TSTP Solution File: SWW632_2 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW632_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 00:21:46 EDT 2023
% Result : Theorem 0.45s 0.67s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW632_2 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 20:16:05 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_ARI
% 0.45/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.nqSHq7h14G/cvc5---1.0.5_6165.p...
% 0.45/0.67 ------- get file name : TPTP file name is SWW632_2
% 0.45/0.67 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6165.smt2...
% 0.45/0.67 --- Run --finite-model-find --decision=internal at 15...
% 0.45/0.67 % SZS status Theorem for SWW632_2
% 0.45/0.67 % SZS output start Proof for SWW632_2
% 0.45/0.67 (
% 0.45/0.67 (let ((_let_1 (not (forall ((X Int) (N Int)) (=> (<= 0 N) (forall ((E Int) (P Int) (R Int)) (let ((_let_1 (tptp.power X N))) (=> (and (<= 0 E) (= (* R (tptp.power P E)) _let_1)) (=> (not (< 0 E)) (= R _let_1)))))))))) (let ((_let_2 (forall ((X Int) (N Int)) (=> (<= 0 N) (= (tptp.power X (+ N 1)) (* X (tptp.power X N))))))) (let ((_let_3 (forall ((X Int)) (= (tptp.power X 0) 1)))) (let ((_let_4 (tptp.power SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (* SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_4))) (let ((_let_6 (* (- 1) _let_5))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_6))) (let ((_let_8 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_9 (>= _let_5 1))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_5))) (let ((_let_11 (or _let_10 _let_7))) (let ((_let_12 (= _let_4 1))) (let ((_let_13 (or _let_12 (= _let_4 (- 1))))) (let ((_let_14 (tptp.power SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 0))) (let ((_let_15 (= _let_14 1))) (let ((_let_16 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 1))) (let ((_let_17 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 0))) (let ((_let_18 (_let_3))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args _let_18)) _let_19 :args (_let_15 false _let_3)))) (let ((_let_21 (tptp.power SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_23 (= _let_21 _let_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_17))) (let ((_let_26 (or (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 0)) _let_25 _let_24 _let_16 _let_22))) (let ((_let_27 (not _let_16))) (let ((_let_28 (forall ((X Int) (N Int) (BOUND_VARIABLE_1399 Int) (BOUND_VARIABLE_1397 Int) (BOUND_VARIABLE_1395 Int)) (let ((_let_1 (tptp.power X N))) (or (not (>= N 0)) (not (>= BOUND_VARIABLE_1395 0)) (not (= _let_1 (* BOUND_VARIABLE_1399 (tptp.power BOUND_VARIABLE_1397 BOUND_VARIABLE_1395)))) (>= BOUND_VARIABLE_1395 1) (= BOUND_VARIABLE_1399 _let_1)))))) (let ((_let_29 (not _let_26))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (or))) (let ((_let_32 (not _let_28))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_31)) _let_30 :args (_let_29 true _let_28)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 3)) _let_33 :args (_let_27 true _let_26)))) (let ((_let_35 (REFL :args (_let_26)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_17))) :args _let_31)) :args ((or _let_17 _let_26))) _let_33 :args (_let_17 true _let_26)))) (let ((_let_37 (_let_12))) (let ((_let_38 (REFL :args ((not _let_15))))) (let ((_let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_16))))) (let ((_let_40 (REFL :args (_let_25)))) (let ((_let_41 (and _let_17 _let_27 _let_15))) (let ((_let_42 (true _let_41))) (let ((_let_43 (_let_17 _let_27 _let_15))) (let ((_let_44 (= _let_14 _let_4))) (let ((_let_45 (_let_15 _let_44))) (let ((_let_46 (ASSUME :args (_let_15)))) (let ((_let_47 (SYMM (SYMM _let_46)))) (let ((_let_48 (SYMM (ASSUME :args (_let_44))))) (let ((_let_49 (TRANS _let_48 _let_47))) (let ((_let_50 ((= 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_51 (ASSUME :args (_let_27)))) (let ((_let_52 (ASSUME :args (_let_17)))) (let ((_let_53 (MODUS_PONENS (MODUS_PONENS (AND_INTRO _let_52 _let_51) (SCOPE (SYMM (ARITH_TRICHOTOMY _let_52 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_51 :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 1)))) :args ((= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 0)))) :args (_let_17 _let_27))) (SCOPE (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (SYMM (SYMM (ASSUME :args _let_50))) :args (APPLY_UF tptp.power)) :args _let_50)))) (let ((_let_54 (AND_INTRO _let_46 _let_53))) (let ((_let_55 (CNF_AND_NEG :args (_let_41)))) (let ((_let_56 (EQ_RESOLVE (RESOLUTION _let_55 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_54 (SCOPE _let_49 :args _let_45)) :args _let_43)) :args _let_42) (CONG _let_40 _let_39 _let_38 (REFL :args _let_37) :args _let_31)))) (let ((_let_57 (REORDERING (CNF_OR_NEG :args (_let_13 0)) :args ((or (not _let_12) _let_13))))) (let ((_let_58 (- SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_59 (- 1))) (let ((_let_60 (or _let_12 (= _let_4 _let_59)))) (let ((_let_61 (=> _let_60 (or (= _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (= _let_5 _let_58))))) (let ((_let_62 (IMPLIES_ELIM (EQ_RESOLVE (THEORY_LEMMA :args (_let_61 THEORY_ARITH)) (REWRITE :args (_let_61)))))) (let ((_let_63 (not _let_10))) (let ((_let_64 (not _let_22))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 4)) _let_33 :args (_let_64 true _let_26)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_31)) :args ((or _let_23 _let_26))) _let_33 :args (_let_23 true _let_26)))) (let ((_let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_22))))) (let ((_let_68 (REFL :args (_let_24)))) (let ((_let_69 (and _let_23 _let_64))) (let ((_let_70 (ASSUME :args (_let_64)))) (let ((_let_71 (FALSE_INTRO _let_70))) (let ((_let_72 (=))) (let ((_let_73 (ASSUME :args (_let_23)))) (let ((_let_74 (SYMM _let_73))) (let ((_let_75 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_70 _let_73) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_74 :args _let_72) _let_71)) :args (_let_64 _let_23))) :args (_let_23 _let_64))) :args (true _let_69)) (CONG _let_68 _let_67 (REFL :args (_let_63)) :args _let_31)))) (let ((_let_76 (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_10 _let_7 (not _let_11)))))) (let ((_let_77 (MACRO_RESOLUTION_TRUST _let_76 (MACRO_RESOLUTION_TRUST _let_75 _let_66 _let_65 :args (_let_63 false _let_23 true _let_22)) (MACRO_RESOLUTION_TRUST _let_62 (MACRO_RESOLUTION_TRUST _let_57 (MACRO_RESOLUTION_TRUST _let_56 _let_36 _let_34 _let_20 :args (_let_12 false _let_17 true _let_16 false _let_15)) :args (_let_13 false _let_12)) :args (_let_11 false _let_13)) :args (_let_7 true _let_10 false _let_11)))) (let ((_let_78 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_79 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (* (- 1) _let_21)))) (let ((_let_80 (>= _let_79 0))) (let ((_let_81 (= _let_5 0))) (let ((_let_82 (= (tptp.power 0 1) 0))) (let ((_let_83 (not _let_78))) (let ((_let_84 (_let_78))) (let ((_let_85 (_let_81))) (let ((_let_86 (ASSUME :args _let_84))) (let ((_let_87 (forall ((X Int) (N Int)) (or (not (>= N 0)) (= (tptp.power X (+ 1 N)) (* X (tptp.power X N))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_83))) (let ((_let_90 (ASSUME :args _let_85))) (let ((_let_91 (ASSUME :args (_let_82)))) (let ((_let_92 (SYMM _let_91))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_91 _let_86 _let_90 _let_73 _let_70) :args (_let_23 _let_64 _let_78 _let_81 _let_82)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_71) (TRUE_INTRO (TRANS (TRANS (SYMM (SYMM _let_86)) _let_92) (SYMM _let_92) (SYMM (TRANS (SYMM _let_74) (SYMM (SYMM _let_90)))))))) :args (_let_82 _let_78 _let_81 _let_23 _let_64)) :args ((not (and _let_23 _let_64 _let_78 _let_81 _let_82)) SB_LITERAL))) (CONG _let_68 _let_67 (REFL :args _let_89) (REFL :args ((not _let_81))) (REFL :args ((not _let_82))) :args _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_88 :args (0 0 QUANTIFIERS_INST_FMF_FMC_EXH)) :args (_let_87)))) _let_88 :args (_let_82 false _let_87)) _let_65 _let_66 (REORDERING (IMPLIES_ELIM (SCOPE (MACRO_SR_PRED_INTRO _let_86 :args _let_85) :args _let_84)) :args ((or _let_81 _let_83))) :args (_let_83 false _let_82 true _let_22 false _let_23 false _let_81)))) (let ((_let_94 (>= _let_79 1))) (let ((_let_95 (>= _let_4 1))) (let ((_let_96 (not _let_8))) (let ((_let_97 (and _let_96 _let_95))) (let ((_let_98 (>= _let_5 0))) (let ((_let_99 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (- 1)))) (let ((_let_100 (not _let_99))) (let ((_let_101 (ite _let_8 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 2) _let_100))) (let ((_let_102 (= _let_4 0))) (let ((_let_103 (not _let_102))) (let ((_let_104 (and _let_101 _let_13 _let_83 _let_103))) (let ((_let_105 (>= _let_5 (- 1)))) (let ((_let_106 (not _let_105))) (let ((_let_107 (ite _let_98 (>= _let_5 2) _let_106))) (let ((_let_108 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_109 (<= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_110 ((or _let_109 _let_108)))) (let ((_let_111 (not _let_108))) (let ((_let_112 (not _let_109))) (let ((_let_113 (false))) (let ((_let_114 (not _let_95))) (let ((_let_115 (= 1 _let_4))) (let ((_let_116 (> _let_4 0))) (let ((_let_117 (_let_114))) (let ((_let_118 (ASSUME :args _let_117))) (let ((_let_119 ((<= _let_4 0)))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_118 (MODUS_PONENS (AND_INTRO _let_53 _let_46) (SCOPE (TRANS (SYMM _let_47) (SYMM _let_48)) :args (_let_44 _let_15)))) :args (_let_17 _let_27 _let_15 _let_114)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_119) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_115)) :args _let_37) :args (1.0 (- 1.0))) :args _let_113) :args _let_119) :args (_let_116)) (MACRO_SR_PRED_TRANSFORM (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_118 :args ((< _let_4 1)))) :args ((not _let_116)))) :args (_let_114 _let_115)) :args ((not (and _let_17 _let_27 _let_15 _let_114)) SB_LITERAL))) (CONG _let_40 _let_39 _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_114) _let_95))) :args _let_31)) _let_20 _let_34 _let_36 :args (_let_95 false _let_15 true _let_16 false _let_17)))) (let ((_let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_8))))) (let ((_let_122 (_let_97))) (let ((_let_123 (not _let_98))) (let ((_let_124 (< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_125 (_let_100))) (let ((_let_126 (not _let_80))) (let ((_let_127 (_let_99))) (let ((_let_128 (ASSUME :args (_let_123)))) (let ((_let_129 (_let_126))) (let ((_let_130 (ASSUME :args _let_129))) (let ((_let_131 (MACRO_SR_PRED_TRANSFORM _let_73 :args ((= (+ _let_21 _let_6) 0))))) (let ((_let_132 (ASSUME :args _let_127))) (let ((_let_133 (_let_8))) (let ((_let_134 (_let_101))) (let ((_let_135 (not _let_13))) (let ((_let_136 (not _let_101))) (let ((_let_137 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_78))))) (let ((_let_138 (_let_104))) (let ((_let_139 (- _let_5))) (let ((_let_140 (>= 1 0))) (let ((_let_141 (=> (and (ite _let_8 (ite _let_140 (> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 1) (> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_59)) (ite _let_140 (> _let_58 1) (> _let_58 _let_59))) _let_60 _let_83 _let_103) (ite _let_98 (ite _let_140 (> _let_5 1) (> _let_5 _let_59)) (ite _let_140 (> _let_139 1) (> _let_139 _let_59)))))) (let ((_let_142 (REFL :args ((not _let_7))))) (let ((_let_143 (not _let_94))) (let ((_let_144 (= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_5) 0))) (let ((_let_145 ((not _let_144)))) (let ((_let_146 (_let_144))) (let ((_let_147 (ASSUME :args (_let_106)))) (let ((_let_148 (ASSUME :args (_let_143)))) (let ((_let_149 (ASSUME :args (_let_7)))) (let ((_let_150 (MACRO_SR_PRED_TRANSFORM _let_149 :args _let_146))) (let ((_let_151 (_let_124))) (let ((_let_152 (ASSUME :args (_let_80)))) (let ((_let_153 (_let_96))) (let ((_let_154 (ASSUME :args _let_153))) (let ((_let_155 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_149 _let_73 _let_152 _let_154) :args (_let_23 _let_80 _let_96 _let_7)) (SCOPE (CONTRA (MACRO_SR_PRED_TRANSFORM _let_154 :args _let_151) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_151) _let_152 _let_131 _let_150 :args (1.0 (/ (- 1) 2) (/ (- 1) 2) (/ (- 1) 2))) :args _let_113) :args _let_151) :args _let_133) :args ((not _let_124)))) :args (_let_7 _let_23 _let_80 _let_96)) :args ((not (and _let_23 _let_80 _let_96 _let_7)) SB_LITERAL))) (CONG _let_68 (REFL :args _let_129) _let_121 _let_142 :args _let_31)) _let_77 _let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_147 _let_148 _let_73 _let_149) :args (_let_23 _let_143 _let_106 _let_7)) (SCOPE (CONTRA _let_150 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_146) _let_131 (MACRO_SR_PRED_TRANSFORM _let_148 :args ((< _let_79 1))) (MACRO_SR_PRED_TRANSFORM _let_147 :args ((< _let_5 (- 1)))) :args ((- 1.0) 1.0 1.0 2.0)) :args _let_113) :args _let_146) :args _let_145) :args _let_145)) :args (_let_106 _let_143 _let_23 _let_7)) :args ((not (and _let_23 _let_143 _let_106 _let_7)) SB_LITERAL))) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_143) _let_94))) (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) _let_142 :args _let_31)) _let_66 _let_76 _let_75 _let_65 _let_66 _let_62 (REORDERING (CNF_ITE_POS2 :args (_let_107)) :args ((or _let_98 _let_106 (not _let_107)))) (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (THEORY_LEMMA :args (_let_141 THEORY_ARITH)) (REWRITE :args (_let_141)))) :args ((or _let_107 (not _let_104)))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_138) (CONG (REFL :args _let_138) (REFL :args (_let_136)) (REFL :args (_let_135)) _let_137 (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_102))) :args _let_31)) :args ((or _let_78 _let_102 _let_104 _let_136 _let_135))) _let_57 _let_56 _let_20 _let_34 _let_36 (EQ_RESOLVE (RESOLUTION _let_55 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_54 (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (REFL :args (0)) _let_49 :args _let_72) (MACRO_SR_PRED_INTRO :args ((= (= 0 1) false)))) :args ((= _let_102 false)))) :args _let_45)) :args _let_43)) :args _let_42) (CONG _let_40 _let_39 _let_38 (REFL :args (_let_103)) :args _let_31)) _let_20 _let_34 _let_36 (REORDERING (EQ_RESOLVE (CNF_ITE_NEG2 :args _let_134) (CONG (REFL :args _let_134) (REFL :args _let_133) (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_99))) :args _let_31)) :args ((or _let_8 _let_99 _let_101))) (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_128 _let_130 _let_73 _let_132) :args (_let_23 _let_126 _let_123 _let_99)) (SCOPE (CONTRA _let_132 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_132 _let_131 (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_130 :args ((< _let_79 0)))) (MACRO_SR_PRED_TRANSFORM _let_128 :args ((< _let_5 0))) :args ((- 1.0) 1.0 1.0 1.0)) :args _let_113) :args _let_127) :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (- 1)))) :args _let_125)) :args (_let_123 _let_126 _let_23 _let_99)) :args ((not (and _let_23 _let_126 _let_123 _let_99)) SB_LITERAL))) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_126) _let_80))) (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_98))) (REFL :args _let_125) :args _let_31)) _let_66 (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ARITH_MULT_SIGN :args (_let_124 _let_116 _let_5)) (REWRITE :args ((=> (and _let_124 _let_116) (> 0 _let_5)))))) :args ((or _let_123 (not _let_97)))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_122) (CONG (REFL :args _let_122) _let_121 (REFL :args _let_117) :args _let_31)) :args ((or _let_8 _let_114 _let_97))) _let_120 (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (NOT_AND (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_112)) :args ((> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_111)) :args ((< SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) :args ((- 1) 1)) :args _let_113) :args (_let_112 _let_111))) :args _let_110) (REWRITE :args _let_110)) :args ((or _let_80 _let_8 _let_78) false _let_23 false _let_7 true _let_10 true _let_22 false _let_23 false _let_11 true _let_105 false _let_107 false _let_104 false _let_13 false _let_12 false _let_15 true _let_16 false _let_17 true _let_102 false _let_15 true _let_16 false _let_17 false _let_101 true _let_99 false _let_23 true _let_98 false _let_97 false _let_95 true _let_94)) _let_93 :args (_let_8 false _let_7 false _let_23 false _let_80 true _let_78)))) (let ((_let_156 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 1))) (let ((_let_157 (and _let_156 _let_95))) (let ((_let_158 (and _let_8 _let_83))) (let ((_let_159 (> SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0))) (let ((_let_160 (ASSUME :args _let_133))) (let ((_let_161 (ASSUME :args _let_89))) (let ((_let_162 (ASSUME :args (_let_9)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_162 _let_149 _let_160) :args (_let_8 _let_9 _let_7)) (SCOPE (CONTRA _let_160 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_160 _let_150 _let_162 :args ((- 1.0) 1.0 (- 1.0))) :args _let_113) :args _let_133) :args _let_151) :args _let_153)) :args (_let_9 _let_7 _let_8)) :args ((not (and _let_8 _let_9 _let_7)) SB_LITERAL))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ARITH_MULT_SIGN :args (_let_159 _let_116 _let_5)) (REWRITE :args ((=> (and _let_159 _let_116) (> _let_5 0)))))) :args ((or _let_9 (not _let_157)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_157)) :args ((or _let_114 (not _let_156) _let_157))) _let_120 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_158)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_160) (SCOPE (INT_TIGHT_LB (ARITH_TRICHOTOMY _let_161 _let_160 :args (_let_159))) :args (_let_83 _let_8))) :args (_let_8 _let_83))) :args (true _let_158)) (CONG (REFL :args _let_153) _let_137 (REFL :args (_let_156)) :args _let_31)) _let_155 _let_93 :args (_let_156 false _let_8 true _let_78)) :args (_let_157 false _let_95 false _let_156)) :args (_let_9 false _let_157)) _let_155 _let_77 :args (false false _let_9 false _let_8 false _let_7)) :args ((forall ((A tptp.ty)) (tptp.sort A (tptp.witness A))) (forall ((A tptp.ty) (X tptp.bool) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort A (tptp.match_bool A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort A Z) (= (tptp.match_bool A tptp.true Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort A Z1) (= (tptp.match_bool A tptp.false Z Z1) Z1))) (not (= tptp.true tptp.false)) (forall ((U tptp.bool)) (or (= U tptp.true) (= U tptp.false))) (forall ((U tptp.tuple0)) (= U tptp.tuple02)) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) _let_3 _let_2 (forall ((X Int) (N Int)) (=> (< 0 N) (= (tptp.power X N) (* X (tptp.power X (- N 1)))))) (forall ((X Int)) (= (tptp.power X 1) X)) (forall ((X Int) (N Int) (M Int)) (=> (<= 0 N) (=> (<= 0 M) (= (tptp.power X (+ N M)) (* (tptp.power X N) (tptp.power X M)))))) (forall ((X Int) (N Int) (M Int)) (=> (<= 0 N) (=> (<= 0 M) (= (tptp.power X (* N M)) (tptp.power (tptp.power X N) M))))) (forall ((X Int) (Y Int) (N Int)) (=> (<= 0 N) (= (tptp.power (* X Y) N) (* (tptp.power X N) (tptp.power Y N))))) (forall ((X Int)) (let ((_let_1 (tptp.abs X))) (let ((_let_2 (<= 0 X))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (- X))))))) (forall ((X Int) (Y Int)) (= (<= (tptp.abs X) Y) (and (<= (- Y) X) (<= X Y)))) (forall ((X Int)) (<= 0 (tptp.abs X))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (= X (+ (* Y (tptp.div X Y)) (tptp.mod X Y))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.div X Y))) (=> (and (<= 0 X) (< 0 Y)) (and (<= 0 _let_1) (<= _let_1 X))))) (forall ((X Int) (Y Int)) (let ((_let_1 (tptp.abs Y))) (let ((_let_2 (tptp.mod 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.div X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (< 0 Y)) (<= (tptp.div X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (not (= Y 0))) (<= 0 (tptp.mod X Y)))) (forall ((X Int) (Y Int)) (=> (and (<= X 0) (not (= Y 0))) (<= (tptp.mod X Y) 0))) (forall ((X Int) (Y Int)) (=> (not (= Y 0)) (<= (tptp.abs (* (tptp.div X Y) Y)) (tptp.abs X)))) (forall ((X Int)) (= (tptp.div X 1) X)) (forall ((X Int)) (= (tptp.mod X 1) 0)) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.div X Y) 0))) (forall ((X Int) (Y Int)) (=> (and (<= 0 X) (< X Y)) (= (tptp.mod X Y) X))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.div (+ (* X Y) Z) X) (+ Y (tptp.div Z X))))) (forall ((X Int) (Y Int) (Z Int)) (=> (and (< 0 X) (<= 0 Y) (<= 0 Z)) (= (tptp.mod (+ (* X Y) Z) X) (tptp.mod Z X)))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort (tptp.ref A) (tptp.mk_ref A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort A (tptp.contents A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort A U) (= (tptp.contents A (tptp.mk_ref A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.45/0.68 )
% 0.45/0.68 % SZS output end Proof for SWW632_2
% 0.45/0.68 % cvc5---1.0.5 exiting
% 0.45/0.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------