TSTP Solution File: NUM859_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM859_1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 : Thu Aug 31 10:48:32 EDT 2023
% Result : Theorem 34.05s 34.25s
% Output : Proof 34.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM859_1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 10:52:33 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_ARI
% 34.05/34.25 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Rg0u0IqgEb/cvc5---1.0.5_7645.p...
% 34.05/34.25 ------- get file name : TPTP file name is NUM859_1
% 34.05/34.25 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7645.smt2...
% 34.05/34.25 --- Run --finite-model-find --decision=internal at 15...
% 34.05/34.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 34.05/34.25 --- Run --no-e-matching --full-saturate-quant at 15...
% 34.05/34.25 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 34.05/34.25 % SZS status Theorem for NUM859_1
% 34.05/34.25 % SZS output start Proof for NUM859_1
% 34.05/34.25 (
% 34.05/34.25 (let ((_let_1 (forall ((X Int) (Y Int) (Z Int)) (= (tptp.minsol_model_ub X Y Z) (tptp.minsol_model_max X Y Z))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z Int)) (=> (tptp.model_ub X Y Z) (<= N Z)))))))) (let ((_let_4 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z Int)) (=> (tptp.model_max X Y Z) (<= N Z)))))))) (let ((_let_5 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_ub X Y N) (exists ((Z Int)) (and (tptp.ub X Y Z) (<= Z N))))))) (let ((_let_6 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_max X Y N) (<= (tptp.max X Y) N))))) (let ((_let_7 (forall ((X Int) (Y Int) (Z Int)) (= (tptp.ub X Y Z) (and (<= X Z) (<= Y Z)))))) (let ((_let_8 (forall ((X Int) (Y Int)) (or (= (tptp.max X Y) Y) (not (<= X Y)))))) (let ((_let_9 (forall ((X Int) (Y Int)) (or (= (tptp.max X Y) X) (not (<= Y X)))))) (let ((_let_10 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77))) (let ((_let_11 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_10) 1))) (let ((_let_12 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_10))) (let ((_let_13 (>= _let_12 1))) (let ((_let_14 (tptp.max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_15 (* (- 1) _let_14))) (let ((_let_16 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_15))) (let ((_let_17 (>= _let_16 1))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_14))) (let ((_let_19 (not _let_11))) (let ((_let_20 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19))) (let ((_let_23 (forall ((Z Int)) (or (not (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Z)) (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) 0))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85))) (let ((_let_26 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_25))) (let ((_let_27 (>= _let_26 1))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (not _let_23))) (let ((_let_33 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_76))) (let ((_let_34 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_33) 1))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_76))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35))) (let ((_let_39 (not _let_31))) (let ((_let_40 (forall ((Z Int)) (or (not (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Z)) (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) 0))))) (let ((_let_41 (not _let_38))) (let ((_let_42 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_43 (and _let_42 _let_40))) (let ((_let_44 (not _let_40))) (let ((_let_45 (forall ((Z Int)) (or (not (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Z)) (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) 1))))) (let ((_let_46 (not _let_45))) (let ((_let_47 (= _let_42 _let_46))) (let ((_let_48 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_ub X Y N) (not (forall ((Z Int)) (or (not (tptp.ub X Y Z)) (not (>= (+ N (* (- 1) Z)) 0))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_48))) (let ((_let_51 ((tptp.model_ub X Y N)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50))) _let_49 :args (_let_47 false _let_48)))) (let ((_let_53 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_54 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_55 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_54))) (let ((_let_56 (>= _let_55 1))) (let ((_let_57 (not _let_56))) (let ((_let_58 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_54))) (let ((_let_59 (>= _let_58 1))) (let ((_let_60 (not _let_59))) (let ((_let_61 (and _let_60 _let_57))) (let ((_let_62 (= _let_53 _let_61))) (let ((_let_63 (forall ((X Int) (Y Int) (Z Int)) (let ((_let_1 (* (- 1) Z))) (= (tptp.ub X Y Z) (and (not (>= (+ X _let_1) 1)) (not (>= (+ Y _let_1) 1)))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((tptp.ub X Y Z)))) (let ((_let_67 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_15))) (let ((_let_68 (>= _let_67 1))) (let ((_let_69 (>= _let_16 0))) (let ((_let_70 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_14))) (let ((_let_71 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) (let ((_let_72 (>= _let_71 1))) (let ((_let_73 (or _let_70 _let_72))) (let ((_let_74 (>= _let_71 0))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_18 _let_75))) (let ((_let_77 (not _let_68))) (let ((_let_78 (_let_70))) (let ((_let_79 (_let_77))) (let ((_let_80 ((< _let_67 1)))) (let ((_let_81 (_let_68))) (let ((_let_82 (false))) (let ((_let_83 (= _let_67 0))) (let ((_let_84 (_let_83))) (let ((_let_85 (ASSUME :args _let_78))) (let ((_let_86 (MACRO_SR_PRED_TRANSFORM _let_85 :args _let_84))) (let ((_let_87 (ASSUME :args _let_81))) (let ((_let_88 (forall ((X Int) (Y Int)) (or (= Y (tptp.max X Y)) (>= (+ X (* (- 1) Y)) 1))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.max X Y)))) :args (_let_88))) _let_89 :args (_let_73 false _let_88)))) (let ((_let_91 (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_70 _let_72 (not _let_73)))))) (let ((_let_92 (_let_72))) (let ((_let_93 (_let_74))) (let ((_let_94 ((< _let_71 0)))) (let ((_let_95 (1.0 (- 1.0)))) (let ((_let_96 (ASSUME :args _let_92))) (let ((_let_97 (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_96 (SCOPE (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_94) _let_96 :args _let_95) :args _let_82) :args _let_94) :args _let_93) :args _let_92)) :args _let_92)) :args ((or _let_74 (not _let_72)))))) (let ((_let_98 (forall ((X Int) (Y Int)) (or (= X (tptp.max X Y)) (not (>= (+ X (* (- 1) Y)) 0)))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.max X Y)))) :args (_let_98))) _let_99 :args (_let_76 false _let_98)))) (let ((_let_101 (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_18 _let_75 (not _let_76)))))) (let ((_let_102 (not _let_18))) (let ((_let_103 (ASSUME :args _let_93))) (let ((_let_104 (= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_15) 0))) (let ((_let_105 (_let_104))) (let ((_let_106 (ASSUME :args (_let_18)))) (let ((_let_107 (MACRO_SR_PRED_TRANSFORM _let_106 :args _let_105))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_103 _let_106 _let_87) :args (_let_18 _let_74 _let_68)) (SCOPE (CONTRA _let_87 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_87 _let_107 _let_103 :args ((- 1.0) 1.0 (- 1.0))) :args _let_82) :args _let_81) :args _let_80) :args _let_79)) :args (_let_74 _let_18 _let_68)) :args ((not (and _let_18 _let_74 _let_68)) SB_LITERAL))) :args ((or _let_75 _let_102 _let_77))) _let_101 _let_100 _let_97 _let_91 _let_90 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_85 (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_87 _let_86 :args ((- 1.0) 1.0)) :args _let_82) :args _let_81) :args _let_80) :args _let_79) :args _let_78)) :args _let_78)) :args (_let_77 false _let_18 false _let_76 false _let_74 false _let_72 false _let_73 true _let_70)))) (let ((_let_109 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_110 (= _let_109 _let_69))) (let ((_let_111 (forall ((X Int) (Y Int) (N Int)) (= (tptp.model_max X Y N) (>= (+ N (* (- 1) (tptp.max X Y))) 0))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (_let_111))) (let ((_let_114 ((tptp.model_max X Y N)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113)) _let_112 :args (_let_110 false _let_111)))) (let ((_let_116 (forall ((Z Int)) (or (not (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Z)) (>= (+ Z (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) 0))))) (let ((_let_117 (and _let_109 _let_116))) (let ((_let_118 (tptp.minsol_model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_119 (= _let_118 _let_117))) (let ((_let_120 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z Int)) (or (not (tptp.model_max X Y Z)) (not (>= (+ N (* (- 1) Z)) 1))))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minsol_model_max X Y N)))) :args (_let_120)))) _let_121 :args (_let_119 false _let_120)))) (let ((_let_123 (tptp.minsol_model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_124 (= _let_123 _let_118))) (let ((_let_125 (not _let_124))) (let ((_let_126 (_let_2))) (let ((_let_127 (ASSUME :args _let_126))) (let ((_let_128 (or))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_127) :args _let_126)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_125)) :args _let_128)) _let_127 :args (_let_125 true _let_1)))) (let ((_let_130 (= _let_123 _let_43))) (let ((_let_131 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_132 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_131))) (let ((_let_133 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_134 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_133) 0))) (let ((_let_135 (not _let_134))) (let ((_let_136 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_137 _let_135))) (let ((_let_139 (= _let_132 _let_32))) (let ((_let_140 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_131))) (let ((_let_141 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_133))) (let ((_let_142 (>= _let_141 1))) (let ((_let_143 (not _let_142))) (let ((_let_144 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_133))) (let ((_let_145 (>= _let_144 1))) (let ((_let_146 (not _let_145))) (let ((_let_147 (and _let_146 _let_143))) (let ((_let_148 (= _let_136 _let_147))) (let ((_let_149 (>= _let_55 0))) (let ((_let_150 (not _let_149))) (let ((_let_151 (>= _let_58 0))) (let ((_let_152 (not _let_151))) (let ((_let_153 (and _let_152 _let_150))) (let ((_let_154 (= _let_140 _let_153))) (let ((_let_155 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38)) 1))) (let ((_let_156 (not _let_155))) (let ((_let_157 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_158 (not _let_157))) (let ((_let_159 (or _let_158 _let_156))) (let ((_let_160 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 _let_15))) (let ((_let_161 (>= _let_160 0))) (let ((_let_162 (= _let_157 _let_161))) (let ((_let_163 (not _let_123))) (let ((_let_164 (_let_124))) (let ((_let_165 (forall ((X Int) (Y Int) (N Int)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z Int)) (or (not (tptp.model_ub X Y Z)) (not (>= (+ N (* (- 1) Z)) 1))))))))) (let ((_let_166 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_167 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_166 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minsol_model_ub X Y N)))) :args (_let_165)))) _let_166 :args (_let_130 false _let_165)))) (let ((_let_168 (not _let_130))) (let ((_let_169 (_let_130))) (let ((_let_170 (not _let_119))) (let ((_let_171 (not _let_117))) (let ((_let_172 (_let_119))) (let ((_let_173 (not _let_43))) (let ((_let_174 (not _let_47))) (let ((_let_175 (_let_47))) (let ((_let_176 (_let_40))) (let ((_let_177 (_let_131 QUANTIFIERS_INST_CEGQI))) (let ((_let_178 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))))) (let ((_let_179 (_let_46))) (let ((_let_180 (not _let_139))) (let ((_let_181 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_23))))) (let ((_let_182 (REFL :args (_let_138)))) (let ((_let_183 (_let_23))) (let ((_let_184 (ASSUME :args _let_183))) (let ((_let_185 (not _let_147))) (let ((_let_186 (not _let_70))) (let ((_let_187 (REFL :args (_let_186)))) (let ((_let_188 (REFL :args (_let_135)))) (let ((_let_189 (not _let_69))) (let ((_let_190 (MACRO_SR_PRED_INTRO :args ((= (not _let_189) _let_69))))) (let ((_let_191 (<= _let_141 0))) (let ((_let_192 (_let_191))) (let ((_let_193 (1.0 1.0 (- 1.0) (- 1.0)))) (let ((_let_194 (ASSUME :args (_let_134)))) (let ((_let_195 ((< _let_16 0)))) (let ((_let_196 (_let_189))) (let ((_let_197 (ASSUME :args _let_196))) (let ((_let_198 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_let_75 _let_77 _let_151)) (SCOPE (CONTRA _let_236 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_236 _let_218 (INT_TIGHT_UB _let_228) _let_224 :args ((- 1.0) 1.0 1.0 (- 1.0))) :args _let_82) :args _let_233) :args _let_195) :args _let_196)) :args (_let_151 _let_75 _let_77 _let_69)) :args ((not (and _let_69 _let_75 _let_77 _let_151)) SB_LITERAL))) (CONG _let_232 _let_226 _let_212 _let_225 :args _let_128)) _let_108 _let_231 (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_238 (SCOPE (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_222) _let_238 :args _let_95) :args _let_82) :args _let_222) :args _let_223) :args _let_237)) :args _let_237)) :args ((or _let_151 _let_60))) :args (_let_60 false _let_69 false _let_18 false _let_76 false _let_74 true _let_68 false _let_69 false _let_151)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_217 _let_235 _let_236) :args (_let_69 _let_77 _let_56)) (SCOPE (CONTRA _let_236 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_236 _let_235 _let_218 :args _let_234) :args _let_82) :args _let_233) :args _let_195) :args _let_196)) :args (_let_77 _let_56 _let_69)) :args ((not (and _let_69 _let_77 _let_56)) SB_LITERAL))) (CONG _let_232 _let_212 (REFL :args (_let_57)) :args _let_128)) _let_231 _let_108 :args (_let_57 false _let_69 true _let_68)) :args (_let_61 true _let_59 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_53 false _let_61 false _let_62)) :args (_let_46 false _let_53)) _let_52 :args (_let_42 true _let_45 false _let_47)) :args (_let_44 true _let_43 false _let_42)) :args (_let_41 true _let_40)) :args (_let_39 true _let_38)) :args (_let_32 true _let_31)) :args (_let_24 true _let_23)))) (let ((_let_255 (REFL :args (_let_22)))) (let ((_let_256 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_255 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_11))) :args _let_128)) :args ((or _let_11 _let_22))) _let_254 :args (_let_11 true _let_22)))) (let ((_let_257 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_10))) (let ((_let_258 (>= _let_257 1))) (let ((_let_259 (not _let_258))) (let ((_let_260 (not _let_13))) (let ((_let_261 (and _let_260 _let_259))) (let ((_let_262 (= _let_20 _let_261))) (let ((_let_263 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_262)) :args ((or _let_21 _let_261 (not _let_262)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_255 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_128)) :args ((or _let_20 _let_22))) _let_254 :args (_let_20 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_262 false _let_63)) :args (_let_261 false _let_20 false _let_262)))) (let ((_let_264 (not _let_261))) (let ((_let_265 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_131))) (let ((_let_266 (= _let_265 _let_17))) (let ((_let_267 (not _let_17))) (let ((_let_268 (_let_116))) (let ((_let_269 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_266)) :args ((or _let_265 _let_267 (not _let_266)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_268) :args _let_177) :args _let_268))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_117 1)) :args ((or _let_116 _let_171))) _let_230 :args (_let_116 false _let_117)) :args ((not _let_265) false _let_116)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_131 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113))) _let_112 :args (_let_266 false _let_111)) :args (_let_267 true _let_265 false _let_266)))) (let ((_let_270 (MACRO_SR_PRED_INTRO :args ((= (not _let_267) _let_17))))) (let ((_let_271 (REFL :args (_let_19)))) (let ((_let_272 ((not _let_83)))) (let ((_let_273 (ASSUME :args (_let_267)))) (let ((_let_274 (MACRO_SR_PRED_TRANSFORM _let_273 :args ((< _let_16 1))))) (let ((_let_275 (ASSUME :args (_let_11)))) (let ((_let_276 (ASSUME :args (_let_259)))) (let ((_let_277 (<= _let_12 0))) (let ((_let_278 (_let_277))) (let ((_let_279 (ASSUME :args (_let_260)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_106 _let_275 _let_273 _let_279) :args (_let_18 _let_11 _let_260 _let_267)) (SCOPE (CONTRA (INT_TIGHT_UB (MACRO_SR_PRED_TRANSFORM _let_279 :args ((< _let_12 1)))) (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_278) _let_274 _let_275 _let_107 :args _let_193) :args _let_82) :args _let_278) :args ((> _let_12 0))) :args ((not _let_277)))) :args (_let_18 _let_11 _let_267 _let_260)) :args ((not (and _let_18 _let_11 _let_260 _let_267)) SB_LITERAL))) (CONG _let_200 _let_271 (MACRO_SR_PRED_INTRO :args ((= (not _let_260) _let_13))) _let_270 :args _let_128)) (MACRO_RESOLUTION_TRUST _let_101 (MACRO_RESOLUTION_TRUST _let_97 (MACRO_RESOLUTION_TRUST _let_91 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_273 _let_275 _let_276 _let_85) :args (_let_70 _let_11 _let_259 _let_267)) (SCOPE (CONTRA _let_86 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB (ASSUME :args _let_84) (MACRO_SR_PRED_TRANSFORM _let_276 :args ((< _let_257 1))) _let_275 (INT_TIGHT_UB _let_274) :args ((- 1.0) 1.0 (- 1.0) 1.0)) :args _let_82) :args _let_84) :args _let_272) :args _let_272)) :args (_let_267 _let_11 _let_259 _let_70)) :args ((not (and _let_70 _let_11 _let_259 _let_267)) SB_LITERAL))) (CONG _let_187 _let_271 (MACRO_SR_PRED_INTRO :args ((= (not _let_259) _let_258))) _let_270 :args _let_128)) _let_256 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_261 1)) :args ((or _let_259 _let_264))) _let_263 :args (_let_259 false _let_261)) _let_269 :args (_let_186 false _let_11 true _let_258 true _let_17)) _let_90 :args (_let_72 true _let_70 false _let_73)) :args (_let_74 false _let_72)) _let_100 :args (_let_18 false _let_74 false _let_76)) _let_269 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_261 0)) :args ((or _let_260 _let_264))) _let_263 :args (_let_260 false _let_261)) _let_256 :args (false false _let_18 true _let_17 true _let_13 false _let_11)) :args ((forall ((X Int) (Y Int)) (= (<= X Y) (<= (tptp.summation X) (tptp.summation Y)))) _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 34.05/34.26 )
% 34.05/34.26 % SZS output end Proof for NUM859_1
% 34.05/34.26 % cvc5---1.0.5 exiting
% 34.05/34.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------