TSTP Solution File: RNG068+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG068+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 13:49:49 EDT 2023
% Result : Theorem 1.10s 1.32s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG068+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n007.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 : Sun Aug 27 01:55:27 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 1.10/1.32 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ALPZB3Wztq/cvc5---1.0.5_32682.p...
% 1.10/1.32 ------- get file name : TPTP file name is RNG068+2
% 1.10/1.32 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32682.smt2...
% 1.10/1.32 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.10/1.32 % SZS status Theorem for RNG068+2
% 1.10/1.32 % SZS output start Proof for RNG068+2
% 1.10/1.32 (
% 1.10/1.32 (let ((_let_1 (tptp.sdtasdt0 tptp.xS tptp.xS))) (let ((_let_2 (tptp.sdtasdt0 tptp.xS tptp.xR))) (let ((_let_3 (tptp.sdtasdt0 tptp.xR tptp.xS))) (let ((_let_4 (tptp.sdtasdt0 tptp.xR tptp.xR))) (let ((_let_5 (tptp.sdtpldt0 _let_4 _let_3))) (let ((_let_6 (tptp.sdtpldt0 _let_5 (tptp.sdtpldt0 _let_2 _let_1)))) (let ((_let_7 (tptp.sdtasdt0 tptp.xP tptp.xP))) (let ((_let_8 (tptp.sdtpldt0 _let_7 _let_7))) (let ((_let_9 (tptp.sdtpldt0 _let_8 _let_8))) (let ((_let_10 (tptp.sdtlseqdt0 _let_9 _let_6))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.sdtpldt0 _let_1 tptp.xN))) (let ((_let_13 (tptp.sdtpldt0 _let_4 tptp.xN))) (let ((_let_14 (tptp.sdtpldt0 _let_13 _let_1))) (let ((_let_15 (= (tptp.sdtpldt0 _let_14 tptp.xN) (tptp.sdtpldt0 _let_13 _let_12)))) (let ((_let_16 (tptp.sdtpldt0 _let_4 _let_1))) (let ((_let_17 (tptp.sdtpldt0 _let_16 tptp.xN))) (let ((_let_18 (tptp.sdtpldt0 _let_17 tptp.xN))) (let ((_let_19 (tptp.sdtpldt0 _let_8 _let_7))) (let ((_let_20 (tptp.sdtpldt0 _let_19 _let_7))) (let ((_let_21 (tptp.sdtlseqdt0 _let_20 _let_18))) (let ((_let_22 (= tptp.xN _let_3))) (let ((_let_23 (tptp.aScalar0 tptp.xN))) (let ((_let_24 (and _let_23 _let_22))) (let ((_let_25 (tptp.aScalar0 tptp.xS))) (let ((_let_26 (and _let_25 (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD))))) (let ((_let_27 (tptp.aScalar0 tptp.xP))) (let ((_let_28 (and _let_27 (= tptp.xP (tptp.sdtasdt0 tptp.xE tptp.xH))))) (let ((_let_29 (tptp.sdtasdt0 tptp.xC tptp.xG))) (let ((_let_30 (= tptp.xR _let_29))) (let ((_let_31 (tptp.aScalar0 tptp.xR))) (let ((_let_32 (and _let_31 _let_30))) (let ((_let_33 (tptp.aScalar0 tptp.xG))) (let ((_let_34 (and _let_33 (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB))))) (let ((_let_35 (tptp.aScalar0 tptp.xC))) (let ((_let_36 (and _let_35 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp))))) (let ((_let_37 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_38 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_39 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))))) (let ((_let_40 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_41 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_42 (tptp.aScalar0 tptp.sz0z00))) (let ((_let_43 (tptp.sdtasdt0 tptp.xG tptp.xS))) (let ((_let_44 (= (tptp.sdtasdt0 _let_29 tptp.xS) (tptp.sdtasdt0 tptp.xC _let_43)))) (let ((_let_45 (tptp.sdtasdt0 tptp.xS tptp.xC))) (let ((_let_46 (= (tptp.sdtasdt0 _let_45 tptp.xG) (tptp.sdtasdt0 tptp.xS _let_29)))) (let ((_let_47 (tptp.sdtasdt0 tptp.xC tptp.xS))) (let ((_let_48 (= _let_45 _let_47))) (let ((_let_49 (= _let_17 (tptp.sdtpldt0 _let_4 _let_12)))) (let ((_let_50 (tptp.sdtpldt0 _let_1 _let_4))) (let ((_let_51 (= _let_16 _let_50))) (let ((_let_52 (tptp.sdtpldt0 _let_1 _let_13))) (let ((_let_53 (= _let_14 _let_52))) (let ((_let_54 (= _let_20 _let_9))) (let ((_let_55 (tptp.sdtpldt0 tptp.xN _let_16))) (let ((_let_56 (= _let_17 _let_55))) (let ((_let_57 (tptp.sdtpldt0 _let_5 _let_2))) (let ((_let_58 (= _let_6 (tptp.sdtpldt0 _let_57 _let_1)))) (let ((_let_59 (tptp.sdtpldt0 _let_2 _let_5))) (let ((_let_60 (= _let_57 _let_59))) (let ((_let_61 (= _let_52 (tptp.sdtpldt0 _let_50 tptp.xN)))) (let ((_let_62 (= (tptp.sdtpldt0 _let_55 tptp.xN) (tptp.sdtpldt0 tptp.xN _let_17)))) (let ((_let_63 (= (tptp.sdtpldt0 _let_59 _let_1) (tptp.sdtpldt0 _let_2 (tptp.sdtpldt0 _let_5 _let_1))))) (let ((_let_64 (tptp.sdtasdt0 tptp.xS tptp.xG))) (let ((_let_65 (= (tptp.sdtasdt0 _let_47 tptp.xG) (tptp.sdtasdt0 tptp.xC _let_64)))) (let ((_let_66 (= _let_43 _let_64))) (let ((_let_67 (1))) (let ((_let_68 (ASSUME :args (_let_32)))) (let ((_let_69 (ASSUME :args (_let_24)))) (let ((_let_70 (AND_ELIM _let_69 :args _let_67))) (let ((_let_71 (ASSUME :args (_let_21)))) (let ((_let_72 (ASSUME :args (_let_11)))) (let ((_let_73 (tptp.sdtpldt0 tptp.xC tptp.xG))) (let ((_let_74 (tptp.sdtpldt0 tptp.xG tptp.xS))) (let ((_let_75 (and (= (tptp.sdtpldt0 _let_73 tptp.xS) (tptp.sdtpldt0 tptp.xC _let_74)) (= _let_73 (tptp.sdtpldt0 tptp.xG tptp.xC)) _let_44 (= _let_29 (tptp.sdtasdt0 tptp.xG tptp.xC))))) (let ((_let_76 (not _let_25))) (let ((_let_77 (not _let_33))) (let ((_let_78 (not _let_35))) (let ((_let_79 (or _let_78 _let_77 _let_76 _let_75))) (let ((_let_80 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (not (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 (0))) (let ((_let_84 (AND_ELIM (ASSUME :args (_let_26)) :args _let_83))) (let ((_let_85 (AND_ELIM (ASSUME :args (_let_34)) :args _let_83))) (let ((_let_86 (AND_ELIM (ASSUME :args (_let_36)) :args _let_83))) (let ((_let_87 (tptp.sdtpldt0 tptp.xC tptp.xS))) (let ((_let_88 (tptp.sdtpldt0 tptp.xS tptp.xC))) (let ((_let_89 (= _let_88 _let_87))) (let ((_let_90 (and (= (tptp.sdtpldt0 _let_88 tptp.xG) (tptp.sdtpldt0 tptp.xS _let_73)) _let_89 _let_46 _let_48))) (let ((_let_91 (or _let_76 _let_78 _let_77 _let_90))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_78 _let_77 _let_76 _let_90 (not _let_91)))) _let_86 _let_85 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.xS tptp.xC tptp.xG QUANTIFIERS_INST_E_MATCHING ((tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) :args _let_82)) _let_81 :args (_let_91 false _let_80)) :args (_let_90 false _let_35 false _let_33 false _let_25 false _let_91)))) (let ((_let_93 (not _let_90))) (let ((_let_94 (tptp.sdtasdt0 _let_1 _let_4))) (let ((_let_95 (tptp.sdtasdt0 _let_4 _let_1))) (let ((_let_96 (= _let_95 _let_94))) (let ((_let_97 (tptp.sdtasdt0 _let_1 tptp.xN))) (let ((_let_98 (and _let_49 _let_51 (= (tptp.sdtasdt0 _let_95 tptp.xN) (tptp.sdtasdt0 _let_4 _let_97)) _let_96))) (let ((_let_99 (not _let_23))) (let ((_let_100 (tptp.aScalar0 _let_1))) (let ((_let_101 (not _let_100))) (let ((_let_102 (tptp.aScalar0 _let_4))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101 _let_99 _let_98))) (let ((_let_105 ((tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2)))) (let ((_let_106 (or _let_76 _let_76 _let_100))) (let ((_let_107 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (_let_107))) (let ((_let_110 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_106))) :args ((or _let_76 _let_100 (not _let_106)))) _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xS tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_109)) _let_108 :args (_let_106 false _let_107)) :args (_let_100 false _let_25 false _let_106)))) (let ((_let_112 (not _let_31))) (let ((_let_113 (or _let_112 _let_112 _let_102))) (let ((_let_114 (AND_ELIM _let_68 :args _let_83))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_113))) :args ((or _let_112 _let_102 (not _let_113)))) _let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xR tptp.xR QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_109)) _let_108 :args (_let_113 false _let_107)) :args (_let_102 false _let_31 false _let_113)))) (let ((_let_116 (AND_ELIM _let_69 :args _let_83))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_99 _let_103 _let_101 _let_98 (not _let_104)))) _let_116 _let_115 _let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_4 _let_1 tptp.xN QUANTIFIERS_INST_E_MATCHING _let_105)) :args _let_82)) _let_81 :args (_let_104 false _let_80)) :args (_let_98 false _let_23 false _let_102 false _let_100 false _let_104)))) (let ((_let_118 (not _let_98))) (let ((_let_119 (tptp.sdtasdt0 _let_13 _let_1))) (let ((_let_120 (and _let_15 _let_53 (= (tptp.sdtasdt0 _let_119 tptp.xN) (tptp.sdtasdt0 _let_13 _let_97)) (= _let_119 (tptp.sdtasdt0 _let_1 _let_13))))) (let ((_let_121 (tptp.aScalar0 _let_13))) (let ((_let_122 (not _let_121))) (let ((_let_123 (or _let_122 _let_101 _let_99 _let_120))) (let ((_let_124 (or _let_103 _let_99 _let_121))) (let ((_let_125 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (_let_125))) (let ((_let_128 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_99 _let_103 _let_121 (not _let_124)))) _let_116 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (_let_4 tptp.xN QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_128)) :args _let_127)) _let_126 :args (_let_124 false _let_125)) :args (_let_121 false _let_23 false _let_102 false _let_124)))) (let ((_let_130 (tptp.sdtasdt0 _let_8 _let_7))) (let ((_let_131 (and _let_54 (= _let_19 (tptp.sdtpldt0 _let_7 _let_8)) (= (tptp.sdtasdt0 _let_130 _let_7) (tptp.sdtasdt0 _let_8 (tptp.sdtasdt0 _let_7 _let_7))) (= _let_130 (tptp.sdtasdt0 _let_7 _let_8))))) (let ((_let_132 (tptp.aScalar0 _let_7))) (let ((_let_133 (not _let_132))) (let ((_let_134 (tptp.aScalar0 _let_8))) (let ((_let_135 (not _let_134))) (let ((_let_136 (or _let_135 _let_133 _let_133 _let_131))) (let ((_let_137 (or _let_133 _let_133 _let_134))) (let ((_let_138 (not _let_27))) (let ((_let_139 (or _let_138 _let_138 _let_132))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_139))) :args ((or _let_138 _let_132 (not _let_139)))) (AND_ELIM (ASSUME :args (_let_28)) :args _let_83) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xP tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_109)) _let_108 :args (_let_139 false _let_107)) :args (_let_132 false _let_27 false _let_139)))) (let ((_let_141 (tptp.sdtasdt0 tptp.xN _let_16))) (let ((_let_142 (tptp.sdtasdt0 _let_16 tptp.xN))) (let ((_let_143 (= _let_142 _let_141))) (let ((_let_144 (and (= _let_18 (tptp.sdtpldt0 _let_16 (tptp.sdtpldt0 tptp.xN tptp.xN))) _let_56 (= (tptp.sdtasdt0 _let_142 tptp.xN) (tptp.sdtasdt0 _let_16 (tptp.sdtasdt0 tptp.xN tptp.xN))) _let_143))) (let ((_let_145 (tptp.aScalar0 _let_16))) (let ((_let_146 (not _let_145))) (let ((_let_147 (or _let_146 _let_99 _let_99 _let_144))) (let ((_let_148 (or _let_103 _let_101 _let_145))) (let ((_let_149 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_148)) :args ((or _let_103 _let_101 _let_145 (not _let_148)))) _let_115 _let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (_let_4 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_128)) :args _let_127)) _let_126 :args (_let_148 false _let_125)) :args (_let_145 false _let_102 false _let_100 false _let_148)))) (let ((_let_150 (tptp.sdtasdt0 _let_2 _let_5))) (let ((_let_151 (tptp.sdtasdt0 _let_5 _let_2))) (let ((_let_152 (= _let_151 _let_150))) (let ((_let_153 (and _let_58 _let_60 (= (tptp.sdtasdt0 _let_151 _let_1) (tptp.sdtasdt0 _let_5 (tptp.sdtasdt0 _let_2 _let_1))) _let_152))) (let ((_let_154 (tptp.aScalar0 _let_2))) (let ((_let_155 (not _let_154))) (let ((_let_156 (tptp.aScalar0 _let_5))) (let ((_let_157 (not _let_156))) (let ((_let_158 (or _let_157 _let_155 _let_101 _let_153))) (let ((_let_159 ((tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (let ((_let_160 (or _let_76 _let_112 _let_154))) (let ((_let_161 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_160)) :args ((or _let_112 _let_76 _let_154 (not _let_160)))) _let_114 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.xS tptp.xR QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_110)) :args _let_109)) _let_108 :args (_let_160 false _let_107)) :args (_let_154 false _let_31 false _let_25 false _let_160)))) (let ((_let_162 (and _let_22 _let_121))) (let ((_let_163 (ASSUME :args (_let_121)))) (let ((_let_164 (APPLY_UF tptp.sdtpldt0))) (let ((_let_165 (ASSUME :args (_let_22)))) (let ((_let_166 (SYMM _let_165))) (let ((_let_167 (CONG (REFL :args (_let_4)) _let_166 :args _let_164))) (let ((_let_168 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_162)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_163 _let_165) (SCOPE (TRUE_ELIM (TRANS (CONG _let_167 :args (APPLY_UF tptp.aScalar0)) (TRUE_INTRO _let_163))) :args (_let_121 _let_22))) :args (_let_22 _let_121))) :args (true _let_162)) _let_70 _let_129 :args (_let_156 false _let_22 false _let_121)))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_158)) :args ((or _let_101 _let_157 _let_155 _let_153 (not _let_158)))) _let_111 _let_168 _let_161 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_5 _let_2 _let_1 QUANTIFIERS_INST_E_MATCHING _let_159)) :args _let_82))) _let_81 :args (_let_158 false _let_80)) :args (_let_153 false _let_100 false _let_156 false _let_154 false _let_158)))) (let 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_let_1 W0) tptp.sz0z00) (= (tptp.smndt0 _let_1) W0) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) _let_39 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W2))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) _let_1)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 _let_1 (tptp.sdtasdt0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W2 W3)) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W0 W3)) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W2) (tptp.sdtasdt0 W1 W3)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.smndt0 (tptp.sdtasdt0 W0 W1)))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (and (= (tptp.sdtasdt0 W0 (tptp.smndt0 W1)) _let_1) (= (tptp.sdtasdt0 (tptp.smndt0 W0) W1) _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (= (tptp.sdtasdt0 (tptp.smndt0 W0) (tptp.smndt0 W1)) (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2) (tptp.aScalar0 W3)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 tptp.sz0z00 W2) (tptp.sdtlseqdt0 W2 W3)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W2) (tptp.sdtasdt0 W1 W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1)) (and (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtpldt0 W0 W1)) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasdt0 W0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (=> (and (tptp.sdtlseqdt0 tptp.sz0z00 W0) (tptp.sdtlseqdt0 tptp.sz0z00 W1) (= (tptp.sdtasdt0 W0 W0) (tptp.sdtasdt0 W1 W1))) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.aNaturalNumber0 (tptp.aDimensionOf0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aScalar0 (tptp.sdtlbdtrb0 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (=> (not (= (tptp.aDimensionOf0 W0) tptp.sz00)) (forall ((W1 $$unsorted)) (= (= W1 (tptp.sziznziztdt0 W0)) (and (tptp.aVector0 W1) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 W1)) (tptp.aDimensionOf0 W0)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtlbdtrb0 W1 W2) (tptp.sdtlbdtrb0 W0 W2)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.aDimensionOf0 (tptp.sziznziztdt0 W0)) (tptp.aDimensionOf0 (tptp.sziznziztdt0 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= (tptp.aDimensionOf0 W0) (tptp.aDimensionOf0 W1)) (tptp.aScalar0 (tptp.sdtasasdt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= (tptp.aDimensionOf0 W0) _let_1) (= _let_1 tptp.sz00)) (= (tptp.sdtasasdt0 W0 W1) tptp.sz0z00))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.aDimensionOf0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (and (= _let_2 _let_1) (not (= _let_1 tptp.sz00))) (= (tptp.sdtasasdt0 W0 W1) (tptp.sdtpldt0 (tptp.sdtasasdt0 (tptp.sziznziztdt0 W0) (tptp.sziznziztdt0 W1)) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 W0 _let_2) (tptp.sdtlbdtrb0 W1 _let_1))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aVector0 W0) (tptp.sdtlseqdt0 tptp.sz0z00 (tptp.sdtasasdt0 W0 W0)))) (and (tptp.aVector0 tptp.xs) (tptp.aVector0 tptp.xt)) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.sdtasasdt0 W0 W1))) (let ((_let_2 (tptp.aDimensionOf0 W0))) (=> (and (tptp.aVector0 W0) (tptp.aVector0 W1)) (=> (= _let_2 (tptp.aDimensionOf0 W1)) (=> (tptp.iLess0 _let_2 (tptp.aDimensionOf0 tptp.xs)) (tptp.sdtlseqdt0 (tptp.sdtasdt0 _let_1 _let_1) (tptp.sdtasdt0 (tptp.sdtasasdt0 W0 W0) (tptp.sdtasasdt0 W1 W1))))))))) (= _let_38 _let_37) (not (= _let_38 tptp.sz00)) (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) _let_38) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xp W0) (tptp.sdtlbdtrb0 tptp.xs W0)))) (= tptp.xp (tptp.sziznziztdt0 tptp.xs))) (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) _let_37) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.sdtlbdtrb0 tptp.xq W0) (tptp.sdtlbdtrb0 tptp.xt W0)))) (= tptp.xq (tptp.sziznziztdt0 tptp.xt))) (and (tptp.aScalar0 tptp.xA) (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs _let_38))) (and (tptp.aScalar0 tptp.xB) (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_37))) _let_36 (and (tptp.aScalar0 tptp.xD) (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq))) (and (tptp.aScalar0 tptp.xE) (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq))) (and (tptp.aScalar0 tptp.xF) (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA))) _let_34 (and (tptp.aScalar0 tptp.xH) (= tptp.xH (tptp.sdtasdt0 tptp.xA tptp.xB))) _let_32 _let_28 _let_26 _let_24 (tptp.sdtlseqdt0 (tptp.sdtasdt0 tptp.xE tptp.xE) (tptp.sdtasdt0 tptp.xC tptp.xD)) (tptp.sdtlseqdt0 _let_7 tptp.xN) (tptp.sdtlseqdt0 _let_8 _let_16) _let_21 _let_15 _let_11 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.10/1.33 )
% 1.10/1.33 % SZS output end Proof for RNG068+2
% 1.10/1.33 % cvc5---1.0.5 exiting
% 1.10/1.33 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------