%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW667_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 : Fri Sep  1 00:21:53 EDT 2023

% Result   : Theorem 16.62s 16.86s
% Output   : Proof 16.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWW667_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 17:38:04 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_ARI
% 16.62/16.86  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qgE7xDP2JC/cvc5---1.0.5_21132.p...
% 16.62/16.86  ------- get file name : TPTP file name is SWW667_2
% 16.62/16.86  ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21132.smt2...
% 16.62/16.86  --- Run --finite-model-find --decision=internal at 15...
% 16.62/16.86  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 16.62/16.86  % SZS status Theorem for SWW667_2
% 16.62/16.86  % SZS output start Proof for SWW667_2
% 16.62/16.86  (
% 16.62/16.86  (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int) (N Int)) (=> (and (<= 0 A) (= N A) (forall ((I Int)) (=> (and (<= 0 I) (< I N)) (<= 0 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb I))))))) (=> (<= 0 (- N 1)) (forall ((M Int) (S Int) (I Int)) (let ((_let_1 (<= 0 I))) (let ((_let_2 (and _let_1 (< I A)))) (let ((_let_3 (tptp.t2tb1 A1))) (=> (and _let_1 (<= I (- N 1))) (=> (and (= S (tptp.sum2 A1 0 I)) (tptp.is_max1 (tptp.tb2t2 (tptp.mk_array1 tptp.int A _let_3)) 0 I M) (<= S (* I M))) (=> _let_2 (=> (< M (tptp.tb2t (tptp.get tptp.int tptp.int _let_3 (tptp.t2tb I)))) (=> _let_2 (forall ((M1 Int)) (=> (= M1 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb I)))) (=> (and (<= 0 I) (< I A)) (forall ((S1 Int)) (let ((_let_1 (tptp.t2tb1 A1))) (=> (= S1 (+ S (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb I))))) (tptp.is_max1 (tptp.tb2t2 (tptp.mk_array1 tptp.int A _let_1)) 0 (+ I 1) M1)))))))))))))))))))))) (let ((_let_2 (forall ((A tptp.array_int) (L Int) (H Int) (M Int)) (let ((_let_1 (tptp.is_max1 A L H M))) (let ((_let_2 (< L H))) (let ((_let_3 (and (<= H L) (= M 0)))) (and (=> _let_1 (and (forall ((K Int)) (=> (and (<= L K) (< K H)) (<= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) K)) M))) (or _let_3 (and _let_2 (exists ((K Int)) (and (<= L K) (< K H) (= M (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) K))))))))) (=> (and (forall ((K Int)) (=> (and (<= L K) (< K H)) (<= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) K)) M))) (or _let_3 (and _let_2 (exists ((K Int)) (and (<= L K) (< K H) (= M (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A) K)))))))) _let_1)))))))) (let ((_let_3 (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)))) (let ((_let_4 (forall ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb1 X))))) (let ((_let_5 (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get2 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb I)))))) (let ((_let_6 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array1 A U U1)) U1))))) (let ((_let_7 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7))) (let ((_let_9 (tptp.tb2t2 _let_8))) (let ((_let_10 (tptp.t2tb2 _let_9))) (let ((_let_11 (= _let_8 _let_10))) (let ((_let_12 (tptp.elts tptp.int _let_8))) (let ((_let_13 (= _let_7 _let_12))) (let ((_let_14 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= (tptp.get2 tptp.int _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.get tptp.int tptp.int _let_12 _let_14)))) (let ((_let_16 (tptp.tb2t (tptp.get2 tptp.int _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64)))) (let ((_let_17 (* (- 1) _let_16))) (let ((_let_18 (tptp.tb2t (tptp.get tptp.int tptp.int _let_7 _let_14)))) (let ((_let_19 (+ _let_18 _let_17))) (let ((_let_20 (>= _let_19 0))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64))) (let ((_let_22 (forall ((J tptp.uni)) (= J (tptp.t2tb2 (tptp.tb2t2 J)))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tb2t2 J)))) :args (_let_22))) _let_23 :args (_let_11 false _let_22)))) (let ((_let_25 (tptp.sort1 (tptp.map tptp.int tptp.int) _let_7))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_13))) (let ((_let_28 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (or (not (tptp.sort1 (tptp.map tptp.int A) U1)) (= U1 (tptp.elts A (tptp.mk_array1 A U U1))))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (_let_4))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_13 (not _let_27)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb1 X)))) :args _let_30)) _let_31 :args (_let_25 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.mk_array1 A U U1)))) :args (_let_28))) _let_29 :args (_let_27 false _let_28)) :args (_let_13 false _let_25 false _let_27)))) (let ((_let_33 (_let_5))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.int _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb I))))) :args _let_33)) _let_34 :args (_let_15 false _let_5)))) (let ((_let_36 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64)))) (let ((_let_37 (>= _let_36 0))) (let ((_let_38 (not _let_37))) (let ((_let_39 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 0))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38 _let_20))) (let ((_let_42 (not _let_20))) (let ((_let_43 (forall ((K Int)) (let ((_let_1 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (not (>= K 0)) (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 1) (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (* (- 1) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 (tptp.tb2t2 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) K)))) 0)))))) (let ((_let_44 (not _let_41))) (let ((_let_45 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (tptp.is_max1 _let_9 0 _let_45 _let_18))) (let ((_let_47 (tptp.tb2t (tptp.get2 tptp.int _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_48 (= _let_18 _let_47))) (let ((_let_49 (not _let_48))) (let ((_let_50 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (and (or _let_50 (not (= _let_18 0))) _let_52))) (let ((_let_54 (not _let_43))) (let ((_let_55 (or _let_54 _let_53 _let_46))) (let ((_let_56 (forall ((BOUND_VARIABLE_1549 tptp.array_int) (BOUND_VARIABLE_1551 Int) (BOUND_VARIABLE_1553 Int) (BOUND_VARIABLE_1555 Int) (BOUND_VARIABLE_1698 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_1698))) (let ((_let_2 (>= (+ BOUND_VARIABLE_1551 (* (- 1) BOUND_VARIABLE_1553)) 0))) (or (not (forall ((K Int)) (or (not (>= (+ K (* (- 1) BOUND_VARIABLE_1551)) 0)) (>= (+ K (* (- 1) BOUND_VARIABLE_1553)) 0) (>= (+ BOUND_VARIABLE_1555 (* (- 1) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1549) K)))) 0)))) (and (or (not _let_2) (not (= BOUND_VARIABLE_1555 0))) (or _let_2 (>= (+ BOUND_VARIABLE_1551 _let_1) 1) (not (>= (+ BOUND_VARIABLE_1553 _let_1) 1)) (not (= BOUND_VARIABLE_1555 (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1549) BOUND_VARIABLE_1698)))))) (tptp.is_max1 BOUND_VARIABLE_1549 BOUND_VARIABLE_1551 BOUND_VARIABLE_1553 BOUND_VARIABLE_1555))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_56))) (let ((_let_59 (not _let_53))) (let ((_let_60 (not _let_52))) (let ((_let_61 (and _let_13 _let_11 _let_15))) (let ((_let_62 ((= _let_47 _let_18)))) (let ((_let_63 (APPLY_UF tptp.tb2t))) (let ((_let_64 (APPLY_UF tptp.get))) (let ((_let_65 (REFL :args (_let_14)))) (let ((_let_66 (ASSUME :args (_let_13)))) (let ((_let_67 (SYMM _let_66))) (let ((_let_68 (REFL :args (tptp.int)))) (let ((_let_69 (ASSUME :args (_let_15)))) (let ((_let_70 (SYMM _let_69))) (let ((_let_71 (APPLY_UF tptp.get2))) (let ((_let_72 (ASSUME :args (_let_11)))) (let ((_let_73 (SYMM _let_72))) (let ((_let_74 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (* (- 1) _let_18)))) (let ((_let_75 (>= _let_74 0))) (let ((_let_76 (tptp.sum2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_77 (tptp.is_max1 _let_9 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_78 (not _let_77))) (let ((_let_79 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_80 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_79) 1)))) (let ((_let_81 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 1)))) (let ((_let_82 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 0)))) (let ((_let_83 (or _let_82 (not (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (>= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.t2tb I))) 0)))) _let_81 _let_51 _let_80 _let_78 (>= (+ _let_76 (* (- 1) (* SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) 1) _let_75 _let_46))) (let ((_let_84 (forall ((A1 tptp.map_int_int) (N Int) (BOUND_VARIABLE_1868 Int) (BOUND_VARIABLE_1866 Int)) (let ((_let_1 (tptp.t2tb1 A1))) (let ((_let_2 (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb BOUND_VARIABLE_1868))))) (let ((_let_3 (tptp.tb2t2 (tptp.mk_array1 tptp.int N _let_1)))) (or (not (>= N 0)) (not (forall ((I Int)) (or (not (>= I 0)) (not (>= (+ N (* (- 1) I)) 1)) (>= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb I))) 0)))) (not (>= N 1)) (not (>= BOUND_VARIABLE_1868 0)) (not (>= (+ N (* (- 1) BOUND_VARIABLE_1868)) 1)) (not (tptp.is_max1 _let_3 0 BOUND_VARIABLE_1868 BOUND_VARIABLE_1866)) (>= (+ (tptp.sum2 A1 0 BOUND_VARIABLE_1868) (* (- 1) (* BOUND_VARIABLE_1866 BOUND_VARIABLE_1868))) 1) (>= (+ BOUND_VARIABLE_1866 (* (- 1) _let_2)) 0) (tptp.is_max1 _let_3 0 (+ 1 BOUND_VARIABLE_1868) _let_2)))))))) (let ((_let_85 (not _let_83))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (or))) (let ((_let_88 (not _let_84))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_86) :args (_let_88)) (REWRITE :args ((=> _let_88 (not (or _let_82 (not (forall ((I Int)) (or (not (>= I 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (* (- 1) I)) 1)) (>= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.t2tb I))) 0)))) _let_81 _let_51 _let_80 _let_78 (>= (+ _let_76 (* (- 1) (* SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) 1) _let_75 _let_46))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_84))) (REFL :args (_let_85)) :args _let_87)) _let_86 :args (_let_85 true _let_84)))) (let ((_let_90 (REFL :args (_let_83)))) (let ((_let_91 (_let_54))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_91)) :args _let_91) (REWRITE :args ((=> _let_54 (not (or _let_40 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 _let_79) 1) _let_20))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_43))) (REFL :args (_let_44)) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_46 _let_54 _let_53 (not _let_55)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_83 8)) _let_89 :args ((not _let_46) true _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 1)) :args ((or _let_52 _let_59))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_49 _let_60))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 3)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_87)) :args ((or _let_50 _let_83))) _let_89 :args (_let_50 true _let_83)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (MODUS_PONENS (AND_INTRO _let_66 _let_69 _let_72) (SCOPE (CONG (TRANS (CONG _let_68 _let_73 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_71) (SYMM _let_70) (CONG _let_68 _let_68 _let_67 _let_65 :args _let_64)) :args _let_63) :args (_let_13 _let_15 _let_11))) (SCOPE (SYMM (ASSUME :args _let_62)) :args _let_62)) :args (_let_13 _let_11 _let_15))) :args (true _let_61)) _let_35 _let_32 _let_24 :args (_let_48 false _let_15 false _let_13 false _let_11)) :args (_let_60 false _let_50 false _let_48)) :args (_let_59 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_58) :args (_let_9 0 _let_45 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1549) BOUND_VARIABLE_1698) (not (= (tptp.is_max1 BOUND_VARIABLE_1549 BOUND_VARIABLE_1551 BOUND_VARIABLE_1553 BOUND_VARIABLE_1555) true))))) :args _let_58))) (AND_ELIM _let_57 :args (1)) :args (_let_55 false _let_56)) :args (_let_54 true _let_46 true _let_53 false _let_55)) :args (_let_44 true _let_43)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 2)) _let_92 :args (_let_42 true _let_41)))) (let ((_let_94 (>= _let_36 1))) (let ((_let_95 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17) 0))) (let ((_let_96 (not _let_94))) (let ((_let_97 (or _let_40 _let_96 _let_95))) (let ((_let_98 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 1))) (let ((_let_99 (and _let_97 (or (and (not _let_98) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 0)) (and _let_98 (not (forall ((K Int)) (or (not (>= K 0)) (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 (tptp.tb2t2 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) K)))))))))))) (let ((_let_100 (or _let_78 _let_99))) (let ((_let_101 (forall ((BOUND_VARIABLE_1502 tptp.array_int) (BOUND_VARIABLE_1504 Int) (BOUND_VARIABLE_1506 Int) (BOUND_VARIABLE_1508 Int) (BOUND_VARIABLE_1631 Int)) (let ((_let_1 (>= (+ BOUND_VARIABLE_1504 (* (- 1) BOUND_VARIABLE_1506)) 0))) (let ((_let_2 (* (- 1) BOUND_VARIABLE_1631))) (or (not (tptp.is_max1 BOUND_VARIABLE_1502 BOUND_VARIABLE_1504 BOUND_VARIABLE_1506 BOUND_VARIABLE_1508)) (and (or (>= (+ BOUND_VARIABLE_1504 _let_2) 1) (not (>= (+ BOUND_VARIABLE_1506 _let_2) 1)) (>= (+ BOUND_VARIABLE_1508 (* (- 1) (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1502) BOUND_VARIABLE_1631)))) 0)) (or (and _let_1 (= BOUND_VARIABLE_1508 0)) (and (not _let_1) (not (forall ((K Int)) (or (not (>= (+ K (* (- 1) BOUND_VARIABLE_1504)) 0)) (>= (+ K (* (- 1) BOUND_VARIABLE_1506)) 0) (not (= BOUND_VARIABLE_1508 (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1502) K)))))))))))))))) (let ((_let_102 (_let_101))) (let ((_let_103 (not _let_95))) (let ((_let_104 (not _let_75))) (let ((_let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_20))))) (let ((_let_106 (< _let_74 0))) (let ((_let_107 (_let_106))) (let ((_let_108 (false))) (let ((_let_109 (_let_42))) (let ((_let_110 (ASSUME :args _let_109))) (let ((_let_111 (MACRO_SR_PRED_TRANSFORM _let_110 :args ((< _let_19 0))))) (let ((_let_112 (ASSUME :args (_let_95)))) (let ((_let_113 (ASSUME :args (_let_104)))) (let ((_let_114 (REFL :args (_let_41)))) (let ((_let_115 (not _let_21))) (let ((_let_116 (= _let_36 0))) (let ((_let_117 (_let_115))) (let ((_let_118 (_let_116))) (let ((_let_119 (not _let_15))) (let ((_let_120 (not _let_11))) (let ((_let_121 (not _let_13))) (let ((_let_122 (= _let_18 _let_16))) (let ((_let_123 (not _let_122))) (let ((_let_124 (_let_122))) (let ((_let_125 (ASSUME :args _let_124))) (let ((_let_126 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS _let_110 (SCOPE (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_125 (INT_TIGHT_UB _let_111) :args ((- 1) 1)) :args _let_108) :args _let_124) :args _let_109)) (MODUS_PONENS (AND_INTRO _let_72 _let_126 _let_69 _let_66) (SCOPE (CONG (TRANS (CONG _let_68 _let_68 (SYMM _let_67) _let_65 :args _let_64) _let_70 (CONG _let_68 (SYMM _let_73) (SYMM (SYMM _let_126)) :args _let_71)) :args _let_63) :args (_let_11 _let_21 _let_15 _let_13)))) :args (_let_13 _let_11 _let_15 _let_21 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_123)))) (TRUE_INTRO _let_125))) :args (_let_123 _let_122)) :args ((not (and _let_13 _let_11 _let_15 _let_21 _let_42)) SB_LITERAL))) (CONG (REFL :args (_let_121)) (REFL :args (_let_120)) (REFL :args (_let_119)) (REFL :args _let_117) _let_105 :args _let_87)) :args ((or _let_121 _let_120 _let_119 _let_20 _let_115))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (ARITH_TRICHOTOMY (ASSUME :args (_let_37)) (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_96)) :args ((< _let_36 1)))) :args _let_118) :args _let_118) (MACRO_SR_PRED_TRANSFORM (ASSUME :args _let_117) :args ((not _let_116)))) :args (_let_37 _let_96 _let_115))) (CONG (REFL :args (_let_38)) (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_94))) (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_21))) :args _let_87)) :args ((or _let_38 _let_21 _let_94))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 1)) (CONG _let_114 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_87)) :args ((or _let_37 _let_41))) _let_92 :args (_let_37 true _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_40 _let_96 _let_95 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG _let_114 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_87)) :args ((or _let_39 _let_41))) _let_92 :args (_let_39 true _let_41)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_110 _let_112 _let_113) :args (_let_104 _let_42 _let_95)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM _let_113 :args _let_107) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_107) _let_112 _let_111 :args (1.0 (- 1.0) 1.0)) :args _let_108) :args _let_107) :args (_let_75)) :args ((not _let_106)))) :args (_let_42 _let_95 _let_104)) :args ((not (and _let_104 _let_42 _let_95)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_75))) _let_105 (REFL :args (_let_103)) :args _let_87)) _let_93 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_83 7)) _let_89 :args (_let_104 true _let_83)) :args (_let_103 true _let_20 true _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_99 0)) :args ((or _let_97 (not _let_99)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_78 _let_99 (not _let_100)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 5)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) :args _let_87)) :args ((or _let_77 _let_83))) _let_89 :args (_let_77 true _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_102) :args (_let_9 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.is_max1 BOUND_VARIABLE_1502 BOUND_VARIABLE_1504 BOUND_VARIABLE_1506 BOUND_VARIABLE_1508) false)) (tptp.get2 tptp.int (tptp.t2tb2 BOUND_VARIABLE_1502) BOUND_VARIABLE_1631)))) :args _let_102))) (AND_ELIM _let_57 :args (0)) :args (_let_100 false _let_101)) :args (_let_99 false _let_77 false _let_100)) :args (_let_97 false _let_99)) :args (_let_96 false _let_39 true _let_95 false _let_97)) :args (_let_21 false _let_37 true _let_94)) _let_93 _let_35 _let_32 _let_24 :args (false false _let_21 true _let_20 false _let_15 false _let_13 false _let_11)) :args ((forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))) (forall ((A tptp.ty) (X tptp.bool1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_bool1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_bool1 A tptp.true1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_bool1 A tptp.false1 Z Z1) Z1))) (not (= tptp.true1 tptp.false1)) (forall ((U tptp.bool1)) (or (= U tptp.true1) (= U tptp.false1))) (forall ((U tptp.tuple02)) (= U tptp.tuple03)) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.ref A) (tptp.mk_ref A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.contents A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.contents A (tptp.mk_ref A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 B (tptp.get B A X X1))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.set B A X X1 X2))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni) (B1 tptp.uni)) (=> (tptp.sort1 B B1) (=> (= A1 A2) (= (tptp.get B A (tptp.set B A M A1 B1) A2) B1)))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni)) (=> (tptp.sort1 A A1) (=> (tptp.sort1 A A2) (forall ((B1 tptp.uni)) (=> (not (= A1 A2)) (= (tptp.get B A (tptp.set B A M A1 B1) A2) (tptp.get B A M A2))))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort1 B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.mk_array1 A X X1))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length1 A (tptp.mk_array1 A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) _let_6 (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array1 A (tptp.length1 A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort1 A (tptp.get2 A X X1))) (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb X))) (forall ((I Int)) (= (tptp.tb2t (tptp.t2tb I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)) _let_5 (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.set2 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set2 A A1 I V) (tptp.mk_array1 A (tptp.length1 A A1) (tptp.set A tptp.int (tptp.elts A A1) (tptp.t2tb I) V)))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make1 A N V) (tptp.mk_array1 A N (tptp.const A tptp.int V)))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (<= J I) (= (tptp.sum2 C I J) 0))) _let_4 (forall ((I tptp.map_int_int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((C tptp.map_int_int) (I Int) (J Int)) (=> (< I J) (= (tptp.sum2 C I J) (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C) (tptp.t2tb I))) (tptp.sum2 C (+ I 1) J))))) (forall ((C tptp.map_int_int) (I Int) (J Int)) (let ((_let_1 (- J 1))) (=> (< I J) (= (tptp.sum2 C I J) (+ (tptp.sum2 C I _let_1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C) (tptp.t2tb _let_1)))))))) (forall ((C tptp.map_int_int) (I Int) (K Int) (J Int)) (=> (and (<= I K) (<= K J)) (= (tptp.sum2 C I J) (+ (tptp.sum2 C I K) (tptp.sum2 C K J))))) (forall ((C1 tptp.map_int_int) (C2 tptp.map_int_int) (I Int) (J Int)) (=> (forall ((K Int)) (let ((_let_1 (tptp.t2tb K))) (=> (and (<= I K) (< K J)) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C1) _let_1)) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 C2) _let_1)))))) (= (tptp.sum2 C1 I J) (tptp.sum2 C2 I J)))) (forall ((X tptp.array_int)) (tptp.sort1 (tptp.array tptp.int) (tptp.t2tb2 X))) (forall ((I tptp.array_int)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) _let_3 (forall ((A tptp.array_int) (L Int) (H Int)) (= (tptp.sum3 A L H) (tptp.sum2 (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 A))) L H))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 16.62/16.87  )
% 16.62/16.87  % SZS output end Proof for SWW667_2
% 16.62/16.87  % cvc5---1.0.5 exiting
% 16.62/16.87  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------