TSTP Solution File: SWW573_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW573_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:21:34 EDT 2023
% Result : Theorem 15.76s 15.93s
% Output : Proof 15.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW573_2 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n009.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 22:59:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_ARI
% 15.76/15.93 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vo3trhRAJX/cvc5---1.0.5_7432.p...
% 15.76/15.93 ------- get file name : TPTP file name is SWW573_2
% 15.76/15.93 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7432.smt2...
% 15.76/15.93 --- Run --finite-model-find --decision=internal at 15...
% 15.76/15.93 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.76/15.93 % SZS status Theorem for SWW573_2
% 15.76/15.93 % SZS output start Proof for SWW573_2
% 15.76/15.93 (
% 15.76/15.93 (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int) (M Int) (N Int)) (=> (and (<= 0 A) (<= 0 M) (< M N) (< N A)) (forall ((F Int)) (=> (and (<= M F) (<= F N)) (=> (and (<= 0 F) (< F A)) (forall ((Ghx Int)) (=> (= Ghx (tptp.get3 A1 F)) (forall ((I Int)) (=> (= I M) (forall ((J Int)) (let ((_let_1 (tptp.get3 A1 F))) (let ((_let_2 (tptp.mk_array3 A A1))) (=> (= J N) (=> (and (<= M J) (<= J N) (<= M I) (<= I N) (tptp.permut_sub2 _let_2 _let_2 M (+ N 1)) (forall ((R Int)) (=> (and (<= M R) (< R I)) (<= (tptp.get3 A1 R) (tptp.get3 A1 F)))) (forall ((R Int)) (=> (and (< J R) (<= R N)) (<= (tptp.get3 A1 F) (tptp.get3 A1 R)))) (= _let_1 _let_1)) (forall ((J1 Int) (I1 Int) (A2 tptp.map_int_int)) (let ((_let_1 (<= M J1))) (let ((_let_2 (= I1 N))) (let ((_let_3 (= J1 I1))) (let ((_let_4 (tptp.get3 A1 F))) (=> (and (<= 0 A) _let_1 (<= J1 I1) (<= I1 N) (tptp.permut_sub2 (tptp.mk_array3 A A1) (tptp.mk_array3 A A2) M (+ N 1)) (or _let_2 (< _let_4 (tptp.get3 A2 I1))) (or (= J1 M) (< (tptp.get3 A2 J1) _let_4)) (= (tptp.get3 A2 F) _let_4) (forall ((R Int)) (=> (and (<= M R) (< R I1)) (<= (tptp.get3 A2 R) (tptp.get3 A1 F)))) (forall ((R Int)) (=> (and (< J1 R) (<= R N)) (<= (tptp.get3 A1 F) (tptp.get3 A2 R))))) (=> (or (< J1 I1) (and _let_3 (= I1 M)) (and _let_3 _let_2)) (=> (not (< I1 F)) (=> (< F J1) (=> (and (<= 0 M) (<= M F) (<= F N) (< N A) _let_1 (<= J1 N)) (forall ((A3 tptp.map_int_int)) (let ((_let_1 (tptp.mk_array3 A A3))) (let ((_let_2 (tptp.mk_array3 A A2))) (=> (and (<= 0 A) (tptp.exchange4 _let_2 _let_1 F J1) (tptp.permut_sub2 _let_2 _let_1 M (+ N 1))) (forall ((J2 Int)) (=> (= J2 (- J1 1)) (forall ((R Int)) (=> (and (<= I1 R) (<= R N)) (<= Ghx (tptp.get3 A3 R))))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((A1 tptp.array_int) (A2 tptp.array_int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb2 A1))) (let ((_let_2 (tptp.length2 tptp.int _let_1))) (let ((_let_3 (tptp.t2tb2 A2))) (= (tptp.exchange4 A1 A2 I J) (and (= _let_2 (tptp.length2 tptp.int _let_3)) (tptp.exchange2 tptp.int (tptp.elts tptp.int _let_1) (tptp.elts tptp.int _let_3) 0 _let_2 I J))))))))) (let ((_let_3 (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))))))))))) (let ((_let_4 (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_5 (forall ((U Int) (U1 tptp.map_int_int)) (= (tptp.tb2t (tptp.elts tptp.int (tptp.t2tb2 (tptp.mk_array3 U U1)))) U1)))) (let ((_let_6 (forall ((U Int) (U1 tptp.map_int_int)) (= (tptp.length2 tptp.int (tptp.t2tb2 (tptp.mk_array3 U U1))) U)))) (let ((_let_7 (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)))) (let ((_let_8 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_10 (>= (+ _let_9 (* (- 1) _let_8)) 1))) (let ((_let_11 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (tptp.t2tb2 _let_11))) (let ((_let_13 (tptp.elts tptp.int _let_12))) (let ((_let_14 (tptp.tb2t _let_13))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_14))) (let ((_let_16 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (tptp.t2tb2 _let_16))) (let ((_let_18 (tptp.elts tptp.int _let_17))) (let ((_let_19 (tptp.tb2t _let_18))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_19))) (let ((_let_21 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_22 (* (- 1) _let_21))) (let ((_let_23 (+ _let_9 _let_22))) (let ((_let_24 (>= _let_23 1))) (let ((_let_25 (tptp.get3 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_26 (tptp.get3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (not _let_10))) (let ((_let_29 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_30 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_29))) (let ((_let_31 (>= _let_30 0))) (let ((_let_32 (not _let_31))) (let ((_let_33 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_34 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_33))) (let ((_let_35 (>= _let_34 0))) (let ((_let_36 (not _let_35))) (let ((_let_37 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_38 (not (tptp.permut_sub2 _let_16 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_37)))) (let ((_let_39 (tptp.exchange4 _let_16 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_40 (not _let_39))) (let ((_let_41 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_42 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_41) 0)))) (let ((_let_43 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_44 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_43))) (let ((_let_45 (>= _let_44 1))) (let ((_let_46 (not _let_45))) (let ((_let_47 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_43))) (let ((_let_48 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_49 (not _let_48))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_54 (or _let_51 _let_53))) (let ((_let_55 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_41))) (let ((_let_56 (>= _let_55 1))) (let ((_let_57 (not _let_56))) (let ((_let_58 (and _let_57 _let_54 _let_52))) (let ((_let_59 (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 1)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 1) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 R))) 1)))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (= _let_9 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_64 (* (- 1) _let_63))) (let ((_let_65 (>= (+ _let_9 _let_64) 1))) (let ((_let_66 (not _let_65))) (let ((_let_67 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_68 (not _let_67))) (let ((_let_69 (and _let_68 _let_66))) (let ((_let_70 (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_71 (+ _let_9 (* (- 1) _let_70)))) (let ((_let_72 (>= _let_71 0))) (let ((_let_73 (and _let_49 _let_72))) (let ((_let_74 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_75 (not (tptp.permut_sub2 _let_74 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_37)))) (let ((_let_76 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_33))) (let ((_let_77 (>= _let_76 0))) (let ((_let_78 (not _let_77))) (let ((_let_79 (>= _let_55 0))) (let ((_let_80 (not _let_79))) (let ((_let_81 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_41))) (let ((_let_82 (>= _let_81 1))) (let ((_let_83 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_43) 1)))) (let ((_let_84 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 0))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_43) 0)))) (let ((_let_87 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43))) (let ((_let_88 (>= _let_87 1))) (let ((_let_89 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_90 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_89))) (let ((_let_91 (>= _let_90 1))) (let ((_let_92 (not (tptp.permut_sub2 _let_74 _let_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_37)))) (let ((_let_93 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_89) 1))) (let ((_let_94 (not _let_93))) (let ((_let_95 (>= _let_90 0))) (let ((_let_96 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0)))) (let ((_let_97 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0)))) (let ((_let_98 (or _let_97 _let_96 _let_95 _let_94 _let_92 _let_91 _let_88 _let_86 _let_85 _let_83 _let_82 _let_80 _let_78 _let_75 _let_73 _let_69 _let_62 (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) 0) (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 R))) 0)))) _let_60 _let_58 (not (>= _let_47 0)) _let_46 _let_42 _let_40 _let_38 _let_36 _let_32 _let_28))) (let ((_let_99 (forall ((A Int) (A1 tptp.map_int_int) (M Int) (N Int) (BOUND_VARIABLE_3831 tptp.map_int_int) (BOUND_VARIABLE_3829 Int) (BOUND_VARIABLE_3827 tptp.map_int_int) (BOUND_VARIABLE_3825 Int) (BOUND_VARIABLE_3823 Int) (BOUND_VARIABLE_3821 Int)) (let ((_let_1 (tptp.get3 A1 BOUND_VARIABLE_3821))) (let ((_let_2 (* (- 1) BOUND_VARIABLE_3829))) (let ((_let_3 (+ 1 N))) (let ((_let_4 (tptp.mk_array3 A BOUND_VARIABLE_3831))) (let ((_let_5 (tptp.mk_array3 A BOUND_VARIABLE_3827))) (let ((_let_6 (* (- 1) BOUND_VARIABLE_3823))) (let ((_let_7 (* (- 1) BOUND_VARIABLE_3825))) (let ((_let_8 (not (= N BOUND_VARIABLE_3825)))) (let ((_let_9 (not (= BOUND_VARIABLE_3823 BOUND_VARIABLE_3825)))) (let ((_let_10 (+ BOUND_VARIABLE_3823 _let_7))) (let ((_let_11 (tptp.mk_array3 A A1))) (let ((_let_12 (* (- 1) BOUND_VARIABLE_3821))) (let ((_let_13 (* (- 1) N))) (let ((_let_14 (+ M _let_13))) (or (not (>= A 0)) (not (>= M 0)) (>= _let_14 0) (not (>= (+ A _let_13) 1)) (not (tptp.permut_sub2 _let_11 _let_11 M _let_3)) (>= _let_14 1) (>= (+ M _let_12) 1) (not (>= (+ N _let_12) 0)) (not (>= BOUND_VARIABLE_3821 0)) (not (>= (+ A _let_12) 1)) (>= (+ M _let_6) 1) (>= _let_10 1) (not (>= (+ N _let_7) 0)) (not (tptp.permut_sub2 _let_11 _let_5 M _let_3)) (and _let_8 (>= (+ _let_1 (* (- 1) (tptp.get3 BOUND_VARIABLE_3827 BOUND_VARIABLE_3825))) 0)) (and (not (= M BOUND_VARIABLE_3823)) (not (>= (+ _let_1 (* (- 1) (tptp.get3 BOUND_VARIABLE_3827 BOUND_VARIABLE_3823))) 1))) (not (= _let_1 (tptp.get3 BOUND_VARIABLE_3827 BOUND_VARIABLE_3821))) (not (forall ((R Int)) (or (>= (+ M (* (- 1) R)) 1) (>= (+ R (* (- 1) BOUND_VARIABLE_3825)) 0) (>= (+ (tptp.get3 A1 BOUND_VARIABLE_3821) (* (- 1) (tptp.get3 BOUND_VARIABLE_3827 R))) 0)))) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) BOUND_VARIABLE_3823)) 1)) (not (>= (+ N (* (- 1) R)) 0)) (not (>= (+ (tptp.get3 A1 BOUND_VARIABLE_3821) (* (- 1) (tptp.get3 BOUND_VARIABLE_3827 R))) 1))))) (and (>= _let_10 0) (or _let_9 (not (= M BOUND_VARIABLE_3825))) (or _let_9 _let_8)) (>= (+ BOUND_VARIABLE_3821 _let_7) 1) (>= (+ BOUND_VARIABLE_3821 _let_6) 0) (not (>= (+ N _let_6) 0)) (not (tptp.exchange4 _let_5 _let_4 BOUND_VARIABLE_3821 BOUND_VARIABLE_3823)) (not (tptp.permut_sub2 _let_5 _let_4 M _let_3)) (>= (+ BOUND_VARIABLE_3825 _let_2) 1) (not (>= (+ N _let_2) 0)) (not (>= (+ _let_1 (* (- 1) (tptp.get3 BOUND_VARIABLE_3831 BOUND_VARIABLE_3829))) 1)))))))))))))))))))) (let ((_let_100 (not _let_98))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (or))) (let ((_let_103 (not _let_99))) (let ((_let_104 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_105 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_33))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_101) :args (_let_103)) (REWRITE :args ((=> _let_103 (not (or _let_97 _let_96 _let_95 _let_94 _let_92 _let_91 _let_88 _let_86 _let_85 _let_83 _let_82 (>= _let_105 1) _let_78 _let_75 _let_73 _let_69 _let_62 (not (forall ((R Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) R)) 1) (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) 0) (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 R))) 0)))) (not (forall ((R Int)) (or (not (>= (+ R (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 1)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (* (- 1) R)) 0)) (not (>= (+ (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (* (- 1) (tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 R))) 1))))) (and (>= _let_105 0) (or _let_104 _let_53) (or _let_104 _let_49)) (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_33) 1) (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_41) 0) _let_42 _let_40 _let_38 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_29) 1) _let_32 _let_28))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_99))) (REFL :args (_let_100)) :args _let_102)) _let_101 :args (_let_100 true _let_99)))) (let ((_let_107 (REFL :args (_let_98)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 27)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_10))) :args _let_102)) :args ((or _let_10 _let_98))) _let_106 :args (_let_10 true _let_98)))) (let ((_let_109 (forall ((U Int) (U1 tptp.map_int_int)) (= U1 (tptp.tb2t (tptp.elts tptp.int (tptp.t2tb2 (tptp.mk_array3 U U1)))))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_109))) (let ((_let_112 ((tptp.mk_array3 U U1)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_111)) _let_110 :args (_let_15 false _let_109)))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_111)) _let_110 :args (_let_20 false _let_109)))) (let ((_let_115 (not _let_24))) (let ((_let_116 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_41))) (let ((_let_117 (>= _let_116 1))) (let ((_let_118 (not _let_117))) (let ((_let_119 (or _let_118 _let_32 _let_115))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 18)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_102)) :args ((or _let_59 _let_98))) _let_106 :args (_let_59 true _let_98)))) (let ((_let_121 (_let_59))) (let ((_let_122 ((tptp.get3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 R)))) (let ((_let_123 (ASSUME :args _let_121))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 25)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_102)) :args ((or _let_35 _let_98))) _let_106 :args (_let_35 true _let_98)))) (let ((_let_125 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 26)) (CONG _let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_102)) :args ((or _let_31 _let_98))) _let_106 :args (_let_31 true _let_98)))) (let ((_let_127 (tptp.get3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_128 (tptp.get3 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_129 (= _let_128 _let_127))) (let ((_let_130 (tptp.length2 tptp.int _let_17))) (let ((_let_131 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_130))) (let ((_let_132 (* (- 1) _let_130))) (let ((_let_133 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_132) 0))) (let ((_let_134 (tptp.get3 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_135 (tptp.tb2t1 (tptp.get4 tptp.int 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:args (_let_61 true _let_98)))) (let ((_let_147 (forall ((K Int)) (let ((_let_1 (tptp.t2tb2 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (or (not (>= K 0)) (>= (+ K (* (- 1) (tptp.length2 tptp.int _let_1))) 0) (= K SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (= K SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) (= (tptp.get3 (tptp.tb2t (tptp.elts tptp.int _let_1)) K) (tptp.get3 (tptp.tb2t (tptp.elts tptp.int (tptp.t2tb2 (tptp.mk_array3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) K))))))) (let ((_let_148 (and _let_84 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_132) 0)) (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 0) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_132) 0)) _let_129 (= (tptp.get3 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) (tptp.get3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) _let_147))) (let ((_let_149 (tptp.t2tb _let_14))) (let ((_let_150 (tptp.t2tb _let_19))) (let ((_let_151 (tptp.exchange2 tptp.int 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(MACRO_SR_PRED_TRANSFORM (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_307 :args ((< _let_44 0)))) :args ((not _let_306)))) :args (_let_305 _let_45)) :args ((not (and _let_45 _let_305)) SB_LITERAL))) (CONG _let_281 (MACRO_SR_PRED_INTRO :args ((= (not _let_305) _let_304))) :args _let_102)) _let_266 :args (_let_304 false _let_45)) _let_297 :args ((not _let_299) false _let_304 false _let_117)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_278 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.get3 _let_14 K)))) :args _let_277))) _let_276 :args (_let_303 false _let_147)) :args (_let_27 true _let_298 false _let_301 true _let_300 true _let_299 false _let_303)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_32 _let_118 _let_115 (not _let_119)))) _let_126 _let_297 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_123 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_121))) _let_120 :args (_let_119 false _let_59)) :args (_let_115 false _let_31 false _let_117 false _let_119)) _let_114 _let_113 _let_108 :args (false false _let_27 true _let_24 false _let_20 false _let_15 false _let_10)) :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 ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb X))) (forall ((I tptp.map_int_int)) (= (tptp.tb2t (tptp.t2tb I)) I)) _let_7 (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb1 X))) (forall ((I Int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((M tptp.map_int_int) (A1 Int) (A2 Int) (B Int)) (=> (= A1 A2) (= (tptp.get3 (tptp.tb2t (tptp.set tptp.int tptp.int (tptp.t2tb M) (tptp.t2tb1 A1) (tptp.t2tb1 B))) A2) B))) (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 ((M tptp.map_int_int) (A1 Int) (A2 Int) (B Int)) (=> (not (= A1 A2)) (= (tptp.get3 (tptp.tb2t (tptp.set tptp.int tptp.int (tptp.t2tb M) (tptp.t2tb1 A1) (tptp.t2tb1 B))) A2) (tptp.get3 M A2)))) (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 ((B Int) (A Int)) (= (tptp.get3 (tptp.tb2t (tptp.const tptp.int tptp.int (tptp.t2tb1 B))) A) B)) (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_array2 A X X1))) (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)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) _let_6 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length2 A (tptp.mk_array2 A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) _let_5 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array2 A U U1)) U1))) (forall ((U tptp.array_int)) (let ((_let_1 (tptp.t2tb2 U))) (= U (tptp.mk_array3 (tptp.length2 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.length2 A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort1 A (tptp.get4 A X X1))) _let_4 (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.length2 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.length2 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.occ2 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.occ2 tptp.int _let_3 _let_2 L U) (tptp.occ2 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.occ2 A V M L U) (tptp.occ2 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.occ2 tptp.int _let_3 _let_2 L U) (+ 1 (tptp.occ2 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.occ2 A V M L U) (+ 1 (tptp.occ2 A V M L _let_1))))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.occ2 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.occ2 A V M L U) (+ (tptp.occ2 A V M L Mid) (tptp.occ2 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.occ2 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.occ2 A V M L U) 0)))) (forall ((V Int) (M tptp.map_int_int) (L Int) (U Int)) (=> (< 0 (tptp.occ2 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.occ2 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.occ2 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.occ2 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.occ2 tptp.int _let_1 (tptp.t2tb M1) L U) (tptp.occ2 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.occ2 A V M1 L U) (tptp.occ2 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.occ2 A V M1 L U) (tptp.occ2 A V M2 L U)))) (=> (forall ((V tptp.uni)) (=> (tptp.sort1 A V) (= (tptp.occ2 A V M1 L U) (tptp.occ2 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.length2 A A1))) (= (tptp.array_eq_sub1 A A1 A2 L U) (and (= _let_1 (tptp.length2 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.length2 A A1))) (= (tptp.array_eq A A1 A2) (and (= _let_1 (tptp.length2 A A2)) (tptp.map_eq_sub1 A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1))))) _let_3 (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)))))) _let_2 (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int)) (let ((_let_1 (tptp.length2 A A1))) (= (tptp.exchange3 A A1 A2 I J) (and (= _let_1 (tptp.length2 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.length2 A A1))) (= (tptp.permut3 A A1 A2 L U) (and (= _let_1 (tptp.length2 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_sub2 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.length2 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_sub1 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.length2 A A1))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni)) (let ((_let_1 (tptp.length2 A A1))) (= (tptp.permut_all A A1 A2) (and (= _let_1 (tptp.length2 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)) (=> (tptp.exchange4 A1 A2 I J) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (=> (<= 0 L) (=> (<= U (tptp.length2 tptp.int (tptp.t2tb2 A1))) (tptp.permut_sub2 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.length2 A A1)) (tptp.permut_sub1 A A1 A2 L U))))))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (L1 Int) (U1 Int) (L2 Int) (U2 Int)) (=> (tptp.permut_sub2 A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length2 tptp.int (tptp.t2tb2 A1)))) (tptp.permut_sub2 A1 A2 L2 U2))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L1 Int) (U1 Int) (L2 Int) (U2 Int)) (=> (tptp.permut_sub1 A A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length2 A A1))) (tptp.permut_sub1 A A1 A2 L2 U2))))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (I Int) (J Int)) (=> (tptp.exchange4 A1 A2 I J) (tptp.permut_all tptp.int (tptp.t2tb2 A1) (tptp.t2tb2 A2)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.76/15.93 )
% 15.76/15.93 % SZS output end Proof for SWW573_2
% 15.76/15.93 % cvc5---1.0.5 exiting
% 15.76/15.93 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------