%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV114+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 21:49:22 EDT 2023

% Result   : Theorem 0.22s 0.69s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWV114+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n005.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 08:16:38 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QHAx6Z7znN/cvc5---1.0.5_29462.p...
% 0.22/0.69  ------- get file name : TPTP file name is SWV114+1
% 0.22/0.69  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29462.smt2...
% 0.22/0.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.69  % SZS status Theorem for SWV114+1
% 0.22/0.69  % SZS output start Proof for SWV114+1
% 0.22/0.69  (
% 0.22/0.69  (let ((_let_1 (tptp.succ tptp.n0))) (let ((_let_2 (tptp.succ _let_1))) (let ((_let_3 (tptp.succ _let_2))) (let ((_let_4 (tptp.succ _let_3))) (let ((_let_5 (tptp.succ _let_4))) (let ((_let_6 (tptp.succ _let_5))) (let ((_let_7 (= _let_6 tptp.n6))) (let ((_let_8 (= _let_5 tptp.n5))) (let ((_let_9 (= _let_4 tptp.n4))) (let ((_let_10 (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n0)) (= X tptp.n0))))) (let ((_let_11 (tptp.gt tptp.n0 tptp.tptp_minus_1))) (let ((_let_12 (tptp.leq tptp.pv5 (tptp.minus tptp.n999 tptp.n1)))) (let ((_let_13 (tptp.leq tptp.n0 tptp.pv5))) (let ((_let_14 (not (=> (and _let_13 _let_12 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 A) (tptp.leq tptp.n0 B) (tptp.leq A _let_1) (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 C) (tptp.leq tptp.n0 D) (tptp.leq C _let_1) (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 E) (tptp.leq tptp.n0 F) (tptp.leq E _let_1) (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E)))))) (and _let_13 _let_12 (forall ((G $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 G) (tptp.leq tptp.n0 H) (tptp.leq G _let_1) (tptp.leq H _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter G H) (tptp.a_select3 tptp.q_ds1_filter H G))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (=> (and (tptp.leq tptp.n0 I) (tptp.leq tptp.n0 J) (tptp.leq I _let_1) (tptp.leq J _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter I J) (tptp.a_select3 tptp.r_ds1_filter J I))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (=> (and (tptp.leq tptp.n0 K) (tptp.leq tptp.n0 L) (tptp.leq K _let_1) (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter K L) (tptp.a_select3 tptp.pminus_ds1_filter L K))))) (forall ((M $$unsorted)) (=> (and (tptp.leq tptp.n0 M) (tptp.leq M (tptp.minus tptp.n0 tptp.n1))) (forall ((N $$unsorted)) (=> (and (tptp.leq tptp.n0 N) (tptp.leq N (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter M N) (tptp.a_select3 tptp.id_ds1_filter N M))))))))))) (let ((_let_15 (forall ((X $$unsorted)) (= (tptp.pred (tptp.succ X)) X)))) (let ((_let_16 (forall ((X $$unsorted)) (= (tptp.minus X tptp.n1) (tptp.pred X))))) (let ((_let_17 (forall ((X $$unsorted)) (= (tptp.plus tptp.n5 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))))) (let ((_let_18 (forall ((X $$unsorted)) (= (tptp.plus tptp.n4 X) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_19 (forall ((X $$unsorted)) (= (tptp.plus tptp.n3 X) (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_20 (forall ((X $$unsorted)) (= (tptp.plus tptp.n2 X) (tptp.succ (tptp.succ X)))))) (let ((_let_21 (forall ((X $$unsorted)) (= (tptp.plus tptp.n1 X) (tptp.succ X))))) (let ((_let_22 (tptp.succ tptp.tptp_minus_1))) (let ((_let_23 (= _let_22 tptp.n0))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.gt Y X) (tptp.leq X Y))))) (let ((_let_25 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.leq X Y) (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_26 (= (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.a_select3 tptp.id_ds1_filter SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_27 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (= tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (tptp.minus tptp.n6 tptp.n1))) (let ((_let_30 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.minus tptp.n0 tptp.n1))) (let ((_let_35 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_34))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.leq tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_33 _let_31 _let_26))) (let ((_let_40 (forall ((M $$unsorted) (BOUND_VARIABLE_2223 $$unsorted)) (or (not (tptp.leq tptp.n0 M)) (not (tptp.leq M (tptp.minus tptp.n0 tptp.n1))) (not (tptp.leq tptp.n0 BOUND_VARIABLE_2223)) (not (tptp.leq BOUND_VARIABLE_2223 (tptp.minus tptp.n6 tptp.n1))) (= (tptp.a_select3 tptp.id_ds1_filter M BOUND_VARIABLE_2223) (tptp.a_select3 tptp.id_ds1_filter BOUND_VARIABLE_2223 M)))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 K)) (not (tptp.leq tptp.n0 L)) (not (tptp.leq K _let_1)) (not (tptp.leq L _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter K L) (tptp.a_select3 tptp.pminus_ds1_filter L K))))))) (let ((_let_43 (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 I)) (not (tptp.leq tptp.n0 J)) (not (tptp.leq I _let_1)) (not (tptp.leq J _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter I J) (tptp.a_select3 tptp.r_ds1_filter J I))))))) (let ((_let_44 (forall ((G $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 G)) (not (tptp.leq tptp.n0 H)) (not (tptp.leq G _let_1)) (not (tptp.leq H _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter G H) (tptp.a_select3 tptp.q_ds1_filter H G))))))) (let ((_let_45 (not _let_40))) (let ((_let_46 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 E)) (not (tptp.leq tptp.n0 F)) (not (tptp.leq E _let_1)) (not (tptp.leq F _let_1)) (= (tptp.a_select3 tptp.pminus_ds1_filter E F) (tptp.a_select3 tptp.pminus_ds1_filter F E))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (NOT_IMPLIES_ELIM1 _let_47))) (let ((_let_49 (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus tptp.n3 tptp.n1))) (or (not (tptp.leq tptp.n0 C)) (not (tptp.leq tptp.n0 D)) (not (tptp.leq C _let_1)) (not (tptp.leq D _let_1)) (= (tptp.a_select3 tptp.r_ds1_filter C D) (tptp.a_select3 tptp.r_ds1_filter D C))))))) (let ((_let_50 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus tptp.n6 tptp.n1))) (or (not (tptp.leq tptp.n0 A)) (not (tptp.leq tptp.n0 B)) (not (tptp.leq A _let_1)) (not (tptp.leq B _let_1)) (= (tptp.a_select3 tptp.q_ds1_filter A B) (tptp.a_select3 tptp.q_ds1_filter B A))))))) (let ((_let_51 (or))) (let ((_let_52 (_let_45))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_40))) (REFL :args (_let_41)) :args _let_51)) (MACRO_RESOLUTION_TRUST (NOT_AND (NOT_IMPLIES_ELIM2 _let_47)) (AND_ELIM _let_48 :args (0)) (AND_ELIM _let_48 :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_50 (= A G) (= B H)))) :args ((or _let_44 (not _let_50)))) (AND_ELIM _let_48 :args (2)) :args (_let_44 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_49 (= C I) (= D J)))) :args ((or _let_43 (not _let_49)))) (AND_ELIM _let_48 :args (3)) :args (_let_43 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_46 (= E K) (= F L)))) :args ((or _let_42 (not _let_46)))) (AND_ELIM _let_48 :args (4)) :args (_let_42 false _let_46)) :args (_let_45 false _let_13 false _let_12 false _let_44 false _let_43 false _let_42)) :args (_let_41 true _let_40)))) (let ((_let_54 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.n0))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_38 _let_55 _let_27))) (let ((_let_57 (forall ((X $$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_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((not (= (tptp.leq tptp.n0 X) false))))) (let ((_let_61 (tptp.leq _let_34 tptp.n0))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_36 _let_62 _let_54))) (let ((_let_64 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq X Y)) (not (tptp.leq Y Z)) (tptp.leq X Z))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 ((not (= (tptp.leq X Y) false)) (not (= (tptp.leq Y Z) false))))) (let ((_let_68 (= tptp.tptp_minus_1 (tptp.pred _let_22)))) (let ((_let_69 (= _let_34 (tptp.pred tptp.n0)))) (let ((_let_70 (tptp.leq tptp.tptp_minus_1 tptp.n0))) (let ((_let_71 (= tptp.n0 _let_22))) (let ((_let_72 (forall ((X $$unsorted)) (= X (tptp.pred (tptp.succ X)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((tptp.succ X)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_68 false _let_72)))) (let ((_let_77 (_let_16))) (let ((_let_78 (ASSUME :args _let_77))) (let ((_let_79 ((tptp.minus X tptp.n1)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_77)) _let_78 :args (_let_69 false _let_16)))) (let ((_let_81 (not _let_11))) (let ((_let_82 (or _let_81 _let_70))) (let ((_let_83 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.gt Y X)) (tptp.leq X Y))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (SYMM (ASSUME :args (_let_23))))) (let ((_let_86 (not _let_68))) (let ((_let_87 (not _let_69))) (let ((_let_88 (not _let_71))) (let ((_let_89 (and _let_71 _let_70 _let_69 _let_68))) (let ((_let_90 (ASSUME :args (_let_70)))) (let ((_let_91 (APPLY_UF tptp.leq))) (let ((_let_92 (ASSUME :args (_let_68)))) (let ((_let_93 (SYMM (SYMM _let_92)))) (let ((_let_94 (APPLY_UF tptp.pred))) (let ((_let_95 (SYMM _let_85))) (let ((_let_96 (ASSUME :args (_let_69)))) (let ((_let_97 (SYMM _let_96))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_89)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_90 _let_92 _let_85 _let_96) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM _let_97) (CONG (SYMM _let_95) :args _let_94) (SYMM _let_93)) (REFL :args (tptp.n0)) :args _let_91) (TRUE_INTRO _let_90))) :args (_let_70 _let_68 _let_71 _let_69))) :args (_let_71 _let_70 _let_69 _let_68))) :args (true _let_89)) :args ((or _let_88 _let_61 (not _let_70) _let_87 _let_86))) _let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_81 _let_70 (not _let_82)))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.tptp_minus_1 tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.gt Y X) false))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_70 false _let_11 false _let_82)) _let_80 _let_76 :args (_let_61 false _let_71 false _let_70 false _let_69 false _let_68)))) (let ((_let_99 (REFL :args (_let_39)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_51)) :args ((or _let_35 _let_39))) _let_53 :args (_let_35 true _let_39)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_51)) :args ((or _let_37 _let_39))) _let_53 :args (_let_37 true _let_39)))) (let ((_let_102 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.n0))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_33 _let_103 _let_28))) (let ((_let_105 (= tptp.n0 _let_34))) (let ((_let_106 (= _let_5 (tptp.pred _let_6)))) (let ((_let_107 (= _let_29 (tptp.pred tptp.n6)))) (let ((_let_108 (= _let_5 (tptp.plus tptp.n5 tptp.n0)))) (let ((_let_109 (tptp.succ _let_22))) (let ((_let_110 (tptp.succ _let_109))) (let ((_let_111 (tptp.succ _let_110))) (let ((_let_112 (= (tptp.succ _let_111) (tptp.plus tptp.n5 tptp.tptp_minus_1)))) (let ((_let_113 (= _let_4 (tptp.plus tptp.n4 tptp.n0)))) (let ((_let_114 (= _let_111 (tptp.plus tptp.n4 tptp.tptp_minus_1)))) (let ((_let_115 (= _let_3 (tptp.plus tptp.n3 tptp.n0)))) (let ((_let_116 (= _let_110 (tptp.plus tptp.n3 tptp.tptp_minus_1)))) (let ((_let_117 (= _let_2 (tptp.plus tptp.n2 tptp.n0)))) (let ((_let_118 (= _let_109 (tptp.plus tptp.n2 tptp.tptp_minus_1)))) (let ((_let_119 (= _let_22 (tptp.plus tptp.n1 tptp.tptp_minus_1)))) (let ((_let_120 (= _let_1 (tptp.plus tptp.n1 tptp.n0)))) (let ((_let_121 (= tptp.n6 _let_6))) (let ((_let_122 (= tptp.n5 _let_5))) (let ((_let_123 (= tptp.n4 _let_4))) (let ((_let_124 (tptp.leq tptp.n0 _let_34))) (let ((_let_125 (not _let_124))) (let ((_let_126 (or _let_125 _let_62 _let_105))) (let ((_let_127 (or _let_38 _let_36 _let_124))) (let ((_let_128 (_let_17))) (let ((_let_129 (ASSUME :args _let_128))) (let ((_let_130 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))))) (let ((_let_131 (_let_18))) (let ((_let_132 (ASSUME :args _let_131))) (let ((_let_133 ((tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) (let ((_let_134 (_let_19))) (let ((_let_135 (ASSUME :args _let_134))) (let ((_let_136 ((tptp.succ (tptp.succ (tptp.succ X)))))) (let ((_let_137 (_let_20))) (let ((_let_138 (ASSUME :args _let_137))) (let ((_let_139 ((tptp.succ (tptp.succ X))))) (let ((_let_140 (_let_21))) (let ((_let_141 (ASSUME :args _let_140))) (let ((_let_142 ((tptp.succ X)))) (let ((_let_143 (SYMM (ASSUME :args (_let_7))))) (let ((_let_144 (SYMM (ASSUME :args (_let_8))))) (let ((_let_145 (SYMM (ASSUME :args (_let_9))))) (let ((_let_146 (and _let_71 _let_123 _let_122 _let_121 _let_30 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_108 _let_69 _let_107 _let_68 _let_106 _let_105))) (let ((_let_147 (ASSUME :args (_let_30)))) (let ((_let_148 (ASSUME :args (_let_107)))) (let ((_let_149 (ASSUME :args (_let_106)))) (let ((_let_150 (SYMM _let_144))) (let ((_let_151 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_152 (ASSUME :args (_let_108)))) (let ((_let_153 (APPLY_UF tptp.plus))) (let ((_let_154 (ASSUME :args (_let_105)))) (let ((_let_155 (TRANS _let_93 (CONG _let_95 :args _let_94) _let_97 (SYMM _let_154)))) (let ((_let_156 (ASSUME :args (_let_112)))) (let ((_let_157 (APPLY_UF tptp.succ))) (let ((_let_158 (CONG _let_85 :args _let_157))) (let ((_let_159 (CONG _let_158 :args _let_157))) (let ((_let_160 (CONG _let_159 :args _let_157))) (let ((_let_161 (SYMM _let_145))) (let ((_let_162 (ASSUME :args (_let_113)))) (let ((_let_163 (ASSUME :args (_let_114)))) (let ((_let_164 (ASSUME :args (_let_115)))) (let ((_let_165 (ASSUME :args (_let_116)))) (let ((_let_166 (ASSUME :args (_let_117)))) (let ((_let_167 (ASSUME :args (_let_118)))) (let ((_let_168 (ASSUME :args (_let_120)))) (let ((_let_169 (ASSUME :args (_let_119)))) (let ((_let_170 (and _let_27 _let_28))) (let ((_let_171 (ASSUME :args (_let_27)))) (let ((_let_172 (ASSUME :args (_let_28)))) (let ((_let_173 (TRANS (SYMM _let_172) (SYMM (SYMM _let_171))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_170)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_172 _let_171) (SCOPE (CONG (REFL :args (tptp.id_ds1_filter)) (SYMM _let_173) _let_173 :args (APPLY_UF tptp.a_select3)) :args (_let_28 _let_27))) :args (_let_27 _let_28))) :args (true _let_170)) :args ((or _let_26 (not _let_27) (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_33 _let_28 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_51)) :args ((or _let_32 _let_39))) _let_53 :args (_let_32 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_146)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_92 _let_96 _let_152 _let_156 _let_154 _let_164 _let_144 _let_149 _let_148 _let_169 _let_143 _let_145 _let_147 _let_163 _let_168 _let_85 _let_162 _let_167 _let_166 _let_165) (SCOPE (TRUE_ELIM (TRANS (CONG _let_151 (TRANS _let_85 (SYMM (SYMM _let_169)) (CONG (REFL :args (tptp.n1)) _let_155 :args _let_153) (SYMM _let_168) _let_158 (SYMM (SYMM _let_167)) (CONG (REFL :args (tptp.n2)) _let_155 :args _let_153) (SYMM _let_166) _let_159 (SYMM (SYMM _let_165)) (CONG (REFL :args (tptp.n3)) _let_155 :args _let_153) (SYMM _let_164) _let_160 (SYMM (SYMM _let_163)) (CONG (REFL :args (tptp.n4)) _let_155 :args _let_153) (SYMM _let_162) _let_161) :args _let_91) (CONG _let_151 (TRANS (SYMM _let_161) (CONG _let_160 :args _let_157) (SYMM (SYMM _let_156)) (CONG (REFL :args (tptp.n5)) _let_155 :args _let_153) (SYMM _let_152) _let_150) :args _let_91) (CONG _let_151 (TRANS (SYMM _let_150) (SYMM (SYMM _let_149)) (CONG (SYMM _let_143) :args _let_94) (SYMM _let_148)) :args _let_91) (TRUE_INTRO _let_147))) :args (_let_68 _let_69 _let_108 _let_112 _let_105 _let_115 _let_122 _let_106 _let_107 _let_119 _let_121 _let_123 _let_30 _let_114 _let_120 _let_71 _let_113 _let_118 _let_117 _let_116))) :args (_let_71 _let_123 _let_122 _let_121 _let_30 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_108 _let_69 _let_107 _let_68 _let_106 _let_105))) :args (true _let_146)) :args ((or _let_88 (not _let_123) (not _let_122) (not _let_121) _let_31 _let_102 (not _let_120) (not _let_119) (not _let_118) (not _let_117) (not _let_116) (not _let_115) (not _let_114) (not _let_113) (not _let_112) (not _let_108) _let_87 (not _let_107) _let_86 (not _let_106) (not _let_105)))) _let_85 _let_145 _let_144 _let_143 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_51)) :args ((or _let_30 _let_39))) _let_53 :args (_let_30 true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_141 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_142)) :args _let_140))) _let_141 :args (_let_120 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_141 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_142)) :args _let_140))) _let_141 :args (_let_119 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_138 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_137))) _let_138 :args (_let_118 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_138 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_137))) _let_138 :args (_let_117 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_135 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_136)) :args _let_134))) _let_135 :args (_let_116 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_135 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_136)) :args _let_134))) _let_135 :args (_let_115 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_133)) :args _let_131))) _let_132 :args (_let_114 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_133)) :args _let_131))) _let_132 :args (_let_113 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_129 :args (tptp.tptp_minus_1 QUANTIFIERS_INST_E_MATCHING _let_130)) :args _let_128))) _let_129 :args (_let_112 false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_129 :args (tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_130)) :args _let_128))) _let_129 :args (_let_108 false _let_17)) _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.n6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_79)) :args _let_77)) _let_78 :args (_let_107 false _let_16)) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74)) _let_73 :args (_let_106 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_62 _let_125 _let_105 (not _let_126)))) _let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_127)) :args ((or _let_38 _let_36 _let_124 (not _let_127)))) _let_101 _let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.n0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_34 QUANTIFIERS_INST_E_MATCHING _let_67)) :args _let_66)) _let_65 :args (_let_127 false _let_64)) :args (_let_124 false _let_37 false _let_35 false _let_127)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_126 false _let_57)) :args (_let_105 false _let_61 false _let_124 false _let_126)) :args (_let_102 false _let_71 false _let_123 false _let_122 false _let_121 false _let_30 false _let_120 false _let_119 false _let_118 false _let_117 false _let_116 false _let_115 false _let_114 false _let_113 false _let_112 false _let_108 false _let_69 false _let_107 false _let_68 false _let_106 false _let_105)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_104 false _let_57)) :args (_let_28 false _let_32 false _let_102 false _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_38 _let_27 _let_55 (not _let_56)))) _let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_36 _let_62 _let_54 (not _let_63)))) _let_100 _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_34 tptp.n0 QUANTIFIERS_INST_E_MATCHING _let_67)) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_54 false _let_35 false _let_61 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_56 false _let_57)) :args (_let_27 false _let_37 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 4)) _let_53 :args ((not _let_26) true _let_39)) :args (false false _let_28 false _let_27 true _let_26)) :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 $$unsorted)) (tptp.leq X X)) _let_25 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lt X Y) (tptp.gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.geq X Y) (tptp.leq Y X))) _let_24 (forall ((X $$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_23 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n1) (tptp.succ X))) _let_21 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n2) (tptp.succ (tptp.succ X)))) _let_20 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n3) (tptp.succ (tptp.succ (tptp.succ X))))) _let_19 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n4) (tptp.succ (tptp.succ (tptp.succ (tptp.succ X)))))) _let_18 (forall ((X $$unsorted)) (= (tptp.plus X tptp.n5) (tptp.succ (tptp.succ (tptp.succ (tptp.succ (tptp.succ X))))))) _let_17 _let_16 _let_15 (forall ((X $$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_14 (tptp.gt tptp.n5 tptp.n4) (tptp.gt tptp.n6 tptp.n4) (tptp.gt tptp.n999 tptp.n4) (tptp.gt tptp.n6 tptp.n5) (tptp.gt tptp.n999 tptp.n5) (tptp.gt tptp.n999 tptp.n6) (tptp.gt tptp.n4 tptp.tptp_minus_1) (tptp.gt tptp.n5 tptp.tptp_minus_1) (tptp.gt tptp.n6 tptp.tptp_minus_1) (tptp.gt tptp.n999 tptp.tptp_minus_1) _let_11 (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.n6 tptp.n0) (tptp.gt tptp.n999 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.n6 tptp.n1) (tptp.gt tptp.n999 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.n6 tptp.n2) (tptp.gt tptp.n999 tptp.n2) (tptp.gt tptp.n3 tptp.n2) (tptp.gt tptp.n4 tptp.n3) (tptp.gt tptp.n5 tptp.n3) (tptp.gt tptp.n6 tptp.n3) (tptp.gt tptp.n999 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)))) (forall ((X $$unsorted)) (=> (and (tptp.leq tptp.n0 X) (tptp.leq X tptp.n6)) (or (= X tptp.n0) (= X tptp.n1) (= X tptp.n2) (= X tptp.n3) (= X tptp.n4) (= X tptp.n5) (= X tptp.n6)))) _let_10 (forall ((X $$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_9 _let_8 _let_7 (= _let_1 tptp.n1) (= _let_2 tptp.n2) (= _let_3 tptp.n3) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.70  )
% 0.22/0.70  % SZS output end Proof for SWV114+1
% 0.22/0.70  % cvc5---1.0.5 exiting
% 0.22/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------