%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW590_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:21:37 EDT 2023

% Result   : Theorem 0.54s 1.00s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SWW590_2 : TPTP v8.1.2. Released v6.1.0.
% 0.03/0.12  % Command    : do_cvc5 %s %d
% 0.11/0.32  % Computer : n009.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sun Aug 27 21:55:35 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.17/0.44  %----Proving TF0_ARI
% 0.54/1.00  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.7QWzLe4Szs/cvc5---1.0.5_14159.p...
% 0.54/1.00  ------- get file name : TPTP file name is SWW590_2
% 0.54/1.00  ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14159.smt2...
% 0.54/1.00  --- Run --finite-model-find --decision=internal at 15...
% 0.54/1.00  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.54/1.00  % SZS status Theorem for SWW590_2
% 0.54/1.00  % SZS output start Proof for SWW590_2
% 0.54/1.00  (
% 0.54/1.00  (let ((_let_1 (not (forall ((N Int)) (=> (< 0 N) (=> (tptp.p1 (- N 1)) (=> (and (= (tptp.mod1 N 3) 0) (= (tptp.mod1 N 5) 0)) (tptp.p1 N)))))))) (let ((_let_2 (forall ((N Int)) (= (= (tptp.mod1 N 15) 0) (and (= (tptp.mod1 N 3) 0) (= (tptp.mod1 N 5) 0)))))) (let ((_let_3 (forall ((N Int)) (= (tptp.p1 N) (= (tptp.sum_multiple_3_5_lt1 (+ N 1)) (tptp.closed_formula_aux1 N)))))) (let ((_let_4 (forall ((N Int)) (= (tptp.closed_formula_aux1 N) (- (+ (* 3 (tptp.tr1 (tptp.div1 N 3))) (* 5 (tptp.tr1 (tptp.div1 N 5)))) (* 15 (tptp.tr1 (tptp.div1 N 15)))))))) (let ((_let_5 (forall ((N Int)) (=> (<= 0 N) (= (tptp.tr1 (+ N 1)) (+ (+ (tptp.tr1 N) N) 1)))))) (let ((_let_6 (forall ((X Int) (Y Int)) (let ((_let_1 (+ X 1))) (=> (and (<= 0 X) (< 0 Y)) (=> (= (tptp.mod1 _let_1 Y) 0) (= (tptp.div1 _let_1 Y) (+ (tptp.div1 X Y) 1)))))))) (let ((_let_7 (forall ((N Int)) (=> (<= 0 N) (=> (or (= (tptp.mod1 N 3) 0) (= (tptp.mod1 N 5) 0)) (= (tptp.sum_multiple_3_5_lt1 (+ N 1)) (+ (tptp.sum_multiple_3_5_lt1 N) N))))))) (let ((_let_8 (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< 0 Y)) (<= 0 (tptp.div1 X Y)))))) (let ((_let_9 (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (= X (+ (* Y (tptp.div1 X Y)) (tptp.mod1 X Y))))))) (let ((_let_10 (tptp.mod1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 3))) (let ((_let_11 (= _let_10 0))) (let ((_let_12 (tptp.mod1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 5))) (let ((_let_13 (= _let_12 0))) (let ((_let_14 (tptp.div1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 3))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (+ _let_10 (* 3 _let_14))))) (let ((_let_16 (tptp.div1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 5))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (+ _let_12 (* 5 _let_16))))) (let ((_let_18 (tptp.closed_formula_aux1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (tptp.sum_multiple_3_5_lt1 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (tptp.closed_formula_aux1 _let_21))) (let ((_let_23 (tptp.sum_multiple_3_5_lt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (tptp.mod1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 15))) (let ((_let_26 (= _let_25 0))) (let ((_let_27 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (+ (* (- 1) _let_23) _let_19)))) (let ((_let_28 (tptp.div1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 15))) (let ((_let_29 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (+ _let_25 (* 15 _let_28))))) (let ((_let_30 (tptp.tr1 _let_28))) (let ((_let_31 (tptp.tr1 _let_16))) (let ((_let_32 (tptp.tr1 _let_14))) (let ((_let_33 (= _let_18 (+ (* 3 _let_32) (* 5 _let_31) (* (- 15) _let_30))))) (let ((_let_34 (tptp.div1 _let_21 15))) (let ((_let_35 (tptp.tr1 _let_34))) (let ((_let_36 (tptp.div1 _let_21 5))) (let ((_let_37 (tptp.tr1 _let_36))) (let ((_let_38 (tptp.div1 _let_21 3))) (let ((_let_39 (tptp.tr1 _let_38))) (let ((_let_40 (= _let_22 (+ (* 3 _let_39) (* 5 _let_37) (* (- 15) _let_35))))) (let ((_let_41 (+ 1 _let_38))) (let ((_let_42 (= _let_14 _let_41))) (let ((_let_43 (+ 1 _let_36))) (let ((_let_44 (= _let_16 _let_43))) (let ((_let_45 (+ 1 _let_34))) (let ((_let_46 (= _let_28 _let_45))) (let ((_let_47 (tptp.tr1 _let_41))) (let ((_let_48 (= _let_38 (+ (- 1) (* (- 1) _let_39) _let_47)))) (let ((_let_49 (tptp.tr1 _let_43))) (let ((_let_50 (= _let_36 (+ (- 1) (* (- 1) _let_37) _let_49)))) (let ((_let_51 (tptp.tr1 _let_45))) (let ((_let_52 (= _let_34 (+ (- 1) (* (- 1) _let_35) _let_51)))) (let ((_let_53 (+ _let_19 (* (- 1) _let_18)))) (let ((_let_54 (>= _let_53 0))) (let ((_let_55 (tptp.p1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_56 (not _let_13))) (let ((_let_57 (not _let_11))) (let ((_let_58 (tptp.p1 _let_21))) (let ((_let_59 (not _let_58))) (let ((_let_60 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 1))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59 _let_57 _let_56 _let_55))) (let ((_let_63 (forall ((N Int)) (or (not (>= N 1)) (not (tptp.p1 (+ (- 1) N))) (not (= (tptp.mod1 N 3) 0)) (not (= (tptp.mod1 N 5) 0)) (tptp.p1 N))))) (let ((_let_64 (not _let_62))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (or))) (let ((_let_67 (not _let_63))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_65) :args (_let_67))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_63))) (REFL :args (_let_64)) :args _let_66)) _let_65 :args (_let_64 true _let_63)))) (let ((_let_69 (REFL :args (_let_62)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 2)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_11))) :args _let_66)) :args ((or _let_11 _let_62))) _let_68 :args (_let_11 true _let_62)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 3)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_13))) :args _let_66)) :args ((or _let_13 _let_62))) _let_68 :args (_let_13 true _let_62)))) (let ((_let_72 (forall ((X Int) (Y Int)) (or (= Y 0) (= X (+ (tptp.mod1 X Y) (* Y (tptp.div1 X Y)))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 ((tptp.mod1 X Y)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74))) _let_73 :args (_let_15 false _let_72)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74))) _let_73 :args (_let_17 false _let_72)))) (let ((_let_78 (= _let_55 _let_20))) (let ((_let_79 (not _let_20))) (let ((_let_80 (forall ((N Int)) (= (tptp.p1 N) (= (tptp.closed_formula_aux1 N) (tptp.sum_multiple_3_5_lt1 (+ 1 N))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.p1 N)))) (let ((_let_84 (= _let_58 _let_24))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_84)) :args ((or _let_59 _let_24 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 1)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_58))) :args _let_66)) :args ((or _let_58 _let_62))) _let_68 :args (_let_58 true _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82))) _let_81 :args (_let_84 false _let_80)) :args (_let_24 false _let_58 false _let_84)))) (let ((_let_86 (and _let_11 _let_13))) (let ((_let_87 (= _let_26 _let_86))) (let ((_let_88 (_let_2))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_87)) :args ((or _let_26 (not _let_86) (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_86)) :args ((or _let_57 _let_56 _let_86))) _let_70 _let_71 :args (_let_86 false _let_11 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.mod1 N 3)))) :args _let_88)) _let_89 :args (_let_87 false _let_2)) :args (_let_26 false _let_86 false _let_87)))) (let ((_let_91 (and _let_57 _let_56))) (let ((_let_92 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 0))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_91 _let_27))) (let ((_let_95 (forall ((N Int)) (or (not (>= N 0)) (and (not (= (tptp.mod1 N 3) 0)) (not (= (tptp.mod1 N 5) 0))) (= N (+ (* (- 1) (tptp.sum_multiple_3_5_lt1 N)) (tptp.sum_multiple_3_5_lt1 (+ 1 N)))))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (not _let_91))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_66)) :args ((or _let_60 _let_62))) _let_68 :args (_let_60 true _let_62)))) (let ((_let_99 (> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (- 1)))) (let ((_let_100 (ASSUME :args (_let_93)))) (let ((_let_101 ((<= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (- 1))))) (let ((_let_102 (false))) (let ((_let_103 (ASSUME :args (_let_60)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_93 _let_91 _let_27 (not _let_94)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_100 _let_103) :args (_let_60 _let_93)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_101) _let_103 :args (1.0 (- 1.0))) :args _let_102) :args _let_101) :args (_let_99)) (MACRO_SR_PRED_TRANSFORM (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_100 :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 0)))) :args ((not _let_99)))) :args (_let_93 _let_60)) :args ((not (and _let_60 _let_93)) SB_LITERAL))) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) :args _let_66)) _let_98 :args (_let_92 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_91 0)) :args ((or _let_57 _let_97))) _let_70 :args (_let_97 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.mod1 N 3)))) :args (_let_95))) _let_96 :args (_let_94 false _let_95)) :args (_let_27 false _let_92 true _let_91 false _let_94)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_75)) :args _let_74))) _let_73 :args (_let_29 false _let_72)))) (let ((_let_106 (forall ((N Int)) (= (tptp.closed_formula_aux1 N) (+ (* 3 (tptp.tr1 (tptp.div1 N 3))) (* 5 (tptp.tr1 (tptp.div1 N 5))) (* (- 15) (tptp.tr1 (tptp.div1 N 15)))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_106))) (let ((_let_109 ((tptp.closed_formula_aux1 N)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_108)) _let_107 :args (_let_33 false _let_106)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (_let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_108)) _let_107 :args (_let_40 false _let_106)))) (let ((_let_112 (or _let_61 _let_57 _let_42))) (let ((_let_113 (forall ((X Int) (Y Int)) (let ((_let_1 (+ 1 X))) (or (not (>= X 0)) (not (>= Y 1)) (not (= (tptp.mod1 _let_1 Y) 0)) (= (tptp.div1 X Y) (+ (- 1) (tptp.div1 _let_1 Y)))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (_let_113))) (let ((_let_116 ((tptp.div1 X Y)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_61 _let_57 _let_42 (not _let_112)))) _let_98 _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_21 3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_116)) :args _let_115))) _let_114 :args (_let_112 false _let_113)) :args (_let_42 false _let_60 false _let_11 false _let_112)))) (let ((_let_118 (or _let_61 _let_56 _let_44))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_61 _let_56 _let_44 (not _let_118)))) _let_98 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_21 5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_116)) :args _let_115))) _let_114 :args (_let_118 false _let_113)) :args (_let_44 false _let_60 false _let_13 false _let_118)))) (let ((_let_120 (not _let_26))) (let ((_let_121 (or _let_61 _let_120 _let_46))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_61 _let_120 _let_46 (not _let_121)))) _let_98 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_21 15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_116)) :args _let_115))) _let_114 :args (_let_121 false _let_113)) :args (_let_46 false _let_60 false _let_26 false _let_121)))) (let ((_let_123 (>= _let_38 0))) (let ((_let_124 (not _let_123))) (let ((_let_125 (or _let_124 _let_48))) (let ((_let_126 (forall ((N Int)) (or (not (>= N 0)) (= N (+ (- 1) (* (- 1) (tptp.tr1 N)) (tptp.tr1 (+ 1 N)))))))) (let ((_let_127 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_128 (_let_126))) (let ((_let_129 ((tptp.tr1 N)))) (let ((_let_130 (or _let_61 _let_123))) (let ((_let_131 (forall ((X Int) (Y Int)) (or (not (>= X 0)) (not (>= Y 1)) (>= (tptp.div1 X Y) 0))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (_let_131))) (let ((_let_134 ((tptp.div1 X Y)))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_124 _let_48 (not _let_125)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_61 _let_123 (not _let_130)))) _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (_let_21 3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_134)) :args _let_133))) _let_132 :args (_let_130 false _let_131)) :args (_let_123 false _let_60 false _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (_let_38 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_128)) _let_127 :args (_let_125 false _let_126)) :args (_let_48 false _let_123 false _let_125)))) (let ((_let_136 (>= _let_36 0))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_137 _let_50))) (let ((_let_139 (or _let_61 _let_136))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_138)) :args ((or _let_137 _let_50 (not _let_138)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_61 _let_136 (not _let_139)))) _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (_let_21 5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_134)) :args _let_133))) _let_132 :args (_let_139 false _let_131)) :args (_let_136 false _let_60 false _let_139)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (_let_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_128)) _let_127 :args (_let_138 false _let_126)) :args (_let_50 false _let_136 false _let_138)))) (let ((_let_141 (>= _let_34 0))) (let ((_let_142 (not _let_141))) (let ((_let_143 (or _let_142 _let_52))) (let ((_let_144 (or _let_61 _let_141))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_142 _let_52 (not _let_143)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_61 _let_141 (not _let_144)))) _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (_let_21 15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_134)) :args _let_133))) _let_132 :args (_let_144 false _let_131)) :args (_let_141 false _let_60 false _let_144)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (_let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_128)) _let_127 :args (_let_143 false _let_126)) :args (_let_52 false _let_141 false _let_143)))) (let 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((or _let_55 _let_79 (not _let_78)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_62 4)) _let_68 :args ((not _let_55) true _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82))) _let_81 :args (_let_78 false _let_80)) :args (_let_79 true _let_55 false _let_78)) _let_77 _let_76 _let_71 _let_70 :args (false false _let_54 false _let_52 false _let_50 false _let_48 false _let_46 false _let_44 false _let_42 false _let_40 false _let_33 false _let_29 false _let_27 false _let_26 false _let_24 true _let_20 false _let_17 false _let_15 false _let_13 false _let_11)) :args ((forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))) (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))) _let_9 (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)))))) _let_8 (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)))) (= (tptp.sum_multiple_3_5_lt1 0) 0) (forall ((N Int)) (=> (<= 0 N) (=> (and (not (= (tptp.mod1 N 3) 0)) (not (= (tptp.mod1 N 5) 0))) (= (tptp.sum_multiple_3_5_lt1 (+ N 1)) (tptp.sum_multiple_3_5_lt1 N))))) _let_7 (forall ((X Int)) (exists ((Y Int)) (let ((_let_1 (* 2 Y))) (or (= X _let_1) (= X (+ _let_1 1)))))) (forall ((X Int) (Y Int) (Q Int) (R Int)) (=> (and (<= 0 X) (< 0 Y) (= X (+ (* Q Y) R)) (<= 0 R) (< R Y)) (and (= Q (tptp.div1 X Y)) (= R (tptp.mod1 X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.mod1 (+ X 1) Y))) (=> (and (<= 0 X) (< 0 Y)) (=> (not (= _let_1 0)) (= _let_1 (+ (tptp.mod1 X Y) 1)))))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< 0 Y)) (=> (= (tptp.mod1 (+ X 1) Y) 0) (= (tptp.mod1 X Y) (- Y 1))))) _let_6 (forall ((X Int) (Y Int)) (let ((_let_1 (+ X 1))) (=> (and (<= 0 X) (< 0 Y)) (=> (not (= (tptp.mod1 _let_1 Y) 0)) (= (tptp.div1 _let_1 Y) (tptp.div1 X Y)))))) (forall ((X Int)) (= (tptp.mod1 (* 2 X) 2) 0)) (forall ((X Int) (Y Int)) (= (tptp.mod1 (* Y (* 2 X)) 2) 0)) (forall ((X Int) (Y Int) (Z Int) (T Int)) (= (tptp.mod1 (+ (* Y (* 2 X)) (* Z (* 2 T))) 2) 0)) (forall ((X Int)) (= (tptp.div1 (* 2 X) 2) X)) (forall ((X Int) (Y Int)) (= (tptp.div1 (* Y (* 2 X)) 2) (* Y X))) (forall ((X Int) (Y Int)) (=> (and (= (tptp.mod1 X 2) 0) (= (tptp.mod1 Y 2) 0)) (= (tptp.div1 (+ X Y) 2) (+ (tptp.div1 X 2) (tptp.div1 Y 2))))) (forall ((X Int) (Y Int)) (=> (and (= (tptp.mod1 X 2) 0) (= (tptp.mod1 Y 2) 0)) (= (tptp.div1 (- X Y) 2) (- (tptp.div1 X 2) (tptp.div1 Y 2))))) (forall ((N Int)) (=> (<= 0 N) (= (tptp.mod1 (* N (+ N 1)) 2) 0))) (forall ((N Int)) (= (tptp.tr1 N) (tptp.div1 (* N (+ N 1)) 2))) (forall ((N Int)) (=> (<= 0 N) (= (* N (+ N 1)) (* 2 (tptp.tr1 N))))) _let_5 _let_4 _let_3 _let_2 (tptp.p1 0) (forall ((N Int)) (=> (< 0 N) (=> (tptp.p1 (- N 1)) (=> (and (not (= (tptp.mod1 N 3) 0)) (not (= (tptp.mod1 N 5) 0))) (tptp.p1 N))))) (forall ((N Int)) (=> (< 0 N) (=> (tptp.p1 (- N 1)) (=> (and (= (tptp.mod1 N 3) 0) (not (= (tptp.mod1 N 5) 0))) (tptp.p1 N))))) (forall ((N Int)) (=> (< 0 N) (=> (tptp.p1 (- N 1)) (=> (and (not (= (tptp.mod1 N 3) 0)) (= (tptp.mod1 N 5) 0)) (tptp.p1 N))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.54/1.01  )
% 0.54/1.01  % SZS output end Proof for SWW590_2
% 0.54/1.01  % cvc5---1.0.5 exiting
% 0.54/1.01  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------