TSTP Solution File: SWW604_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW604_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:21:40 EDT 2023
% Result : Theorem 46.56s 46.78s
% Output : Proof 46.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW604_2 : TPTP v8.1.2. Released v6.1.0.
% 0.15/0.14 % Command : do_cvc5 %s %d
% 0.16/0.35 % Computer : n010.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 20:48:19 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_ARI
% 46.56/46.78 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.lW4gmnW3wJ/cvc5---1.0.5_12670.p...
% 46.56/46.78 ------- get file name : TPTP file name is SWW604_2
% 46.56/46.78 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12670.smt2...
% 46.56/46.78 --- Run --finite-model-find --decision=internal at 15...
% 46.56/46.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 46.56/46.78 --- Run --no-e-matching --full-saturate-quant at 15...
% 46.56/46.78 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 46.56/46.78 % SZS status Theorem for SWW604_2
% 46.56/46.78 % SZS output start Proof for SWW604_2
% 46.56/46.78 (
% 46.56/46.78 (let ((_let_1 (not (forall ((H Int) (H1 tptp.map_int_lplist_lpkeycm_a1rprp) (H2 tptp.map_key_lpoption_a1rp)) (=> (and (< 0 H) (forall ((I Int)) (=> (and (<= 0 I) (< I H)) (tptp.good_hash1 tptp.a (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 H1)) I))) (forall ((K tptp.key1) (V tptp.a1)) (tptp.good_data1 tptp.a K (tptp.t2tb7 V) (tptp.t2tb3 H2) (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 H1)))) (<= 0 H)) (forall ((Rho Int)) (=> (= Rho 0) (and (<= 0 0) (<= 0 H) (<= (+ 0 H) H) (forall ((O tptp.map_int_lplist_lpkeycm_a1rprp)) (=> (and (<= 0 H) (forall ((I Int)) (let ((_let_1 (tptp.t2tb I))) (let ((_let_2 (tptp.list (tptp.tuple2 tptp.key tptp.a)))) (=> (or (and (<= 0 I) (< I 0)) (and (<= (+ 0 H) I) (< I H))) (= (tptp.tb2t6 (tptp.get _let_2 tptp.int (tptp.t2tb2 O) _let_1)) (tptp.tb2t6 (tptp.get _let_2 tptp.int (tptp.t2tb2 H1) _let_1))))))) (forall ((I Int)) (let ((_let_1 (tptp.tuple2 tptp.key tptp.a))) (=> (and (<= 0 I) (< I (+ 0 H))) (= (tptp.tb2t6 (tptp.get (tptp.list _let_1) tptp.int (tptp.t2tb2 O) (tptp.t2tb I))) (tptp.tb2t6 (tptp.nil _let_1))))))) (forall ((Rho1 tptp.map_key_lpoption_a1rp)) (let ((_let_1 (= Rho1 (tptp.tb2t3 (tptp.const (tptp.option tptp.a) tptp.key (tptp.none tptp.a)))))) (=> _let_1 (and (< 0 H) (forall ((I Int)) (=> (and (<= 0 I) (< I H)) (tptp.good_hash1 tptp.a (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 O)) I))) (forall ((K tptp.key1) (V tptp.a1)) (tptp.good_data1 tptp.a K (tptp.t2tb7 V) (tptp.t2tb3 Rho1) (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 O)))) (<= 0 H) _let_1)))))))))))))) (let ((_let_2 (forall ((J tptp.uni)) (= (tptp.t2tb6 (tptp.tb2t6 J)) J)))) (let ((_let_3 (forall ((J tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.key (tptp.option tptp.a)) J) (= (tptp.t2tb3 (tptp.tb2t3 J)) J))))) (let ((_let_4 (forall ((X tptp.map_int_lplist_lpkeycm_a1rprp)) (tptp.sort1 (tptp.map tptp.int (tptp.list (tptp.tuple2 tptp.key tptp.a))) (tptp.t2tb2 X))))) (let ((_let_5 (forall ((A tptp.ty) (D tptp.uni) (I Int)) (let ((_let_1 (tptp.good_hash1 A D I))) (and (=> _let_1 (forall ((K tptp.key1) (V tptp.uni)) (let ((_let_1 (tptp.tuple2 tptp.key A))) (let ((_let_2 (tptp.list _let_1))) (=> (tptp.mem _let_1 (tptp.tuple21 tptp.key A (tptp.t2tb1 K) V) (tptp.get2 _let_2 D I)) (= (tptp.bucket1 K (tptp.length1 _let_2 D)) I)))))) (=> (forall ((K tptp.key1) (V tptp.uni)) (let ((_let_1 (tptp.tuple2 tptp.key A))) (let ((_let_2 (tptp.list _let_1))) (=> (tptp.sort1 A V) (=> (tptp.mem _let_1 (tptp.tuple21 tptp.key A (tptp.t2tb1 K) V) (tptp.get2 _let_2 D I)) (= (tptp.bucket1 K (tptp.length1 _let_2 D)) I)))))) _let_1)))))) (let ((_let_6 (forall ((A tptp.ty) (K tptp.key1) (V tptp.uni) (M tptp.uni) (D tptp.uni)) (= (tptp.good_data1 A K V M D) (= (= (tptp.get (tptp.option A) tptp.key M (tptp.t2tb1 K)) (tptp.some A V)) (tptp.in_data1 A K V D)))))) (let ((_let_7 (forall ((A tptp.ty) (K tptp.key1) (V tptp.uni) (D tptp.uni)) (let ((_let_1 (tptp.tuple2 tptp.key A))) (let ((_let_2 (tptp.list _let_1))) (= (tptp.in_data1 A K V D) (tptp.mem _let_1 (tptp.tuple21 tptp.key A (tptp.t2tb1 K) V) (tptp.get2 _let_2 D (tptp.bucket1 K (tptp.length1 _let_2 D)))))))))) (let ((_let_8 (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.tuple2 A1 A) (tptp.tuple21 A1 A X X1))))) (let ((_let_9 (forall ((N Int)) (=> (< 0 N) (forall ((K tptp.key1)) (let ((_let_1 (tptp.bucket1 K N))) (and (<= 0 _let_1) (< _let_1 N)))))))) (let ((_let_10 (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_11 (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_12 (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length1 A (tptp.mk_array1 A U U1)) U)))) (let ((_let_13 (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))))) (let ((_let_14 (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.const B A X))))) (let ((_let_15 (forall ((A tptp.ty) (X tptp.uni)) (=> (tptp.sort1 A X) (and (not (tptp.mem A X (tptp.nil A))) (forall ((X1 tptp.uni) (X2 tptp.uni)) (=> (tptp.sort1 A X1) (= (tptp.mem A X (tptp.cons A X1 X2)) (or (= X X1) (tptp.mem A X X2)))))))))) (let ((_let_16 (forall ((A tptp.ty) (V tptp.uni)) (not (= (tptp.none A) (tptp.some A V)))))) (let ((_let_17 (forall ((A tptp.ty)) (tptp.sort1 (tptp.option A) (tptp.none A))))) (let ((_let_18 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_120))) (let ((_let_19 (tptp.tuple2 tptp.key tptp.a))) (let ((_let_20 (tptp.list _let_19))) (let ((_let_21 (tptp.mk_array1 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 _let_18))) (let ((_let_22 (tptp.get2 _let_20 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117))) (let ((_let_23 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_256))) (let ((_let_24 (tptp.tuple21 tptp.key tptp.a _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_257))) (let ((_let_25 (tptp.mem _let_19 _let_24 _let_22))) (let ((_let_26 (tptp.length1 _let_20 _let_21))) (let ((_let_27 (tptp.bucket1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_256 _let_26))) (let ((_let_28 (not _let_25))) (let ((_let_29 (or (not (tptp.sort1 tptp.a SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_257)) _let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117 _let_27)))) (let ((_let_30 (tptp.nil _let_19))) (let ((_let_31 (tptp.mem _let_19 _let_24 _let_30))) (let ((_let_32 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117))) (let ((_let_33 (tptp.get _let_20 tptp.int _let_18 _let_32))) (let ((_let_34 (tptp.tb2t6 _let_33))) (let ((_let_35 (= _let_33 (tptp.t2tb6 _let_34)))) (let ((_let_36 (tptp.tb2t6 _let_30))) (let ((_let_37 (= _let_36 _let_34))) (let ((_let_38 (tptp.elts _let_20 _let_21))) (let ((_let_39 (= _let_22 (tptp.get _let_20 tptp.int _let_38 _let_32)))) (let ((_let_40 (= _let_30 (tptp.t2tb6 _let_36)))) (let ((_let_41 (= _let_18 _let_38))) (let ((_let_42 (tptp.none tptp.a))) (let ((_let_43 (tptp.option tptp.a))) (let ((_let_44 (tptp.const _let_43 tptp.key _let_42))) (let ((_let_45 (tptp.cons _let_19 _let_44 _let_44))) (let ((_let_46 (not (tptp.sort1 _let_19 _let_44)))) (let ((_let_47 (not _let_31))) (let ((_let_48 (and _let_47 (or _let_46 (= (tptp.mem _let_19 _let_24 _let_45) (or (= _let_44 _let_24) (tptp.mem _let_19 _let_24 _let_44))))))) (let ((_let_49 (tptp.sort1 _let_19 _let_24))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48))) (let ((_let_52 (forall ((A tptp.ty) (X tptp.uni) (BOUND_VARIABLE_2138 tptp.uni) (BOUND_VARIABLE_2136 tptp.uni)) (or (not (tptp.sort1 A X)) (and (not (tptp.mem A X (tptp.nil A))) (or (not (tptp.sort1 A BOUND_VARIABLE_2136)) (= (tptp.mem A X (tptp.cons A BOUND_VARIABLE_2136 BOUND_VARIABLE_2138)) (or (= X BOUND_VARIABLE_2136) (tptp.mem A X BOUND_VARIABLE_2138))))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (_let_8))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 ((tptp.tuple21 A1 A X X1)))) (let ((_let_58 (forall ((J tptp.uni)) (= J (tptp.t2tb6 (tptp.tb2t6 J)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117)) 1))) (let ((_let_62 (not _let_61))) (let ((_let_63 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117 0))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_62 _let_37))) (let ((_let_66 (forall ((I Int)) (let ((_let_1 (tptp.tuple2 tptp.key tptp.a))) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114)) 0) (= (tptp.tb2t6 (tptp.nil _let_1)) (tptp.tb2t6 (tptp.get (tptp.list _let_1) tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_120) (tptp.t2tb I))))))))) (let ((_let_67 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 0))) (let ((_let_68 (tptp.t2tb3 (tptp.tb2t3 _let_44)))) (let ((_let_69 (tptp.t2tb7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_118))) (let ((_let_70 (tptp.good_data1 tptp.a SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119 _let_69 _let_68 _let_21))) (let ((_let_71 (tptp.good_hash1 tptp.a _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117))) (let ((_let_72 (or _let_64 _let_62 _let_71))) (let ((_let_73 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 1))) (let ((_let_74 (and _let_73 _let_72 _let_70 _let_67))) (let ((_let_75 (not _let_66))) (let ((_let_76 (not _let_67))) (let ((_let_77 (or _let_76 _let_75 _let_74))) (let ((_let_78 (and _let_67 _let_77))) (let ((_let_79 (not _let_77))) (let ((_let_80 (not (forall ((K tptp.key1) (V tptp.a1)) (tptp.good_data1 tptp.a K (tptp.t2tb7 V) (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116) (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115))))))) (let ((_let_81 (not _let_73))) (let ((_let_82 (or _let_81 (not (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114)) 0) (tptp.good_hash1 tptp.a (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115)) I)))) _let_80 _let_76 _let_78))) (let ((_let_83 (forall ((H Int) (H1 tptp.map_int_lplist_lpkeycm_a1rprp) (H2 tptp.map_key_lpoption_a1rp) (BOUND_VARIABLE_2677 Int) (BOUND_VARIABLE_2675 tptp.a1) (BOUND_VARIABLE_2673 tptp.key1) (BOUND_VARIABLE_2671 tptp.map_int_lplist_lpkeycm_a1rprp)) (let ((_let_1 (>= H 0))) (let ((_let_2 (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 BOUND_VARIABLE_2671)))) (let ((_let_3 (>= H 1))) (let ((_let_4 (not _let_1))) (or (not _let_3) (not (forall ((I Int)) (or (not (>= I 0)) (not (>= (+ H (* (- 1) I)) 1)) (tptp.good_hash1 tptp.a (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 H1)) I)))) (not (forall ((K tptp.key1) (V tptp.a1)) (tptp.good_data1 tptp.a K (tptp.t2tb7 V) (tptp.t2tb3 H2) (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) H (tptp.t2tb2 H1))))) _let_4 (and _let_1 (or _let_4 (not (forall ((I Int)) (let ((_let_1 (tptp.tuple2 tptp.key tptp.a))) (or (not (>= I 0)) (not (>= (+ H (* (- 1) I)) 1)) (= (tptp.tb2t6 (tptp.nil _let_1)) (tptp.tb2t6 (tptp.get (tptp.list _let_1) tptp.int (tptp.t2tb2 BOUND_VARIABLE_2671) (tptp.t2tb I)))))))) (and _let_3 (or (not (>= BOUND_VARIABLE_2677 0)) (not (>= (+ H (* (- 1) BOUND_VARIABLE_2677)) 1)) (tptp.good_hash1 tptp.a _let_2 BOUND_VARIABLE_2677)) (tptp.good_data1 tptp.a BOUND_VARIABLE_2673 (tptp.t2tb7 BOUND_VARIABLE_2675) (tptp.t2tb3 (tptp.tb2t3 (tptp.const (tptp.option tptp.a) tptp.key (tptp.none tptp.a)))) _let_2) _let_1))))))))))) (let ((_let_84 (not _let_82))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or))) (let ((_let_87 (not _let_83))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_85) :args (_let_87)) (REWRITE :args ((=> _let_87 (not (or _let_81 (not (forall ((I Int)) (or (not (>= I 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (* (- 1) I)) 1)) (tptp.good_hash1 tptp.a (tptp.mk_array1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115)) I)))) _let_80 _let_76 (and _let_67 (or _let_76 (not (forall ((I Int)) (let ((_let_1 (tptp.tuple2 tptp.key tptp.a))) (or (not (>= I 0)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 (* (- 1) I)) 1)) (= (tptp.tb2t6 (tptp.nil _let_1)) (tptp.tb2t6 (tptp.get (tptp.list _let_1) tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_120) (tptp.t2tb I)))))))) _let_74))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_83))) (REFL :args (_let_84)) :args _let_86)) _let_85 :args (_let_84 true _let_83)))) (let ((_let_89 (REFL :args (_let_82)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_82 3)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_67))) :args _let_86)) :args ((or _let_67 _let_82))) _let_88 :args (_let_67 true _let_82)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_78)) :args ((or _let_76 _let_78 _let_79))) _let_90 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_82 4)) _let_88 :args ((not _let_78) true _let_82)) :args (_let_79 false _let_67 true _let_78)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG (REFL :args (_let_77)) (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_66))) :args _let_86)) :args ((or _let_66 _let_77))) _let_91 :args (_let_66 true _let_77)))) (let ((_let_93 (_let_66))) (let ((_let_94 ((tptp.t2tb I)))) (let ((_let_95 (ASSUME :args _let_93))) (let ((_let_96 (not _let_72))) (let ((_let_97 (tptp.in_data1 tptp.a SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119 _let_69 _let_21))) (let ((_let_98 (tptp.some tptp.a _let_69))) (let ((_let_99 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119))) (let ((_let_100 (= (tptp.get _let_43 tptp.key _let_68 _let_99) _let_98))) (let ((_let_101 (= _let_100 _let_97))) (let ((_let_102 (= _let_70 _let_101))) (let ((_let_103 (_let_6))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 (tptp.bucket1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119 _let_26))) (let ((_let_106 (tptp.get2 _let_20 _let_21 _let_105))) (let ((_let_107 (tptp.tuple21 tptp.key tptp.a _let_99 _let_69))) (let ((_let_108 (tptp.mem _let_19 _let_107 _let_106))) (let ((_let_109 (= _let_97 _let_108))) (let ((_let_110 (not _let_97))) (let ((_let_111 (_let_7))) (let ((_let_112 (ASSUME :args _let_111))) (let ((_let_113 (tptp.t2tb _let_105))) (let ((_let_114 (tptp.get _let_20 tptp.int _let_18 _let_113))) (let ((_let_115 (tptp.tb2t6 _let_114))) (let ((_let_116 (= _let_114 (tptp.t2tb6 _let_115)))) (let ((_let_117 (= _let_36 _let_115))) (let ((_let_118 (tptp.mem 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_let_232 _let_71))) (let ((_let_234 (forall ((BOUND_VARIABLE_2353 tptp.ty) (BOUND_VARIABLE_2355 tptp.uni) (BOUND_VARIABLE_2357 Int)) (or (not (forall ((K tptp.key1) (V tptp.uni)) (let ((_let_1 (tptp.tuple2 tptp.key BOUND_VARIABLE_2353))) (let ((_let_2 (tptp.list _let_1))) (or (not (tptp.sort1 BOUND_VARIABLE_2353 V)) (not (tptp.mem _let_1 (tptp.tuple21 tptp.key BOUND_VARIABLE_2353 (tptp.t2tb1 K) V) (tptp.get2 _let_2 BOUND_VARIABLE_2355 BOUND_VARIABLE_2357))) (= BOUND_VARIABLE_2357 (tptp.bucket1 K (tptp.length1 _let_2 BOUND_VARIABLE_2355)))))))) (tptp.good_hash1 BOUND_VARIABLE_2353 BOUND_VARIABLE_2355 BOUND_VARIABLE_2357))))) (let ((_let_235 (_let_234))) (let ((_let_236 (_let_232))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG (REFL :args (_let_29)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_25))) :args _let_86)) :args ((or _let_25 _let_29))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_236)) :args _let_236)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_232) _let_230))) (REFL :args (_let_231)) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_233)) :args ((or _let_71 _let_232 (not _let_233)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_72 2)) _let_220 :args ((not _let_71) true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_235) :args (tptp.a _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.good_hash1 BOUND_VARIABLE_2353 BOUND_VARIABLE_2355 BOUND_VARIABLE_2357) true))))) :args _let_235)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_233 false _let_234)) :args (_let_232 true _let_71 false _let_233)) :args (_let_231 true _let_230)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_225)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_226 _let_180 _let_227 _let_228 _let_186 _let_229) (SCOPE (FALSE_ELIM (TRANS (CONG _let_191 (REFL :args (_let_24)) (TRANS (SYMM (SYMM _let_229)) (CONG _let_189 _let_188 _let_187 (REFL :args (_let_32)) :args _let_185) (SYMM (SYMM _let_228)) (CONG (SYMM _let_227) :args _let_182) _let_181) :args _let_179) (FALSE_INTRO _let_226))) :args (_let_47 _let_40 _let_37 _let_35 _let_41 _let_39))) :args (_let_41 _let_40 _let_39 _let_37 _let_35 _let_47))) :args (true _let_225)) (CONG _let_177 _let_175 (REFL :args (_let_224)) (REFL :args (_let_223)) (REFL :args (_let_222)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_31))) (REFL :args (_let_28)) :args _let_86)) :args ((or _let_176 _let_174 _let_28 _let_224 _let_223 _let_222 _let_31))) _let_173 _let_165 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_163 :args (_let_20 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_164)) :args _let_162)) _let_163 :args (_let_39 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_64 _let_62 _let_37 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_221 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_86)) :args ((or _let_63 _let_72))) _let_220 :args (_let_63 true _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_221 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_86)) :args ((or _let_61 _let_72))) _let_220 :args (_let_61 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_94)) :args _let_93))) _let_92 :args (_let_65 false _let_66)) :args (_let_37 false _let_63 false _let_61 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_33 QUANTIFIERS_INST_CBQI_PROP)) :args _let_60)) _let_59 :args (_let_35 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_48 0)) :args ((or _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_48 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.a tptp.key _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_257 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_55)) _let_56 :args (_let_49 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_19 _let_24 _let_44 _let_44 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_54))) _let_53 :args (_let_51 false _let_52)) :args (_let_48 false _let_49 false _let_51)) :args (_let_47 false _let_48)) :args (_let_28 false _let_41 false _let_40 false _let_39 false _let_37 false _let_35 true _let_31)) :args (false true _let_29 true _let_25)) :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 ((X Int)) (let ((_let_1 (tptp.abs1 X))) (let ((_let_2 (<= 0 X))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (- X))))))) (forall ((X Int) (Y Int)) (= (<= (tptp.abs1 X) Y) (and (<= (- Y) X) (<= X Y)))) (forall ((X Int)) (<= 0 (tptp.abs1 X))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (= X (+ (* Y (tptp.div1 X Y)) (tptp.mod1 X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.div1 X Y))) (=> (and (<= 0 X) (< 0 Y)) (and (<= 0 _let_1) (<= _let_1 X))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.abs1 Y))) (let ((_let_2 (tptp.mod1 X Y))) (=> (not (= Y 0)) (and (< (- _let_1) _let_2) (< _let_2 _let_1)))))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< 0 Y)) (<= 0 (tptp.div1 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (< 0 Y)) (<= (tptp.div1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (not (= Y 0))) (<= 0 (tptp.mod1 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (not (= Y 0))) (<= (tptp.mod1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (<= (tptp.abs1 (* (tptp.div1 X Y) Y)) (tptp.abs1 X)))) (forall ((X Int)) (= (tptp.div1 X 1) X)) (forall ((X Int)) (= (tptp.mod1 X 1) 0)) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.div1 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.mod1 X Y) X))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.div1 (+ (* X Y) Z) X) (+ Y (tptp.div1 Z X))))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.mod1 (+ (* X Y) Z) X) (tptp.mod1 Z X)))) _let_17 (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.option A) (tptp.some A X))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A1 (tptp.match_option1 A1 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A1 Z) (= (tptp.match_option1 A1 A (tptp.none A) Z Z1) Z))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U tptp.uni)) (=> (tptp.sort1 A1 Z1) (= (tptp.match_option1 A1 A (tptp.some A U) Z Z1) Z1))) _let_16 (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.some_proj_11 A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.some_proj_11 A (tptp.some A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 (tptp.option A) U) (or (= U (tptp.none A)) (= U (tptp.some A (tptp.some_proj_11 A U)))))) (forall ((A tptp.ty)) (tptp.sort1 (tptp.list A) (tptp.nil A))) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.cons A X X1))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A1 (tptp.match_list1 A1 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A1 Z) (= (tptp.match_list1 A1 A (tptp.nil A) Z Z1) Z))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A1 Z1) (= (tptp.match_list1 A1 A (tptp.cons A U U1) Z Z1) Z1))) (forall ((A tptp.ty) (V tptp.uni) (V1 tptp.uni)) (not (= (tptp.nil A) (tptp.cons A V V1)))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.cons_proj_11 A X))) (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.cons_proj_11 A (tptp.cons A U U1)) U))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.cons_proj_21 A X))) (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (= (tptp.cons_proj_21 A (tptp.cons A U U1)) U1)) (forall ((A tptp.ty) (U tptp.uni)) (or (= U (tptp.nil A)) (= U (tptp.cons A (tptp.cons_proj_11 A U) (tptp.cons_proj_21 A U))))) _let_15 (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))))))) _let_14 _let_13 (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.mk_array1 A X X1))) _let_12 (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) _let_11 (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_10 (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.set2 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set2 A A1 I V) (tptp.mk_array1 A (tptp.length1 A A1) (tptp.set A tptp.int (tptp.elts A A1) (tptp.t2tb I) V)))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make1 A N V) (tptp.mk_array1 A N (tptp.const A tptp.int V)))) (forall ((K tptp.key1)) (<= 0 (tptp.hash1 K))) (forall ((K tptp.key1) (N Int)) (= (tptp.bucket1 K N) (tptp.mod1 (tptp.hash1 K) N))) _let_9 _let_8 (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni)) (tptp.sort1 A1 (tptp.tuple2_proj_11 A1 A X))) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A1 U) (= (tptp.tuple2_proj_11 A1 A (tptp.tuple21 A1 A U U1)) U))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.tuple2_proj_21 A1 A X))) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A U1) (= (tptp.tuple2_proj_21 A1 A (tptp.tuple21 A1 A U U1)) U1))) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni)) (=> (tptp.sort1 (tptp.tuple2 A1 A) U) (= U (tptp.tuple21 A1 A (tptp.tuple2_proj_11 A1 A U) (tptp.tuple2_proj_21 A1 A U))))) (forall ((X tptp.key1)) (tptp.sort1 tptp.key (tptp.t2tb1 X))) (forall ((I tptp.key1)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort1 tptp.key J) (= (tptp.t2tb1 (tptp.tb2t1 J)) J))) _let_7 _let_6 _let_5 (forall ((A tptp.ty) (X Int) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 (tptp.t A) (tptp.mk_t1 A X X1 X2))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni) (U2 tptp.uni)) (= (tptp.size1 A (tptp.mk_t1 A U U1 U2)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.array (tptp.list (tptp.tuple2 tptp.key A))) (tptp.data A X))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni) (U2 tptp.uni)) (= (tptp.data A (tptp.mk_t1 A U U1 U2)) U1)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.key (tptp.option A)) (tptp.view A X))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni) (U2 tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.key (tptp.option A)) U2) (= (tptp.view A (tptp.mk_t1 A U U1 U2)) U2))) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_t1 A (tptp.size1 A U) (tptp.data A U) (tptp.view A U)))) _let_4 (forall ((I tptp.map_int_lplist_lpkeycm_a1rprp)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) (forall ((X tptp.map_key_lpoption_a1rp)) (tptp.sort1 (tptp.map tptp.key (tptp.option tptp.a)) (tptp.t2tb3 X))) (forall ((I tptp.map_key_lpoption_a1rp)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) _let_3 (forall ((X tptp.option_a1)) (tptp.sort1 (tptp.option tptp.a) (tptp.t2tb4 X))) (forall ((I tptp.option_a1)) (= (tptp.tb2t4 (tptp.t2tb4 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort1 (tptp.option tptp.a) J) (= (tptp.t2tb4 (tptp.tb2t4 J)) J))) (forall ((X tptp.array_lplist_lpkeycm_a1rprp)) (tptp.sort1 (tptp.array (tptp.list (tptp.tuple2 tptp.key tptp.a))) (tptp.t2tb5 X))) (forall ((I tptp.array_lplist_lpkeycm_a1rprp)) (= (tptp.tb2t5 (tptp.t2tb5 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb5 (tptp.tb2t5 J)) J)) (forall ((X tptp.list_lpkeycm_a1rp)) (tptp.sort1 (tptp.list (tptp.tuple2 tptp.key tptp.a)) (tptp.t2tb6 X))) (forall ((I tptp.list_lpkeycm_a1rp)) (= (tptp.tb2t6 (tptp.t2tb6 I)) I)) _let_2 (forall ((X tptp.a1)) (tptp.sort1 tptp.a (tptp.t2tb7 X))) (forall ((I tptp.a1)) (= (tptp.tb2t7 (tptp.t2tb7 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort1 tptp.a J) (= (tptp.t2tb7 (tptp.tb2t7 J)) J))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 46.56/46.78 )
% 46.56/46.78 % SZS output end Proof for SWW604_2
% 46.56/46.79 % cvc5---1.0.5 exiting
% 46.56/46.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------