%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW612_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:21:42 EDT 2023

% Result   : Theorem 15.53s 16.02s
% Output   : Proof 15.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SWW612_2 : TPTP v8.1.2. Released v6.1.0.
% 0.14/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 19:19:51 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_ARI
% 15.53/16.02  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.FxAhRVyZ8Z/cvc5---1.0.5_31928.p...
% 15.53/16.02  ------- get file name : TPTP file name is SWW612_2
% 15.53/16.02  ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31928.smt2...
% 15.53/16.02  --- Run --finite-model-find --decision=internal at 15...
% 15.53/16.02  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.53/16.02  % SZS status Theorem for SWW612_2
% 15.53/16.02  % SZS output start Proof for SWW612_2
% 15.53/16.02  (
% 15.53/16.02  (let ((_let_1 (not (forall ((M Int)) (let ((_let_1 (<= 0 M))) (=> (<= 2 M) (=> _let_1 (=> _let_1 (=> (and (<= 0 0) (< 0 M)) (forall ((P tptp.map_int_int)) (let ((_let_1 (tptp.t2tb1 0))) (=> (and (<= 0 M) (= P (tptp.tb2t3 (tptp.set tptp.int tptp.int (tptp.const tptp.int tptp.int _let_1) _let_1 (tptp.t2tb1 2))))) (=> (and (<= 0 1) (< 1 M)) (forall ((P1 tptp.map_int_int)) (=> (and (<= 0 M) (= P1 (tptp.tb2t3 (tptp.set tptp.int tptp.int (tptp.t2tb3 P) (tptp.t2tb1 1) (tptp.t2tb1 3))))) (=> (<= 2 (- M 1)) (forall ((N Int) (P2 tptp.map_int_int) (J Int)) (let ((_let_1 (tptp.t2tb3 P2))) (let ((_let_2 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb1 (- J 1)))))) (let ((_let_3 (tptp.no_prime_in1 _let_2 N))) (let ((_let_4 (tptp.odd1 N))) (let ((_let_5 (< N (* 2 _let_2)))) (let ((_let_6 (< _let_2 N))) (let ((_let_7 (tptp.first_primes1 (tptp.tb2t2 (tptp.mk_array1 tptp.int M _let_1)) J))) (=> (and (<= 2 J) (<= J (- M 1))) (=> (and _let_7 _let_6 _let_5 _let_4 _let_3) (=> (and (<= 0 M) (<= 1 1) (< 1 J) _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((I Int)) (=> (and (<= 0 I) (< I 1)) (not (tptp.divides1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 P2) (tptp.t2tb1 I))) N))))) (forall ((N1 Int)) (let ((_let_1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 P2) (tptp.t2tb1 (- J 1)))))) (=> (and (< _let_1 N1) (tptp.prime1 N1) (tptp.no_prime_in1 _let_1 N1)) (=> (and (<= 0 J) (< J M)) (forall ((P3 tptp.map_int_int)) (=> (and (<= 0 M) (= P3 (tptp.tb2t3 (tptp.set tptp.int tptp.int (tptp.t2tb3 P2) (tptp.t2tb1 J) (tptp.t2tb1 N1))))) (forall ((N2 Int)) (=> (= N2 (+ N1 2)) (tptp.no_prime_in1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 P3) (tptp.t2tb1 (- (+ J 1) 1)))) N2)))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((J tptp.uni)) (= (tptp.t2tb3 (tptp.tb2t3 J)) J)))) (let ((_let_3 (forall ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb3 X))))) (let ((_let_4 (forall ((P tptp.array_int) (U Int)) (= (tptp.first_primes1 P U) (and (= (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) 0)) 2) (forall ((I Int) (J Int)) (let ((_let_1 (tptp.t2tb2 P))) (=> (and (<= 0 I) (< I J) (< J U)) (< (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 J)))))) (forall ((I Int)) (=> (and (<= 0 I) (< I U)) (tptp.prime1 (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) I))))) (forall ((I Int)) (let ((_let_1 (tptp.t2tb2 P))) (=> (and (<= 0 I) (< I (- U 1))) (tptp.no_prime_in1 (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 (+ I 1)))))))))))) (let ((_let_5 (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)))) (let ((_let_6 (forall ((L Int) (U Int)) (= (tptp.no_prime_in1 L U) (forall ((X Int)) (=> (and (< L X) (< X U)) (not (tptp.prime1 X)))))))) (let ((_let_7 (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get2 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb1 I)))))) (let ((_let_8 (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_9 (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)))))) (let ((_let_10 (forall ((P Int)) (=> (tptp.prime1 P) (=> (<= 3 P) (tptp.odd1 P)))))) (let ((_let_11 (forall ((P Int)) (=> (tptp.prime1 P) (=> (tptp.even1 P) (= P 2)))))) (let ((_let_12 (forall ((N Int)) (=> (tptp.odd1 N) (tptp.even1 (+ N 1)))))) (let ((_let_13 (forall ((I Int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)))) (let ((_let_14 (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb1 X))))) (let ((_let_15 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_181 3))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_181 2))) (let ((_let_17 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_18 (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_19 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_18))) (let ((_let_20 (tptp.tb2t2 _let_19))) (let ((_let_21 (tptp.t2tb2 _let_20))) (let ((_let_22 (tptp.get2 tptp.int _let_21 _let_17))) (let ((_let_23 (tptp.tb2t1 _let_22))) (let ((_let_24 (tptp.t2tb1 _let_17))) (let ((_let_25 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_18 _let_24)))) (let ((_let_26 (= _let_25 _let_23))) (let ((_let_27 (* (- 1) _let_23))) (let ((_let_28 (tptp.tb2t1 (tptp.get2 tptp.int _let_21 0)))) (let ((_let_29 (+ _let_28 _let_27))) (let ((_let_30 (>= _let_29 0))) (let ((_let_31 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_32 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_33 (tptp.set tptp.int tptp.int _let_18 _let_31 _let_32))) (let ((_let_34 (tptp.t2tb3 (tptp.tb2t3 _let_33)))) (let ((_let_35 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_34 _let_31)))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_35))) (let ((_let_37 (* (- 1) _let_35))) (let ((_let_38 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_181 _let_37) 1))) (let ((_let_39 (= _let_28 2))) (let ((_let_40 (* (- 1) _let_25))) (let ((_let_41 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_40) 1))) (let ((_let_42 (= _let_22 (tptp.get tptp.int tptp.int (tptp.elts tptp.int _let_21) _let_24)))) (let ((_let_43 (= _let_19 _let_21))) (let ((_let_44 (= _let_18 (tptp.elts tptp.int _let_19)))) (let ((_let_45 (_let_7))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (forall ((J tptp.uni)) (= J (tptp.t2tb2 (tptp.tb2t2 J)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (tptp.sort1 (tptp.map tptp.int tptp.int) _let_18))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_44))) (let ((_let_52 (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_53 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_3))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (and _let_44 _let_43 _let_42))) (let ((_let_57 (_let_44 _let_43 _let_42))) (let ((_let_58 (= _let_23 _let_25))) (let ((_let_59 (_let_58))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (APPLY_UF tptp.tb2t1))) (let ((_let_62 (APPLY_UF tptp.get))) (let ((_let_63 (ASSUME :args (_let_44)))) (let ((_let_64 (ASSUME :args (_let_43)))) (let ((_let_65 (REFL :args (tptp.int)))) (let ((_let_66 (ASSUME :args (_let_42)))) (let ((_let_67 (not _let_30))) (let ((_let_68 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 2))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_67))) (let ((_let_71 (forall ((I Int) (J Int)) (let ((_let_1 (tptp.t2tb2 (tptp.tb2t2 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29)))))) (or (not (>= I 0)) (>= (+ I (* (- 1) J)) 0) (>= (+ J (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) 0) (not (>= (+ (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (* (- 1) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 J)))) 0))))))) (let ((_let_72 (and _let_39 _let_71 (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) 0) (tptp.prime1 (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 (tptp.tb2t2 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29)))) I))))) (forall ((I Int)) (let ((_let_1 (tptp.t2tb2 (tptp.tb2t2 (tptp.mk_array1 tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29)))))) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) (- 1)) (tptp.no_prime_in1 (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 (+ 1 I)))))))))) (let ((_let_73 (tptp.first_primes1 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_74 (= _let_73 _let_72))) (let ((_let_75 (forall ((P tptp.array_int) (U Int)) (= (tptp.first_primes1 P U) (and (= (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) 0)) 2) (forall ((I Int) (J Int)) (let ((_let_1 (tptp.t2tb2 P))) (let ((_let_2 (* (- 1) J))) (or (not (>= I 0)) (>= (+ I _let_2) 0) (not (>= (+ U _let_2) 1)) (not (>= (+ (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (* (- 1) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 J)))) 0)))))) (forall ((I Int)) (or (not (>= I 0)) (not (>= (+ U (* (- 1) I)) 1)) (tptp.prime1 (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) I))))) (forall ((I Int)) (let ((_let_1 (tptp.t2tb2 P))) (or (not (>= I 0)) (not (>= (+ U (* (- 1) I)) 2)) (tptp.no_prime_in1 (tptp.tb2t1 (tptp.get2 tptp.int _let_1 I)) (tptp.tb2t1 (tptp.get2 tptp.int _let_1 (+ 1 I)))))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (+ 2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_78 (tptp.no_prime_in1 _let_35 _let_77))) (let ((_let_79 (tptp.no_prime_in1 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_80 (not _let_79))) (let ((_let_81 (tptp.prime1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_82 (not _let_81))) (let ((_let_83 (not _let_41))) (let ((_let_84 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 (* (- 2) _let_25)))) (let ((_let_85 (>= _let_84 0))) (let ((_let_86 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 _let_40) 1))) (let ((_let_87 (not _let_86))) (let ((_let_88 (not _let_73))) (let ((_let_89 (or (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 2)) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 0)) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 1)) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 3)) _let_69 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) 1)) _let_88 _let_87 _let_85 (not (tptp.odd1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) (not (tptp.no_prime_in1 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) (not (forall ((I Int)) (or (not (>= I 0)) (>= I 1) (not (tptp.divides1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29) (tptp.t2tb1 I))) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))))) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 0)) _let_83 _let_82 _let_80 _let_78))) (let ((_let_90 (forall ((M Int) (BOUND_VARIABLE_3364 Int) (BOUND_VARIABLE_3362 Int) (BOUND_VARIABLE_3360 tptp.map_int_int) (BOUND_VARIABLE_3358 Int)) (let ((_let_1 (tptp.t2tb1 BOUND_VARIABLE_3358))) (let ((_let_2 (tptp.t2tb3 BOUND_VARIABLE_3360))) (let ((_let_3 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_2 (tptp.t2tb1 (+ (- 1) BOUND_VARIABLE_3358)))))) (let ((_let_4 (* (- 1) _let_3))) (or (not (>= M 2)) (not (>= M 0)) (not (>= M 1)) (not (>= M 3)) (not (>= BOUND_VARIABLE_3358 2)) (not (>= (+ M (* (- 1) BOUND_VARIABLE_3358)) 1)) (not (tptp.first_primes1 (tptp.tb2t2 (tptp.mk_array1 tptp.int M _let_2)) BOUND_VARIABLE_3358)) (not (>= (+ BOUND_VARIABLE_3362 _let_4) 1)) (>= (+ BOUND_VARIABLE_3362 (* (- 2) _let_3)) 0) (not (tptp.odd1 BOUND_VARIABLE_3362)) (not (tptp.no_prime_in1 _let_3 BOUND_VARIABLE_3362)) (not (forall ((I Int)) (or (not (>= I 0)) (>= I 1) (not (tptp.divides1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 BOUND_VARIABLE_3360) (tptp.t2tb1 I))) BOUND_VARIABLE_3362))))) (not (>= BOUND_VARIABLE_3358 0)) (not (>= (+ BOUND_VARIABLE_3364 _let_4) 1)) (not (tptp.prime1 BOUND_VARIABLE_3364)) (not (tptp.no_prime_in1 _let_3 BOUND_VARIABLE_3364)) (tptp.no_prime_in1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb3 (tptp.tb2t3 (tptp.set tptp.int tptp.int _let_2 _let_1 (tptp.t2tb1 BOUND_VARIABLE_3364)))) _let_1)) (+ 2 BOUND_VARIABLE_3364)))))))))) (let ((_let_91 (not _let_89))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (or))) (let ((_let_94 (not _let_90))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_92) :args (_let_94))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_90))) (REFL :args (_let_91)) :args _let_93)) _let_92 :args (_let_91 true _let_90)))) (let ((_let_96 (REFL :args (_let_89)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_74)) :args ((or _let_88 _let_72 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 6)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_73))) :args _let_93)) :args ((or _let_73 _let_89))) _let_95 :args (_let_73 true _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_primes1 P U)))) :args (_let_75)))) _let_76 :args (_let_74 false _let_75)) :args (_let_72 false _let_73 false _let_74)))) (let ((_let_98 (not _let_72))) (let ((_let_99 (_let_71))) (let ((_let_100 (= _let_33 _let_34))) (let ((_let_101 (= _let_32 (tptp.get tptp.int tptp.int _let_33 _let_31)))) (let ((_let_102 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 (tptp.tb2t1 _let_32)))) (let ((_let_103 (forall ((J tptp.uni)) (= J (tptp.t2tb3 (tptp.tb2t3 J)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tb2t3 J)))) :args (_let_103))) _let_104 :args (_let_100 false _let_103)))) (let ((_let_106 (tptp.sort1 tptp.int _let_32))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_101))) (let ((_let_109 (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A2 tptp.uni) (B1 tptp.uni)) (or (not (tptp.sort1 B B1)) (= B1 (tptp.get B A (tptp.set B A M A2 B1) A2)))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_14))) (let ((_let_112 (ASSUME :args _let_111))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_107 _let_101 (not _let_108)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 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(CNF_AND_POS :args (_let_72 0)) :args ((or _let_39 _let_98))) _let_97 :args (_let_39 false _let_72)) _let_145 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_126 (SCOPE _let_122 :args _let_120)) :args _let_118)) :args (true _let_117)) _let_116 _let_113 _let_105 :args (_let_36 false _let_102 false _let_101 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_67 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 4)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_93)) :args ((or _let_68 _let_89))) _let_95 :args (_let_68 true _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (0 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.get2 tptp.int _let_21 I) (tptp.get2 tptp.int _let_21 J)))) :args _let_99))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_72 1)) :args ((or _let_71 _let_98))) _let_97 :args (_let_71 false _let_72)) :args (_let_70 false _let_71)) :args (_let_67 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_56)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (MODUS_PONENS (AND_INTRO _let_63 _let_64 _let_66) (SCOPE (CONG (TRANS (SYMM (SYMM _let_66)) (CONG _let_65 _let_65 (TRANS (CONG _let_65 (SYMM _let_64) :args (APPLY_UF tptp.elts)) (SYMM _let_63)) (REFL :args (_let_24)) :args _let_62)) :args _let_61) :args _let_57)) (SCOPE (SYMM _let_60) :args _let_59)) :args _let_57)) :args (true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_44 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb3 X)))) :args _let_54)) _let_55 :args (_let_49 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.mk_array1 A U U1)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_44 false _let_49 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tb2t2 J)))) :args (_let_47))) _let_48 :args (_let_43 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.int _let_21 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.get2 A A1 I)))) :args _let_45)) _let_46 :args (_let_42 false _let_7)) :args (_let_26 false _let_44 false _let_43 false _let_42)) :args (_let_15 false _let_41 false _let_39 false _let_38 false _let_36 true _let_30 false _let_26)) :args (false false _let_16 false _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 ((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.div2 X Y)) (tptp.mod2 X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.div2 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.mod2 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.div2 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (< 0 Y)) (<= (tptp.div2 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (not (= Y 0))) (<= 0 (tptp.mod2 X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (not (= Y 0))) (<= (tptp.mod2 X Y) 0))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (<= (tptp.abs1 (* (tptp.div2 X Y) Y)) (tptp.abs1 X)))) (forall ((X Int)) (= (tptp.div2 X 1) X)) (forall ((X Int)) (= (tptp.mod2 X 1) 0)) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.div2 X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.mod2 X Y) X))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.div2 (+ (* X Y) Z) X) (+ Y (tptp.div2 Z X))))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.mod2 (+ (* X Y) Z) X) (tptp.mod2 Z X)))) (forall ((X Int) (Y Int)) (= (tptp.lt_nat1 X Y) (and (<= 0 Y) (< X Y)))) (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))) (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.lpintcm_intrp)) (tptp.sort1 (tptp.tuple2 tptp.int tptp.int) (tptp.t2tb X))) (forall ((I tptp.lpintcm_intrp)) (= (tptp.tb2t (tptp.t2tb I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)) _let_14 _let_13 (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((X1 Int) (X2 Int) (Y1 Int) (Y2 Int)) (=> (tptp.lt_nat1 X1 X2) (tptp.lex1 (tptp.tb2t (tptp.tuple21 tptp.int tptp.int (tptp.t2tb1 X1) (tptp.t2tb1 Y1))) (tptp.tb2t (tptp.tuple21 tptp.int tptp.int (tptp.t2tb1 X2) (tptp.t2tb1 Y2)))))) (forall ((X Int) (Y1 Int) (Y2 Int)) (let ((_let_1 (tptp.t2tb1 X))) (=> (tptp.lt_nat1 Y1 Y2) (tptp.lex1 (tptp.tb2t (tptp.tuple21 tptp.int tptp.int _let_1 (tptp.t2tb1 Y1))) (tptp.tb2t (tptp.tuple21 tptp.int tptp.int _let_1 (tptp.t2tb1 Y2))))))) (forall ((Z tptp.lpintcm_intrp) (Z1 tptp.lpintcm_intrp)) (=> (tptp.lex1 Z Z1) (or (exists ((X1 Int) (X2 Int) (Y1 Int) (Y2 Int)) (and (tptp.lt_nat1 X1 X2) (= Z (tptp.tb2t (tptp.tuple21 tptp.int tptp.int (tptp.t2tb1 X1) (tptp.t2tb1 Y1)))) (= Z1 (tptp.tb2t (tptp.tuple21 tptp.int tptp.int (tptp.t2tb1 X2) (tptp.t2tb1 Y2)))))) (exists ((X Int) (Y1 Int) (Y2 Int)) (let ((_let_1 (tptp.t2tb1 X))) (and (tptp.lt_nat1 Y1 Y2) (= Z (tptp.tb2t (tptp.tuple21 tptp.int tptp.int _let_1 (tptp.t2tb1 Y1)))) (= Z1 (tptp.tb2t (tptp.tuple21 tptp.int tptp.int _let_1 (tptp.t2tb1 Y2)))))))))) (forall ((N Int)) (= (tptp.even1 N) (exists ((K Int)) (= N (* 2 K))))) (forall ((N Int)) (= (tptp.odd1 N) (exists ((K Int)) (= N (+ (* 2 K) 1))))) (forall ((N Int)) (or (tptp.even1 N) (tptp.odd1 N))) (forall ((N Int)) (=> (tptp.even1 N) (not (tptp.odd1 N)))) (forall ((N Int)) (=> (tptp.odd1 N) (not (tptp.even1 N)))) (forall ((N Int)) (=> (tptp.even1 N) (tptp.odd1 (+ N 1)))) _let_12 (forall ((N Int)) (=> (tptp.even1 N) (tptp.even1 (+ N 2)))) (forall ((N Int)) (=> (tptp.odd1 N) (tptp.odd1 (+ N 2)))) (forall ((K Int)) (tptp.even1 (* 2 K))) (forall ((K Int)) (tptp.odd1 (+ (* 2 K) 1))) (forall ((D Int) (N Int)) (= (tptp.divides1 D N) (exists ((Q Int)) (= N (* Q D))))) (forall ((N Int)) (tptp.divides1 N N)) (forall ((N Int)) (tptp.divides1 1 N)) (forall ((N Int)) (tptp.divides1 N 0)) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (tptp.divides1 (* C A) (* C B)))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (tptp.divides1 (* A C) (* B C)))) (forall ((A Int) (B Int)) (=> (tptp.divides1 A B) (tptp.divides1 A (- B)))) (forall ((A Int) (B Int)) (=> (tptp.divides1 A B) (tptp.divides1 (- A) B))) (forall ((A Int) (B Int)) (=> (tptp.divides1 (- A) B) (tptp.divides1 A B))) (forall ((A Int) (B Int)) (=> (tptp.divides1 A (- B)) (tptp.divides1 A B))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (=> (tptp.divides1 A C) (tptp.divides1 A (+ B C))))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (=> (tptp.divides1 A C) (tptp.divides1 A (- B C))))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (tptp.divides1 A (* C B)))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (tptp.divides1 A (* B C)))) (forall ((A Int) (B Int)) (tptp.divides1 A (* B A))) (forall ((A Int) (B Int)) (tptp.divides1 A (* A B))) (forall ((N Int)) (=> (tptp.divides1 N 1) (or (= N 1) (= N (- 1))))) (forall ((A Int) (B Int)) (=> (tptp.divides1 A B) (=> (tptp.divides1 B A) (or (= A B) (= A (- B)))))) (forall ((A Int) (B Int) (C Int)) (=> (tptp.divides1 A B) (=> (tptp.divides1 B C) (tptp.divides1 A C)))) (forall ((A Int) (B Int)) (=> (tptp.divides1 A B) (=> (not (= B 0)) (<= (tptp.abs1 A) (tptp.abs1 B))))) (forall ((X Int) (Y Int) (Z Int)) (let ((_let_1 (to_real X))) (let ((_let_2 (/ (to_real Z) _let_1))) (let ((_let_3 (>= _let_1 0.0))) (let ((_let_4 (/ (to_real (+ (* X Y) Z)) _let_1))) (=> (< 0 X) (= (ite _let_3 (to_int _let_4) (- (to_int (- _let_4)))) (+ Y (ite _let_3 (to_int _let_2) (- (to_int (- _let_2)))))))))))) (forall ((X Int) (Y Int) (Z Int)) (let ((_let_1 (to_real X))) (let ((_let_2 (to_real Z))) (let ((_let_3 (/ _let_2 _let_1))) (let ((_let_4 (>= _let_1 0.0))) (let ((_let_5 (to_real (+ (* X Y) Z)))) (let ((_let_6 (/ _let_5 _let_1))) (=> (< 0 X) (= (to_int (- _let_5 (* (ite _let_4 (to_int _let_6) (- (to_int (- _let_6)))) _let_1))) (to_int (- _let_2 (* (ite _let_4 (to_int _let_3) (- (to_int (- _let_3)))) _let_1)))))))))))) (forall ((A Int) (B Int)) (let ((_let_1 (to_real B))) (let ((_let_2 (to_real A))) (let ((_let_3 (/ _let_2 _let_1))) (=> (not (= B 0)) (=> (= (to_int (- _let_2 (* (ite (>= _let_1 0.0) (to_int _let_3) (- (to_int (- _let_3)))) _let_1))) 0) (tptp.divides1 B A))))))) (forall ((A Int) (B Int)) (let ((_let_1 (to_real B))) (let ((_let_2 (to_real A))) (let ((_let_3 (/ _let_2 _let_1))) (=> (not (= B 0)) (=> (tptp.divides1 B A) (= (to_int (- _let_2 (* (ite (>= _let_1 0.0) (to_int _let_3) (- (to_int (- _let_3)))) _let_1))) 0))))))) (forall ((A Int) (B Int)) (=> (not (= B 0)) (=> (= (tptp.mod2 A B) 0) (tptp.divides1 B A)))) (forall ((A Int) (B Int)) (=> (not (= B 0)) (=> (tptp.divides1 B A) (= (tptp.mod2 A B) 0)))) (forall ((A Int)) (= (tptp.even1 A) (tptp.divides1 2 A))) (forall ((A Int)) (= (tptp.odd1 A) (not (tptp.divides1 2 A)))) (forall ((P Int)) (= (tptp.prime1 P) (and (<= 2 P) (forall ((N Int)) (=> (and (< 1 N) (< N P)) (not (tptp.divides1 N P))))))) (not (tptp.prime1 1)) (tptp.prime1 2) (tptp.prime1 3) (forall ((P Int)) (=> (tptp.prime1 P) (forall ((D Int)) (=> (tptp.divides1 D P) (or (= D 1) (= D (- 1)) (= D P) (= D (- P))))))) (forall ((P Int)) (=> (<= 2 P) (=> (forall ((D Int)) (let ((_let_1 (* D D))) (=> (<= 2 D) (=> (tptp.prime1 D) (=> (and (< 1 _let_1) (<= _let_1 P)) (not (tptp.divides1 D P))))))) (tptp.prime1 P)))) _let_11 _let_10 (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))) _let_9 (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))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length1 A (tptp.mk_array1 A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) _let_8 (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))) _let_7 (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.t2tb1 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_6 (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)) _let_5 _let_4 (forall ((P tptp.array_int) (U Int)) (=> (<= 1 U) (=> (tptp.first_primes1 P U) (forall ((D Int)) (=> (and (<= 2 D) (<= D (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) (- U 1))))) (=> (tptp.prime1 D) (exists ((I Int)) (and (<= 0 I) (< I U) (= D (tptp.tb2t1 (tptp.get2 tptp.int (tptp.t2tb2 P) I))))))))))) (forall ((P Int)) (=> (tptp.prime1 P) (not (tptp.no_prime_in1 P (* 2 P))))) _let_3 (forall ((I tptp.map_int_int)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.53/16.02  )
% 15.53/16.02  % SZS output end Proof for SWW612_2
% 15.53/16.03  % cvc5---1.0.5 exiting
% 15.53/16.03  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------