TSTP Solution File: SWV089+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV089+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 21:49:15 EDT 2023
% Result : Theorem 0.35s 0.84s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV089+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 04:48:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.35/0.84 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.14xch3VNhK/cvc5---1.0.5_16406.p...
% 0.35/0.84 ------- get file name : TPTP file name is SWV089+1
% 0.35/0.84 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16406.smt2...
% 0.35/0.84 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.35/0.84 % SZS status Theorem for SWV089+1
% 0.35/0.84 % SZS output start Proof for SWV089+1
% 0.35/0.84 (
% 0.35/0.84 (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 (tptp.gt tptp.n5 tptp.n4))) (let ((_let_12 (tptp.tptp_update2 (tptp.tptp_update2 tptp.xinit_defuse tptp.n5 tptp.use) tptp.n4 tptp.use))) (let ((_let_13 (tptp.tptp_update2 _let_12 tptp.n5 tptp.use))) (let ((_let_14 (tptp.tptp_update2 _let_13 tptp.n3 tptp.use))) (let ((_let_15 (tptp.tptp_update2 _let_14 tptp.n4 tptp.use))) (let ((_let_16 (tptp.tptp_update2 _let_15 tptp.n3 tptp.use))) (let ((_let_17 (tptp.a_select2 _let_16 tptp.n5))) (let ((_let_18 (tptp.a_select2 _let_16 tptp.n4))) (let ((_let_19 (tptp.a_select2 _let_16 tptp.n3))) (let ((_let_20 (tptp.tptp_update3 tptp.u_defuse tptp.n2 tptp.n0 tptp.use))) (let ((_let_21 (tptp.tptp_update3 _let_20 tptp.n1 tptp.n0 tptp.use))) (let ((_let_22 (tptp.tptp_update3 _let_21 tptp.n2 tptp.n0 tptp.use))) (let ((_let_23 (tptp.tptp_update3 _let_22 tptp.n0 tptp.n0 tptp.use))) (let ((_let_24 (tptp.tptp_update3 _let_23 tptp.n1 tptp.n0 tptp.use))) (let ((_let_25 (tptp.tptp_update3 _let_24 tptp.n0 tptp.n0 tptp.use))) (let ((_let_26 (tptp.a_select3 _let_25 tptp.n2 tptp.n0))) (let ((_let_27 (tptp.a_select3 _let_25 tptp.n1 tptp.n0))) (let ((_let_28 (tptp.a_select3 _let_25 tptp.n0 tptp.n0))) (let ((_let_29 (not (=> tptp.true (and (= _let_28 tptp.use) (= _let_27 tptp.use) (= _let_26 tptp.use) (= _let_19 tptp.use) (= _let_18 tptp.use) (= _let_17 tptp.use)))))) (let ((_let_30 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))) (let ((_let_31 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))) (let ((_let_32 (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= J V) (= (tptp.a_select3 X U V) VAL)) (= (tptp.a_select3 (tptp.tptp_update3 X I J VAL2) U V) VAL))))) (let ((_let_33 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V) VAL)))) (let ((_let_34 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))))) (let ((_let_35 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_36 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_37 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))))) (let ((_let_38 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))))) (let ((_let_39 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_40 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))))) (let ((_let_41 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_42 (= tptp.n1 _let_1))) (let ((_let_43 (= tptp.n2 _let_2))) (let ((_let_44 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_45 (= _let_1 (tptp.pred _let_2)))) (let ((_let_46 (= tptp.n0 _let_2))) (let ((_let_47 (= tptp.n1 tptp.n2))) (let ((_let_48 (SYMM (ASSUME :args (_let_6))))) (let ((_let_49 (SYMM (ASSUME :args (_let_5))))) (let ((_let_50 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 ((tptp.succ X)))) (let ((_let_54 (= tptp.n0 tptp.n2))) (let ((_let_55 (not _let_46))) (let ((_let_56 (= tptp.n5 _let_8))) (let ((_let_57 (= tptp.n3 _let_3))) (let ((_let_58 (= _let_8 (tptp.plus _let_3 tptp.n2)))) (let ((_let_59 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_60 (= tptp.n3 tptp.n5))) (let ((_let_61 (not _let_54))) (let ((_let_62 (SYMM (ASSUME :args (_let_9))))) (let ((_let_63 (SYMM (ASSUME :args (_let_4))))) (let ((_let_64 (_let_37))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (_let_36))) (let ((_let_67 (ASSUME :args _let_66))) (let ((_let_68 (tptp.leq tptp.n4 tptp.n5))) (let ((_let_69 (tptp.leq tptp.n4 tptp.n3))) (let ((_let_70 (not _let_60))) (let ((_let_71 (not _let_11))) (let ((_let_72 (or _let_71 _let_68))) (let ((_let_73 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (ASSUME :args (_let_11)))) (let ((_let_76 (tptp.leq _let_7 _let_3))) (let ((_let_77 (= tptp.n4 _let_7))) (let ((_let_78 (not _let_69))) (let ((_let_79 (tptp.leq _let_3 _let_2))) (let ((_let_80 (= _let_76 _let_79))) (let ((_let_81 (not _let_76))) (let ((_let_82 (_let_34))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (tptp.gt _let_3 _let_3))) (let ((_let_85 (= _let_79 _let_84))) (let ((_let_86 (not _let_79))) (let ((_let_87 (_let_38))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (_let_41))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (SYMM (ASSUME :args (_let_10))))) (let ((_let_92 (not _let_57))) (let ((_let_93 (not _let_77))) (let ((_let_94 (or))) (let ((_let_95 (_let_78))) (let ((_let_96 (REFL :args (_let_92)))) (let ((_let_97 (REFL :args (_let_93)))) (let ((_let_98 (and _let_77 _let_57 _let_81))) (let ((_let_99 (ASSUME :args (_let_81)))) (let ((_let_100 (APPLY_UF tptp.leq))) (let ((_let_101 (SYMM _let_63))) (let ((_let_102 (SYMM _let_101))) (let ((_let_103 (SYMM (SYMM _let_91)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_98)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_91 _let_63) (SCOPE (FALSE_ELIM (TRANS (CONG _let_103 _let_102 :args _let_100) (FALSE_INTRO _let_99))) :args (_let_81 _let_77 _let_57))) :args (_let_77 _let_57 _let_81))) :args (true _let_98)) (CONG _let_97 _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_76))) (REFL :args _let_95) :args _let_94)) :args ((or _let_93 _let_92 _let_78 _let_76))) _let_91 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_80)) :args ((or _let_79 _let_81 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_85)) :args ((or _let_86 _let_84 (not _let_85)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_89)) _let_90 :args ((not _let_84) false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_3 _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.gt (tptp.succ Y) X)))) :args _let_87)) _let_88 :args (_let_85 false _let_38)) :args (_let_86 true _let_84 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (_let_3 _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.leq (tptp.succ X) (tptp.succ Y))))) :args _let_82)) _let_83 :args (_let_80 false _let_34)) :args (_let_81 true _let_79 false _let_80)) :args (_let_78 false _let_77 false _let_57 true _let_76)))) (let ((_let_105 (not _let_68))) (let ((_let_106 (ASSUME :args _let_95))) (let ((_let_107 (ASSUME :args (_let_60)))) (let ((_let_108 (REFL :args (tptp.n4)))) (let ((_let_109 (ASSUME :args (_let_68)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_106 _let_107 _let_109) :args (_let_68 _let_60 _let_78)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_109)) (CONG _let_108 (SYMM _let_107) :args _let_100) (FALSE_INTRO _let_106))) :args (_let_78 _let_60 _let_68)) :args ((not (and _let_68 _let_60 _let_78)) SB_LITERAL))) (CONG (REFL :args (_let_105)) (REFL :args (_let_70)) (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_69))) :args _let_94)) :args ((or _let_69 _let_105 _let_70))) _let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_71 _let_68 (not _let_72)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.n4 tptp.n5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_68 false _let_11 false _let_72)) :args (_let_70 true _let_69 false _let_68)))) (let ((_let_111 (not _let_43))) (let ((_let_112 (and _let_56 _let_43 _let_57 _let_58 _let_59 _let_54))) (let ((_let_113 (ASSUME :args (_let_58)))) (let ((_let_114 (APPLY_UF tptp.plus))) (let ((_let_115 (SYMM _let_49))) (let ((_let_116 (ASSUME :args (_let_54)))) (let ((_let_117 (ASSUME :args (_let_59)))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_113 _let_63 _let_49 _let_116 _let_117) (SCOPE (TRANS _let_102 (SYMM (SYMM _let_117)) (CONG (REFL :args (tptp.n3)) (TRANS (SYMM (SYMM _let_116)) _let_49) :args _let_114) (CONG _let_102 _let_115 :args _let_114) (SYMM _let_113) (SYMM _let_62)) :args (_let_56 _let_58 _let_57 _let_43 _let_54 _let_59))) :args (_let_56 _let_43 _let_57 _let_58 _let_59 _let_54))) :args (true _let_112)) :args ((or (not _let_56) _let_111 _let_92 _let_60 (not _let_58) (not _let_59) _let_61))) _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ (tptp.succ X)))))) :args _let_66))) _let_67 :args (_let_59 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.succ (tptp.succ X))))) :args _let_64))) _let_65 :args (_let_58 false _let_37)) _let_63 _let_49 _let_62 :args (_let_61 true _let_60 false _let_59 false _let_58 false _let_57 false _let_43 false _let_56)))) (let ((_let_119 (and _let_43 _let_61))) (let ((_let_120 (ASSUME :args (_let_61)))) (let ((_let_121 (REFL :args (tptp.n0)))) (let ((_let_122 (tptp.a_select3 _let_23 tptp.n2 tptp.n0))) (let ((_let_123 (tptp.a_select3 _let_24 tptp.n2 tptp.n0))) (let ((_let_124 (= _let_123 _let_122))) (let ((_let_125 (or _let_47 _let_124))) (let ((_let_126 (forall ((I $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select3 X U V) (tptp.a_select3 (tptp.tptp_update3 X I V VAL2) U V)))))) (let ((_let_127 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_128 (_let_126))) (let ((_let_129 ((tptp.a_select3 (tptp.tptp_update3 X I V VAL2) U V)))) (let ((_let_130 (tptp.a_select3 _let_22 tptp.n2 tptp.n0))) (let ((_let_131 (= _let_130 _let_122))) (let ((_let_132 (= _let_26 _let_123))) (let ((_let_133 (= tptp.use _let_130))) (let ((_let_134 (= tptp.use (tptp.a_select3 _let_20 tptp.n2 tptp.n0)))) (let ((_let_135 (= tptp.use _let_26))) (let ((_let_136 (not _let_124))) (let ((_let_137 (or _let_54 _let_131))) (let ((_let_138 (or _let_54 _let_132))) (let ((_let_139 (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select3 (tptp.tptp_update3 X U V VAL) U V))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (_let_139))) (let ((_let_142 ((tptp.tptp_update3 X U V VAL)))) (let ((_let_143 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (tptp.u_defuse tptp.n2 tptp.n0 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_142)) :args _let_141)) _let_140 :args (_let_134 false _let_139)))) (let ((_let_144 (= tptp.use _let_17))) (let ((_let_145 (= tptp.use _let_18))) (let ((_let_146 (= tptp.use _let_19))) (let ((_let_147 (= tptp.use _let_27))) (let ((_let_148 (= tptp.use _let_28))) (let ((_let_149 (not _let_135))) (let ((_let_150 (tptp.a_select2 _let_14 tptp.n5))) (let ((_let_151 (tptp.a_select2 _let_13 tptp.n5))) (let ((_let_152 (= _let_151 _let_150))) (let ((_let_153 (tptp.a_select2 _let_15 tptp.n5))) (let ((_let_154 (= _let_153 _let_150))) (let ((_let_155 (= _let_17 _let_153))) (let ((_let_156 (= tptp.use _let_151))) (let ((_let_157 (or _let_60 _let_152))) (let ((_let_158 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL2 $$unsorted)) (or (= I U) (= (tptp.a_select2 X U) (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))))) (let ((_let_159 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_160 (_let_158))) (let ((_let_161 ((tptp.a_select2 (tptp.tptp_update2 X I VAL2) U)))) (let ((_let_162 (= tptp.n4 tptp.n5))) (let ((_let_163 (or _let_162 _let_154))) (let ((_let_164 (tptp.succ tptp.n3))) (let ((_let_165 (tptp.lt tptp.n4 _let_164))) (let ((_let_166 (tptp.lt tptp.n4 tptp.n5))) (let ((_let_167 (not _let_162))) (let ((_let_168 (tptp.gt _let_164 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((_let_190 (ASSUME :args (_let_156)))) (let ((_let_191 (ASSUME :args (_let_152)))) (let ((_let_192 (ASSUME :args (_let_154)))) (let ((_let_193 (ASSUME :args (_let_155)))) (let ((_let_194 (ASSUME :args (_let_187)))) (let ((_let_195 (tptp.a_select2 _let_15 tptp.n4))) (let ((_let_196 (= tptp.use _let_195))) (let ((_let_197 (= tptp.n3 tptp.n4))) (let ((_let_198 (= _let_18 _let_195))) (let ((_let_199 (or _let_197 _let_198))) (let ((_let_200 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_182 :args (_let_14 tptp.n4 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_184)) :args _let_183)) _let_182 :args (_let_196 false _let_181)))) (let ((_let_201 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_182 :args (_let_15 tptp.n3 tptp.use QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_184)) :args _let_183)) :args ((or _let_146 (not _let_181)))) _let_182 :args (_let_146 false _let_181)))) (let ((_let_202 (not _let_197))) (let ((_let_203 (not _let_196))) (let ((_let_204 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Y))) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))) (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) _let_38 (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))) (= (tptp.succ tptp.tptp_minus_1) tptp.n0) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))) _let_37 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_36 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) (forall ((X $$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 $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_35 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) _let_34 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.succ X) Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq (tptp.minus X Y) X) (tptp.leq tptp.n0 Y))) _let_33 _let_32 (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_31 _let_30 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_29 _let_11 (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (forall ((X $$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)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) (forall ((X $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.35/0.85 )
% 0.35/0.85 % SZS output end Proof for SWV089+1
% 0.35/0.85 % cvc5---1.0.5 exiting
% 0.35/0.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------