptp.n1 tptp.n5))) (let ((_let_130 (not _let_114))) (let ((_let_131 (SYMM (ASSUME :args (_let_9))))) (let ((_let_132 (SYMM (ASSUME :args (_let_4))))) (let ((_let_133 (_let_88))) (let ((_let_134 (ASSUME :args _let_133))) (let ((_let_135 ((tptp.succ X)))) (let ((_let_136 (_let_87))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (_let_85))) (let ((_let_139 (ASSUME :args _let_138))) (let ((_let_140 (tptp.gt tptp.n1 tptp.n1))) (let ((_let_141 (not _let_129))) (let ((_let_142 (ASSUME :args (_let_18)))) (let ((_let_143 (not _let_140))) (let ((_let_144 (_let_94))) (let ((_let_145 (ASSUME :args _let_144))) (let ((_let_146 ((not (= (tptp.gt X X) false))))) (let ((_let_147 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (tptp.n1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_146)) :args _let_144)) _let_145 :args (_let_143 false _let_94)))) (let ((_let_148 (or))) (let ((_let_149 (not _let_123))) (let ((_let_150 (not _let_18))) (let ((_let_151 (APPLY_UF tptp.gt))) (let ((_let_152 (REFL :args (tptp.n1)))) (let ((_let_153 (SYMM _let_131))) (let ((_let_154 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_143)))) (CONG (TRANS (SYMM (SYMM (ASSUME :args (_let_129)))) _let_131) _let_152 :args _let_151) (CONG _let_153 _let_152 :args _let_151) (TRUE_INTRO _let_142))) :args (_let_18 _let_123 _let_129 _let_143))) (CONG (REFL :args (_let_150)) (REFL :args (_let_149)) (REFL :args (_let_141)) (MACRO_SR_PRED_INTRO :args ((= (not _let_143) _let_140))) :args _let_148)) _let_147 _let_131 _let_142 :args (_let_141 true _let_140 false _let_123 false _let_18)))) (let ((_let_155 (not _let_124))) (let ((_let_156 (not _let_109))) (let ((_let_157 (not _let_97))) (let ((_let_158 (and _let_123 _let_97 _let_109 _let_124 _let_125 _let_126 _let_127 _let_128 _let_114))) (let ((_let_159 (ASSUME :args (_let_127)))) (let ((_let_160 (APPLY_UF tptp.plus))) (let ((_let_161 (SYMM _let_116))) (let ((_let_162 (SYMM _let_132))) (let ((_let_163 (SYMM _let_162))) (let ((_let_164 (ASSUME :args (_let_114)))) (let ((_let_165 (SYMM (SYMM _let_164)))) (let ((_let_166 (REFL :args (tptp.n3)))) (let ((_let_167 (ASSUME :args (_let_128)))) (let ((_let_168 (ASSUME :args (_let_126)))) (let ((_let_169 (SYMM _let_107))) (let ((_let_170 (ASSUME :args (_let_125)))) (let ((_let_171 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_158)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_131 _let_159 _let_132 _let_116 _let_164 _let_167 _let_168 _let_107 _let_170) (SCOPE (TRANS _let_107 (SYMM (SYMM _let_170)) (CONG _let_107 _let_165 :args _let_160) (CONG _let_169 _let_116 :args _let_160) (SYMM _let_168) (SYMM (SYMM _let_167)) (CONG _let_166 (TRANS _let_165 _let_116) :args _let_160) (CONG _let_163 _let_161 :args _let_160) (SYMM _let_159) _let_153) :args (_let_123 _let_127 _let_124 _let_109 _let_114 _let_128 _let_126 _let_97 _let_125))) :args (_let_123 _let_97 _let_109 _let_124 _let_125 _let_126 _let_127 _let_128 _let_114))) :args (true _let_158)) :args ((or _let_149 _let_157 _let_156 _let_155 _let_129 (not _let_125) (not _let_126) (not _let_127) (not _let_128) _let_130))) _let_154 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_139 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ (tptp.succ X)))))) :args _let_138))) _let_139 :args (_let_128 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_137 :args (_let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ X))))) :args _let_136))) _let_137 :args (_let_127 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_134 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_135)) :args _let_133))) _let_134 :args (_let_126 false _let_88)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_134 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_135)) :args _let_133))) _let_134 :args (_let_125 false _let_88)) _let_132 _let_116 _let_107 _let_131 :args (_let_130 true _let_129 false _let_128 false _let_127 false _let_126 false _let_125 false _let_124 false _let_109 false _let_97 false _let_123)))) (let ((_let_172 (not _let_113))) (let ((_let_173 (not _let_111))) (let ((_let_174 (_let_115))) (let ((_let_175 (REFL :args (_let_156)))) (let ((_let_176 (= tptp.n0 _let_2))) (let ((_let_177 (ASSUME :args (_let_130)))) (let ((_let_178 (SYMM _let_161))) (let ((_let_179 (ASSUME :args (_let_108)))) (let ((_let_180 (SYMM (SYMM _let_179)))) (let ((_let_181 (ASSUME :args (_let_113)))) (let ((_let_182 (SYMM _let_181))) (let ((_let_183 (APPLY_UF tptp.pred))) (let ((_let_184 (ASSUME :args (_let_111)))) (let ((_let_185 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_116 (MODUS_PONENS (AND_INTRO _let_116 _let_179 _let_107 _let_181 _let_184) (SCOPE (TRANS (SYMM (SYMM _let_184)) (CONG _let_169 :args _let_183) (CONG (TRANS _let_180 _let_178) :args _let_183) _let_182 _let_169 _let_180 _let_178) :args (_let_109 _let_108 _let_97 _let_113 _let_111))) _let_177) :args (_let_97 _let_109 _let_111 _let_113 _let_108 _let_130)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_177)) (TRUE_INTRO (TRANS (SYMM (SYMM (ASSUME :args (_let_176)))) _let_161)))) :args (_let_109 _let_176 _let_130)) :args ((not (and _let_97 _let_109 _let_111 _let_113 _let_108 _let_130)) SB_LITERAL))) (CONG (REFL :args (_let_157)) _let_175 (REFL :args (_let_173)) (REFL :args (_let_172)) (REFL :args _let_174) (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_114))) :args _let_148)) :args ((or _let_157 _let_156 _let_173 _let_172 _let_114 _let_115))))) (let ((_let_186 (MACRO_RESOLUTION_TRUST _let_185 _let_171 _let_122 _let_121 _let_116 _let_107 :args (_let_115 true _let_114 false _let_113 false _let_111 false _let_109 false _let_97)))) (let ((_let_187 (and _let_109 _let_115))) (let ((_let_188 (ASSUME :args _let_174))) (let ((_let_189 (=))) (let ((_let_190 (forall ((X $$unsorted)) (= X (tptp.succ (tptp.pred X)))))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_192 (_let_86))) (let ((_let_193 (ASSUME :args _let_192))) (let ((_let_194 (_let_84))) (let ((_let_195 (ASSUME :args _let_194))) (let ((_let_196 (tptp.a_select2 _let_26 tptp.n3))) (let ((_let_197 (tptp.a_select2 _let_25 tptp.n3))) (let ((_let_198 (= _let_197 _let_196))) (let ((_let_199 (or _let_105 _let_198))) (let ((_let_200 (forall ((I $$unsorted) (U 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_let_107 _let_106 :args (false false _let_105 false _let_104 false _let_103 false _let_101 true _let_98 false _let_97 false _let_96)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) _let_95 _let_94 (forall ((X $$unsorted)) (tptp.leq X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))) _let_93 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_92 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) _let_91 (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))) (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L1 I) (tptp.leq I U1) (tptp.leq L2 J) (tptp.leq J U2)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim L1 U1) (tptp.dim L2 U2) Val) I J) Val))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.trans A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.inv A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (let ((_let_1 (tptp.tptp_update3 A K K VAL))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N) (tptp.leq tptp.n0 K) (tptp.leq K N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_msub A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 D I J) (tptp.a_select3 D J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 F I J) (tptp.a_select3 F J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)) (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_90 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_88 _let_87 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) _let_86 _let_85 _let_84 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_83 _let_82 _let_81 _let_80 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) _let_79 _let_78 _let_77 tptp.true (not (= tptp.def tptp.use)) _let_76 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) _let_21 _let_20 _let_19 (tptp.gt tptp.n4 tptp.n1) _let_18 (tptp.gt tptp.n2 tptp.n1) _let_17 (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) _let_16 _let_15 _let_14 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) _let_13 _let_12 _let_11 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))) _let_10 _let_9 _let_6 _let_5 _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.37/0.87 )
% 0.37/0.87 % SZS output end Proof for SWV091+1
% 0.37/0.87 % cvc5---1.0.5 exiting
% 0.37/0.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------