%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP021_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 03:16:27 EDT 2023

% Result   : Theorem 30.17s 30.55s
% Output   : Proof 30.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ITP021_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n008.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   : Sun Aug 27 12:54:32 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 30.17/30.55  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.1UvpdGKkGs/cvc5---1.0.5_6385.p...
% 30.17/30.55  ------- get file name : TPTP file name is ITP021_2
% 30.17/30.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6385.smt2...
% 30.17/30.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 30.17/30.55  --- Run --no-e-matching --full-saturate-quant at 5...
% 30.17/30.55  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 30.17/30.55  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 30.17/30.55  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.17/30.55  % SZS status Theorem for ITP021_2
% 30.17/30.55  % SZS output start Proof for ITP021_2
% 30.17/30.55  (
% 30.17/30.55  (let ((_let_1 (forall ((V0z tptp.tp__ty_2Eextreal_2Eextreal) (V1x tptp.tp__ty_2Eextreal_2Eextreal) (V2y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (tptp.inj__ty_2Eextreal_2Eextreal V0z))) (let ((_let_2 (tptp.inj__ty_2Eextreal_2Eextreal V2y))) (let ((_let_3 (tptp.inj__ty_2Eextreal_2Eextreal V1x))) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max _let_3) _let_2)) _let_1)) (and (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_3) _let_1)) (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_2) _let_1)))))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (tptp.inj__ty_2Eextreal_2Eextreal V1y))) (= (tptp.surj__ty_2Eextreal_2Eextreal (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max _let_1) _let_2)) (tptp.surj__ty_2Eextreal_2Eextreal (tptp.ap (tptp.ap (tptp.ap (tptp.c_2Ebool_2ECOND tptp.ty_2Eextreal_2Eextreal) (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_1) _let_2)) _let_2) _let_1)))))))) (let ((_let_4 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (tptp.inj__ty_2Eextreal_2Eextreal V1y))) (or (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_1) _let_2)) (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_2) _let_1)))))))) (let ((_let_5 (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_2 (tptp.ap tptp.c_2Eextreal_2Eextreal__le (tptp.inj__ty_2Eextreal_2Eextreal V0x)))) (let ((_let_3 (tptp.inj__ty_2Eextreal_2Eextreal V1y))) (=> (and (tptp.p (tptp.ap _let_2 _let_3)) (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_3) _let_1))) (tptp.p (tptp.ap _let_2 _let_1))))))))) (let ((_let_6 (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (tptp.mem V0t1 A_27a) (forall ((V1t2 $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2ECOND A_27a))) (=> (tptp.mem V1t2 A_27a) (and (= (tptp.ap (tptp.ap (tptp.ap _let_1 (tptp.inj__o tptp.fo__c_2Ebool_2ET)) V0t1) V1t2) V0t1) (= (tptp.ap (tptp.ap (tptp.ap _let_1 (tptp.inj__o tptp.fo__c_2Ebool_2EF)) V0t1) V1t2) V1t2))))))))) (let ((_let_7 (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E Q)) (not (tptp.p Q))))))) (let ((_let_8 (tptp.arr tptp.bool tptp.bool))) (let ((_let_9 (tptp.arr tptp.bool _let_8))) (let ((_let_10 (not (tptp.p tptp.c_2Ebool_2EF)))) (let ((_let_11 (tptp.inj__o tptp.fo__c_2Ebool_2EF))) (let ((_let_12 (= _let_11 tptp.c_2Ebool_2EF))) (let ((_let_13 (tptp.mem tptp.c_2Ebool_2EF tptp.bool))) (let ((_let_14 (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (tptp.inj__ty_2Eextreal_2Eextreal (tptp.fo__c_2Eextreal_2Eextreal__max X0 X1)) (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max (tptp.inj__ty_2Eextreal_2Eextreal X0)) (tptp.inj__ty_2Eextreal_2Eextreal X1)))))) (let ((_let_15 (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (tptp.inj__o (tptp.fo__c_2Eextreal_2Eextreal__le X0 X1)) (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le (tptp.inj__ty_2Eextreal_2Eextreal X0)) (tptp.inj__ty_2Eextreal_2Eextreal X1)))))) (let ((_let_16 (forall ((X $$unsorted)) (=> (tptp.mem X tptp.ty_2Eextreal_2Eextreal) (= X (tptp.inj__ty_2Eextreal_2Eextreal (tptp.surj__ty_2Eextreal_2Eextreal X))))))) (let ((_let_17 (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (tptp.mem (tptp.inj__ty_2Eextreal_2Eextreal X) tptp.ty_2Eextreal_2Eextreal)))) (let ((_let_18 (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (= (tptp.surj__ty_2Eextreal_2Eextreal (tptp.inj__ty_2Eextreal_2Eextreal X)) X)))) (let ((_let_19 (tptp.p tptp.c_2Ebool_2ET))) (let ((_let_20 (tptp.inj__o tptp.fo__c_2Ebool_2ET))) (let ((_let_21 (= _let_20 tptp.c_2Ebool_2ET))) (let ((_let_22 (tptp.mem tptp.c_2Ebool_2ET tptp.bool))) (let ((_let_23 (forall ((X tptp.tp__o)) (tptp.mem (tptp.inj__o X) tptp.bool)))) (let ((_let_24 (forall ((X tptp.tp__o)) (= (tptp.surj__o (tptp.inj__o X)) X)))) (let ((_let_25 (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.i A) X) X))))) (let ((_let_26 (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (=> (= (tptp.p Q) (tptp.p R)) (= Q R)))))))) (let ((_let_27 (tptp.p _let_20))) (let ((_let_28 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (tptp.inj__o _let_28))) (let ((_let_30 (tptp.inj__ty_2Eextreal_2Eextreal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (tptp.inj__ty_2Eextreal_2Eextreal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_31))) (let ((_let_33 (tptp.ap _let_32 _let_30))) (let ((_let_34 (= _let_33 _let_29))) (let ((_let_35 (tptp.fo__c_2Eextreal_2Eextreal__max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_36 (tptp.inj__ty_2Eextreal_2Eextreal _let_35))) (let ((_let_37 (tptp.inj__ty_2Eextreal_2Eextreal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_38 (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max _let_37) _let_31))) (let ((_let_39 (= _let_38 _let_36))) (let ((_let_40 (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_37))) (let ((_let_41 (tptp.ap _let_40 _let_31))) (let ((_let_42 (tptp.c_2Ebool_2ECOND tptp.ty_2Eextreal_2Eextreal))) (let ((_let_43 (tptp.ap (tptp.ap (tptp.ap _let_42 _let_41) _let_31) _let_37))) (let ((_let_44 (tptp.surj__ty_2Eextreal_2Eextreal _let_43))) (let ((_let_45 (= (tptp.surj__ty_2Eextreal_2Eextreal _let_38) _let_44))) (let ((_let_46 (= _let_35 (tptp.surj__ty_2Eextreal_2Eextreal _let_36)))) (let ((_let_47 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (tptp.inj__o _let_47))) (let ((_let_49 (= _let_41 _let_48))) (let ((_let_50 (tptp.ap _let_42 _let_20))) (let ((_let_51 (tptp.ap _let_50 _let_31))) (let ((_let_52 (= _let_31 (tptp.ap _let_51 _let_37)))) (let ((_let_53 (tptp.p (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_38) _let_30)))) (let ((_let_54 (= _let_20 _let_29))) (let ((_let_55 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_56 (tptp.inj__o _let_55))) (let ((_let_57 (= _let_20 _let_56))) (let ((_let_58 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_35))) (let ((_let_59 (tptp.inj__o _let_58))) (let ((_let_60 (= _let_56 _let_59))) (let ((_let_61 (= _let_43 (tptp.inj__ty_2Eextreal_2Eextreal _let_44)))) (let ((_let_62 (= _let_48 _let_59))) (let ((_let_63 (SYMM (ASSUME :args (_let_21))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO _let_63 :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_15))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (tptp.inj__ty_2Eextreal_2Eextreal X1))) (let ((_let_68 (tptp.inj__ty_2Eextreal_2Eextreal X0))) (let ((_let_69 ((tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_68) _let_67)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_69)) :args _let_65))) _let_66 :args (_let_34 false _let_15)))) (let ((_let_71 (_let_14))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 ((tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max (tptp.inj__ty_2Eextreal_2Eextreal X0)) (tptp.inj__ty_2Eextreal_2Eextreal X1))))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_73)) :args _let_71))) _let_72 :args (_let_39 false _let_14)))) (let ((_let_75 (_let_3))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_78 (tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max _let_78) _let_77)))) :args _let_75)) _let_76 :args (_let_45 false _let_3)))) (let ((_let_80 (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (= X (tptp.surj__ty_2Eextreal_2Eextreal (tptp.inj__ty_2Eextreal_2Eextreal X)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_35 QUANTIFIERS_INST_CBQI_PROP)) :args _let_82)) _let_81 :args (_let_46 false _let_80)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_69)) :args _let_65))) _let_66 :args (_let_49 false _let_15)))) (let ((_let_85 (tptp.ap _let_42 _let_11))) (let ((_let_86 (tptp.ap _let_85 _let_31))) (let ((_let_87 (= _let_37 (tptp.ap _let_86 _let_37)))) (let ((_let_88 (and _let_52 _let_87))) (let ((_let_89 (tptp.mem _let_37 tptp.ty_2Eextreal_2Eextreal))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.mem _let_31 tptp.ty_2Eextreal_2Eextreal))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_90 _let_88))) (let ((_let_94 (forall ((A_27a tptp.del) (V0t1 $$unsorted) (BOUND_VARIABLE_1620 $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2ECOND A_27a))) (or (not (tptp.mem V0t1 A_27a)) (not (tptp.mem BOUND_VARIABLE_1620 A_27a)) (and (= V0t1 (tptp.ap (tptp.ap (tptp.ap _let_1 (tptp.inj__o tptp.fo__c_2Ebool_2ET)) V0t1) BOUND_VARIABLE_1620)) (= BOUND_VARIABLE_1620 (tptp.ap (tptp.ap (tptp.ap _let_1 (tptp.inj__o tptp.fo__c_2Ebool_2EF)) V0t1) BOUND_VARIABLE_1620)))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_94))) (let ((_let_97 ((not (= (tptp.mem V0t1 A_27a) false)) (not (= (tptp.mem BOUND_VARIABLE_1620 A_27a) false))))) (let ((_let_98 (_let_17))) (let ((_let_99 (ASSUME :args _let_98))) (let ((_let_100 ((tptp.inj__ty_2Eextreal_2Eextreal X)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_100)) :args _let_98)) _let_99 :args (_let_91 false _let_17)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_100)) :args _let_98)) _let_99 :args (_let_89 false _let_17)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_90 _let_92 _let_88 (not _let_93)))) _let_102 _let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.ty_2Eextreal_2Eextreal _let_31 _let_37 QUANTIFIERS_INST_E_MATCHING _let_97)) :args _let_96)) _let_95 :args (_let_93 false _let_94)) :args (_let_88 false _let_89 false _let_91 false _let_93)))) (let ((_let_104 (not _let_88))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_88 0)) :args ((or _let_52 _let_104))) _let_103 :args (_let_52 false _let_88)))) (let ((_let_106 (tptp.p _let_33))) (let ((_let_107 (tptp.ap _let_40 _let_30))) (let ((_let_108 (tptp.p _let_107))) (let ((_let_109 (and _let_108 _let_106))) (let ((_let_110 (= _let_53 _let_109))) (let ((_let_111 (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_36))) (let ((_let_112 (tptp.ap _let_111 _let_30))) (let ((_let_113 (tptp.p _let_112))) (let ((_let_114 (tptp.fo__c_2Eextreal_2Eextreal__le _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_115 (tptp.inj__o _let_114))) (let ((_let_116 (= _let_115 _let_112))) (let ((_let_117 (tptp.p _let_115))) (let ((_let_118 (not _let_27))) (let ((_let_119 (= _let_118 _let_117))) (let ((_let_120 (tptp.mem _let_20 tptp.bool))) (let ((_let_121 (tptp.mem _let_115 tptp.bool))) (let ((_let_122 (= _let_20 _let_115))) (let ((_let_123 (not _let_121))) (let ((_let_124 (not _let_120))) (let ((_let_125 (or _let_124 _let_123 _let_119 _let_122))) (let ((_let_126 (tptp.ap tptp.c_2Eextreal_2Eextreal__le _let_30))) (let ((_let_127 (tptp.ap _let_126 _let_31))) (let ((_let_128 (tptp.p _let_127))) (let ((_let_129 (or _let_106 _let_128))) (let ((_let_130 (tptp.ap _let_111 _let_31))) (let ((_let_131 (tptp.p _let_130))) (let ((_let_132 (not _let_128))) (let ((_let_133 (not _let_113))) (let ((_let_134 (or _let_133 _let_132 _let_131))) (let ((_let_135 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_136 (tptp.inj__o _let_135))) (let ((_let_137 (= _let_127 _let_136))) (let ((_let_138 (tptp.p _let_136))) (let ((_let_139 (tptp.fo__c_2Eextreal_2Eextreal__le _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_140 (tptp.inj__o _let_139))) (let ((_let_141 (= _let_140 _let_130))) (let ((_let_142 (tptp.p _let_140))) (let ((_let_143 (not _let_142))) (let ((_let_144 (= _let_27 _let_143))) (let ((_let_145 (= _let_143 _let_138))) (let ((_let_146 (tptp.mem _let_140 tptp.bool))) (let ((_let_147 (= _let_20 _let_140))) (let ((_let_148 (not _let_146))) (let ((_let_149 (or _let_148 _let_124 _let_144 _let_147))) (let ((_let_150 (tptp.mem _let_136 tptp.bool))) (let ((_let_151 (= _let_136 _let_140))) (let ((_let_152 (not _let_150))) (let ((_let_153 (or _let_148 _let_152 _let_145 _let_151))) (let ((_let_154 (= tptp.fo__c_2Ebool_2ET (tptp.surj__o _let_20)))) (let ((_let_155 (= 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((_let_431 (tptp.mem _let_29 tptp.bool))) (let ((_let_432 (not _let_431))) (let ((_let_433 (or _let_432 _let_124 _let_430 _let_54))) (let ((_let_434 (not _let_430))) (let ((_let_435 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_183) :args ((or _let_53 _let_109 _let_110))) _let_427 _let_182 :args (_let_109 true _let_53 true _let_110)))) (let ((_let_436 (not _let_109))) (let ((_let_437 (and _let_106 _let_34))) (let ((_let_438 (_let_106 _let_34))) (let ((_let_439 (ASSUME :args (_let_106)))) (let ((_let_440 (= _let_27 _let_211))) (let ((_let_441 (or _let_215 _let_124 _let_440 _let_57))) (let ((_let_442 (not _let_440))) (let ((_let_443 (and _let_108 _let_209))) (let ((_let_444 (_let_108 _let_209))) (let ((_let_445 (ASSUME :args (_let_108)))) (let ((_let_446 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_443)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_445 _let_237) (SCOPE (TRUE_ELIM (TRANS _let_239 (TRUE_INTRO _let_445))) :args _let_444)) :args 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false _let_457)) :args (_let_448 false _let_456 false _let_455)))) (let ((_let_468 (not _let_448))) (let ((_let_469 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_202 :args (_let_58 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_203)) :args _let_201)) _let_202 :args (_let_450 false _let_23)))) (let ((_let_470 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_452)) :args ((or _let_215 _let_451 _let_449 _let_60 (not _let_452)))) _let_243 _let_469 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_449)) :args ((or _let_211 _let_468 _let_453))) _let_446 _let_467 :args (_let_453 false _let_210 false _let_448)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_205 :args (_let_56 _let_59 QUANTIFIERS_INST_CBQI_PROP)) :args _let_206)) _let_205 :args (_let_452 false _let_204)) :args (_let_60 false _let_213 false _let_450 true _let_449 false _let_452)))) (let ((_let_471 (tptp.mem _let_43 tptp.ty_2Eextreal_2Eextreal))) (let ((_let_472 (not _let_471))) (let ((_let_473 (or _let_472 _let_61))) (let ((_let_474 (forall ((X $$unsorted)) (or (not (tptp.mem X tptp.ty_2Eextreal_2Eextreal)) (= X (tptp.inj__ty_2Eextreal_2Eextreal (tptp.surj__ty_2Eextreal_2Eextreal X))))))) (let ((_let_475 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_476 (_let_474))) (let ((_let_477 ((tptp.surj__ty_2Eextreal_2Eextreal X)))) (let ((_let_478 (tptp.ap _let_32 _let_31))) (let ((_let_479 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_480 (tptp.inj__o _let_479))) (let ((_let_481 (= _let_480 _let_478))) (let ((_let_482 (tptp.ap (tptp.ap tptp.c_2Eextreal_2Eextreal__max _let_31) _let_31))) (let ((_let_483 (tptp.surj__ty_2Eextreal_2Eextreal _let_482))) (let ((_let_484 (= _let_483 (tptp.surj__ty_2Eextreal_2Eextreal (tptp.ap (tptp.ap (tptp.ap _let_42 _let_478) _let_31) _let_31))))) (let ((_let_485 (tptp.fo__c_2Eextreal_2Eextreal__max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_486 (tptp.inj__ty_2Eextreal_2Eextreal _let_485))) (let ((_let_487 (= _let_482 _let_486))) (let ((_let_488 (= _let_31 (tptp.ap _let_51 _let_31)))) (let ((_let_489 (tptp.mem _let_486 tptp.ty_2Eextreal_2Eextreal))) (let ((_let_490 (= _let_482 (tptp.inj__ty_2Eextreal_2Eextreal _let_483)))) (let ((_let_491 (tptp.fo__c_2Eextreal_2Eextreal__le SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_492 (tptp.inj__o _let_491))) (let ((_let_493 (= _let_20 _let_492))) (let ((_let_494 (= _let_480 _let_492))) (let ((_let_495 (= _let_448 _let_160))) (let ((_let_496 (or _let_162 _let_451 _let_495 _let_62))) (let ((_let_497 (tptp.ap _let_40 _let_37))) (let ((_let_498 (= _let_492 _let_497))) (let ((_let_499 (= _let_37 (tptp.ap (tptp.ap _let_50 _let_37) _let_37)))) (let ((_let_500 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 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(SYMM _let_529))) (let ((_let_531 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_527)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_528 _let_529) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_530) :args _let_188) (TRUE_INTRO _let_528))) :args (_let_523 _let_498))) :args (_let_498 _let_523))) :args (true _let_527)) :args ((or (not _let_523) _let_526 _let_517))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_227 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_525)) :args _let_226))) _let_227 :args (_let_523 false _let_4)) _let_524 :args (_let_517 false _let_523 false _let_498)))) (let ((_let_532 (not _let_517))) (let ((_let_533 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_202 :args (_let_491 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_203)) :args _let_201)) _let_202 :args (_let_519 false _let_23)))) (let ((_let_534 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_521)) :args ((or _let_124 _let_520 _let_518 _let_493 (not _let_521)))) _let_200 _let_533 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_518)) :args ((or _let_118 _let_532 _let_522))) _let_64 _let_531 :args (_let_522 false _let_27 false _let_517)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_205 :args (_let_20 _let_492 QUANTIFIERS_INST_CBQI_PROP)) :args _let_206)) _let_205 :args (_let_521 false _let_204)) :args (_let_493 false _let_120 false _let_519 true _let_518 false _let_521)))) (let ((_let_535 (tptp.p _let_480))) (let ((_let_536 (not _let_535))) (let ((_let_537 (= _let_517 _let_536))) (let ((_let_538 (tptp.mem _let_480 tptp.bool))) (let ((_let_539 (not _let_538))) (let ((_let_540 (or _let_539 _let_520 _let_537 _let_494))) (let ((_let_541 (not _let_537))) (let ((_let_542 (tptp.p _let_478))) (let ((_let_543 (not _let_481))) (let ((_let_544 (and _let_481 _let_542))) (let ((_let_545 (ASSUME :args (_let_542)))) (let ((_let_546 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((_let_565 (ASSUME :args (_let_472)))) (let ((_let_566 (SYMM (FALSE_INTRO _let_565)))) (let ((_let_567 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_205 :args (_let_48 _let_59 QUANTIFIERS_INST_CBQI_PROP)) :args _let_206))) _let_205 :args (_let_496 false _let_204)))) (let ((_let_568 (REORDERING (CNF_OR_POS :args (_let_496)) :args ((or _let_162 _let_451 _let_62 _let_495 (not _let_496)))))) (let ((_let_569 (not _let_495))) (let ((_let_570 (REORDERING (CNF_EQUIV_POS1 :args (_let_495)) :args ((or _let_468 _let_160 _let_569))))) (let ((_let_571 (and _let_499 (= _let_37 (tptp.ap (tptp.ap _let_85 _let_37) _let_37))))) (let ((_let_572 (or _let_90 _let_90 _let_571))) (let ((_let_573 (ASSUME :args (_let_89)))) (let ((_let_574 (ASSUME :args (_let_499)))) (let ((_let_575 (TRANS (CONG (CONG (CONG _let_350 (TRANS _let_530 _let_558) :args _let_189) _let_343 :args _let_189) _let_343 :args _let_189) (SYMM _let_574)))) (let ((_let_576 (CONG (CONG (CONG _let_350 (TRANS _let_366 _let_348) :args _let_189) _let_344 :args _let_189) _let_343 :args _let_189))) (let ((_let_577 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_473)) :args ((or _let_472 _let_61 (not _let_473)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_573 _let_574 _let_557 _let_529 _let_351 _let_347 _let_345 _let_565) :args (_let_89 _let_498 _let_472 _let_49 _let_499 _let_493 _let_87 _let_168)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_566 (CONG (TRANS (TRANS _let_576 _let_352) (SYMM _let_575)) _let_514 :args _let_513) (CONG _let_575 _let_514 :args _let_513) (TRUE_INTRO _let_573))) :args (_let_89 _let_499 _let_493 _let_498 _let_87 _let_168 _let_49 _let_472)) :args ((not (and _let_89 _let_498 _let_472 _let_49 _let_499 _let_493 _let_87 _let_168)) SB_LITERAL))) (CONG (REFL :args (_let_90)) (REFL :args (_let_526)) _let_552 _let_313 (REFL :args ((not _let_499))) _let_551 _let_310 _let_308 :args _let_181)) _let_293 _let_534 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_571 0)) :args ((or _let_499 (not _let_571)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_572))) :args ((or _let_90 _let_571 (not _let_572)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.ty_2Eextreal_2Eextreal _let_37 _let_37 QUANTIFIERS_INST_E_MATCHING _let_97)) :args _let_96)) _let_95 :args (_let_572 false _let_94)) :args (_let_571 false _let_89 false _let_572)) :args (_let_499 false _let_571)) _let_84 _let_524 _let_102 _let_361 _let_360 _let_359 _let_242 _let_363 _let_240 _let_570 _let_467 _let_568 _let_567 _let_469 _let_359 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_562 _let_414 _let_515 _let_546 _let_560 _let_555 _let_565 _let_556 _let_553 _let_412 _let_345 _let_559 _let_557 _let_511 _let_563) :args (_let_155 _let_481 _let_484 _let_472 _let_490 _let_49 _let_487 _let_488 _let_489 _let_493 _let_494 _let_52 _let_62 _let_57 _let_60)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_566 (CONG (TRANS (TRANS _let_564 _let_413) (TRANS (CONG (TRANS _let_415 (CONG (TRANS (SYMM (SYMM _let_559)) (CONG (CONG (CONG _let_350 (TRANS (SYMM _let_558) (SYMM _let_556) _let_547) :args _let_189) _let_344 :args _let_189) _let_344 :args _let_189)) :args _let_339)) :args _let_554) (CONG (SYMM _let_555) :args _let_554) (SYMM _let_553)) _let_516) _let_514 :args _let_513) _let_512)) :args (_let_60 _let_155 _let_487 _let_481 _let_57 _let_484 _let_472 _let_494 _let_490 _let_52 _let_49 _let_488 _let_493 _let_489 _let_62)) :args ((not (and _let_155 _let_481 _let_484 _let_472 _let_490 _let_49 _let_487 _let_488 _let_489 _let_493 _let_494 _let_52 _let_62 _let_57 _let_60)) SB_LITERAL))) (CONG _let_405 (REFL :args (_let_543)) (REFL :args ((not _let_484))) _let_552 (REFL :args ((not _let_490))) _let_313 (REFL :args (_let_509)) (REFL :args ((not _let_488))) (REFL :args (_let_508)) _let_551 (REFL :args ((not _let_494))) _let_403 _let_550 _let_549 _let_548 :args _let_181)) _let_470 _let_447 _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_540)) :args ((or _let_539 _let_520 _let_494 _let_537 (not _let_540)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_202 :args (_let_479 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_203)) :args _let_201)) _let_202 :args (_let_538 false _let_23)) _let_533 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_537)) :args ((or _let_536 _let_532 _let_541))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_544)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_545 _let_546) (SCOPE (TRUE_ELIM (TRANS (CONG _let_547 :args _let_188) (TRUE_INTRO _let_545))) :args (_let_542 _let_481))) :args (_let_481 _let_542))) :args (true _let_544)) :args ((or (not _let_542) _let_543 _let_535))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_227 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_525)) :args _let_226))) _let_227 :args (_let_542 false _let_4)) _let_500 :args (_let_535 false _let_542 false _let_481)) _let_531 :args (_let_541 false _let_535 false _let_517)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_205 :args (_let_480 _let_492 QUANTIFIERS_INST_CBQI_PROP)) :args _let_206))) _let_205 :args (_let_540 false _let_204)) :args (_let_494 false _let_538 false _let_519 true _let_537 false _let_540)) _let_534 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_507)) :args ((or _let_506 _let_490 (not _let_507)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_510)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_511 _let_515) (SCOPE (TRUE_ELIM (TRANS (CONG _let_516 _let_514 :args _let_513) _let_512)) :args (_let_489 _let_487))) :args (_let_487 _let_489))) :args (true _let_510)) :args ((or _let_505 _let_509 _let_508))) _let_501 _let_504 :args (_let_505 false _let_487 false _let_489)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_475 :args (_let_482 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_477)) :args _let_476)) _let_475 :args (_let_507 false _let_474)) :args (_let_490 false _let_505 false _let_507)) _let_504 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_502 0)) :args ((or _let_488 (not _let_502)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_503))) :args ((or _let_92 _let_502 (not _let_503)))) _let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.ty_2Eextreal_2Eextreal _let_31 _let_31 QUANTIFIERS_INST_E_MATCHING _let_97)) :args _let_96)) _let_95 :args (_let_503 false _let_94)) :args (_let_502 false _let_91 false _let_503)) :args (_let_488 false _let_502)) _let_501 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING (_let_78 _let_77))) :args _let_75)) _let_76 :args (_let_484 false _let_3)) _let_500 _let_396 :args (_let_471 false _let_87 false _let_493 false _let_499 false _let_49 false _let_498 false _let_89 false _let_168 false _let_170 false _let_158 false _let_167 true _let_166 true _let_164 true _let_159 false _let_448 false _let_495 false _let_496 false _let_450 false _let_158 true _let_62 false _let_60 false _let_57 false _let_52 false _let_494 false _let_493 false _let_490 false _let_489 false _let_488 false _let_487 false _let_49 false _let_484 false _let_481 false _let_155)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_475 :args (_let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_477)) :args _let_476)) _let_475 :args (_let_473 false _let_474)) :args (_let_61 false _let_471 false _let_473)))) (let ((_let_578 (REFL :args ((not _let_61))))) (let ((_let_579 (ASSUME :args (_let_61)))) (let ((_let_580 (SYMM _let_579))) (let ((_let_581 (CONG (TRANS (SYMM _let_338) (CONG _let_192 :args _let_339) (SYMM _let_342)) :args _let_554))) (let ((_let_582 (CONG (CONG (SYMM _let_463) _let_190 :args _let_189) :args _let_188))) (let ((_let_583 (SYMM _let_462))) (let ((_let_584 (ASSUME :args (_let_54)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_584 _let_345 _let_563 _let_579 _let_337 _let_341 _let_191 _let_560 _let_412 _let_416 _let_562 _let_461 _let_64) :args (_let_27 _let_177 _let_34 _let_39 _let_45 _let_46 _let_61 _let_49 _let_54 _let_52 _let_62 _let_57 _let_60)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_583 _let_582 (CONG (TRANS (CONG (TRANS _let_463 (CONG _let_194 (TRANS _let_191 _let_581 _let_580 _let_564 _let_413) :args _let_189)) _let_190 :args _let_189) _let_417 (SYMM _let_584)) :args _let_188) _let_260)) :args (_let_54 _let_49 _let_62 _let_61 _let_46 _let_45 _let_39 _let_57 _let_52 _let_34 _let_60 _let_177 _let_27)) :args ((not (and _let_27 _let_177 _let_34 _let_39 _let_45 _let_46 _let_61 _let_49 _let_54 _let_52 _let_62 _let_57 _let_60)) SB_LITERAL))) (CONG _let_259 _let_458 _let_404 _let_316 _let_315 _let_314 _let_578 _let_313 (REFL :args ((not _let_54))) _let_403 _let_550 _let_549 _let_548 :args _let_181)) (MACRO_RESOLUTION_TRUST _let_568 _let_359 _let_469 (MACRO_RESOLUTION_TRUST _let_570 _let_467 (MACRO_RESOLUTION_TRUST _let_363 _let_240 (MACRO_RESOLUTION_TRUST _let_361 _let_242 _let_359 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_560 _let_347 _let_351 _let_345 _let_579 _let_337 _let_341 _let_191 _let_237 _let_461 _let_64) :args (_let_27 _let_177 _let_209 _let_39 _let_45 _let_46 _let_61 _let_49 _let_87 _let_168 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_583 _let_582 (CONG (TRANS (CONG (TRANS _let_463 (CONG _let_194 (TRANS _let_191 _let_581 _let_580 _let_576 _let_352) :args _let_189)) _let_190 :args _let_189) (SYMM _let_238) _let_561) :args _let_188) _let_260)) :args (_let_57 _let_168 _let_87 _let_49 _let_61 _let_46 _let_45 _let_39 _let_209 _let_177 _let_27)) :args ((not (and _let_27 _let_177 _let_209 _let_39 _let_45 _let_46 _let_61 _let_49 _let_87 _let_168 _let_57)) SB_LITERAL))) (CONG _let_259 _let_458 _let_232 _let_316 _let_315 _let_314 _let_578 _let_313 _let_310 _let_308 _let_549 :args _let_181)) _let_64 _let_427 _let_231 _let_74 _let_79 _let_83 _let_577 _let_84 _let_293 _let_447 :args (_let_294 false _let_27 true _let_53 false _let_209 false _let_39 false _let_45 false _let_46 false _let_61 false _let_49 false _let_87 false _let_57)) _let_360 :args (_let_166 false _let_167 false _let_158 true _let_168 false _let_170)) :args (_let_159 true _let_164 false _let_166)) :args (_let_569 false _let_448 false _let_159)) _let_567 :args (_let_62 false _let_158 false _let_450 true _let_495 false _let_496)) _let_577 _let_470 _let_447 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_433)) :args ((or _let_124 _let_432 _let_430 _let_54 (not _let_433)))) _let_200 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_202 :args (_let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_203)) :args _let_201)) _let_202 :args (_let_431 false _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_430)) :args ((or _let_118 _let_429 _let_434))) _let_64 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_437)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_439 _let_416) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_417) :args _let_188) (TRUE_INTRO _let_439))) :args _let_438)) :args _let_438)) :args (true _let_437)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_109 1)) :args ((or _let_106 _let_436))) _let_435 :args (_let_106 false _let_109)) _let_70 :args (_let_428 false _let_106 false _let_34)) :args (_let_434 false _let_27 false _let_428)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_205 :args (_let_29 _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args _let_206))) _let_205 :args (_let_433 false _let_204)) :args (_let_54 false _let_120 false _let_431 true _let_430 false _let_433)) _let_427 _let_105 _let_84 _let_83 _let_79 _let_74 _let_70 _let_64 :args (false false _let_62 false _let_61 false _let_60 false _let_57 false _let_54 true _let_53 false _let_52 false _let_49 false _let_46 false _let_45 false _let_39 false _let_34 false _let_27)) :args ((forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.mem (tptp.ap F X) B))))) _let_26 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((G $$unsorted)) (=> (tptp.mem G (tptp.arr A B)) (=> (forall ((X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap F X) (tptp.ap G X)))) (= F G)))))) (forall ((A tptp.del) (Y $$unsorted) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.k A Y) X) Y))) _let_25 _let_24 _let_23 (forall ((X $$unsorted)) (=> (tptp.mem X tptp.bool) (= X (tptp.inj__o (tptp.surj__o X))))) _let_22 _let_21 _let_19 _let_18 _let_17 _let_16 (tptp.mem tptp.c_2Eextreal_2Eextreal__le (tptp.arr tptp.ty_2Eextreal_2Eextreal (tptp.arr tptp.ty_2Eextreal_2Eextreal tptp.bool))) _let_15 (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2ECOND A_27a) (tptp.arr tptp.bool (tptp.arr A_27a (tptp.arr A_27a A_27a))))) (tptp.mem tptp.c_2Eextreal_2Eextreal__max (tptp.arr tptp.ty_2Eextreal_2Eextreal (tptp.arr tptp.ty_2Eextreal_2Eextreal tptp.ty_2Eextreal_2Eextreal))) _let_14 _let_13 _let_12 _let_10 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E _let_9) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E X0 X1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E Q) R)) (=> (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_5C_2F _let_9) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_5C_2F X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F Q) R)) (or (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_2F_5C _let_9) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C Q) R)) (and (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_7E _let_8) (forall ((X0 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E X0)) (tptp.ap tptp.c_2Ebool_2E_7E (tptp.inj__o X0)))) _let_7 (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Emin_2E_3D A_27a) (tptp.arr A_27a (tptp.arr A_27a tptp.bool)))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (forall ((Y $$unsorted)) (=> (tptp.mem Y A) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A) X) Y)) (= X Y)))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 A) Q)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.p (tptp.ap Q X))))))) true (forall ((V0t1 tptp.tp__o) (V1t2 tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1t2)))) (let ((_let_2 (tptp.p (tptp.inj__o V0t1)))) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1)))))) (forall ((V0t tptp.tp__o)) (=> false (tptp.p (tptp.inj__o V0t)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (or _let_1 (not _let_1)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (=> (=> _let_1 false) (not _let_1)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (=> (not _let_1) (=> _let_1 false)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1))))) (and (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (= (not (not _let_1)) _let_1))) (= (not true) false) (= (not false) true)) (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (tptp.mem V0x A_27a) (forall ((V1y $$unsorted)) (=> (tptp.mem V1y A_27a) (= (= V0x V1y) (= V1y V0x)))))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (let ((_let_2 (not _let_1))) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2))))) _let_6 (forall ((V0A tptp.tp__o) (V1B tptp.tp__o) (V2C tptp.tp__o)) (let ((_let_1 (or (tptp.p (tptp.inj__o V0A)) (tptp.p (tptp.inj__o V1B)) (tptp.p (tptp.inj__o V2C))))) (= _let_1 _let_1))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (let ((_let_2 (tptp.p (tptp.inj__o V1B)))) (= (or _let_1 _let_2) (or _let_2 _let_1))))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V0A)))) (let ((_let_4 (not _let_3))) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2)))))))) _let_5 _let_4 _let_3 (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (= (not (not _let_1)) _let_1))) (forall ((V0A tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (=> _let_1 (=> (not _let_1) false)))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (tptp.p (tptp.inj__o V0A)))) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false)))))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (tptp.p (tptp.inj__o V0A)))) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false)))))) (forall ((V0A tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false)))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.p (tptp.inj__o V2r)))) (let ((_let_6 (not _let_5))) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2)))))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V2r)))) (let ((_let_4 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V2r)))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V2r)))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V1q)))) (let ((_let_3 (not _let_2))) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1)))))))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.17/30.55  )
% 30.17/30.55  % SZS output end Proof for ITP021_2
% 30.17/30.55  % cvc5---1.0.5 exiting
% 30.17/30.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------