TSTP Solution File: SWW636_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW636_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 00:21:47 EDT 2023
% Result : Theorem 15.60s 15.87s
% Output : Proof 15.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW636_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Aug 27 17:44:25 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.51 %----Proving TF0_ARI
% 15.60/15.87 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YvpPziHzXX/cvc5---1.0.5_32334.p...
% 15.60/15.87 ------- get file name : TPTP file name is SWW636_2
% 15.60/15.87 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32334.smt2...
% 15.60/15.87 --- Run --finite-model-find --decision=internal at 15...
% 15.60/15.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.60/15.87 % SZS status Theorem for SWW636_2
% 15.60/15.87 % SZS output start Proof for SWW636_2
% 15.60/15.87 (
% 15.60/15.87 (let ((_let_1 (not (forall ((A Int) (A1 tptp.map_int_int) (L Int) (R Int)) (let ((_let_1 (<= 0 L))) (=> (and (<= 0 A) _let_1 (<= L R) (<= R A)) (=> (< (+ L 1) R) (=> (and _let_1 (< L A)) (forall ((I Int) (Mr Int) (Ml Int) (A2 tptp.map_int_int)) (let ((_let_1 (< I A))) (let ((_let_2 (<= 0 I))) (let ((_let_3 (tptp.t2tb1 A1))) (let ((_let_4 (tptp.t2tb1 A2))) (=> (and (<= L Ml) (< Ml I) (<= I Mr) (<= Mr R) (forall ((J Int)) (=> (and (<= L J) (< J Ml)) (< (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A2) (tptp.t2tb J))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L)))))) (forall ((J Int)) (=> (and (<= Ml J) (< J I)) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A2) (tptp.t2tb J))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L)))))) (forall ((J Int)) (=> (and (<= Mr J) (< J R)) (< (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A2) (tptp.t2tb J)))))) (tptp.permut_sub1 tptp.int (tptp.mk_array1 tptp.int A _let_3) (tptp.mk_array1 tptp.int A _let_4) L R)) (=> (< I Mr) (=> (and (<= 0 A) _let_2 _let_1) (=> (< (tptp.tb2t (tptp.get tptp.int tptp.int _let_4 (tptp.t2tb I))) (tptp.tb2t (tptp.get tptp.int tptp.int _let_3 (tptp.t2tb L)))) (=> (and (<= 0 Ml) (< Ml A) _let_2 _let_1) (forall ((A3 tptp.map_int_int)) (=> (and (<= 0 A) (tptp.exchange3 tptp.int (tptp.mk_array1 tptp.int A (tptp.t2tb1 A2)) (tptp.mk_array1 tptp.int A (tptp.t2tb1 A3)) Ml I)) (forall ((Ml1 Int)) (=> (= Ml1 (+ Ml 1)) (forall ((I1 Int)) (=> (= I1 (+ I 1)) (=> (tptp.permut_sub1 tptp.int (tptp.mk_array1 tptp.int A (tptp.t2tb1 A2)) (tptp.mk_array1 tptp.int A (tptp.t2tb1 A3)) L R) (forall ((J Int)) (=> (and (<= L J) (< J Ml1)) (< (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A3) (tptp.t2tb J))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L))))))))))))))))))))))))))))))) (let ((_let_2 (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))))))) (let ((_let_3 (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.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.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)))))))))))))) (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 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length1 A (tptp.mk_array1 A U U1)) U)))) (let ((_let_8 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_10 (tptp.tb2t (tptp.get tptp.int tptp.int _let_9 _let_8)))) (let ((_let_11 (* (- 1) _let_10))) (let ((_let_12 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.tb2t (tptp.get tptp.int tptp.int _let_12 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_14 (+ _let_13 _let_11))) (let ((_let_15 (>= _let_14 1))) (let ((_let_16 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9))) (let ((_let_17 (tptp.elts tptp.int _let_16))) (let ((_let_18 (= _let_9 _let_17))) (let ((_let_19 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_20 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_19))) (let ((_let_21 (tptp.elts tptp.int _let_20))) (let ((_let_22 (= _let_19 _let_21))) (let ((_let_23 (tptp.tb2t (tptp.get tptp.int tptp.int _let_19 _let_8)))) (let ((_let_24 (* (- 1) _let_23))) (let ((_let_25 (>= (+ _let_13 _let_24) 1))) (let ((_let_26 (tptp.get tptp.int tptp.int _let_17 _let_8))) (let ((_let_27 (= _let_26 (tptp.get tptp.int tptp.int _let_21 _let_8)))) (let ((_let_28 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_29 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_28))) (let ((_let_30 (>= _let_29 1))) (let ((_let_31 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_32 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_31))) (let ((_let_33 (>= _let_32 1))) (let ((_let_34 (not (tptp.permut_sub1 tptp.int _let_20 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_35 (tptp.exchange3 tptp.int _let_20 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_36 (not _let_35))) (let ((_let_37 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_28) 1)))) (let ((_let_38 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 0))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_41 (tptp.tb2t (tptp.get tptp.int tptp.int _let_19 _let_40)))) (let ((_let_42 (>= (+ _let_13 (* (- 1) _let_41)) 1))) (let ((_let_43 (not _let_42))) (let ((_let_44 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_45 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_44) 1)))) (let ((_let_46 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 0))) (let ((_let_47 (not _let_46))) (let ((_let_48 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_44))) (let ((_let_49 (>= _let_48 1))) (let ((_let_50 (not _let_49))) (let ((_let_51 (not (tptp.permut_sub1 tptp.int (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12) _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_52 (not (forall ((J Int)) (or (not (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 0)) (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) 0) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.t2tb J))))))))) (let ((_let_53 (forall ((J Int)) (or (not (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 0)) (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 0) (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.t2tb J))))) 1))))) (let ((_let_54 (not _let_53))) (let ((_let_55 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_56 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_55) 0))) (let ((_let_57 (not _let_56))) (let ((_let_58 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_28) 1))) (let ((_let_59 (not _let_58))) (let ((_let_60 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_28) 1))) (let ((_let_61 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) 1)))) (let ((_let_62 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_63 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_62))) (let ((_let_64 (>= _let_63 (- 1)))) (let ((_let_65 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_62) 0))) (let ((_let_66 (not _let_65))) (let ((_let_67 (>= _let_63 1))) (let ((_let_68 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_69 (not _let_68))) (let ((_let_70 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 0)))) (let ((_let_71 (or _let_70 _let_69 _let_67 _let_66 _let_64 _let_61 _let_60 _let_59 (not (>= _let_48 0)) _let_57 _let_54 _let_52 (not (forall ((J Int)) (or (not (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) 0)) (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) 0) (not (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.t2tb J))))) 0))))) _let_51 _let_50 _let_47 _let_45 _let_43 _let_39 _let_37 _let_36 _let_34 _let_33 _let_30 _let_15))) (let ((_let_72 (not _let_15))) (let ((_let_73 (forall ((A Int) (A1 tptp.map_int_int) (L Int) (R Int) (BOUND_VARIABLE_2807 tptp.map_int_int) (BOUND_VARIABLE_2805 Int) (BOUND_VARIABLE_2803 tptp.map_int_int) (BOUND_VARIABLE_2801 Int) (BOUND_VARIABLE_2799 Int) (BOUND_VARIABLE_2797 Int)) (let ((_let_1 (tptp.t2tb1 BOUND_VARIABLE_2807))) (let ((_let_2 (tptp.t2tb1 A1))) (let ((_let_3 (tptp.tb2t (tptp.get tptp.int tptp.int _let_2 (tptp.t2tb L))))) (let ((_let_4 (* (- 1) BOUND_VARIABLE_2805))) (let ((_let_5 (tptp.mk_array1 tptp.int A _let_1))) (let ((_let_6 (tptp.t2tb1 BOUND_VARIABLE_2803))) (let ((_let_7 (tptp.mk_array1 tptp.int A _let_6))) (let ((_let_8 (* (- 1) BOUND_VARIABLE_2797))) (let ((_let_9 (* (- 1) BOUND_VARIABLE_2799))) (let ((_let_10 (* (- 1) BOUND_VARIABLE_2801))) (let ((_let_11 (+ BOUND_VARIABLE_2799 _let_10))) (let ((_let_12 (* (- 1) R))) (let ((_let_13 (+ L _let_12))) (or (not (>= A 0)) (not (>= L 0)) (>= _let_13 1) (not (>= (+ A _let_12) 0)) (>= _let_13 (- 1)) (not (>= (+ A (* (- 1) L)) 1)) (>= (+ L _let_8) 1) (>= (+ BOUND_VARIABLE_2797 _let_9) 0) (>= _let_11 1) (not (>= (+ R _let_10) 0)) (not (forall ((J Int)) (or (>= (+ L (* (- 1) J)) 1) (>= (+ J (* (- 1) BOUND_VARIABLE_2797)) 0) (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 BOUND_VARIABLE_2803) (tptp.t2tb J))))) 1)))) (not (forall ((J Int)) (or (not (>= (+ J (* (- 1) BOUND_VARIABLE_2797)) 0)) (>= (+ J (* (- 1) BOUND_VARIABLE_2799)) 0) (= (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L))) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 BOUND_VARIABLE_2803) (tptp.t2tb J))))))) (not (forall ((J Int)) (or (not (>= (+ J (* (- 1) BOUND_VARIABLE_2801)) 0)) (not (>= (+ R (* (- 1) J)) 1)) (not (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 A1) (tptp.t2tb L))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 BOUND_VARIABLE_2803) (tptp.t2tb J))))) 0))))) (not (tptp.permut_sub1 tptp.int (tptp.mk_array1 tptp.int A _let_2) _let_7 L R)) (>= _let_11 0) (not (>= BOUND_VARIABLE_2799 0)) (not (>= (+ A _let_9) 1)) (not (>= (+ _let_3 (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int _let_6 (tptp.t2tb BOUND_VARIABLE_2799))))) 1)) (not (>= BOUND_VARIABLE_2797 0)) (not (>= (+ A _let_8) 1)) (not (tptp.exchange3 tptp.int _let_7 _let_5 BOUND_VARIABLE_2797 BOUND_VARIABLE_2799)) (not (tptp.permut_sub1 tptp.int _let_7 _let_5 L R)) (>= (+ L _let_4) 1) (not (>= (+ BOUND_VARIABLE_2797 _let_4) 0)) (>= (+ _let_3 (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb BOUND_VARIABLE_2805))))) 1)))))))))))))))))) (let ((_let_74 (not _let_71))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (or))) (let ((_let_77 (not _let_73))) (let ((_let_78 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_55))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_75) :args (_let_77)) (REWRITE :args ((=> _let_77 (not (or _let_70 _let_69 _let_67 _let_66 _let_64 _let_61 _let_60 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_44) 0) (>= _let_78 1) _let_57 (not (forall ((J Int)) (or (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) J)) 1) (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) 0) (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.t2tb J))))) 1)))) _let_52 (not (forall ((J Int)) (or (not (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (* (- 1) J)) 1)) (not (>= (+ (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (* (- 1) (tptp.tb2t (tptp.get tptp.int tptp.int (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.t2tb J))))) 0))))) _let_51 (>= _let_78 0) _let_47 _let_45 _let_43 _let_39 _let_37 _let_36 _let_34 _let_33 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_31) 0)) _let_15))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_73))) (REFL :args (_let_74)) :args _let_76)) _let_75 :args (_let_74 true _let_73)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_71 24)) _let_79 :args (_let_72 true _let_71)))) (let ((_let_81 (tptp.map tptp.int tptp.int))) (let ((_let_82 (tptp.sort1 _let_81 _let_9))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_18))) (let ((_let_85 (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_86 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_85))) (let ((_let_88 ((tptp.mk_array1 A U U1)))) (let ((_let_89 (_let_4))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 ((tptp.t2tb1 X)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_18 (not _let_84)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_89)) _let_90 :args (_let_82 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_88)) :args _let_87)) _let_86 :args (_let_84 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(_let_183 false _let_65 false _let_56 false _let_58 false _let_49 true _let_30 true _let_101 false _let_182)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_181 (SCOPE (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_180) (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_181 :args ((< _let_171 0)))) :args ((- 1) 1)) :args _let_138) :args _let_180) :args _let_179)) :args _let_179)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_174) _let_172))) (REFL :args (_let_173)) :args _let_76)) (MACRO_RESOLUTION_TRUST (MACRO_SR_PRED_TRANSFORM (NOT_AND (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args _let_178) :args _let_178) _let_177 _let_176 :args ((- 1.0) (- 1.0) 1.0)) :args _let_138) :args (_let_58 _let_155 _let_108 _let_172))) :args ((or _let_59 _let_30 _let_101 _let_174))) _let_175 _let_156 _let_154 :args (_let_174 false _let_58 true _let_30 true _let_101)) :args (_let_173 true _let_172)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_170) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb K)))) :args _let_170))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_115 6)) :args ((or _let_112 _let_125))) _let_124 :args (_let_112 false _let_115)) :args (_let_169 false _let_112)) :args (_let_27 true _let_101 false _let_167 true _let_166 true _let_165 false _let_169)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_33 _let_97 _let_25 (not _let_98)))) _let_164 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_158)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_160) (SCOPE (MACRO_SR_PRED_TRANSFORM _let_162 :args _let_157) :args _let_159)) :args _let_159)) :args (true _let_158)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_155) _let_30))) (MACRO_SR_PRED_INTRO :args ((= (not _let_108) _let_101))) (REFL :args _let_157) :args _let_76)) _let_156 _let_154 :args (_let_102 true _let_30 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb J)))) :args _let_100))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 10)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_76)) :args ((or _let_53 _let_71))) _let_79 :args (_let_53 true _let_71)) :args (_let_98 false _let_53)) :args (_let_25 true _let_33 true _let_97 false _let_98)) _let_96 _let_92 _let_80 :args (false false _let_27 false _let_25 false _let_22 false _let_18 true _let_15)) :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))) _let_7 (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)))) _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 ((A tptp.map_int_int) (L Int) (U Int)) (= (tptp.sorted_sub2 A L U) (forall ((I1 Int) (I2 Int)) (let ((_let_1 (tptp.t2tb1 A))) (=> (and (<= L I1) (<= I1 I2) (< I2 U)) (<= (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb I1))) (tptp.tb2t (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb I2))))))))) (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)) (forall ((A tptp.array_int) (L Int) (U Int)) (= (tptp.sorted_sub3 A L U) (tptp.sorted_sub2 (tptp.tb2t1 (tptp.elts tptp.int (tptp.t2tb2 A))) L U))) (forall ((A tptp.array_int)) (let ((_let_1 (tptp.t2tb2 A))) (= (tptp.sorted1 A) (tptp.sorted_sub2 (tptp.tb2t1 (tptp.elts tptp.int _let_1)) 0 (tptp.length1 tptp.int _let_1))))) _let_3 (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.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) (V tptp.uni) (M tptp.uni) (L Int) (U Int)) (=> (<= U L) (= (tptp.occ1 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.sort1 A V) (=> (< L U) (=> (not (= (tptp.get A tptp.int M (tptp.t2tb _let_1)) V)) (= (tptp.occ1 A V M L U) (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 (- U 1))) (=> (< L U) (=> (= (tptp.get A tptp.int M (tptp.t2tb _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 ((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.t2tb I)) V)))) (= (tptp.occ1 A V M L U) 0)))) (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.t2tb I)) V)))))) (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.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.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 ((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.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_sub1 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.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 ((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 ((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.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 ((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_sub1 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_sub1 A A1 A2 L1 U1) (=> (and (<= 0 L2) (<= L2 L1)) (=> (and (<= U1 U2) (<= U2 (tptp.length1 A A1))) (tptp.permut_sub1 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))) (forall ((A1 tptp.array_int) (A2 tptp.array_int) (L Int) (Ml Int) (Mr Int) (R Int) (V Int)) (= (tptp.qs_partition2 A1 A2 L Ml Mr R V) (and (tptp.permut_sub1 tptp.int (tptp.t2tb2 A1) (tptp.t2tb2 A2) L R) (forall ((J Int)) (=> (and (<= L J) (< J Ml)) (< (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A2) J)) V))) (forall ((J Int)) (=> (and (<= Ml J) (< J Mr)) (= (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A2) J)) V))) (forall ((J Int)) (=> (and (<= Mr J) (< J R)) (< V (tptp.tb2t (tptp.get2 tptp.int (tptp.t2tb2 A2) J)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.60/15.87 )
% 15.60/15.87 % SZS output end Proof for SWW636_2
% 15.60/15.87 % cvc5---1.0.5 exiting
% 15.60/15.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------