TSTP Solution File: SWV167+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV167+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 21:49:33 EDT 2023
% Result : Theorem 0.23s 0.69s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWV167+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.16/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Aug 29 07:17:07 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.69 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.E7zATrEhrx/cvc5---1.0.5_26972.p...
% 0.23/0.69 ------- get file name : TPTP file name is SWV167+1
% 0.23/0.69 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26972.smt2...
% 0.23/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.69 % SZS status Theorem for SWV167+1
% 0.23/0.69 % SZS output start Proof for SWV167+1
% 0.23/0.69 (
% 0.23/0.69 (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 $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))))) (let ((_let_14 (tptp.gt tptp.n4 tptp.n3))) (let ((_let_15 (tptp.gt tptp.n3 tptp.n2))) (let ((_let_16 (tptp.gt tptp.n3 tptp.n1))) (let ((_let_17 (tptp.gt tptp.n2 tptp.n1))) (let ((_let_18 (tptp.gt tptp.n3 tptp.n0))) (let ((_let_19 (tptp.gt tptp.n2 tptp.n0))) (let ((_let_20 (tptp.gt tptp.n1 tptp.n0))) (let ((_let_21 (tptp.gt tptp.loopcounter tptp.n1))) (let ((_let_22 (tptp.leq tptp.pv40 tptp.n4))) (let ((_let_23 (tptp.leq tptp.n0 tptp.pv40))) (let ((_let_24 (tptp.a_select2 tptp.mu_init tptp.pv40))) (let ((_let_25 (not (=> (and (= _let_24 tptp.init) (= (tptp.a_select2 tptp.sigma_init tptp.pv40) tptp.init) _let_23 _let_22 (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n135299)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n4)) (= (tptp.a_select3 tptp.q_init A B) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C tptp.n4)) (= (tptp.a_select2 tptp.rho_init C) tptp.init))) (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D (tptp.pred tptp.pv40))) (= (tptp.a_select2 tptp.mu_init D) tptp.init))) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E (tptp.pred tptp.pv40))) (= (tptp.a_select2 tptp.sigma_init E) tptp.init))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select3 tptp.center_init F tptp.n0) tptp.init))) (=> _let_21 (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.muold_init G) tptp.init)))) (=> _let_21 (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init H) tptp.init)))) (=> _let_21 (forall ((I $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init I) tptp.init))))) (forall ((J $$unsorted)) (=> (and (tptp.leq tptp.n0 J) (tptp.leq J tptp.pv40)) (= (tptp.a_select2 tptp.mu_init J) tptp.init))))))) (let ((_let_26 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_28 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_29 (= tptp.n4 _let_7))) (let ((_let_30 (= tptp.n3 _let_3))) (let ((_let_31 (= _let_3 (tptp.pred _let_7)))) (let ((_let_32 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.pred tptp.pv40)))) (let ((_let_33 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n3))) (let ((_let_34 (= tptp.n4 tptp.pv40))) (let ((_let_35 (SYMM (ASSUME :args (_let_8))))) (let ((_let_36 (SYMM (ASSUME :args (_let_4))))) (let ((_let_37 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((tptp.succ X)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_31 false _let_37)))) (let ((_let_42 (= tptp.init (tptp.a_select2 tptp.mu_init SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_43 (not _let_32))) (let ((_let_44 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 _let_42))) (let ((_let_47 (forall ((D $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D (tptp.pred tptp.pv40))) (= tptp.init (tptp.a_select2 tptp.mu_init D)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (NOT_IMPLIES_ELIM1 _let_48))) (let ((_let_50 (_let_47))) (let ((_let_51 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.pv40))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_45 _let_52 _let_42))) (let ((_let_54 (forall ((J $$unsorted)) (or (not (tptp.leq tptp.n0 J)) (not (tptp.leq J tptp.pv40)) (= tptp.init (tptp.a_select2 tptp.mu_init J)))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (or))) (let ((_let_57 (not _let_54))) (let ((_let_58 (_let_57))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_54))) (REFL :args (_let_55)) :args _let_56)) (NOT_IMPLIES_ELIM2 _let_48) :args (_let_55 true _let_54)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 2)) _let_59 :args ((not _let_42) true _let_53)))) (let ((_let_61 (REFL :args (_let_53)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_56)) :args ((or _let_44 _let_53))) _let_59 :args (_let_44 true _let_53)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_42 _let_43 (not _let_46)))) _let_62 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 D) false))))) :args _let_50)) (AND_ELIM _let_49 :args (6)) :args (_let_46 false _let_47)) :args (_let_43 false _let_44 true _let_42 false _let_46)))) (let ((_let_64 (= tptp.n3 tptp.pv40))) (let ((_let_65 (tptp.leq tptp.n0 tptp.n3))) (let ((_let_66 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_67 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_45 _let_68 _let_66))) (let ((_let_70 (= tptp.n0 tptp.pv40))) (let ((_let_71 (tptp.leq tptp.n1 tptp.n3))) (let ((_let_72 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_73 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n1))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_45 _let_74 _let_66 _let_72))) (let ((_let_76 (= tptp.n1 tptp.pv40))) (let ((_let_77 (tptp.leq tptp.n2 tptp.n3))) (let ((_let_78 (= tptp.n2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_79 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n2))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_45 _let_80 _let_66 _let_72 _let_78))) (let ((_let_82 (= tptp.n2 tptp.pv40))) (let ((_let_83 (not _let_22))) (let ((_let_84 (not _let_23))) (let ((_let_85 (or _let_84 _let_83 _let_70 _let_76 _let_82 _let_64 _let_34))) (let ((_let_86 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n4))) (let ((_let_87 (tptp.leq tptp.n3 (tptp.pred tptp.n4)))) (let ((_let_88 (= tptp.n3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_89 (= tptp.n4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_90 (not _let_86))) (let ((_let_91 (or _let_45 _let_90 _let_66 _let_72 _let_78 _let_88 _let_89))) (let ((_let_92 (= tptp.init _let_24))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_56)) :args ((or _let_51 _let_53))) _let_59 :args (_let_51 true _let_53)))) (let ((_let_94 (not _let_64))) (let ((_let_95 (not _let_33))) (let ((_let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_33))))) (let ((_let_97 (REFL :args (_let_94)))) (let ((_let_98 (REFL :args (_let_52)))) (let ((_let_99 (_let_95))) (let ((_let_100 (ASSUME :args _let_99))) (let ((_let_101 (FALSE_INTRO _let_100))) (let ((_let_102 (APPLY_UF tptp.leq))) (let ((_let_103 (ASSUME :args (_let_64)))) (let ((_let_104 (SYMM _let_103))) (let ((_let_105 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_106 (ASSUME :args (_let_51)))) (let ((_let_107 (SYMM (TRUE_INTRO _let_106)))) (let ((_let_108 (not _let_18))) (let ((_let_109 (or _let_108 _let_65))) (let ((_let_110 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (_let_110))) (let ((_let_113 ((not (= (tptp.gt Y X) false))))) (let ((_let_114 (not _let_66))) (let ((_let_115 (not _let_65))) (let ((_let_116 (not _let_30))) (let ((_let_117 (REFL :args (_let_114)))) (let ((_let_118 (REFL :args (_let_116)))) (let ((_let_119 (ASSUME :args (_let_65)))) (let ((_let_120 (SYMM _let_36))) (let ((_let_121 (REFL :args (tptp.n0)))) (let ((_let_122 (ASSUME :args (_let_66)))) (let ((_let_123 (SYMM _let_122))) (let ((_let_124 (SYMM _let_101))) (let ((_let_125 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_125))) _let_126 :args (_let_69 false _let_125)))) (let ((_let_128 (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_45 _let_66 _let_68 (not _let_69)))))) (let ((_let_129 (not _let_70))) (let ((_let_130 (ASSUME :args (_let_68)))) (let ((_let_131 (ASSUME :args (_let_70)))) (let ((_let_132 (SYMM _let_131))) (let ((_let_133 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_130 _let_131 _let_106) :args (_let_51 _let_70 _let_68)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_107 (CONG _let_105 _let_132 :args _let_102) (FALSE_INTRO _let_130))) :args (_let_68 _let_70 _let_51)) :args ((not (and _let_51 _let_70 _let_68)) SB_LITERAL))) (CONG _let_98 (REFL :args (_let_129)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_56)) :args ((or _let_52 _let_67 _let_129))))) (let ((_let_134 (not _let_16))) (let ((_let_135 (or _let_134 _let_71))) (let ((_let_136 (not _let_72))) (let ((_let_137 (not _let_71))) (let ((_let_138 (REFL :args (_let_136)))) (let ((_let_139 (ASSUME :args (_let_71)))) (let ((_let_140 (REFL :args (tptp.n1)))) (let ((_let_141 (ASSUME :args (_let_72)))) (let ((_let_142 (SYMM _let_141))) (let ((_let_143 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n1)) (= tptp.n0 X) (= tptp.n1 X))))) (let ((_let_144 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_144 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_143))) _let_144 :args (_let_75 false _let_143)))) (let ((_let_146 (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_45 _let_66 _let_72 _let_74 (not _let_75)))))) (let ((_let_147 (not _let_76))) (let ((_let_148 (REFL :args (_let_147)))) (let ((_let_149 (ASSUME :args (_let_74)))) (let ((_let_150 (ASSUME :args (_let_76)))) (let ((_let_151 (SYMM _let_150))) (let ((_let_152 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_149 _let_150 _let_106) :args (_let_51 _let_76 _let_74)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_107 (CONG _let_105 _let_151 :args _let_102) (FALSE_INTRO _let_149))) :args (_let_74 _let_76 _let_51)) :args ((not (and _let_51 _let_76 _let_74)) SB_LITERAL))) (CONG _let_98 _let_148 (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_56)) :args ((or _let_52 _let_73 _let_147))))) (let ((_let_153 (not _let_15))) (let ((_let_154 (or _let_153 _let_77))) (let ((_let_155 (ASSUME :args (_let_15)))) (let ((_let_156 (not _let_78))) (let ((_let_157 (not _let_77))) (let ((_let_158 (REFL :args (_let_156)))) (let ((_let_159 (ASSUME :args (_let_77)))) (let ((_let_160 (REFL :args (tptp.n2)))) (let ((_let_161 (ASSUME :args (_let_78)))) (let ((_let_162 (SYMM _let_161))) (let ((_let_163 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n2)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X))))) (let ((_let_164 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_165 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_164 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_163))) _let_164 :args (_let_81 false _let_163)))) (let ((_let_166 (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_45 _let_66 _let_72 _let_78 _let_80 (not _let_81)))))) (let ((_let_167 (not _let_82))) (let ((_let_168 (REFL :args (_let_167)))) (let ((_let_169 (ASSUME :args (_let_80)))) (let ((_let_170 (ASSUME :args (_let_82)))) (let ((_let_171 (SYMM _let_170))) (let ((_let_172 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_169 _let_170 _let_106) :args (_let_51 _let_82 _let_80)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_107 (CONG _let_105 _let_171 :args _let_102) (FALSE_INTRO _let_169))) :args (_let_80 _let_82 _let_51)) :args ((not (and _let_51 _let_82 _let_80)) SB_LITERAL))) (CONG _let_98 _let_168 (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_79))) :args _let_56)) :args ((or _let_52 _let_79 _let_167))))) (let ((_let_173 (AND_ELIM _let_49 :args (2)))) (let ((_let_174 (AND_ELIM _let_49 :args (3)))) (let ((_let_175 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n4)) (= tptp.n0 X) (= tptp.n1 X) (= tptp.n2 X) (= tptp.n3 X) (= tptp.n4 X))))) (let ((_let_176 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_177 (_let_175))) (let ((_let_178 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_176 :args (tptp.pv40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq X tptp.n4) false))))) :args _let_177)) _let_176 :args (_let_85 false _let_175)))) (let ((_let_179 (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_84 _let_83 _let_70 _let_34 _let_76 _let_82 _let_64 (not _let_85)))))) (let ((_let_180 (not _let_34))) (let ((_let_181 (REFL :args (_let_180)))) (let ((_let_182 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_let_248 _let_247 _let_43 _let_76)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_235 (CONG _let_123 (TRANS (CONG (TRANS _let_151 _let_249) :args _let_199) _let_260) :args _let_102) (CONG _let_121 (TRANS (SYMM _let_260) (CONG _let_258 :args _let_199)) :args _let_102) (TRUE_INTRO _let_257))) :args (_let_248 _let_246 _let_247 _let_66 _let_76 _let_43)) :args ((not (and _let_246 _let_66 _let_248 _let_247 _let_43 _let_76)) SB_LITERAL))) (CONG _let_256 _let_117 (REFL :args (_let_254)) (REFL :args (_let_253)) _let_226 _let_148 :args _let_56)) :args ((or _let_255 _let_32 _let_114 _let_254 _let_253 _let_147))) _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_250)) :args ((or _let_252 _let_248 (not _let_250)))) _let_251 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_187 :args (tptp.n0 tptp.n1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_188)) :args _let_186))) _let_187 :args (_let_250 false _let_27)) :args (_let_248 false _let_20 false _let_250)) 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X Y) (tptp.leq Y X))) _let_28 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) _let_27 (forall ((X $$unsorted)) (tptp.gt (tptp.succ X) X)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.leq X Y) (tptp.leq X (tptp.succ Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X Y) (tptp.gt (tptp.succ Y) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq (tptp.uniform_int_rnd C X) X))) (forall ((X $$unsorted) (C $$unsorted)) (=> (tptp.leq tptp.n0 X) (tptp.leq tptp.n0 (tptp.uniform_int_rnd C X)))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_const_array1 (tptp.dim L U) Val) I) Val))) (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (tptp.leq L1 I) (tptp.leq I U1) (tptp.leq L2 J) (tptp.leq J U2)) (= (tptp.a_select3 (tptp.tptp_const_array2 (tptp.dim L1 U1) (tptp.dim L2 U2) Val) I J) Val))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.trans A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.inv A))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (let ((_let_1 (tptp.tptp_update3 A K K VAL))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N) (tptp.leq tptp.n0 K) (tptp.leq K N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_msub A B))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 B I J) (tptp.a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_mmul A (tptp.tptp_mmul B (tptp.trans A))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I M) (tptp.leq tptp.n0 J) (tptp.leq J M)) (= (tptp.a_select3 D I J) (tptp.a_select3 D J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 A I J) (tptp.a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 F I J) (tptp.a_select3 F J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.tptp_madd A (tptp.tptp_mmul B (tptp.tptp_mmul (tptp.tptp_madd (tptp.tptp_mmul C (tptp.tptp_mmul D (tptp.trans C))) (tptp.tptp_mmul E (tptp.tptp_mmul F (tptp.trans E)))) (tptp.trans B)))))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq I N) (tptp.leq tptp.n0 J) (tptp.leq J N)) (= (tptp.a_select3 _let_1 I J) (tptp.a_select3 _let_1 J I))))))) (forall ((Body $$unsorted)) (= (tptp.sum tptp.n0 tptp.tptp_minus_1 Body) tptp.n0)) (forall ((Body $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) (= (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 $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))) _let_26 (forall ((X $$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_25 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.69 )
% 0.23/0.69 % SZS output end Proof for SWV167+1
% 0.23/0.69 % cvc5---1.0.5 exiting
% 0.23/0.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------