TSTP Solution File: SWV033+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV033+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 21:49:02 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV033+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 08:12:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8NF6sbPdQC/cvc5---1.0.5_12852.p...
% 0.21/0.64 ------- get file name : TPTP file name is SWV033+1
% 0.21/0.64 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12852.smt2...
% 0.21/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.64 % SZS status Theorem for SWV033+1
% 0.21/0.64 % SZS output start Proof for SWV033+1
% 0.21/0.64 (
% 0.21/0.64 (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 (tptp.gt tptp.n3 tptp.n2))) (let ((_let_14 (tptp.gt tptp.n3 tptp.n1))) (let ((_let_15 (tptp.gt tptp.n2 tptp.n1))) (let ((_let_16 (tptp.gt tptp.n2 tptp.n0))) (let ((_let_17 (tptp.gt tptp.n1 tptp.n0))) (let ((_let_18 (= tptp.init tptp.init))) (let ((_let_19 (tptp.leq tptp.pv1376 tptp.n3))) (let ((_let_20 (tptp.leq tptp.n0 tptp.pv1376))) (let ((_let_21 (not (=> (and _let_18 _let_20 _let_19 (forall ((A $$unsorted)) (=> (and (tptp.leq tptp.n0 A) (tptp.leq A tptp.n2)) (forall ((B $$unsorted)) (=> (and (tptp.leq tptp.n0 B) (tptp.leq B tptp.n3)) (= (tptp.a_select3 tptp.simplex7_init B A) tptp.init))))) (forall ((C $$unsorted)) (=> (and (tptp.leq tptp.n0 C) (tptp.leq C (tptp.minus tptp.pv1376 tptp.n1))) (= (tptp.a_select2 tptp.s_values7_init C) tptp.init)))) (and _let_18 (forall ((D $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n2)) (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n3)) (= (tptp.a_select3 tptp.simplex7_init E D) tptp.init))))) (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F (tptp.minus (tptp.plus tptp.n1 tptp.pv1376) tptp.n1))) (= (tptp.a_select2 (tptp.tptp_update2 tptp.s_values7_init tptp.pv1376 tptp.init) F) tptp.init)))))))) (let ((_let_22 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (tptp.a_select2 X U) VAL)) (= (tptp.a_select2 (tptp.tptp_update2 X I VAL2) U) VAL))))) (let ((_let_23 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) U) VAL)))) (let ((_let_24 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_25 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_26 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_27 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))))) (let ((_let_28 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_29 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_30 (= tptp.n3 _let_3))) (let ((_let_31 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (= tptp.n0 tptp.pv1376))) (let ((_let_33 (= tptp.n3 tptp.pv1376))) (let ((_let_34 (= tptp.pv1376 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (SYMM (ASSUME :args (_let_4))))) (let ((_let_36 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_36))) (let ((_let_40 (or _let_39 _let_38 _let_31))) (let ((_let_41 (= tptp.n1 tptp.pv1376))) (let ((_let_42 (= tptp.n1 _let_1))) (let ((_let_43 (tptp.plus tptp.n1 tptp.pv1376))) (let ((_let_44 (tptp.minus _let_43 tptp.n1))) (let ((_let_45 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_44))) (let ((_let_46 (= _let_43 (tptp.succ tptp.pv1376)))) (let ((_let_47 (= _let_44 (tptp.pred _let_43)))) (let ((_let_48 (= tptp.n0 (tptp.pred _let_1)))) (let ((_let_49 (= tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (tptp.a_select2 tptp.s_values7_init SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (tptp.tptp_update2 tptp.s_values7_init tptp.pv1376 tptp.init))) (let ((_let_52 (tptp.a_select2 _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (= _let_52 _let_50))) (let ((_let_54 (or _let_34 _let_53))) (let ((_let_55 (= tptp.init _let_52))) (let ((_let_56 (= tptp.init _let_50))) (let ((_let_57 (tptp.minus tptp.pv1376 tptp.n1))) (let ((_let_58 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_57))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_39 _let_59 _let_56))) (let ((_let_61 (= tptp.n2 _let_2))) (let ((_let_62 (= _let_2 (tptp.pred _let_3)))) (let ((_let_63 (tptp.leq tptp.n1 tptp.n2))) (let ((_let_64 (= _let_57 (tptp.pred tptp.pv1376)))) (let ((_let_65 (= tptp.n2 tptp.pv1376))) (let ((_let_66 (not _let_19))) (let ((_let_67 (not _let_20))) (let ((_let_68 (or _let_67 _let_66 _let_32 _let_41 _let_65 _let_33))) (let ((_let_69 (= _let_1 (tptp.pred _let_2)))) (let ((_let_70 (tptp.leq tptp.n1 (tptp.pred tptp.n2)))) (let ((_let_71 (not _let_45))) (let ((_let_72 (or _let_39 _let_71 _let_55))) (let ((_let_73 (forall ((F $$unsorted)) (or (not (tptp.leq tptp.n0 F)) (not (tptp.leq F (tptp.minus (tptp.plus tptp.n1 tptp.pv1376) tptp.n1))) (= tptp.init (tptp.a_select2 (tptp.tptp_update2 tptp.s_values7_init tptp.pv1376 tptp.init) F)))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (forall ((D $$unsorted) (BOUND_VARIABLE_2140 $$unsorted)) (or (not (tptp.leq tptp.n0 D)) (not (tptp.leq D tptp.n2)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2140)) (not (tptp.leq BOUND_VARIABLE_2140 tptp.n3)) (= tptp.init (tptp.a_select3 tptp.simplex7_init BOUND_VARIABLE_2140 D)))))) (let ((_let_76 (not _let_73))) (let ((_let_77 (forall ((A $$unsorted) (BOUND_VARIABLE_2098 $$unsorted)) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq A tptp.n2)) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2098)) (not (tptp.leq BOUND_VARIABLE_2098 tptp.n3)) (= tptp.init (tptp.a_select3 tptp.simplex7_init BOUND_VARIABLE_2098 A)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (NOT_IMPLIES_ELIM1 _let_78))) (let ((_let_80 (AND_ELIM _let_79 :args (2)))) (let ((_let_81 (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_77 (= BOUND_VARIABLE_2098 BOUND_VARIABLE_2140) (= A D)))) :args ((or _let_75 (not _let_77)))))) (let ((_let_82 (NOT_AND (NOT_IMPLIES_ELIM2 _let_78)))) (let ((_let_83 (or))) (let ((_let_84 (_let_76))) (let ((_let_85 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_73))) (REFL :args (_let_74)) :args _let_83)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST _let_85 (MACRO_RESOLUTION_TRUST _let_82 (MACRO_RESOLUTION_TRUST _let_81 _let_80 :args (_let_75 false _let_77)) :args (_let_76 false _let_75)) :args (_let_74 true _let_73)))) (let ((_let_87 (REFL :args (_let_72)))) (let ((_let_88 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_87 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_36))) :args _let_83)) :args ((or _let_36 _let_72))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST _let_88 _let_86 :args (_let_36 true _let_72)))) (let ((_let_90 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_90))))) (let ((_let_93 (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_31 _let_38 (not _let_40)))))) (let ((_let_94 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n1))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_39 _let_95 _let_31 _let_49))) (let ((_let_97 (= tptp.init (tptp.a_select2 _let_51 tptp.pv1376)))) (let ((_let_98 (not _let_41))) (let ((_let_99 (SYMM (ASSUME :args (_let_6))))) (let ((_let_100 (SYMM (ASSUME :args (_let_5))))) (let ((_let_101 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_87 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_45))) :args _let_83)) :args ((or _let_45 _let_72))))) (let ((_let_102 (MACRO_RESOLUTION_TRUST _let_101 _let_86 :args (_let_45 true _let_72)))) (let ((_let_103 (_let_26))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.pv1376 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.plus tptp.n1 X)))) :args _let_103)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST _let_105 _let_104 :args (_let_46 false _let_26)))) (let ((_let_107 (_let_25))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 ((tptp.minus X tptp.n1)))) (let ((_let_110 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_107)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST _let_110 _let_108 :args (_let_47 false _let_25)))) (let ((_let_112 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (_let_112))) (let ((_let_115 ((tptp.succ X)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_114)) _let_113 :args (_let_69 false _let_112)))) (let ((_let_117 (not _let_69))) (let ((_let_118 (not _let_47))) (let ((_let_119 (not _let_46))) (let ((_let_120 (not _let_61))) (let ((_let_121 (not _let_42))) (let ((_let_122 (and _let_42 _let_61 _let_45 _let_46 _let_47 _let_69 _let_41))) (let ((_let_123 (ASSUME :args (_let_45)))) (let ((_let_124 (TRUE_INTRO _let_123))) (let ((_let_125 (APPLY_UF tptp.leq))) (let ((_let_126 (ASSUME :args (_let_47)))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (APPLY_UF tptp.pred))) (let ((_let_129 (ASSUME :args (_let_46)))) (let ((_let_130 (SYMM _let_129))) (let ((_let_131 (APPLY_UF tptp.succ))) (let ((_let_132 (ASSUME :args (_let_41)))) (let ((_let_133 (SYMM _let_132))) (let ((_let_134 (SYMM _let_99))) (let ((_let_135 (SYMM _let_100))) (let ((_let_136 (SYMM _let_135))) (let ((_let_137 (CONG _let_135 :args _let_128))) (let ((_let_138 (ASSUME :args (_let_69)))) (let ((_let_139 (SYMM _let_138))) (let ((_let_140 (SYMM _let_139))) (let ((_let_141 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_142 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n1)) (= tptp.n0 X) (= tptp.n1 X))))) (let ((_let_143 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_144 (not _let_55))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_72 2)) _let_86 :args (_let_144 true _let_72)))) (let ((_let_146 (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (tptp.a_select2 (tptp.tptp_update2 X U VAL) U))))) (let ((_let_147 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_148 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (tptp.s_values7_init tptp.pv1376 tptp.init QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tptp_update2 X U VAL)))) :args (_let_146))) _let_147 :args (_let_97 false _let_146)))) (let ((_let_149 (not _let_49))) (let ((_let_150 (not _let_97))) (let ((_let_151 (and _let_97 _let_41 _let_49))) (let ((_let_152 (APPLY_UF tptp.a_select2))) (let ((_let_153 (ASSUME :args (_let_49)))) (let ((_let_154 (SYMM _let_153))) (let ((_let_155 (SYMM _let_154))) (let ((_let_156 (REFL :args (_let_51)))) (let ((_let_157 (ASSUME :args (_let_97)))) (let ((_let_158 (SYMM (SYMM _let_157)))) (let ((_let_159 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_151)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_153 _let_132 _let_157) (SCOPE (TRANS _let_158 (CONG _let_156 (TRANS _let_133 _let_155) :args _let_152)) :args (_let_49 _let_41 _let_97))) :args (_let_97 _let_41 _let_49))) :args (true _let_151)) :args ((or _let_55 _let_150 _let_98 _let_149))))) (let ((_let_160 (MACRO_RESOLUTION_TRUST _let_159 _let_148 _let_145 (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_39 _let_31 _let_49 _let_95 (not _let_96)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_143 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_142))) _let_143 :args (_let_96 false _let_142)) _let_89 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_122)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_126 _let_129 _let_132 _let_99 _let_100 _let_138) (SCOPE (TRUE_ELIM (TRANS (CONG _let_141 (TRANS _let_99 _let_140 _let_137 (CONG (TRANS _let_136 (CONG (TRANS _let_134 (SYMM _let_133)) :args _let_131) _let_130) :args _let_128) _let_127) :args _let_125) _let_124)) :args 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:args (_let_38)))) (let ((_let_171 (ASSUME :args (_let_48)))) (let ((_let_172 (SYMM _let_171))) (let ((_let_173 (CONG (SYMM _let_134) :args _let_128))) (let ((_let_174 (ASSUME :args (_let_32)))) (let ((_let_175 (SYMM _let_174))) (let ((_let_176 (SYMM _let_130))) (let ((_let_177 (SYMM _let_127))) (let ((_let_178 (SYMM _let_124))) (let ((_let_179 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_170 _let_171 _let_99 _let_174 _let_129 _let_126 _let_123) :args (_let_42 _let_45 _let_32 _let_46 _let_47 _let_48 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_178 (CONG _let_141 (TRANS _let_177 (CONG (TRANS _let_176 (CONG _let_175 :args _let_131) _let_134) :args _let_128) _let_173 _let_172) :args _let_125) (FALSE_INTRO _let_170))) :args (_let_38 _let_48 _let_42 _let_32 _let_46 _let_47 _let_45)) :args ((not (and _let_42 _let_45 _let_32 _let_46 _let_47 _let_48 _let_38)) SB_LITERAL))) (CONG (REFL :args (_let_121)) _let_169 _let_168 _let_166 _let_165 (REFL :args 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(_let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_214 :args (tptp.n0 tptp.n2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_216)) :args _let_215)) _let_214 :args (_let_359 false _let_213)) :args (_let_357 false _let_16 false _let_359)) _let_331 _let_356 _let_162 _let_229 _let_294 :args (_let_58 false _let_42 false _let_61 false _let_30 false _let_357 false _let_31 false _let_33 false _let_48 false _let_62 false _let_64)) _let_310 :args (_let_56 false _let_36 false _let_58 false _let_60)) :args (_let_312 true _let_55 false _let_56)) _let_306 :args (_let_34 true _let_53 false _let_54)) _let_356 _let_334 _let_331 _let_35 :args (false false _let_34 false _let_33 true _let_32 false _let_31 false _let_30)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) (forall ((X $$unsorted)) (not (tptp.gt X X))) (forall ((X $$unsorted)) (tptp.leq X X)) _let_29 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq 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))) _let_26 (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))))))) _let_25 _let_24 (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))) _let_23 _let_22 (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (forall ((I0 $$unsorted)) (=> (and (tptp.leq tptp.n0 I0) (tptp.leq I0 U)) (= (tptp.a_select2 X I0) VAL))) (tptp.leq tptp.n0 I) (tptp.leq I U)) (= (tptp.a_select2 (tptp.tptp_update2 X U VAL) I) VAL))) tptp.true (not (= tptp.def tptp.use)) _let_21 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n0 tptp.tptp_minus_1) (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) (tptp.gt tptp.n4 tptp.n0) (tptp.gt tptp.n5 tptp.n0) _let_17 _let_16 (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) _let_15 _let_14 (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) _let_13 (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n4)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n5)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5)))) _let_12 _let_11 _let_10 _let_9 _let_8 (= (tptp.succ _let_7) tptp.n5) _let_6 _let_5 _let_4 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65 )
% 0.21/0.65 % SZS output end Proof for SWV033+1
% 0.21/0.65 % cvc5---1.0.5 exiting
% 0.21/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------