TSTP Solution File: RNG078+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG078+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 13:49:53 EDT 2023
% Result : Theorem 1.06s 1.26s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG078+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 01:37:35 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 1.06/1.26 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.efd4thdF6t/cvc5---1.0.5_15338.p...
% 1.06/1.26 ------- get file name : TPTP file name is RNG078+1
% 1.06/1.26 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15338.smt2...
% 1.06/1.26 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.06/1.26 % SZS status Theorem for RNG078+1
% 1.06/1.26 % SZS output start Proof for RNG078+1
% 1.06/1.26 (
% 1.06/1.26 (let ((_let_1 (tptp.sdtasdt0 tptp.xF tptp.xG))) (let ((_let_2 (tptp.sdtasdt0 tptp.xF tptp.xD))) (let ((_let_3 (tptp.sdtasdt0 tptp.xC tptp.xG))) (let ((_let_4 (tptp.sdtasdt0 tptp.xC tptp.xD))) (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.xH tptp.xH))) (let ((_let_8 (tptp.sdtasdt0 tptp.xH tptp.xE))) (let ((_let_9 (tptp.sdtpldt0 _let_8 _let_7))) (let ((_let_10 (tptp.sdtasdt0 tptp.xE tptp.xH))) (let ((_let_11 (tptp.sdtasdt0 tptp.xE tptp.xE))) (let ((_let_12 (tptp.sdtpldt0 _let_11 _let_10))) (let ((_let_13 (tptp.sdtpldt0 _let_12 _let_9))) (let ((_let_14 (tptp.sdtlseqdt0 _let_13 _let_6))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.sdtpldt0 _let_10 _let_9))) (let ((_let_17 (tptp.sdtpldt0 tptp.xP tptp.xP))) (let ((_let_18 (tptp.sdtpldt0 _let_17 _let_7))) (let ((_let_19 (= _let_18 _let_16))) (let ((_let_20 (tptp.sdtpldt0 tptp.xR tptp.xS))) (let ((_let_21 (tptp.sdtpldt0 _let_4 (tptp.sdtpldt0 _let_20 _let_7)))) (let ((_let_22 (tptp.sdtlseqdt0 (tptp.sdtpldt0 _let_11 _let_18) _let_21))) (let ((_let_23 (= tptp.xS _let_2))) (let ((_let_24 (tptp.aScalar0 tptp.xS))) (let ((_let_25 (and _let_24 _let_23))) (let ((_let_26 (= tptp.xP _let_10))) (let ((_let_27 (tptp.aScalar0 tptp.xP))) (let ((_let_28 (and _let_27 _let_26))) (let ((_let_29 (= tptp.xR _let_3))) (let ((_let_30 (tptp.aScalar0 tptp.xR))) (let ((_let_31 (and _let_30 _let_29))) (let ((_let_32 (tptp.sdtasdt0 tptp.xA tptp.xB))) (let ((_let_33 (= tptp.xH _let_32))) (let ((_let_34 (tptp.aScalar0 tptp.xH))) (let ((_let_35 (and _let_34 _let_33))) (let ((_let_36 (tptp.sdtasdt0 tptp.xB tptp.xB))) (let ((_let_37 (= tptp.xG _let_36))) (let ((_let_38 (tptp.aScalar0 tptp.xG))) (let ((_let_39 (and _let_38 _let_37))) (let ((_let_40 (tptp.sdtasdt0 tptp.xA tptp.xA))) (let ((_let_41 (= tptp.xF _let_40))) (let ((_let_42 (tptp.aScalar0 tptp.xF))) (let ((_let_43 (and _let_42 _let_41))) (let ((_let_44 (tptp.aScalar0 tptp.xE))) (let ((_let_45 (and _let_44 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq))))) (let ((_let_46 (tptp.aScalar0 tptp.xD))) (let ((_let_47 (and _let_46 (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq))))) (let ((_let_48 (tptp.aScalar0 tptp.xC))) (let ((_let_49 (and _let_48 (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp))))) (let ((_let_50 (tptp.aDimensionOf0 tptp.xt))) (let ((_let_51 (tptp.aScalar0 tptp.xB))) (let ((_let_52 (and _let_51 (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt _let_50))))) (let ((_let_53 (tptp.aDimensionOf0 tptp.xs))) (let ((_let_54 (tptp.aScalar0 tptp.xA))) (let ((_let_55 (and _let_54 (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs _let_53))))) (let ((_let_56 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtasdt0 W0 W1))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1) (tptp.aScalar0 W2)) (and (= (tptp.sdtpldt0 _let_2 W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))) (= _let_2 (tptp.sdtpldt0 W1 W0)) (= (tptp.sdtasdt0 _let_1 W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))) (= _let_1 (tptp.sdtasdt0 W1 W0))))))))) (let ((_let_57 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_58 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aScalar0 W0) (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_59 (tptp.sdtasdt0 tptp.xB tptp.xA))) (let ((_let_60 (= _let_32 _let_59))) (let ((_let_61 (tptp.sdtasdt0 tptp.xA tptp.xH))) (let ((_let_62 (tptp.sdtasdt0 tptp.xH tptp.xA))) (let ((_let_63 (= _let_62 _let_61))) (let ((_let_64 (tptp.sdtasdt0 tptp.xF tptp.xB))) (let ((_let_65 (= (tptp.sdtasdt0 _let_64 tptp.xB) (tptp.sdtasdt0 tptp.xF _let_36)))) (let ((_let_66 (tptp.sdtasdt0 tptp.xB tptp.xF))) (let ((_let_67 (= _let_64 _let_66))) (let ((_let_68 (tptp.sdtpldt0 _let_4 _let_20))) (let ((_let_69 (= _let_21 (tptp.sdtpldt0 _let_68 _let_7)))) (let ((_let_70 (= _let_68 (tptp.sdtpldt0 _let_20 _let_4)))) (let ((_let_71 (tptp.sdtpldt0 _let_5 _let_2))) (let ((_let_72 (= _let_6 (tptp.sdtpldt0 _let_71 _let_1)))) (let ((_let_73 (= _let_71 (tptp.sdtpldt0 _let_2 _let_5)))) (let ((_let_74 (= _let_13 (tptp.sdtpldt0 _let_11 _let_16)))) (let ((_let_75 (= _let_71 (tptp.sdtpldt0 _let_4 (tptp.sdtpldt0 _let_3 _let_2))))) (let ((_let_76 (= (tptp.sdtasdt0 _let_59 tptp.xH) (tptp.sdtasdt0 tptp.xB _let_61)))) (let ((_let_77 (= (tptp.sdtasdt0 _let_66 tptp.xB) (tptp.sdtasdt0 tptp.xB _let_64)))) (let ((_let_78 (= (tptp.sdtasdt0 _let_59 tptp.xA) (tptp.sdtasdt0 tptp.xB _let_40)))) (let ((_let_79 (1))) (let ((_let_80 (ASSUME :args (_let_43)))) (let ((_let_81 (ASSUME :args (_let_39)))) (let ((_let_82 (ASSUME :args (_let_35)))) (let ((_let_83 (_let_31))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 (AND_ELIM _let_84 :args _let_79))) (let ((_let_86 (_let_25))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (AND_ELIM _let_87 :args _let_79))) (let ((_let_89 (ASSUME :args (_let_22)))) (let ((_let_90 (ASSUME :args (_let_19)))) (let ((_let_91 (ASSUME :args (_let_15)))) (let ((_let_92 (tptp.sdtpldt0 tptp.xB tptp.xA))) (let ((_let_93 (tptp.sdtpldt0 tptp.xA tptp.xB))) (let ((_let_94 (= _let_93 _let_92))) (let ((_let_95 (and (= (tptp.sdtpldt0 _let_93 tptp.xH) (tptp.sdtpldt0 tptp.xA (tptp.sdtpldt0 tptp.xB tptp.xH))) _let_94 (= (tptp.sdtasdt0 _let_32 tptp.xH) (tptp.sdtasdt0 tptp.xA (tptp.sdtasdt0 tptp.xB tptp.xH))) _let_60))) (let ((_let_96 (not _let_34))) (let ((_let_97 (not _let_51))) (let ((_let_98 (not _let_54))) (let ((_let_99 (or _let_98 _let_97 _let_96 _let_95))) (let ((_let_100 (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_101 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (_let_100))) (let ((_let_103 ((tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2)))) (let ((_let_104 (0))) (let ((_let_105 (AND_ELIM _let_82 :args _let_104))) (let ((_let_106 (AND_ELIM (ASSUME :args (_let_52)) :args _let_104))) (let ((_let_107 (AND_ELIM (ASSUME :args (_let_55)) :args _let_104))) (let ((_let_108 (tptp.sdtpldt0 tptp.xA tptp.xH))) (let ((_let_109 (tptp.sdtpldt0 tptp.xH tptp.xA))) (let ((_let_110 (and (= (tptp.sdtpldt0 _let_109 tptp.xB) (tptp.sdtpldt0 tptp.xH _let_93)) (= _let_109 _let_108) (= (tptp.sdtasdt0 _let_62 tptp.xB) (tptp.sdtasdt0 tptp.xH _let_32)) _let_63))) (let ((_let_111 (or _let_96 _let_98 _let_97 _let_110))) (let ((_let_112 ((tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (let ((_let_113 (tptp.sdtpldt0 tptp.xB tptp.xF))) (let ((_let_114 (tptp.sdtpldt0 tptp.xF tptp.xB))) (let ((_let_115 (= _let_114 _let_113))) (let ((_let_116 (and (= (tptp.sdtpldt0 _let_114 tptp.xB) (tptp.sdtpldt0 tptp.xF (tptp.sdtpldt0 tptp.xB tptp.xB))) _let_115 _let_65 _let_67))) (let ((_let_117 (not _let_42))) (let ((_let_118 (or _let_117 _let_97 _let_97 _let_116))) (let ((_let_119 (AND_ELIM _let_80 :args _let_104))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_118))) :args ((or _let_97 _let_117 _let_116 (not _let_118)))) _let_106 _let_119 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (tptp.xF tptp.xB tptp.xB QUANTIFIERS_INST_E_MATCHING _let_112)) :args _let_102)) _let_101 :args (_let_118 false _let_100)) :args (_let_116 false _let_51 false _let_42 false _let_118)))) (let ((_let_121 (not _let_116))) (let ((_let_122 (tptp.sdtasdt0 _let_4 _let_20))) (let ((_let_123 (and _let_69 _let_70 (= (tptp.sdtasdt0 _let_122 _let_7) (tptp.sdtasdt0 _let_4 (tptp.sdtasdt0 _let_20 _let_7))) (= _let_122 (tptp.sdtasdt0 _let_20 _let_4))))) (let ((_let_124 (tptp.aScalar0 _let_7))) (let ((_let_125 (not _let_124))) (let ((_let_126 (tptp.aScalar0 _let_20))) (let ((_let_127 (not _let_126))) (let ((_let_128 (tptp.aScalar0 _let_4))) (let ((_let_129 (not _let_128))) (let ((_let_130 (or _let_129 _let_127 _let_125 _let_123))) (let ((_let_131 ((tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (let ((_let_132 (not _let_24))) (let ((_let_133 (not _let_30))) (let ((_let_134 (or _let_133 _let_132 _let_126))) (let ((_let_135 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtpldt0 W0 W1)))))) (let ((_let_136 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (_let_135))) (let ((_let_138 ((tptp.sdtpldt0 W0 W1)))) (let ((_let_139 (AND_ELIM _let_87 :args _let_104))) (let ((_let_140 (AND_ELIM _let_84 :args _let_104))) (let ((_let_141 (or _let_96 _let_96 _let_124))) (let ((_let_142 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aScalar0 W0)) (not (tptp.aScalar0 W1)) (tptp.aScalar0 (tptp.sdtasdt0 W0 W1)))))) (let ((_let_143 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_144 (_let_142))) (let ((_let_145 ((tptp.sdtasdt0 W0 W1)))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_141))) :args ((or _let_96 _let_124 (not _let_141)))) _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (tptp.xH tptp.xH QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_145)) :args _let_144)) _let_143 :args (_let_141 false _let_142)) :args (_let_124 false _let_34 false _let_141)))) (let ((_let_147 (not _let_46))) (let ((_let_148 (not _let_48))) (let ((_let_149 (or _let_148 _let_147 _let_128))) (let ((_let_150 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_148 _let_147 _let_128 (not _let_149)))) (AND_ELIM (ASSUME :args (_let_49)) :args _let_104) (AND_ELIM (ASSUME :args (_let_47)) :args _let_104) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (tptp.xC tptp.xD QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_145)) :args _let_144)) _let_143 :args (_let_149 false _let_142)) :args (_let_128 false _let_48 false _let_46 false _let_149)))) (let ((_let_151 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_129 _let_125 _let_127 _let_123 (not _let_130)))) _let_150 _let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_133 _let_132 _let_126 (not _let_134)))) _let_140 _let_139 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (tptp.xR tptp.xS QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_138)) :args _let_137)) _let_136 :args (_let_134 false _let_135)) :args (_let_126 false _let_30 false _let_24 false _let_134)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_4 _let_20 _let_7 QUANTIFIERS_INST_E_MATCHING _let_131)) :args _let_102))) _let_101 :args (_let_130 false _let_100)) :args (_let_123 false _let_128 false _let_124 false _let_126 false _let_130)))) (let ((_let_152 (not _let_123))) (let ((_let_153 (tptp.sdtasdt0 _let_5 _let_2))) (let ((_let_154 (and _let_72 _let_73 (= (tptp.sdtasdt0 _let_153 _let_1) (tptp.sdtasdt0 _let_5 (tptp.sdtasdt0 _let_2 _let_1))) (= _let_153 (tptp.sdtasdt0 _let_2 _let_5))))) (let ((_let_155 (tptp.aScalar0 _let_1))) (let ((_let_156 (not _let_155))) (let ((_let_157 (tptp.aScalar0 _let_2))) (let ((_let_158 (not _let_157))) (let ((_let_159 (tptp.aScalar0 _let_5))) (let ((_let_160 (not _let_159))) (let ((_let_161 (or _let_160 _let_158 _let_156 _let_154))) (let ((_let_162 (tptp.aScalar0 _let_3))) (let ((_let_163 (not _let_162))) (let ((_let_164 (or _let_129 _let_163 _let_159))) (let ((_let_165 (_let_30 _let_29))) (let ((_let_166 (ASSUME :args (_let_30)))) (let ((_let_167 (APPLY_UF tptp.aScalar0))) (let ((_let_168 (ASSUME :args (_let_29)))) (let ((_let_169 (SYMM (SYMM _let_168)))) (let ((_let_170 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args _let_83) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_166 _let_168) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_169) :args _let_167) (TRUE_INTRO _let_166))) :args _let_165)) :args _let_165)) :args (true _let_31)) _let_140 _let_85 :args (_let_162 false _let_30 false _let_29)))) (let ((_let_171 (not _let_38))) (let ((_let_172 (or _let_117 _let_171 _let_155))) (let ((_let_173 (_let_24 _let_23))) (let ((_let_174 (ASSUME :args (_let_24)))) (let ((_let_175 (ASSUME :args (_let_23)))) (let ((_let_176 (SYMM (SYMM _let_175)))) (let ((_let_177 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args _let_86) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_174 _let_175) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_176) :args _let_167) (TRUE_INTRO _let_174))) :args _let_173)) :args _let_173)) :args (true _let_25)) _let_139 _let_88 :args (_let_157 false _let_24 false _let_23)))) (let ((_let_178 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_161)) :args ((or _let_158 _let_156 _let_160 _let_154 (not _let_161)))) _let_177 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_172)) :args ((or _let_117 _let_171 _let_155 (not _let_172)))) _let_119 (AND_ELIM _let_81 :args _let_104) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (tptp.xF tptp.xG QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_145)) :args _let_144)) _let_143 :args (_let_172 false _let_142)) :args (_let_155 false _let_42 false _let_38 false _let_172)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_164)) :args ((or _let_129 _let_163 _let_159 (not _let_164)))) _let_150 _let_170 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (_let_4 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_138)) :args _let_137)) _let_136 :args (_let_164 false _let_135)) :args (_let_159 false _let_128 false _let_162 false _let_164)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 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W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) true)) (tptp.aScalar0 tptp.sz0z00) _let_58 _let_57 (forall ((W0 $$unsorted)) (=> (tptp.aScalar0 W0) (tptp.aScalar0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aScalar0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz0z00) W0) (= (tptp.sdtpldt0 tptp.sz0z00 W0) W0) (= (tptp.sdtasdt0 W0 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 W0) tptp.sz0z00) (= (tptp.sdtpldt0 W0 _let_1) tptp.sz0z00) (= (tptp.sdtpldt0 _let_1 W0) tptp.sz0z00) (= (tptp.smndt0 _let_1) W0) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) _let_56 (forall ((W0 $$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_53 _let_50) (not (= _let_53 tptp.sz00)) (and (tptp.aVector0 tptp.xp) (= tptp.xp (tptp.sziznziztdt0 tptp.xs))) (and (tptp.aVector0 tptp.xq) (= tptp.xq (tptp.sziznziztdt0 tptp.xt))) _let_55 _let_52 _let_49 _let_47 _let_45 _let_43 _let_39 _let_35 _let_31 _let_28 _let_25 (and (tptp.aScalar0 tptp.xN) (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS))) (tptp.sdtlseqdt0 _let_11 _let_4) (tptp.sdtlseqdt0 _let_17 _let_20) _let_22 _let_19 _let_15 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.06/1.27 )
% 1.06/1.27 % SZS output end Proof for RNG078+1
% 1.06/1.27 % cvc5---1.0.5 exiting
% 1.06/1.27 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------