%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 21:49:38 EDT 2023

% Result   : Theorem 0.39s 0.77s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 04:07:35 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.23/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.39/0.77  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.tMIe9Kjl1g/cvc5---1.0.5_32036.p...
% 0.39/0.77  ------- get file name : TPTP file name is SWV188+1
% 0.39/0.77  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32036.smt2...
% 0.39/0.77  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.39/0.77  % SZS status Theorem for SWV188+1
% 0.39/0.77  % SZS output start Proof for SWV188+1
% 0.39/0.77  (
% 0.39/0.77  (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (tptp.succ _let_3))) (let ((_let_5 (= _let_4 tptp.n4))) (let ((_let_6 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_7 (tptp.gt tptp.n4 tptp.n0))) (let ((_let_8 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_9 (tptp.gt tptp.loopcounter tptp.n1))) (let ((_let_10 (not (=> (and (forall ((A $$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 $$unsorted)) (=> (and (tptp.leq tptp.n0 D) (tptp.leq D tptp.n4)) (= (tptp.a_select3 tptp.center_init D tptp.n0) tptp.init))) (=> _let_9 (forall ((E $$unsorted)) (=> (and (tptp.leq tptp.n0 E) (tptp.leq E tptp.n4)) (= (tptp.a_select2 tptp.muold_init E) tptp.init)))) (=> _let_9 (forall ((F $$unsorted)) (=> (and (tptp.leq tptp.n0 F) (tptp.leq F tptp.n4)) (= (tptp.a_select2 tptp.rhoold_init F) tptp.init)))) (=> _let_9 (forall ((G $$unsorted)) (=> (and (tptp.leq tptp.n0 G) (tptp.leq G tptp.n4)) (= (tptp.a_select2 tptp.sigmaold_init G) tptp.init))))) (forall ((H $$unsorted)) (=> (and (tptp.leq tptp.n0 H) (tptp.leq H tptp.tptp_minus_1)) (= (tptp.a_select2 tptp.mu_init H) tptp.init))))))) (let ((_let_11 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_13 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))) (let ((_let_14 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_15 (tptp.succ tptp.tptp_minus_1))) (let ((_let_16 (= _let_15 tptp.n0))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_19 (forall ((X $$unsorted)) (not (tptp.gt X X))))) (let ((_let_20 (= tptp.n0 _let_15))) (let ((_let_21 (= tptp.n4 _let_4))) (let ((_let_22 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_23 (= _let_15 (tptp.plus tptp.n1 tptp.tptp_minus_1)))) (let ((_let_24 (tptp.succ _let_15))) (let ((_let_25 (= _let_24 (tptp.plus tptp.n2 tptp.tptp_minus_1)))) (let ((_let_26 (= _let_2 (tptp.plus tptp.n2 tptp.n0)))) (let ((_let_27 (tptp.succ _let_24))) (let ((_let_28 (= _let_27 (tptp.plus tptp.n3 tptp.tptp_minus_1)))) (let ((_let_29 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_30 (= (tptp.succ _let_27) (tptp.plus tptp.n4 tptp.tptp_minus_1)))) (let ((_let_31 (= _let_4 (tptp.plus tptp.n4 tptp.n0)))) (let ((_let_32 (tptp.gt tptp.n4 tptp.n4))) (let ((_let_33 (= tptp.n0 tptp.tptp_minus_1))) (let ((_let_34 (SYMM (ASSUME :args (_let_16))))) (let ((_let_35 (ASSUME :args (_let_7)))) (let ((_let_36 (SYMM (ASSUME :args (_let_5))))) (let ((_let_37 (_let_14))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 ((tptp.succ X)))) (let ((_let_40 (_let_13))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 ((tptp.succ (tptp.succ X))))) (let ((_let_43 (_let_12))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 ((tptp.succ (tptp.succ (tptp.succ X)))))) (let ((_let_46 (_let_11))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_49 (not _let_32))) (let ((_let_50 (_let_19))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.leq tptp.n0 tptp.tptp_minus_1))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_33))) (let ((_let_57 (forall ((X $$unsorted)) (or (not (tptp.leq tptp.n0 X)) (not (tptp.leq X tptp.n0)) (= tptp.n0 X))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (not _let_8))) (let ((_let_60 (or _let_59 _let_52))) (let ((_let_61 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.tptp_minus_1))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_54))) (let ((_let_68 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (or _let_66 _let_64 (= tptp.init (tptp.a_select2 tptp.mu_init SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_71 (forall ((H $$unsorted)) (or (not (tptp.leq tptp.n0 H)) (not (tptp.leq H tptp.tptp_minus_1)) (= tptp.init (tptp.a_select2 tptp.mu_init H)))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (or))) (let ((_let_74 (not _let_71))) (let ((_let_75 (_let_74))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_71))) (REFL :args (_let_72)) :args _let_73)) (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_72 true _let_71)))) (let ((_let_77 (REFL :args (_let_70)))) (let ((_let_78 (not _let_33))) (let ((_let_79 (not _let_31))) (let ((_let_80 (not _let_30))) (let ((_let_81 (not _let_29))) (let ((_let_82 (not _let_28))) (let ((_let_83 (not _let_26))) (let ((_let_84 (not _let_25))) (let ((_let_85 (not _let_23))) (let ((_let_86 (not _let_22))) (let ((_let_87 (not _let_21))) (let ((_let_88 (not _let_7))) (let ((_let_89 (not _let_20))) (let ((_let_90 (APPLY_UF tptp.gt))) (let ((_let_91 (SYMM _let_34))) (let ((_let_92 (ASSUME :args (_let_23)))) (let ((_let_93 (APPLY_UF tptp.plus))) (let ((_let_94 (ASSUME :args (_let_33)))) (let ((_let_95 (SYMM (SYMM _let_94)))) (let ((_let_96 (ASSUME :args (_let_22)))) (let ((_let_97 (APPLY_UF tptp.succ))) (let ((_let_98 (CONG _let_91 :args _let_97))) (let ((_let_99 (ASSUME :args (_let_25)))) (let ((_let_100 (ASSUME :args (_let_26)))) (let ((_let_101 (CONG _let_98 :args _let_97))) (let ((_let_102 (ASSUME :args (_let_28)))) (let ((_let_103 (ASSUME :args (_let_29)))) (let ((_let_104 (ASSUME :args (_let_30)))) (let ((_let_105 (REFL :args (tptp.n4)))) (let ((_let_106 (ASSUME :args (_let_31)))) (let ((_let_107 (SYMM _let_36))) (let ((_let_108 (SYMM _let_107))) (let ((_let_109 (ASSUME :args (_let_49)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_94 _let_104 _let_102 _let_100 _let_99 _let_92 _let_109 _let_106 _let_103 _let_34 _let_96 _let_36 _let_35) :args (_let_7 _let_20 _let_21 _let_22 _let_23 _let_25 _let_26 _let_28 _let_29 _let_30 _let_31 _let_33 _let_49)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_109)) (CONG _let_108 _let_105 :args _let_90) (CONG _let_107 (TRANS _let_108 (SYMM (SYMM _let_106)) (CONG _let_105 _let_95 :args _let_93) (SYMM _let_104) (CONG _let_101 :args _let_97) (SYMM (SYMM _let_103)) (CONG (REFL :args (tptp.n3)) _let_95 :args _let_93) (SYMM _let_102) _let_101 (SYMM (SYMM _let_100)) (CONG (REFL :args (tptp.n2)) _let_95 :args _let_93) (SYMM _let_99) _let_98 (SYMM (SYMM _let_96)) (CONG (REFL :args (tptp.n1)) _let_95 :args _let_93) (SYMM _let_92) _let_91) :args _let_90) (TRUE_INTRO _let_35))) :args (_let_33 _let_30 _let_28 _let_26 _let_25 _let_23 _let_49 _let_31 _let_29 _let_20 _let_22 _let_21 _let_7)) :args ((not (and _let_7 _let_20 _let_21 _let_22 _let_23 _let_25 _let_26 _let_28 _let_29 _let_30 _let_31 _let_33 _let_49)) SB_LITERAL))) (CONG (REFL :args (_let_88)) (REFL :args (_let_89)) (REFL :args (_let_87)) (REFL :args (_let_86)) (REFL :args (_let_85)) (REFL :args (_let_84)) (REFL :args (_let_83)) (REFL :args (_let_82)) (REFL :args (_let_81)) (REFL :args (_let_80)) (REFL :args (_let_79)) (REFL :args (_let_78)) (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_32))) :args _let_73)) :args ((or _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_32 _let_78))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_53 _let_33 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_64 _let_54 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG _let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_73)) :args ((or _let_65 _let_70))) _let_76 :args (_let_65 true _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 1)) (CONG _let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_73)) :args ((or _let_63 _let_70))) _let_76 :args (_let_63 true _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_54 false _let_65 false _let_63 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_52 (not _let_60)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_52 false _let_8 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.leq tptp.n0 X) false))))) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_33 false _let_54 false _let_52 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.n4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt X X) false))))) :args _let_50)) _let_51 :args (_let_49 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_48)) :args _let_46))) _let_47 :args (_let_31 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_48)) :args _let_46))) _let_47 :args (_let_30 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_45)) :args _let_43))) _let_44 :args (_let_29 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_45)) :args _let_43))) _let_44 :args (_let_28 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_40))) _let_41 :args (_let_26 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_42)) :args _let_40))) _let_41 :args (_let_25 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_37))) _let_38 :args (_let_23 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_37))) _let_38 :args (_let_22 false _let_14)) _let_36 _let_35 _let_34 :args (false false _let_33 true _let_32 false _let_31 false _let_30 false _let_29 false _let_28 false _let_26 false _let_25 false _let_23 false _let_22 false _let_21 false _let_7 false _let_20)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.gt X Y) (tptp.gt Y X) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.gt X Y) (tptp.gt Y Z)) (tptp.gt X Z))) _let_19 (forall ((X $$unsorted)) (tptp.leq X X)) _let_18 (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_17 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.leq X Y) (not (= X Y))) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.leq X (tptp.pred Y)) (tptp.gt Y X))) (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 $$unsorted)) (= tptp.tptp_float_0_0 (tptp.sum tptp.n0 tptp.tptp_minus_1 Body))) _let_16 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_14 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) _let_13 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_12 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) _let_11 (forall ((X $$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))) (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)) (forall ((X $$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_10 (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) _let_8 (tptp.gt tptp.n1 tptp.tptp_minus_1) (tptp.gt tptp.n2 tptp.tptp_minus_1) (tptp.gt tptp.n3 tptp.tptp_minus_1) _let_7 (tptp.gt tptp.n5 tptp.n0) (tptp.gt tptp.n135299 tptp.n0) (tptp.gt tptp.n1 tptp.n0) (tptp.gt tptp.n2 tptp.n0) (tptp.gt tptp.n3 tptp.n0) (tptp.gt tptp.n4 tptp.n1) (tptp.gt tptp.n5 tptp.n1) (tptp.gt tptp.n135299 tptp.n1) (tptp.gt tptp.n2 tptp.n1) (tptp.gt tptp.n3 tptp.n1) (tptp.gt tptp.n4 tptp.n2) (tptp.gt tptp.n5 tptp.n2) (tptp.gt tptp.n135299 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n135299 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_6 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n1)) (or (= X tptp.n0) (= X tptp.n1)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n2)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2)))) (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_5 (= (tptp.succ _let_4) tptp.n5) (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.39/0.77  )
% 0.39/0.77  % SZS output end Proof for SWV188+1
% 0.39/0.77  % cvc5---1.0.5 exiting
% 0.39/0.77  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------