%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW575_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 00:21:34 EDT 2023

% Result   : Theorem 15.52s 15.90s
% Output   : Proof 15.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : SWW575_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n006.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun Aug 27 18:44:52 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_ARI
% 15.52/15.90  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.GoRTrzLNW7/cvc5---1.0.5_15298.p...
% 15.52/15.90  ------- get file name : TPTP file name is SWW575_2
% 15.52/15.90  ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15298.smt2...
% 15.52/15.90  --- Run --finite-model-find --decision=internal at 15...
% 15.52/15.90  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.52/15.90  % SZS status Theorem for SWW575_2
% 15.52/15.90  % SZS output start Proof for SWW575_2
% 15.52/15.90  (
% 15.52/15.90  (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int) (M Int) (N Int) (K Int)) (let ((_let_1 (< N A))) (let ((_let_2 (< M N))) (let ((_let_3 (<= 0 M))) (=> (and (<= 0 A) _let_3 (<= M K) (<= K N) _let_1) (=> _let_2 (=> (and _let_3 _let_2 _let_1) (forall ((J Int) (I Int) (A2 tptp.map_int_int)) (let ((_let_1 (<= K J))) (=> (and (<= 0 A) (<= M J) (< J I) (<= I N) (tptp.permut_sub3 (tptp.mk_array3 A A1) (tptp.mk_array3 A A2) M (+ N 1)) (forall ((R Int)) (=> (and (<= M R) (<= R J)) (<= (tptp.get3 A2 R) 42))) (forall ((R Int)) (=> (and (< J R) (< R I)) (= (tptp.get3 A2 R) 42))) (forall ((R Int)) (=> (and (<= I R) (<= R N)) (<= 42 (tptp.get3 A2 R))))) (=> _let_1 (=> (and (<= 0 M) (<= M K) _let_1 (< J A)) (forall ((A3 tptp.map_int_int)) (let ((_let_1 (+ N 1))) (let ((_let_2 (tptp.mk_array3 A A3))) (let ((_let_3 (tptp.mk_array3 A A2))) (=> (and (<= 0 A) (tptp.permut_sub3 _let_3 _let_2 M (+ J 1)) (forall ((R Int)) (=> (and (<= M R) (<= R K)) (<= (tptp.get3 A3 R) (tptp.get3 A3 K)))) (forall ((R Int)) (=> (and (<= K R) (<= R J)) (<= (tptp.get3 A3 K) (tptp.get3 A3 R))))) (=> (tptp.permut_sub3 _let_3 _let_2 M _let_1) (=> (forall ((R Int)) (=> (and (< J R) (<= R N)) (= (tptp.get3 A3 R) (tptp.get3 A2 R)))) (=> (forall ((R Int)) (=> (and (<= M R) (<= R J)) (and (exists ((S Int)) (and (<= M S) (<= S J) (= (tptp.get3 A3 R) (tptp.get3 A2 S)))) (<= (tptp.get3 A3 R) (tptp.get3 A3 (+ J 1)))))) (=> (not (<= I K)) (=> (tptp.permut_sub3 _let_2 _let_2 M _let_1) (forall ((R Int)) (=> (and (<= I R) (<= R N)) (and (exists ((S Int)) (and (<= I S) (<= S N) (= (tptp.get3 A3 R) (tptp.get3 A3 S)))) (<= (tptp.get3 A3 (- I 1)) (tptp.get3 A3 R)))))))))))))))))))))))))))))) (let ((_let_2 (forall ((A tptp.array_int) (I Int)) (let ((_let_1 (tptp.t2tb2 A))) (= (tptp.tb2t1 (tptp.get4 tptp.int _let_1 I)) (tptp.get3 (tptp.tb2t (tptp.elts tptp.int _let_1)) I)))))) (let ((_let_3 (forall ((U Int) (U1 tptp.map_int_int)) (= (tptp.tb2t (tptp.elts tptp.int (tptp.t2tb2 (tptp.mk_array3 U U1)))) U1)))) (let ((_let_4 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_5 (tptp.t2tb2 _let_4))) (let ((_let_6 (tptp.tb2t (tptp.elts tptp.int _let_5)))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_6))) (let ((_let_8 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_10 (= _let_9 _let_8))) (let ((_let_11 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_12 (tptp.get3 _let_6 _let_11))) (let ((_let_13 (tptp.tb2t1 (tptp.get4 tptp.int _let_5 _let_11)))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (>= _let_8 42))) (let ((_let_16 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11))) (let ((_let_17 (* (- 1) _let_16))) (let ((_let_18 (+ _let_9 _let_17))) (let ((_let_19 (>= _let_18 0))) (let ((_let_20 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_11))) (let ((_let_21 (= _let_16 _let_20))) (let ((_let_22 (= _let_20 42))) (let ((_let_23 (forall ((U Int) (U1 tptp.map_int_int)) (= U1 (tptp.tb2t (tptp.elts tptp.int (tptp.t2tb2 (tptp.mk_array3 U U1)))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_26 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_25) 0))) (let ((_let_27 (not _let_26))) (let ((_let_28 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_29 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_28))) (let ((_let_30 (>= _let_29 1))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_27 _let_10))) (let ((_let_33 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 1) (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R)))))) (let ((_let_34 (forall ((S Int)) (or (not (>= (+ S (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 0)) (>= (+ S (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 1) (not (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 S) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (and _let_35 _let_19))) (let ((_let_37 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_38 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_37) 0))) (let ((_let_39 (not _let_38))) (let ((_let_40 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_41 (not (tptp.permut_sub3 _let_4 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_40)))) (let ((_let_42 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (and (not (forall ((S Int)) (or (not (>= (+ S (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ S (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 S) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R)))))) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) 1))))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (not _let_33))) (let ((_let_45 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_46 (not (tptp.permut_sub3 _let_45 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_40)))) (let ((_let_47 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_48 (not (tptp.permut_sub3 _let_45 _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_47)))) (let ((_let_49 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_37) 0))) (let ((_let_50 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_28) 1)))) (let ((_let_51 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_28) 1))) (let ((_let_52 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 1) (>= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) 42))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 0) (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) 42))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (>= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) 43)))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (not (tptp.permut_sub3 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_40)))) (let ((_let_59 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_37))) (let ((_let_60 (>= _let_59 0))) (let ((_let_61 (not _let_60))) (let ((_let_62 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_28))) (let ((_let_63 (>= _let_62 1))) (let ((_let_64 (not _let_63))) (let ((_let_65 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_28))) (let ((_let_66 (>= _let_65 1))) (let ((_let_67 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_68 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_67) 0))) (let ((_let_69 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_67) 1)))) (let ((_let_70 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_71 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_70) 0)))) (let ((_let_72 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_70) 1))) (let ((_let_73 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0)))) (let ((_let_74 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0)))) (let ((_let_75 (or _let_74 _let_73 _let_72 _let_71 _let_69 _let_68 _let_66 _let_64 _let_61 _let_58 _let_57 _let_55 _let_53 _let_51 _let_50 _let_49 _let_48 (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) 1) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) 1))))) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R))) 1))))) _let_46 _let_44 _let_43 _let_41 _let_39 _let_27 _let_36))) (let ((_let_76 (forall ((A Int) (A1 tptp.map_int_int) (M Int) (N Int) (K Int) (BOUND_VARIABLE_3567 tptp.map_int_int) (BOUND_VARIABLE_3565 Int) (BOUND_VARIABLE_3563 tptp.map_int_int) (BOUND_VARIABLE_3561 Int) (BOUND_VARIABLE_3559 Int)) (let ((_let_1 (* (- 1) BOUND_VARIABLE_3565))) (let ((_let_2 (+ 1 N))) (let ((_let_3 (tptp.mk_array3 A BOUND_VARIABLE_3567))) (let ((_let_4 (tptp.mk_array3 A BOUND_VARIABLE_3563))) (let ((_let_5 (* (- 1) BOUND_VARIABLE_3561))) (let ((_let_6 (* (- 1) BOUND_VARIABLE_3559))) (let ((_let_7 (* (- 1) N))) (let ((_let_8 (* (- 1) K))) (or (not (>= A 0)) (not (>= M 0)) (>= (+ M _let_8) 1) (not (>= (+ N _let_8) 0)) (not (>= (+ A _let_7) 1)) (>= (+ M _let_7) 0) (>= (+ M _let_6) 1) (>= (+ BOUND_VARIABLE_3559 _let_5) 0) (not (>= (+ N _let_5) 0)) (not (tptp.permut_sub3 (tptp.mk_array3 A A1) _let_4 M _let_2)) (not (forall ((R Int)) (or (>= (+ M (* (- 1) R)) 1) (>= (+ R (* (- 1) BOUND_VARIABLE_3559)) 1) (not (>= (tptp.get3 BOUND_VARIABLE_3563 R) 43))))) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) BOUND_VARIABLE_3559)) 1)) (>= (+ R (* (- 1) BOUND_VARIABLE_3561)) 0) (= (tptp.get3 BOUND_VARIABLE_3563 R) 42)))) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) BOUND_VARIABLE_3561)) 0)) (not (>= (+ N (* (- 1) R)) 0)) (>= (tptp.get3 BOUND_VARIABLE_3563 R) 42)))) (>= (+ K _let_6) 1) (not (>= (+ A _let_6) 1)) (>= (+ K _let_5) 0) (not (tptp.permut_sub3 _let_4 _let_3 M (+ 1 BOUND_VARIABLE_3559))) (not (forall ((R Int)) (let ((_let_1 (* (- 1) R))) (or (>= (+ M _let_1) 1) (not (>= (+ K _let_1) 0)) (not (>= (+ (tptp.get3 BOUND_VARIABLE_3567 R) (* (- 1) (tptp.get3 BOUND_VARIABLE_3567 K))) 1)))))) (not (forall ((R Int)) (or (>= (+ K (* (- 1) R)) 1) (>= (+ R (* (- 1) BOUND_VARIABLE_3559)) 1) (not (>= (+ (tptp.get3 BOUND_VARIABLE_3567 K) (* (- 1) (tptp.get3 BOUND_VARIABLE_3567 R))) 1))))) (not (tptp.permut_sub3 _let_4 _let_3 M _let_2)) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) BOUND_VARIABLE_3559)) 1)) (not (>= (+ N (* (- 1) R)) 0)) (= (tptp.get3 BOUND_VARIABLE_3563 R) (tptp.get3 BOUND_VARIABLE_3567 R))))) (not (forall ((R Int)) (or (>= (+ M (* (- 1) R)) 1) (>= (+ R (* (- 1) BOUND_VARIABLE_3559)) 1) (and (not (forall ((S Int)) (or (>= (+ M (* (- 1) S)) 1) (>= (+ S (* (- 1) BOUND_VARIABLE_3559)) 1) (not (= (tptp.get3 BOUND_VARIABLE_3563 S) (tptp.get3 BOUND_VARIABLE_3567 R)))))) (not (>= (+ (tptp.get3 BOUND_VARIABLE_3567 R) (* (- 1) (tptp.get3 BOUND_VARIABLE_3567 (+ 1 BOUND_VARIABLE_3559)))) 1)))))) (not (tptp.permut_sub3 _let_3 _let_3 M _let_2)) (>= (+ BOUND_VARIABLE_3561 _let_1) 1) (not (>= (+ N _let_1) 0)) (and (not (forall ((S Int)) (or (not (>= (+ S (* (- 1) BOUND_VARIABLE_3561)) 0)) (not (>= (+ N (* (- 1) S)) 0)) (not (= (tptp.get3 BOUND_VARIABLE_3567 S) (tptp.get3 BOUND_VARIABLE_3567 BOUND_VARIABLE_3565)))))) (>= (+ (tptp.get3 BOUND_VARIABLE_3567 BOUND_VARIABLE_3565) (* (- 1) (tptp.get3 BOUND_VARIABLE_3567 (+ (- 1) BOUND_VARIABLE_3561)))) 0)))))))))))))) (let ((_let_77 (not _let_75))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (or))) (let ((_let_80 (not _let_76))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_78) :args (_let_80)) (REWRITE :args ((=> _let_80 (not (or _let_74 _let_73 _let_72 _let_71 _let_69 _let_68 _let_66 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_37) 0) _let_61 _let_58 (not (forall ((R Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) R)) 1) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (>= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) 43))))) _let_55 (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (* (- 1) R)) 0)) (>= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) 42)))) _let_51 _let_50 _let_49 _let_48 (not (forall ((R Int)) (let ((_let_1 (* (- 1) R))) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_1) 1) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_1) 0)) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) 1)))))) (not (forall ((R Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (* (- 1) R)) 1) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R))) 1))))) _let_46 (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (* (- 1) R)) 0)) (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 R) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R))))) (not (forall ((R Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) R)) 1) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (and (not (forall ((S Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) S)) 1) (>= (+ S (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 1) (not (= (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 S) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R)))))) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 R) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (+ 1 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(forall ((U tptp.array_int)) (let ((_let_1 (tptp.t2tb2 U))) (= U (tptp.mk_array3 (tptp.length1 tptp.int _let_1) (tptp.tb2t (tptp.elts tptp.int _let_1)))))) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array2 A (tptp.length1 A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort1 A (tptp.get4 A X X1))) _let_2 (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get4 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb1 I)))) (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.array_int) (I Int) (V Int)) (let ((_let_1 (tptp.t2tb1 V))) (let ((_let_2 (tptp.t2tb2 A))) (= (tptp.tb2t2 (tptp.set2 tptp.int _let_2 I _let_1)) (tptp.mk_array3 (tptp.length1 tptp.int _let_2) (tptp.tb2t (tptp.set tptp.int tptp.int (tptp.elts tptp.int _let_2) (tptp.t2tb1 I) _let_1))))))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set2 A A1 I V) (tptp.mk_array2 A (tptp.length1 A A1) (tptp.set A tptp.int (tptp.elts A A1) (tptp.t2tb1 I) V)))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) (forall ((N Int) (V Int)) (let ((_let_1 (tptp.t2tb1 V))) (= (tptp.tb2t2 (tptp.make1 tptp.int N _let_1)) (tptp.mk_array3 N (tptp.tb2t (tptp.const tptp.int tptp.int _let_1)))))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make1 A N V) (tptp.mk_array2 A N (tptp.const A tptp.int V)))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (<= U L) (= (tptp.occ1 A V M L U) 0))) (forall ((V Int) (M tptp.map_int_int) (L Int) (U Int)) (let ((_let_1 (- U 1))) (let ((_let_2 (tptp.t2tb M))) (let ((_let_3 (tptp.t2tb1 V))) (=> (< L U) (=> (not (= (tptp.get3 M _let_1) V)) (= (tptp.occ1 tptp.int _let_3 _let_2 L U) (tptp.occ1 tptp.int _let_3 _let_2 L _let_1)))))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (- U 1))) (=> (tptp.sort1 A V) (=> (< L U) (=> (not (= (tptp.get A tptp.int M (tptp.t2tb1 _let_1)) V)) (= (tptp.occ1 A V M L U) (tptp.occ1 A V M L _let_1))))))) (forall ((V Int) (M tptp.map_int_int) (L Int) (U Int)) (let ((_let_1 (- U 1))) (let ((_let_2 (tptp.t2tb M))) (let ((_let_3 (tptp.t2tb1 V))) (=> (< L U) (=> (= (tptp.get3 M _let_1) V) (= (tptp.occ1 tptp.int _let_3 _let_2 L U) (+ 1 (tptp.occ1 tptp.int _let_3 _let_2 L _let_1))))))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (- U 1))) (=> (< L U) (=> (= (tptp.get A tptp.int M (tptp.t2tb1 _let_1)) V) (= (tptp.occ1 A V M L U) (+ 1 (tptp.occ1 A V M L _let_1))))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.occ1 A V M L U))) (=> (<= L U) (and (<= 0 _let_1) (<= _let_1 (- U L)))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (Mid Int) (U Int)) (=> (and (<= L Mid) (<= Mid U)) (= (tptp.occ1 A V M L U) (+ (tptp.occ1 A V M L Mid) (tptp.occ1 A V M Mid U))))) (forall ((V Int) (M tptp.map_int_int) (L Int) (U Int)) (=> (forall ((I Int)) (=> (and (<= L I) (< I U)) (not (= (tptp.get3 M I) V)))) (= (tptp.occ1 tptp.int (tptp.t2tb1 V) (tptp.t2tb M) L U) 0))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (tptp.sort1 A V) (=> (forall ((I Int)) (=> (and (<= L I) (< I U)) (not (= (tptp.get A tptp.int M (tptp.t2tb1 I)) V)))) (= (tptp.occ1 A V M L U) 0)))) (forall ((V Int) (M tptp.map_int_int) (L Int) (U Int)) (=> (< 0 (tptp.occ1 tptp.int (tptp.t2tb1 V) (tptp.t2tb M) L U)) (exists ((I Int)) (and (<= L I) (< I U) (= (tptp.get3 M I) V))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (tptp.sort1 A V) (=> (< 0 (tptp.occ1 A V M L U)) (exists ((I Int)) (and (<= L I) (< I U) (= (tptp.get A tptp.int M (tptp.t2tb1 I)) V)))))) (forall ((M tptp.map_int_int) (L Int) (U Int) (I Int)) (=> (and (<= L I) (< I U)) (< 0 (tptp.occ1 tptp.int (tptp.t2tb1 (tptp.get3 M I)) (tptp.t2tb M) L U)))) (forall ((A tptp.ty) (M tptp.uni) (L Int) (U Int) (I Int)) (=> (and (<= L I) (< I U)) (< 0 (tptp.occ1 A (tptp.get A tptp.int M (tptp.t2tb1 I)) M L U)))) (forall ((V Int) (M1 tptp.map_int_int) (M2 tptp.map_int_int) (L Int) (U Int)) (let ((_let_1 (tptp.t2tb1 V))) (=> (forall ((I Int)) (=> (and (<= L I) (< I U)) (= (tptp.get3 M1 I) (tptp.get3 M2 I)))) (= (tptp.occ1 tptp.int _let_1 (tptp.t2tb M1) L U) (tptp.occ1 tptp.int _let_1 (tptp.t2tb M2) L U))))) (forall ((A tptp.ty) (V tptp.uni) (M1 tptp.uni) (M2 tptp.uni) (L Int) (U Int)) (=> (forall ((I Int)) (let ((_let_1 (tptp.t2tb1 I))) (=> (and (<= L I) (< I U)) (= (tptp.get A tptp.int M1 _let_1) (tptp.get A tptp.int M2 _let_1))))) (= (tptp.occ1 A V M1 L U) (tptp.occ1 A V M2 L U)))) (forall ((A tptp.ty) (M1 tptp.uni) (M2 tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.permut2 A M1 M2 L U))) (and (=> _let_1 (forall ((V tptp.uni)) (= (tptp.occ1 A V M1 L U) (tptp.occ1 A V M2 L U)))) (=> (forall ((V tptp.uni)) (=> (tptp.sort1 A V) (= (tptp.occ1 A V M1 L U) (tptp.occ1 A V M2 L U)))) _let_1)))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (A3 tptp.uni) (L Int) (U Int)) (=> (tptp.permut2 A A1 A2 L U) (=> (tptp.permut2 A A2 A3 L U) (tptp.permut2 A A1 A3 L U)))) (forall ((A1 tptp.map_int_int) (A2 tptp.map_int_int) (L Int) (U Int) (I Int)) (=> (tptp.permut2 tptp.int (tptp.t2tb A1) (tptp.t2tb A2) L U) (=> (and (<= L I) (< I U)) (exists ((J Int)) (and (<= L J) (< J U) (= (tptp.get3 A1 J) (tptp.get3 A2 I))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int) (I Int)) (=> (tptp.permut2 A A1 A2 L U) (=> (and (<= L I) (< I U)) (exists ((J Int)) (and (<= L J) (< J U) (= (tptp.get A tptp.int A1 (tptp.t2tb1 J)) (tptp.get A tptp.int A2 (tptp.t2tb1 I)))))))) (forall ((A1 tptp.map_int_int) (A2 tptp.map_int_int) (L Int) (U Int)) (= (tptp.map_eq_sub1 tptp.int (tptp.t2tb A1) (tptp.t2tb A2) L U) (forall ((I Int)) (=> (and (<= L I) (< I U)) (= (tptp.get3 A1 I) (tptp.get3 A2 I)))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int)) (= (tptp.map_eq_sub1 A A1 A2 L U) (forall ((I Int)) (let ((_let_1 (tptp.t2tb1 I))) (=> (and (<= L I) (< I U)) (= (tptp.get A tptp.int A1 _let_1) (tptp.get A tptp.int A2 _let_1))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.length1 A A1))) (= (tptp.array_eq_sub1 A A1 A2 L U) (and (= _let_1 (tptp.length1 A A2)) (<= 0 L) (<= L _let_1) (<= 0 U) (<= U _let_1) (tptp.map_eq_sub1 A (tptp.elts A A1) (tptp.elts A A2) L U))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni)) (let ((_let_1 (tptp.length1 A A1))) (= (tptp.array_eq A A1 A2) (and (= _let_1 (tptp.length1 A A2)) (tptp.map_eq_sub1 A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1))))) (forall ((A1 tptp.map_int_int) (A2 tptp.map_int_int) (L Int) (U Int) (I Int) (J Int)) (= (tptp.exchange2 tptp.int (tptp.t2tb A1) (tptp.t2tb A2) L U I J) (and (<= L I) (< I U) (<= L J) (< J U) (= (tptp.get3 A1 I) (tptp.get3 A2 J)) (= (tptp.get3 A1 J) (tptp.get3 A2 I)) (forall ((K Int)) (=> (and (<= L K) (< K U)) (=> (not (= K I)) (=> (not (= K J)) (= (tptp.get3 A1 K) (tptp.get3 A2 K))))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb1 I))) (let ((_let_2 (tptp.t2tb1 J))) (= (tptp.exchange2 A A1 A2 L U I J) (and (<= L I) (< I U) (<= L J) (< J U) (= (tptp.get A tptp.int A1 _let_1) (tptp.get A tptp.int A2 _let_2)) (= (tptp.get A tptp.int A1 _let_2) (tptp.get A tptp.int A2 _let_1)) (forall ((K Int)) (let ((_let_1 (tptp.t2tb1 K))) (=> (and (<= L K) (< K U)) (=> (not (= K I)) (=> (not (= K J)) (= (tptp.get A tptp.int A1 _let_1) (tptp.get A tptp.int A2 _let_1)))))))))))) (forall ((A tptp.map_int_int) (L Int) (U Int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb A))) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (tptp.exchange2 tptp.int _let_1 (tptp.set tptp.int tptp.int (tptp.set tptp.int tptp.int _let_1 (tptp.t2tb1 I) (tptp.t2tb1 (tptp.get3 A J))) (tptp.t2tb1 J) (tptp.t2tb1 (tptp.get3 A I))) L U I J))))) (forall ((A tptp.ty) (A1 tptp.uni) (L Int) (U Int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb1 I))) (let ((_let_2 (tptp.t2tb1 J))) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (tptp.exchange2 A A1 (tptp.set A tptp.int (tptp.set A tptp.int A1 _let_1 (tptp.get A tptp.int A1 _let_2)) _let_2 (tptp.get A tptp.int A1 _let_1)) L U I J)))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int)) (let ((_let_1 (tptp.length1 A A1))) (= (tptp.exchange3 A A1 A2 I J) (and (= _let_1 (tptp.length1 A A2)) (tptp.exchange2 A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1 I J))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.length1 A A1))) (= (tptp.permut3 A A1 A2 L U) (and (= _let_1 (tptp.length1 A A2)) (<= 0 L) (<= L _let_1) (<= 0 U) (<= U _let_1) (tptp.permut2 A (tptp.elts A A1) (tptp.elts A A2) L U))))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (L Int) (U Int)) (let ((_let_1 (tptp.t2tb2 A1))) (let ((_let_2 (tptp.t2tb2 A2))) (let ((_let_3 (tptp.elts tptp.int _let_2))) (let ((_let_4 (tptp.elts tptp.int _let_1))) (= (tptp.permut_sub3 A1 A2 L U) (and (tptp.map_eq_sub1 tptp.int _let_4 _let_3 0 L) (tptp.permut3 tptp.int _let_1 _let_2 L U) (tptp.map_eq_sub1 tptp.int _let_4 _let_3 U (tptp.length1 tptp.int _let_1))))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.elts A A2))) (let ((_let_2 (tptp.elts A A1))) (= (tptp.permut_sub2 A A1 A2 L U) (and (tptp.map_eq_sub1 A _let_2 _let_1 0 L) (tptp.permut3 A A1 A2 L U) (tptp.map_eq_sub1 A _let_2 _let_1 U (tptp.length1 A A1))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni)) (let ((_let_1 (tptp.length1 A A1))) (= (tptp.permut_all A A1 A2) (and (= _let_1 (tptp.length1 A A2)) (tptp.permut2 A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1))))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (I Int) (J Int) (L Int) (U Int)) (let ((_let_1 (tptp.t2tb2 A1))) (=> (tptp.exchange3 tptp.int _let_1 (tptp.t2tb2 A2) I J) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (=> (<= 0 L) (=> (<= U (tptp.length1 tptp.int _let_1)) (tptp.permut_sub3 A1 A2 L U)))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int) (L Int) (U Int)) (=> (tptp.exchange3 A A1 A2 I J) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (=> (<= 0 L) (=> (<= U (tptp.length1 A A1)) (tptp.permut_sub2 A A1 A2 L U))))))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (L1 Int) (U1 Int) (L2 Int) (U2 Int)) (=> (tptp.permut_sub3 A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length1 tptp.int (tptp.t2tb2 A1)))) (tptp.permut_sub3 A1 A2 L2 U2))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L1 Int) (U1 Int) (L2 Int) (U2 Int)) (=> (tptp.permut_sub2 A A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length1 A A1))) (tptp.permut_sub2 A A1 A2 L2 U2))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int)) (=> (tptp.exchange3 A A1 A2 I J) (tptp.permut_all A A1 A2))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.52/15.90  )
% 15.52/15.90  % SZS output end Proof for SWW575_2
% 15.52/15.90  % cvc5---1.0.5 exiting
% 15.52/15.90  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------