%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM861+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:48:35 EDT 2023

% Result   : Theorem 0.60s 0.87s
% Output   : Proof 0.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : NUM861+1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 17:25:50 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.60/0.87  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.73O0YVKHq3/cvc5---1.0.5_12095.p...
% 0.60/0.87  ------- get file name : TPTP file name is NUM861+1
% 0.60/0.87  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12095.smt2...
% 0.60/0.87  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.60/0.87  % SZS status Theorem for NUM861+1
% 0.60/0.87  % SZS output start Proof for NUM861+1
% 0.60/0.87  (
% 0.60/0.87  (let ((_let_1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.minsol_model_ub X Y Z) (tptp.minsol_model_max X Y Z))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z $$unsorted)) (=> (tptp.model_ub X Y Z) (tptp.lesseq N Z)))))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z $$unsorted)) (=> (tptp.model_max X Y Z) (tptp.lesseq N Z)))))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.model_ub X Y N) (exists ((Z $$unsorted)) (and (tptp.ub X Y Z) (tptp.lesseq (tptp.sum tptp.c Z) N))))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.model_max X Y N) (tptp.lesseq (tptp.sum tptp.c (tptp.max X Y)) N))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.ub X Y Z) (and (tptp.lesseq X Z) (tptp.lesseq Y Z)))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (or (= (tptp.max X Y) Y) (not (tptp.lesseq X Y)))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (or (= (tptp.max X Y) X) (not (tptp.lesseq Y X)))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.lesseq X Y) (tptp.lesseq (tptp.sum Z X) (tptp.sum Z Y)))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.lesseq X Y) (tptp.lesseq Y X))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.lesseq X Y) (tptp.lesseq Y X)) (= X Y))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.lesseq X Y) (tptp.lesseq Y Z)) (tptp.lesseq X Z))))) (let ((_let_14 (forall ((X $$unsorted)) (tptp.lesseq X X)))) (let ((_let_15 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_16 (tptp.max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (tptp.lesseq _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16))) (let ((_let_19 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_20 (and _let_15 _let_19))) (let ((_let_21 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (_let_7))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 ((tptp.ub X Y Z)))) (let ((_let_26 (tptp.sum tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_27 (tptp.lesseq _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_21))) (let ((_let_30 (or _let_29 _let_28))) (let ((_let_31 (forall ((Z $$unsorted)) (or (not (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (not (tptp.lesseq (tptp.sum tptp.c Z) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (not _let_31))) (let ((_let_34 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_35 (= _let_34 _let_33))) (let ((_let_36 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.model_ub X Y N) (not (forall ((Z $$unsorted)) (or (not (tptp.ub X Y Z)) (not (tptp.lesseq (tptp.sum tptp.c Z) N))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((tptp.model_ub X Y N)))) (let ((_let_40 (tptp.sum tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_41 (tptp.lesseq _let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_42 (not _let_34))) (let ((_let_43 (or _let_42 _let_41))) (let ((_let_44 (forall ((Z $$unsorted)) (or (not (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (tptp.lesseq (tptp.sum tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Z))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_40))) (let ((_let_47 (and _let_46 _let_44))) (let ((_let_48 (not _let_44))) (let ((_let_49 (tptp.minsol_model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_40))) (let ((_let_50 (= _let_49 _let_47))) (let ((_let_51 (not _let_47))) (let ((_let_52 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.minsol_model_ub X Y N) (and (tptp.model_ub X Y N) (forall ((Z $$unsorted)) (or (not (tptp.model_ub X Y Z)) (tptp.lesseq N Z)))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_40))) (let ((_let_56 (tptp.minsol_model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_57 (not _let_49))) (let ((_let_58 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_40))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.lesseq _let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59 _let_55))) (let ((_let_63 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.lesseq X Y)) (not (tptp.lesseq Y X)) (= X Y))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.lesseq X Y) false))))) :args (_let_63)))) _let_64 :args (_let_62 false _let_63)))) (let ((_let_66 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_40))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_58))) (let ((_let_69 (forall ((Z $$unsorted)) (or (not (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Z))))) (let ((_let_70 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_71 (and _let_70 _let_69))) (let ((_let_72 (tptp.minsol_model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_73 (= _let_72 _let_71))) (let ((_let_74 (= _let_56 _let_72))) (let ((_let_75 (forall ((Z $$unsorted)) (or (not (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Z))))) (let ((_let_76 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_77 (and _let_76 _let_75))) (let ((_let_78 (= _let_56 _let_77))) (let ((_let_79 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_80 (tptp.model_ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_79))) (let ((_let_83 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_79))) (let ((_let_86 (tptp.sum tptp.c _let_16))) (let ((_let_87 (tptp.lesseq _let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_88 (= _let_83 _let_87))) (let ((_let_89 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_90 (not _let_87))) (let ((_let_91 (not _let_89))) (let ((_let_92 (or _let_91 _let_90))) (let ((_let_93 (forall ((Z $$unsorted)) (or (not (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (not (tptp.lesseq (tptp.sum tptp.c Z) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))) (let ((_let_94 (not _let_93))) (let ((_let_95 (= _let_80 _let_94))) (let ((_let_96 (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (= (tptp.minsol_model_max X Y N) (and (tptp.model_max X Y N) (forall ((Z $$unsorted)) (or (not (tptp.model_max X Y Z)) (tptp.lesseq N Z)))))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minsol_model_max X Y N)))) :args (_let_96))) _let_97 :args (_let_73 false _let_96)))) (let ((_let_99 (not _let_73))) (let ((_let_100 (_let_73))) (let ((_let_101 (REORDERING (CNF_EQUIV_POS1 :args _let_100) :args ((or (not _let_72) _let_71 _let_99))))) (let ((_let_102 (not _let_74))) (let ((_let_103 (_let_2))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 (or))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_104) :args _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_102)) :args _let_105)) _let_104 :args (_let_102 true _let_1)))) (let ((_let_107 (_let_74))) (let ((_let_108 (REORDERING (CNF_EQUIV_NEG1 :args _let_107) :args ((or _let_56 _let_72 _let_74))))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.minsol_model_ub X Y N)))) :args _let_54)) _let_53 :args (_let_78 false _let_52)))) (let ((_let_110 (not _let_56))) (let ((_let_111 (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_110 _let_77 (not _let_78)))))) (let ((_let_112 (not _let_77))) (let ((_let_113 (_let_75))) (let ((_let_114 (tptp.lesseq _let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_115 (= _let_70 _let_114))) (let ((_let_116 (tptp.lesseq _let_86 _let_40))) (let ((_let_117 (not _let_69))) (let ((_let_118 (_let_69))) (let ((_let_119 (ASSUME :args _let_118))) (let ((_let_120 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (_let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Z) true))))) :args _let_118)))) (let ((_let_121 (_let_6))) (let ((_let_122 (ASSUME :args _let_121))) (let ((_let_123 ((tptp.model_max X Y N)))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_123)) :args _let_121)) _let_122 :args (_let_115 false _let_6)))) (let ((_let_125 (not _let_115))) (let ((_let_126 (not _let_114))) (let ((_let_127 (_let_115))) (let ((_let_128 (= _let_66 _let_116))) (let ((_let_129 (tptp.lesseq _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_130 (= _let_116 _let_129))) (let ((_let_131 (_let_10))) (let ((_let_132 (ASSUME :args _let_131))) (let ((_let_133 ((tptp.sum Z X) (tptp.sum Z Y)))) (let ((_let_134 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_135 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_136 (and _let_135 _let_134))) (let ((_let_137 (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_138 (= _let_137 _let_136))) (let ((_let_139 (not _let_137))) (let ((_let_140 (or _let_139 _let_61))) (let ((_let_141 (forall ((Z $$unsorted)) (or (not (tptp.ub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (not (tptp.lesseq (tptp.sum tptp.c Z) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_142 (not _let_140))) (let ((_let_143 (not _let_141))) (let ((_let_144 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_145 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16))) (let ((_let_146 (and _let_145 _let_144))) (let ((_let_147 (= _let_89 _let_146))) (let ((_let_148 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_149 (not _let_148))) (let ((_let_150 (or _let_18 _let_149))) (let ((_let_151 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_152 (or _let_151 _let_148))) (let ((_let_153 (not _let_151))) (let ((_let_154 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16))) (let ((_let_155 (or _let_154 _let_153))) (let ((_let_156 (tptp.lesseq _let_16 _let_16))) (let ((_let_157 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_23)) _let_24 :args (_let_147 false _let_7)))) (let ((_let_158 (REORDERING (CNF_EQUIV_POS2 :args (_let_147)) :args ((or _let_89 (not _let_146) (not _let_147)))))) (let ((_let_159 (and _let_156 _let_145))) (let ((_let_160 (tptp.ub _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16))) (let ((_let_161 (= _let_160 _let_159))) (let ((_let_162 (not _let_18))) (let ((_let_163 (_let_14))) (let ((_let_164 (ASSUME :args _let_163))) (let ((_let_165 ((not (= (tptp.lesseq X X) true))))) (let ((_let_166 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_164 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_165)) :args _let_163)))) (let ((_let_167 (and _let_18 _let_156))) (let ((_let_168 (ASSUME :args (_let_156)))) (let ((_let_169 (TRUE_INTRO _let_168))) (let ((_let_170 (APPLY_UF tptp.lesseq))) (let ((_let_171 (ASSUME :args (_let_18)))) (let ((_let_172 (SYMM _let_171))) (let ((_let_173 (SYMM _let_172))) (let ((_let_174 (REFL :args (_let_16)))) (let ((_let_175 (not _let_145))) (let ((_let_176 (not _let_144))) (let ((_let_177 (REORDERING (CNF_AND_NEG :args (_let_146)) :args ((or _let_175 _let_146 _let_176))))) (let ((_let_178 (REFL :args (_let_162)))) (let ((_let_179 (and _let_18 _let_176))) (let ((_let_180 (ASSUME :args (_let_176)))) (let ((_let_181 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_182 (_let_11))) (let ((_let_183 (ASSUME :args _let_182))) (let ((_let_184 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_183 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.lesseq X Y) true))))) :args _let_182)) _let_183 :args (_let_152 false _let_11)))) (let ((_let_185 (REORDERING (CNF_OR_POS :args (_let_152)) :args ((or _let_148 _let_151 (not _let_152)))))) (let ((_let_186 (forall ((X $$unsorted) (Y $$unsorted)) (or (= Y (tptp.max X Y)) (not (tptp.lesseq X Y)))))) (let ((_let_187 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(SCOPE (FALSE_ELIM (TRANS (CONG _let_207 _let_181 _let_241 :args (APPLY_UF tptp.minsol_model_ub)) (FALSE_INTRO _let_252))) :args _let_251)) :args _let_251)) :args (true _let_250)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_110) _let_56))) _let_238 (REFL :args (_let_57)) :args _let_105)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_107) _let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_100) :args ((or _let_72 _let_217 _let_99))) _let_247 _let_98 :args (_let_72 false _let_71 false _let_73)) :args (_let_110 true _let_74 false _let_72)) _let_249 :args (_let_57 true _let_56 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.model_ub X Y N)))) :args _let_54)) _let_53 :args (_let_50 false _let_52)) :args (_let_51 true _let_49 false _let_50)) :args (_let_48 false _let_46 true _let_47)) :args (_let_45 true _let_44)))) (let ((_let_259 (_let_33))) (let ((_let_260 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_259)) :args _let_259)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_31))) (REFL :args (_let_32)) :args _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or _let_42 _let_33 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_34))) :args _let_105)) :args ((or _let_34 _let_43))) _let_258 :args (_let_34 true _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_35 false _let_36)) :args (_let_33 false _let_34 false _let_35)) :args (_let_32 true _let_31)))) (let ((_let_261 (REFL :args (_let_30)))) (let ((_let_262 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_29 _let_20 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_261 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_21))) :args _let_105)) :args ((or _let_21 _let_30))) _let_260 :args (_let_21 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_23)) _let_24 :args (_let_22 false _let_7)) :args (_let_20 false _let_21 false _let_22)))) (let ((_let_263 (not _let_20))) (let ((_let_264 (tptp.lesseq _let_86 _let_26))) (let ((_let_265 (= _let_17 _let_264))) (let ((_let_266 (not _let_17))) (let ((_let_267 (tptp.lesseq _let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_268 (not _let_264))) (let ((_let_269 (or _let_268 _let_28 _let_267))) (let ((_let_270 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.lesseq X Y)) (not (tptp.lesseq Y Z)) (tptp.lesseq X Z))))) (let ((_let_271 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_272 (tptp.max _let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_273 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_272))) (let ((_let_274 (= _let_86 _let_272))) (let ((_let_275 (not _let_267))) (let ((_let_276 (not _let_41))) (let ((_let_277 (or _let_273 _let_126))) (let ((_let_278 (tptp.lesseq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_86))) (let ((_let_279 (not _let_278))) (let ((_let_280 (or _let_274 _let_279))) (let ((_let_281 (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_86))) (let ((_let_282 (not _let_281))) (let ((_let_283 (or _let_282 _let_278))) (let ((_let_284 (tptp.lesseq _let_86 _let_86))) (let ((_let_285 (= _let_284 _let_281))) (let ((_let_286 (and _let_55 _let_274 _let_273 _let_276))) (let ((_let_287 (ASSUME :args (_let_276)))) (let ((_let_288 (ASSUME :args (_let_273)))) (let ((_let_289 (ASSUME :args (_let_274)))) (let ((_let_290 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_265)) :args ((or _let_264 _let_266 (not _let_265)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_269)) :args ((or _let_28 _let_268 _let_267 (not _let_269)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_261 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_105)) :args ((or _let_27 _let_30))) _let_260 :args (_let_27 true _let_30)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_286)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_287 _let_240 _let_288 _let_289) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (TRANS (SYMM (SYMM _let_289)) (SYMM _let_288)) _let_242) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) :args _let_170) (FALSE_INTRO _let_287))) :args (_let_276 _let_55 _let_273 _let_274))) :args (_let_55 _let_274 _let_273 _let_276))) :args (true _let_286)) (CONG _let_238 (REFL :args ((not _let_274))) (REFL :args ((not _let_273))) (MACRO_SR_PRED_INTRO :args ((= (not _let_276) _let_41))) (REFL :args (_let_275)) :args _let_105)) _let_249 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_280)) :args ((or _let_279 _let_274 (not _let_280)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_283)) :args ((or _let_278 _let_282 (not _let_283)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_285)) :args ((or (not _let_284) _let_281 (not _let_285)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_164 :args (_let_86 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_165)) :args _let_163)) _let_164 :args (_let_284 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_122 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_86 QUANTIFIERS_INST_E_MATCHING ((tptp.lesseq (tptp.sum tptp.c (tptp.max X Y)) N)))) :args _let_121))) _let_122 :args (_let_285 false _let_6)) :args (_let_281 false _let_284 false _let_285)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (_let_86 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.model_max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z) false))))) :args _let_118)) _let_248 :args (_let_283 false _let_69)) :args (_let_278 false _let_281 false _let_283)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_200 :args (_let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.lesseq Y X) false))))) :args _let_201)) _let_200 :args (_let_280 false _let_199)) :args (_let_274 false _let_278 false _let_280)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_277)) :args ((or _let_126 _let_273 (not _let_277)))) (MACRO_RESOLUTION_TRUST _let_216 (MACRO_RESOLUTION_TRUST _let_218 _let_247 :args (_let_70 false _let_71)) _let_124 :args (_let_114 false _let_70 false _let_115)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_187 :args (_let_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_189)) :args _let_188)) _let_187 :args (_let_277 false _let_186)) :args (_let_273 false _let_114 false _let_277)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 1)) _let_258 :args (_let_276 true _let_43)) :args (_let_275 false _let_55 false _let_274 false _let_273 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_271 :args (_let_86 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.lesseq X Y) false)) (not (= (tptp.lesseq Y Z) false))))) :args (_let_270))) _let_271 :args (_let_269 false _let_270)) :args (_let_268 false _let_27 true _let_267 false _let_269)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_132 :args (_let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 tptp.c QUANTIFIERS_INST_E_MATCHING _let_133)) :args _let_131)) _let_132 :args (_let_265 false _let_10)) :args (_let_266 true _let_264 false _let_265)))) (let ((_let_291 (not _let_19))) (let ((_let_292 (MACRO_SR_PRED_INTRO :args ((= (not _let_266) _let_17))))) (let ((_let_293 (ASSUME :args (_let_19)))) (let ((_let_294 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)))) (let ((_let_295 (ASSUME :args (_let_266)))) (let ((_let_296 (SYMM (FALSE_INTRO _let_295)))) (let ((_let_297 (not _let_15))) (let ((_let_298 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_298 _let_171 _let_295) :args (_let_18 _let_15 _let_266)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_296 (CONG _let_172 _let_294 :args _let_170) (TRUE_INTRO _let_298))) :args (_let_15 _let_18 _let_266)) :args ((not (and _let_18 _let_15 _let_266)) SB_LITERAL))) (CONG _let_178 (REFL :args (_let_297)) _let_292 :args _let_105)) :args ((or _let_162 _let_17 _let_297))) (MACRO_RESOLUTION_TRUST _let_203 (MACRO_RESOLUTION_TRUST _let_185 (MACRO_RESOLUTION_TRUST _let_191 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_293 _let_196 _let_295) :args (_let_154 _let_19 _let_266)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_296 (CONG _let_197 _let_294 :args _let_170) (TRUE_INTRO _let_293))) :args (_let_19 _let_154 _let_266)) :args ((not (and _let_154 _let_19 _let_266)) SB_LITERAL))) (CONG _let_194 (REFL :args (_let_291)) _let_292 :args _let_105)) :args ((or _let_193 _let_17 _let_291))) _let_290 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_19 _let_263))) _let_262 :args (_let_19 false _let_20)) :args (_let_193 true _let_17 false _let_19)) _let_190 :args (_let_153 true _let_154 false _let_155)) _let_184 :args (_let_148 true _let_151 false _let_152)) _let_202 :args (_let_18 false _let_148 false _let_150)) _let_290 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_15 _let_263))) _let_262 :args (_let_15 false _let_20)) :args (false false _let_18 true _let_17 false _let_15)) :args (_let_14 _let_13 _let_12 _let_11 _let_10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.lesseq X Y) (tptp.lesseq (tptp.summation X) (tptp.summation Y)))) _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.60/0.88  )
% 0.60/0.88  % SZS output end Proof for NUM861+1
% 0.60/0.88  % cvc5---1.0.5 exiting
% 0.60/0.88  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------