TSTP Solution File: SWW594_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW594_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 00:21:38 EDT 2023
% Result : Theorem 15.50s 15.81s
% Output : Proof 15.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW594_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n018.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 : Sun Aug 27 22:38:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_ARI
% 15.50/15.81 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Ci5HN1yMyK/cvc5---1.0.5_18894.p...
% 15.50/15.81 ------- get file name : TPTP file name is SWW594_2
% 15.50/15.81 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18894.smt2...
% 15.50/15.81 --- Run --finite-model-find --decision=internal at 15...
% 15.50/15.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.50/15.81 % SZS status Theorem for SWW594_2
% 15.50/15.81 % SZS output start Proof for SWW594_2
% 15.50/15.81 (
% 15.50/15.81 (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int)) (=> (and (<= 0 A) (= A (+ tptp.usN 1))) (forall ((N Int) (M Int) (A2 tptp.map_int_int)) (let ((_let_1 (tptp.mk_array tptp.int A (tptp.t2tb2 A2)))) (let ((_let_2 (tptp.tb2t1 _let_1))) (=> (and (tptp.m_invariant M _let_2) (tptp.n_invariant N _let_2) (tptp.permut_all tptp.int _let_1 (tptp.mk_array tptp.int A (tptp.t2tb2 A1))) (<= 1 M) (<= N tptp.usN)) (=> (< M N) (=> (and (<= 0 A) (<= 0 tptp.f) (< tptp.f A)) (forall ((J Int) (I Int) (A3 tptp.map_int_int)) (let ((_let_1 (tptp.mk_array tptp.int A (tptp.t2tb2 A3)))) (let ((_let_2 (tptp.tb2t1 _let_1))) (let ((_let_3 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb2 A2) (tptp.t2tb tptp.f))))) (=> (and (tptp.i_invariant M N I _let_3 _let_2) (tptp.j_invariant M N J _let_3 _let_2) (tptp.m_invariant M _let_2) (tptp.n_invariant N _let_2) (<= 0 J) (<= I (+ tptp.usN 1)) (tptp.termination I J M N _let_3 _let_2) (tptp.permut_all tptp.int _let_1 (tptp.mk_array tptp.int A (tptp.t2tb2 A1)))) (=> (<= I J) (forall ((I1 Int)) (let ((_let_1 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb2 A2) (tptp.t2tb tptp.f))))) (let ((_let_2 (tptp.t2tb2 A3))) (let ((_let_3 (tptp.tb2t1 (tptp.mk_array tptp.int A _let_2)))) (=> (and (tptp.i_invariant M N I1 _let_1 _let_3) (<= I I1) (<= I1 N) (tptp.termination I1 J M N _let_1 _let_3)) (=> (and (<= 0 A) (<= 0 I1) (< I1 A)) (=> (not (< (tptp.tb2t (tptp.get tptp.int tptp.int _let_2 (tptp.t2tb I1))) _let_1)) (forall ((J1 Int)) (let ((_let_1 (tptp.t2tb2 A3))) (let ((_let_2 (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb2 A2) (tptp.t2tb tptp.f))))) (let ((_let_3 (tptp.tb2t1 (tptp.mk_array tptp.int A _let_1)))) (=> (and (tptp.j_invariant M N J1 _let_2 _let_3) (<= J1 J) (<= M J1) (tptp.termination I1 J1 M N _let_2 _let_3)) (=> (and (<= 0 J1) (< J1 A)) (=> (< _let_2 (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb J1)))) (forall ((J2 Int)) (=> (= J2 (- J1 1)) (tptp.termination I1 J2 M N (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb2 A2) (tptp.t2tb tptp.f))) (tptp.tb2t1 (tptp.mk_array tptp.int A (tptp.t2tb2 A3))))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((X tptp.map_int_int)) (tptp.sort (tptp.map tptp.int tptp.int) (tptp.t2tb2 X))))) (let ((_let_3 (forall ((I Int) (J Int) (I0 Int) (J0 Int) (R Int) (A tptp.array_int)) (= (tptp.termination I J I0 J0 R A) (or (and (< I0 I) (< J J0)) (and (<= I tptp.f) (<= tptp.f J) (= (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) tptp.f)) R))))))) (let ((_let_4 (forall ((M Int) (N Int) (J Int) (R Int) (A tptp.array_int)) (= (tptp.j_invariant M N J R A) (and (<= J N) (forall ((Q Int)) (=> (and (< J Q) (<= Q tptp.usN)) (<= R (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) Q))))) (=> (<= M J) (exists ((Q Int)) (and (<= M Q) (<= Q J) (<= (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) Q)) R))))))))) (let ((_let_5 (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)))) (let ((_let_6 (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get1 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb I)))))) (let ((_let_7 (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)))) (let ((_let_8 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array A U U1)) U1))))) (let ((_let_9 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_10 (tptp.tb2t (tptp.get tptp.int tptp.int _let_9 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))))) (let ((_let_11 (tptp.t2tb tptp.f))) (let ((_let_12 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (tptp.get tptp.int tptp.int _let_12 _let_11))) (let ((_let_14 (tptp.tb2t _let_13))) (let ((_let_15 (+ _let_14 (* (- 1) _let_10)))) (let ((_let_16 (>= _let_15 0))) (let ((_let_17 (= _let_13 (tptp.t2tb _let_14)))) (let ((_let_18 (+ 1 tptp.usN))) (let ((_let_19 (tptp.mk_array tptp.int _let_18 _let_9))) (let ((_let_20 (tptp.tb2t1 _let_19))) (let ((_let_21 (tptp.t2tb1 _let_20))) (let ((_let_22 (= _let_19 _let_21))) (let ((_let_23 (= _let_9 (tptp.elts tptp.int _let_19)))) (let ((_let_24 (tptp.get1 tptp.int _let_21 tptp.f))) (let ((_let_25 (tptp.tb2t _let_24))) (let ((_let_26 (= _let_14 _let_25))) (let ((_let_27 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_28 (+ tptp.f _let_27))) (let ((_let_29 (>= _let_28 1))) (let ((_let_30 (>= _let_28 0))) (let ((_let_31 (= _let_24 (tptp.t2tb _let_25)))) (let ((_let_32 (= _let_24 (tptp.get tptp.int tptp.int (tptp.elts tptp.int _let_21) _let_11)))) (let ((_let_33 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_34 (tptp.termination SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14 _let_20))) (let ((_let_35 (not (>= (+ tptp.usN _let_27) 0)))) (let ((_let_36 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 0)))) (let ((_let_37 (tptp.termination SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14 _let_20))) (let ((_let_38 (not _let_37))) (let ((_let_39 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_27) 1))) (let ((_let_40 (tptp.j_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_14 _let_20))) (let ((_let_41 (not _let_40))) (let ((_let_42 (>= (+ _let_14 (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int _let_9 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) 1))) (let ((_let_43 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_44 (not (>= (+ tptp.usN _let_43) 0)))) (let ((_let_45 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 0)))) (let ((_let_46 (tptp.termination SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14 _let_20))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43) 0)))) (let ((_let_49 (not (tptp.i_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_14 _let_20)))) (let ((_let_50 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_51 (tptp.mk_array tptp.int _let_18 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_52 (not (tptp.permut_all tptp.int _let_19 _let_51)))) (let ((_let_53 (not (tptp.termination SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14 _let_20)))) (let ((_let_54 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_55 (not (>= (+ tptp.usN _let_54) (- 1))))) (let ((_let_56 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 0)))) (let ((_let_57 (not (tptp.n_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20)))) (let ((_let_58 (not (tptp.m_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20)))) (let ((_let_59 (not (tptp.j_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_14 _let_20)))) (let ((_let_60 (not (tptp.i_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_14 _let_20)))) (let ((_let_61 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_62 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_61) 0))) (let ((_let_63 (not (>= (+ tptp.usN _let_61) 0)))) (let ((_let_64 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 1)))) (let ((_let_65 (tptp.mk_array tptp.int _let_18 _let_12))) (let ((_let_66 (not (tptp.permut_all tptp.int _let_65 _let_51)))) (let ((_let_67 (tptp.tb2t1 _let_65))) (let ((_let_68 (not (tptp.n_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_67)))) (let ((_let_69 (not (tptp.m_invariant SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_67)))) (let ((_let_70 (or _let_69 _let_68 _let_66 _let_64 _let_63 _let_62 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_53 _let_52 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_50) 1) _let_49 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_43) 1) _let_48 _let_47 _let_45 _let_44 _let_42 _let_41 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_27) 0)) _let_39 _let_38 _let_36 _let_35 _let_16 _let_34))) (let ((_let_71 (not _let_16))) (let ((_let_72 (forall ((BOUND_VARIABLE_3033 tptp.map_int_int) (BOUND_VARIABLE_3031 Int) (BOUND_VARIABLE_3035 Int) (A1 tptp.map_int_int) (BOUND_VARIABLE_3045 Int) (BOUND_VARIABLE_3043 tptp.map_int_int) (BOUND_VARIABLE_3041 Int) (BOUND_VARIABLE_3037 Int) (BOUND_VARIABLE_3039 Int)) (let ((_let_1 (tptp.t2tb2 BOUND_VARIABLE_3043))) (let ((_let_2 (+ 1 tptp.usN))) (let ((_let_3 (tptp.mk_array tptp.int _let_2 _let_1))) (let ((_let_4 (tptp.tb2t1 _let_3))) (let ((_let_5 (tptp.t2tb2 BOUND_VARIABLE_3033))) (let ((_let_6 (tptp.tb2t (tptp.get tptp.int tptp.int _let_5 (tptp.t2tb tptp.f))))) (let ((_let_7 (* (- 1) BOUND_VARIABLE_3039))) (let ((_let_8 (* (- 1) BOUND_VARIABLE_3037))) (let ((_let_9 (* (- 1) BOUND_VARIABLE_3045))) (let ((_let_10 (tptp.mk_array tptp.int _let_2 (tptp.t2tb2 A1)))) (let ((_let_11 (* (- 1) BOUND_VARIABLE_3035))) (let ((_let_12 (tptp.mk_array tptp.int _let_2 _let_5))) (let ((_let_13 (tptp.tb2t1 _let_12))) (or (not (tptp.m_invariant BOUND_VARIABLE_3031 _let_13)) (not (tptp.n_invariant BOUND_VARIABLE_3035 _let_13)) (not (tptp.permut_all tptp.int _let_12 _let_10)) (not (>= BOUND_VARIABLE_3031 1)) (not (>= (+ tptp.usN _let_11) 0)) (>= (+ BOUND_VARIABLE_3031 _let_11) 0) (not (tptp.i_invariant BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 BOUND_VARIABLE_3045 _let_6 _let_4)) (not (tptp.j_invariant BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 BOUND_VARIABLE_3041 _let_6 _let_4)) (not (tptp.m_invariant BOUND_VARIABLE_3031 _let_4)) (not (tptp.n_invariant BOUND_VARIABLE_3035 _let_4)) (not (>= BOUND_VARIABLE_3041 0)) (not (>= (+ tptp.usN _let_9) (- 1))) (not (tptp.termination BOUND_VARIABLE_3045 BOUND_VARIABLE_3041 BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 _let_6 _let_4)) (not (tptp.permut_all tptp.int _let_3 _let_10)) (not (>= (+ BOUND_VARIABLE_3041 _let_9) 0)) (not (tptp.i_invariant BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 BOUND_VARIABLE_3037 _let_6 _let_4)) (not (>= (+ BOUND_VARIABLE_3037 _let_9) 0)) (not (>= (+ BOUND_VARIABLE_3035 _let_8) 0)) (not (tptp.termination BOUND_VARIABLE_3037 BOUND_VARIABLE_3041 BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 _let_6 _let_4)) (not (>= BOUND_VARIABLE_3037 0)) (not (>= (+ tptp.usN _let_8) 0)) (>= (+ _let_6 (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb BOUND_VARIABLE_3037))))) 1) (not (tptp.j_invariant BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 BOUND_VARIABLE_3039 _let_6 _let_4)) (>= (+ BOUND_VARIABLE_3039 (* (- 1) BOUND_VARIABLE_3041)) 1) (>= (+ BOUND_VARIABLE_3031 _let_7) 1) (not (tptp.termination BOUND_VARIABLE_3037 BOUND_VARIABLE_3039 BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 _let_6 _let_4)) (not (>= BOUND_VARIABLE_3039 0)) (not (>= (+ tptp.usN _let_7) 0)) (>= (+ _let_6 (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb BOUND_VARIABLE_3039))))) 0) (tptp.termination BOUND_VARIABLE_3037 (+ (- 1) BOUND_VARIABLE_3039) BOUND_VARIABLE_3031 BOUND_VARIABLE_3035 _let_6 _let_4)))))))))))))))))) (let ((_let_73 (not _let_70))) (let ((_let_74 (or))) (let ((_let_75 (not _let_72))) (let ((_let_76 (_let_75))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_76)) :args _let_76) (REWRITE :args ((=> _let_75 (not (or _let_69 _let_68 _let_66 _let_64 _let_63 _let_62 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_53 _let_52 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_54) 0)) _let_49 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_54) 0)) _let_48 _let_47 _let_45 _let_44 _let_42 _let_41 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_50) 1) _let_39 _let_38 _let_36 _let_35 _let_16 _let_34))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_72))) (REFL :args (_let_73)) :args _let_74)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (3)) :args (_let_73 true _let_72)))) (let ((_let_78 (forall ((J tptp.uni)) (= J (tptp.t2tb (tptp.tb2t J)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((tptp.tb2t J)))) (let ((_let_82 (forall ((J tptp.uni)) (= J (tptp.t2tb1 (tptp.tb2t1 J)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (tptp.sort (tptp.map tptp.int tptp.int) _let_9))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_23))) (let ((_let_87 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (or (not (tptp.sort (tptp.map tptp.int A) U1)) (= U1 (tptp.elts A (tptp.mk_array A U U1))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_2))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (>= (+ tptp.f _let_43) 0))) (let ((_let_92 (and _let_91 (not (>= (+ tptp.f _let_50) 1)) _let_26))) (let ((_let_93 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_43) 0))) (let ((_let_94 (not _let_93))) (let ((_let_95 (and _let_94 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_50) 1)))) (let ((_let_96 (or _let_95 _let_92))) (let ((_let_97 (= _let_46 _let_96))) (let ((_let_98 (forall ((I Int) (J Int) (I0 Int) (J0 Int) (R Int) (A tptp.array_int)) (= (tptp.termination I J I0 J0 R A) (or (and (>= (+ I (* (- 1) I0)) 1) (not (>= (+ J (* (- 1) J0)) 0))) (and (>= (+ tptp.f (* (- 1) I)) 0) (not (>= (+ tptp.f (* (- 1) J)) 1)) (= R (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) tptp.f))))))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (_let_98))) (let ((_let_101 ((tptp.termination I J I0 J0 R A)))) (let ((_let_102 (REFL :args (_let_70)))) (let ((_let_103 (not 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(tptp.sort 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.sort A A1) (=> (tptp.sort 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.sort (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort (tptp.array A) (tptp.mk_array A X X1))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length A (tptp.mk_array A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort (tptp.map tptp.int A) (tptp.elts A X))) _let_8 (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array A (tptp.length A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort A (tptp.get1 A X X1))) (forall ((X Int)) (tptp.sort tptp.int (tptp.t2tb X))) (forall ((I Int)) (= (tptp.tb2t (tptp.t2tb I)) I)) _let_7 _let_6 (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort (tptp.array A) (tptp.set1 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set1 A A1 I V) (tptp.mk_array A (tptp.length 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.sort (tptp.array A) (tptp.make A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make A N V) (tptp.mk_array 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.occ A V M L U) 0))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (- U 1))) (=> (tptp.sort A V) (=> (< L U) (=> (not (= (tptp.get A tptp.int M (tptp.t2tb _let_1)) V)) (= (tptp.occ A V M L U) (tptp.occ A V M 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.t2tb _let_1)) V) (= (tptp.occ A V M L U) (+ 1 (tptp.occ A V M L _let_1))))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.occ 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.occ A V M L U) (+ (tptp.occ A V M L Mid) (tptp.occ A V M Mid U))))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (tptp.sort A V) (=> (forall ((I Int)) (=> (and (<= L I) (< I U)) (not (= (tptp.get A tptp.int M (tptp.t2tb I)) V)))) (= (tptp.occ A V M L U) 0)))) (forall ((A tptp.ty) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (tptp.sort A V) (=> (< 0 (tptp.occ A V M L U)) (exists ((I Int)) (and (<= L I) (< I U) (= (tptp.get A tptp.int M (tptp.t2tb I)) V)))))) (forall ((A tptp.ty) (M tptp.uni) (L Int) (U Int) (I Int)) (=> (and (<= L I) (< I U)) (< 0 (tptp.occ A (tptp.get A tptp.int M (tptp.t2tb I)) M 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.t2tb I))) (=> (and (<= L I) (< I U)) (= (tptp.get A tptp.int M1 _let_1) (tptp.get A tptp.int M2 _let_1))))) (= (tptp.occ A V M1 L U) (tptp.occ A V M2 L U)))) (forall ((A tptp.ty) (M1 tptp.uni) (M2 tptp.uni) (L Int) (U Int)) (let ((_let_1 (tptp.permut A M1 M2 L U))) (and (=> _let_1 (forall ((V tptp.uni)) (= (tptp.occ A V M1 L U) (tptp.occ A V M2 L U)))) (=> (forall ((V tptp.uni)) (=> (tptp.sort A V) (= (tptp.occ A V M1 L U) (tptp.occ 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.permut A A1 A2 L U) (=> (tptp.permut A A2 A3 L U) (tptp.permut A A1 A3 L U)))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int) (I Int)) (=> (tptp.permut 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.t2tb J)) (tptp.get A tptp.int A2 (tptp.t2tb I)))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int)) (= (tptp.map_eq_sub A A1 A2 L U) (forall ((I Int)) (let ((_let_1 (tptp.t2tb 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.length A A1))) (= (tptp.array_eq_sub A A1 A2 L U) (and (= _let_1 (tptp.length A A2)) (<= 0 L) (<= L _let_1) (<= 0 U) (<= U _let_1) (tptp.map_eq_sub 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.length A A1))) (= (tptp.array_eq A A1 A2) (and (= _let_1 (tptp.length A A2)) (tptp.map_eq_sub A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L Int) (U Int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb I))) (let ((_let_2 (tptp.t2tb J))) (= (tptp.exchange 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.t2tb 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.ty) (A1 tptp.uni) (L Int) (U Int) (I Int) (J Int)) (let ((_let_1 (tptp.t2tb I))) (let ((_let_2 (tptp.t2tb J))) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (tptp.exchange 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.length A A1))) (= (tptp.exchange1 A A1 A2 I J) (and (= _let_1 (tptp.length A A2)) (tptp.exchange 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.length A A1))) (= (tptp.permut1 A A1 A2 L U) (and (= _let_1 (tptp.length A A2)) (<= 0 L) (<= L _let_1) (<= 0 U) (<= U _let_1) (tptp.permut A (tptp.elts A A1) (tptp.elts A A2) L U))))) (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_sub A A1 A2 L U) (and (tptp.map_eq_sub A _let_2 _let_1 0 L) (tptp.permut1 A A1 A2 L U) (tptp.map_eq_sub A _let_2 _let_1 U (tptp.length A A1))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni)) (let ((_let_1 (tptp.length A A1))) (= (tptp.permut_all A A1 A2) (and (= _let_1 (tptp.length A A2)) (tptp.permut A (tptp.elts A A1) (tptp.elts A A2) 0 _let_1))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int) (L Int) (U Int)) (=> (tptp.exchange1 A A1 A2 I J) (=> (and (<= L I) (< I U)) (=> (and (<= L J) (< J U)) (=> (<= 0 L) (=> (<= U (tptp.length A A1)) (tptp.permut_sub A A1 A2 L U))))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (L1 Int) (U1 Int) (L2 Int) (U2 Int)) (=> (tptp.permut_sub A A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length A A1))) (tptp.permut_sub A A1 A2 L2 U2))))) (forall ((A tptp.ty) (A1 tptp.uni) (A2 tptp.uni) (I Int) (J Int)) (=> (tptp.exchange1 A A1 A2 I J) (tptp.permut_all A A1 A2))) (and (<= 1 tptp.f) (<= tptp.f tptp.usN)) (forall ((X tptp.array_int)) (tptp.sort (tptp.array tptp.int) (tptp.t2tb1 X))) (forall ((I tptp.array_int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) _let_5 (forall ((A tptp.array_int)) (= (tptp.found A) (forall ((P Int) (Q Int)) (let ((_let_1 (tptp.t2tb1 A))) (let ((_let_2 (tptp.tb2t (tptp.get1 tptp.int _let_1 tptp.f)))) (=> (and (<= 1 P) (<= P tptp.f) (<= tptp.f Q) (<= Q tptp.usN)) (and (<= (tptp.tb2t (tptp.get1 tptp.int _let_1 P)) _let_2) (<= _let_2 (tptp.tb2t (tptp.get1 tptp.int _let_1 Q)))))))))) (forall ((M Int) (A tptp.array_int)) (= (tptp.m_invariant M A) (and (<= M tptp.f) (forall ((P Int) (Q Int)) (let ((_let_1 (tptp.t2tb1 A))) (=> (and (<= 1 P) (< P M) (<= M Q) (<= Q tptp.usN)) (<= (tptp.tb2t (tptp.get1 tptp.int _let_1 P)) (tptp.tb2t (tptp.get1 tptp.int _let_1 Q))))))))) (forall ((N Int) (A tptp.array_int)) (= (tptp.n_invariant N A) (and (<= tptp.f N) (forall ((P Int) (Q Int)) (let ((_let_1 (tptp.t2tb1 A))) (=> (and (<= 1 P) (<= P N) (< N Q) (<= Q tptp.usN)) (<= (tptp.tb2t (tptp.get1 tptp.int _let_1 P)) (tptp.tb2t (tptp.get1 tptp.int _let_1 Q))))))))) (forall ((M Int) (N Int) (I Int) (R Int) (A tptp.array_int)) (= (tptp.i_invariant M N I R A) (and (<= M I) (forall ((P Int)) (=> (and (<= 1 P) (< P I)) (<= (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) P)) R))) (=> (<= I N) (exists ((P Int)) (and (<= I P) (<= P N) (<= R (tptp.tb2t (tptp.get1 tptp.int (tptp.t2tb1 A) P))))))))) _let_4 _let_3 _let_2 (forall ((I tptp.map_int_int)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.50/15.81 )
% 15.50/15.81 % SZS output end Proof for SWW594_2
% 15.50/15.81 % cvc5---1.0.5 exiting
% 15.50/15.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------