TSTP Solution File: SWV153+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 21:49:30 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV153+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 05:36:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.66 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.P2d0iUqdPL/cvc5---1.0.5_28532.p...
% 0.21/0.66 ------- get file name : TPTP file name is SWV153+1
% 0.21/0.66 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28532.smt2...
% 0.21/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.66 % SZS status Theorem for SWV153+1
% 0.21/0.66 % SZS output start Proof for SWV153+1
% 0.21/0.66 (
% 0.21/0.66 (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 (= _let_7 tptp.n4))) (let ((_let_9 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n3)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3)))))) (let ((_let_10 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))))) (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))))) (let ((_let_14 (tptp.gt tptp.n4 tptp.n3))) (let ((_let_15 (tptp.gt tptp.n3 tptp.n2))) (let ((_let_16 (tptp.gt tptp.n3 tptp.n1))) (let ((_let_17 (tptp.gt tptp.n2 tptp.n1))) (let ((_let_18 (tptp.gt tptp.n3 tptp.n0))) (let ((_let_19 (tptp.gt tptp.n2 tptp.n0))) (let ((_let_20 (tptp.gt tptp.n1 tptp.n0))) (let ((_let_21 (tptp.leq tptp.pv12 tptp.n4))) (let ((_let_22 (tptp.leq tptp.n0 tptp.pv12))) (let ((_let_23 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_24 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_23))) (let ((_let_25 (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_24 _let_24))))) (let ((_let_26 (not (=> (and (= tptp.pv70 _let_25) (tptp.leq tptp.n0 tptp.pv10) _let_22 (tptp.leq tptp.pv10 tptp.n135299) _let_21 (forall ((A $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) _let_1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2)))))))))) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B (tptp.pred tptp.pv10))) (= (tptp.sum tptp.n0 tptp.n4 (tptp.a_select3 tptp.q B tptp.tptp_sum_index)) tptp.n1)))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) _let_1))) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.pv12)) (=> (not (= tptp.pv12 C)) (= (tptp.a_select3 tptp.q tptp.pv10 C) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2))))))))))))))) (let ((_let_27 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_28 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_29 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_30 (= tptp.n2 _let_2))) (let ((_let_31 (= _let_1 (tptp.pred _let_2)))) (let ((_let_32 (tptp.leq tptp.n1 (tptp.pred tptp.n2)))) (let ((_let_33 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.pred tptp.pv12)))) (let ((_let_34 (= tptp.n2 tptp.pv12))) (let ((_let_35 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (SYMM (ASSUME :args (_let_5))))) (let ((_let_37 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((tptp.succ X)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_31 false _let_37)))) (let ((_let_42 (= _let_17 _let_32))) (let ((_let_43 (_let_28))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 ((tptp.gt Y X)))) (let ((_let_46 (ASSUME :args (_let_17)))) (let ((_let_47 (not _let_17))) (let ((_let_48 (tptp.minus (tptp.a_select3 tptp.center SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0) _let_23))) (let ((_let_49 (= (tptp.a_select3 tptp.q tptp.pv10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.divide (tptp.sqrt (tptp.times _let_48 _let_48)) _let_25)))) (let ((_let_50 (not _let_33))) (let ((_let_51 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50 _let_49))) (let ((_let_54 (forall ((A $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center A tptp.n0) _let_1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A (tptp.pred tptp.pv12))) (= (tptp.a_select3 tptp.q tptp.pv10 A) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (NOT_IMPLIES_ELIM1 _let_55))) (let ((_let_57 (_let_54))) (let ((_let_58 (= tptp.pv12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_59 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.pv12))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_52 _let_60 _let_58 _let_49))) (let ((_let_62 (forall ((C $$unsorted)) (let ((_let_1 (tptp.a_select2 tptp.x tptp.pv10))) (let ((_let_2 (tptp.minus (tptp.a_select3 tptp.center tptp.tptp_sum_index tptp.n0) _let_1))) (let ((_let_3 (tptp.minus (tptp.a_select3 tptp.center C tptp.n0) _let_1))) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq C tptp.pv12)) (= tptp.pv12 C) (= (tptp.a_select3 tptp.q tptp.pv10 C) (tptp.divide (tptp.sqrt (tptp.times _let_3 _let_3)) (tptp.sum tptp.n0 tptp.n4 (tptp.sqrt (tptp.times _let_2 _let_2)))))))))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (or))) (let ((_let_65 (not _let_62))) (let ((_let_66 (_let_65))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_62))) (REFL :args (_let_63)) :args _let_64)) (NOT_IMPLIES_ELIM2 _let_55) :args (_let_63 true _let_62)))) (let ((_let_68 (REFL :args (_let_61)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_64)) :args ((or _let_51 _let_61))) _let_67 :args (_let_51 true _let_61)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_49 _let_50 (not _let_53)))) _let_69 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 3)) _let_67 :args ((not _let_49) true _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 A) false))))) :args _let_57)) (AND_ELIM _let_56 :args (5)) :args (_let_53 false _let_54)) :args (_let_50 false _let_51 true _let_49 false _let_53)))) (let ((_let_71 (= tptp.n4 tptp.pv12))) (let ((_let_72 (= tptp.n3 tptp.pv12))) (let ((_let_73 (= tptp.n1 tptp.pv12))) (let ((_let_74 (= tptp.n0 tptp.pv12))) (let ((_let_75 (not _let_21))) (let ((_let_76 (not _let_22))) (let ((_let_77 (or _let_76 _let_75 _let_74 _let_73 _let_34 _let_72 _let_71))) (let ((_let_78 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n4)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X) (= tptp.n3 X) (= tptp.n4 X))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((not (= (tptp.leq tptp.n0 X) false))))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.pv12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_80)) _let_79 :args (_let_77 false _let_78)))) (let ((_let_83 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n3))) (let ((_let_84 (= tptp.n3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_85 (= tptp.n3 _let_3))) (let ((_let_86 (= _let_2 (tptp.pred _let_3)))) (let ((_let_87 (tptp.leq tptp.n1 tptp.n2))) (let ((_let_88 (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_89 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_90 (not _let_83))) (let ((_let_91 (or _let_52 _let_90 _let_89 _let_35 _let_88 _let_84))) (let ((_let_92 (tptp.leq tptp.n2 (tptp.pred tptp.n3)))) (let ((_let_93 (not _let_72))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_64)) :args ((or _let_59 _let_61))) _let_67 :args (_let_59 true _let_61)))) (let ((_let_95 (REFL :args (_let_93)))) (let ((_let_96 (REFL :args (_let_60)))) (let ((_let_97 (ASSUME :args (_let_90)))) (let ((_let_98 (APPLY_UF tptp.leq))) (let ((_let_99 (ASSUME :args (_let_72)))) (let ((_let_100 (SYMM _let_99))) (let ((_let_101 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_102 (ASSUME :args (_let_59)))) (let ((_let_103 (SYMM (TRUE_INTRO _let_102)))) (let ((_let_104 (not _let_58))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 2)) _let_67 :args (_let_104 true _let_61)))) (let ((_let_106 (not _let_84))) (let ((_let_107 (REFL :args (_let_106)))) (let ((_let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_58))))) (let ((_let_109 (and _let_104 _let_72))) (let ((_let_110 (_let_104 _let_72))) (let ((_let_111 (ASSUME :args (_let_104)))) (let ((_let_112 (FALSE_INTRO _let_111))) (let ((_let_113 (=))) (let ((_let_114 (SYMM (ASSUME :args (_let_4))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_86 false _let_37)))) (let ((_let_116 (or _let_47 _let_87))) (let ((_let_117 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (_let_117))) (let ((_let_120 ((not (= (tptp.gt Y X) false))))) (let ((_let_121 (not _let_35))) (let ((_let_122 (not _let_86))) (let ((_let_123 (not _let_87))) (let ((_let_124 (not _let_85))) (let ((_let_125 (not _let_30))) (let ((_let_126 (REFL :args (_let_121)))) (let ((_let_127 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_33))))) (let ((_let_128 (REFL :args (_let_122)))) (let ((_let_129 (REFL :args (_let_124)))) (let ((_let_130 (REFL :args (_let_125)))) (let ((_let_131 (ASSUME :args (_let_87)))) (let ((_let_132 (SYMM _let_36))) (let ((_let_133 (ASSUME :args (_let_86)))) (let ((_let_134 (SYMM _let_133))) (let ((_let_135 (APPLY_UF tptp.pred))) (let ((_let_136 (SYMM _let_114))) (let ((_let_137 (SYMM _let_136))) (let ((_let_138 (CONG _let_100 :args _let_135))) (let ((_let_139 (TRANS _let_138 (CONG _let_137 :args _let_135) _let_134 _let_132))) (let ((_let_140 (ASSUME :args (_let_35)))) (let ((_let_141 (SYMM _let_140))) (let ((_let_142 (ASSUME :args (_let_50)))) (let ((_let_143 (FALSE_INTRO _let_142))) (let ((_let_144 (SYMM _let_143))) (let ((_let_145 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n3)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X) (= tptp.n3 X))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (= tptp.n1 _let_1))) (let ((_let_148 (tptp.leq tptp.n0 tptp.n1))) (let ((_let_149 (tptp.leq tptp.n0 tptp.n2))) (let ((_let_150 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_151 (tptp.leq tptp.n0 (tptp.pred tptp.n1)))) (let ((_let_152 (= tptp.n4 _let_7))) (let ((_let_153 (= _let_3 (tptp.pred _let_7)))) (let ((_let_154 (tptp.leq tptp.n0 tptp.n3))) (let ((_let_155 (not _let_89))) (let ((_let_156 (SYMM (ASSUME :args (_let_6))))) (let ((_let_157 (not _let_20))) (let ((_let_158 (or _let_157 _let_148))) (let ((_let_159 (ASSUME :args (_let_20)))) (let ((_let_160 (not _let_34))) (let ((_let_161 (not _let_31))) (let ((_let_162 (not _let_148))) (let ((_let_163 (not _let_147))) (let ((_let_164 (REFL :args (_let_160)))) (let ((_let_165 (REFL :args (_let_161)))) (let ((_let_166 (REFL :args (_let_155)))) (let ((_let_167 (REFL :args (_let_163)))) (let ((_let_168 (ASSUME :args (_let_148)))) (let ((_let_169 (SYMM _let_156))) (let ((_let_170 (ASSUME :args (_let_31)))) (let ((_let_171 (SYMM _let_170))) (let ((_let_172 (SYMM _let_132))) (let ((_let_173 (ASSUME :args (_let_34)))) (let ((_let_174 (SYMM _let_173))) (let ((_let_175 (CONG _let_174 :args _let_135))) (let ((_let_176 (ASSUME :args (_let_89)))) (let ((_let_177 (SYMM _let_176))) (let ((_let_178 (not _let_19))) (let ((_let_179 (or _let_178 _let_149))) (let ((_let_180 (not _let_149))) (let ((_let_181 (ASSUME :args (_let_149)))) (let ((_let_182 (= _let_20 _let_151))) (let ((_let_183 (not _let_73))) (let ((_let_184 (not _let_150))) (let ((_let_185 (not _let_151))) (let ((_let_186 (REFL :args (_let_183)))) (let ((_let_187 (ASSUME :args (_let_151)))) (let ((_let_188 (CONG _let_169 :args _let_135))) (let ((_let_189 (ASSUME :args (_let_150)))) (let ((_let_190 (SYMM _let_189))) (let ((_let_191 (ASSUME :args (_let_73)))) (let ((_let_192 (SYMM _let_191))) (let ((_let_193 (AND_ELIM _let_56 :args (2)))) (let ((_let_194 (AND_ELIM _let_56 :args (4)))) (let ((_let_195 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0))) (let ((_let_196 (not _let_195))) (let ((_let_197 (or _let_52 _let_196 _let_89))) (let ((_let_198 (not _let_74))) (let ((_let_199 (REFL :args (_let_198)))) (let ((_let_200 (ASSUME :args (_let_196)))) (let ((_let_201 (ASSUME :args (_let_74)))) (let ((_let_202 (SYMM _let_201))) (let ((_let_203 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_204 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_205 (and _let_104 _let_74))) (let ((_let_206 (_let_104 _let_74))) (let ((_let_207 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_205)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_111 _let_201) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_202) _let_101 :args _let_113) _let_112)) :args _let_206)) :args _let_206)) :args (true _let_205)) (CONG _let_108 _let_199 _let_166 :args _let_64)) _let_105 (REORDERING (CNF_OR_POS :args (_let_197)) :args ((or _let_52 _let_89 _let_196 (not _let_197)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_204 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args 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(tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$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))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))) (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))) (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 $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_27 (forall ((X $$unsorted)) (= (tptp.succ (tptp.pred X)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq (tptp.succ X) (tptp.succ Y)) (tptp.leq X Y))) (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))) (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq tptp.n0 J0) (tptp.leq I0 U) (tptp.leq J0 V)) (= (tptp.a_select3 X I0 J0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U) (tptp.leq tptp.n0 J) (tptp.leq J V)) (= (tptp.a_select3 (tptp.tptp_update3 X U V VAL) I J) VAL))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))) (forall ((I $$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_26 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n135299 tptp.n4) (tptp.gt tptp.n135299 tptp.n5) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n135299 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.n135299 tptp.n0) _let_20 _let_19 _let_18 (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n135299 tptp.n1) _let_17 _let_16 (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n135299 tptp.n2) _let_15 _let_14 (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n135299 tptp.n3) _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_12 _let_11 _let_10 _let_9 _let_8 (= (tptp.succ _let_7) tptp.n5) _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.66 )
% 0.21/0.66 % SZS output end Proof for SWV153+1
% 0.21/0.66 % cvc5---1.0.5 exiting
% 0.21/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------