TSTP Solution File: LCL823-1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL823-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 07:03:53 EDT 2023

% Result   : Unsatisfiable 81.32s 81.67s
% Output   : Proof 81.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23  % Problem    : LCL823-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.24  % Command    : do_cvc5 %s %d
% 0.23/0.45  % Computer : n011.cluster.edu
% 0.23/0.45  % Model    : x86_64 x86_64
% 0.23/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.45  % Memory   : 8042.1875MB
% 0.23/0.45  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.45  % CPULimit   : 300
% 0.23/0.45  % WCLimit    : 300
% 0.23/0.45  % DateTime   : Fri Aug 25 07:23:23 EDT 2023
% 0.23/0.45  % CPUTime    : 
% 0.53/0.70  %----Proving TF0_NAR, FOF, or CNF
% 0.53/0.71  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.iTl0hVJCj9/cvc5---1.0.5_1791.p...
% 0.54/0.91  ------- get file name : TPTP file name is LCL823-1
% 0.54/0.92  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1791.smt2...
% 0.54/0.92  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.69/10.98  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.69/16.02  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.82/21.07  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.82/26.14  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.00/31.21  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 36.02/36.27  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.04/41.35  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.22/46.44  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.24/51.52  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.33/56.59  --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.37/61.67  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 66.45/66.71  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 76.52/76.79  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 81.32/81.67  % SZS status Unsatisfiable for LCL823-1
% 81.32/81.67  % SZS output start Proof for LCL823-1
% 81.32/81.70  (
% 81.32/81.70  (let ((_let_1 (tptp.c_Type_Oshift tptp.tc_Type_Otype))) (let ((_let_2 (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 tptp.v_e____) tptp.v_i____) tptp.v_T____)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Type_Otype tptp.tc_bool))) (let ((_let_4 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_Ex tptp.tc_Type_Otype)) _let_2))) (let ((_let_5 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (let ((_let_6 (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB))) (let ((_let_7 (tptp.tc_fun tptp.tc_Lambda_OdB _let_5))) (let ((_let_8 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Lambda_OdB _let_6) _let_7 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_6 _let_5 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB tptp.tc_Lambda_OdB tptp.tc_bool tptp.tc_nat) tptp.c_InductTermi_OIT))) tptp.c_Lambda_Osubst))) (let ((_let_9 (tptp.tc_fun tptp.tc_nat tptp.tc_Type_Otype))) (let ((_let_10 (tptp.tc_fun tptp.tc_Lambda_OdB tptp.tc_bool))) (let ((_let_11 (tptp.tc_fun tptp.tc_Type_Otype _let_10))) (let ((_let_12 (tptp.tc_fun tptp.tc_Lambda_OdB _let_3))) (let ((_let_13 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_9 tptp.tc_Type_Otype _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_12 _let_11 _let_9) (tptp.c_COMBC tptp.tc_Lambda_OdB tptp.tc_Type_Otype tptp.tc_bool)) tptp.c_Type_Otyping)) tptp.v_T____))) (let ((_let_14 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_15 (tptp.c_COMBB tptp.tc_bool _let_14 tptp.tc_Lambda_OdB))) (let ((_let_16 (tptp.hAPP _let_15 tptp.c_implies))) (let ((_let_17 (tptp.tc_fun tptp.tc_Lambda_OdB _let_14))) (let ((_let_18 (tptp.c_COMBB _let_10 _let_17 _let_9))) (let ((_let_19 (tptp.tc_fun _let_5 _let_5))) (let ((_let_20 (tptp.hAPP (tptp.c_COMBB _let_14 _let_19 tptp.tc_Lambda_OdB) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool tptp.tc_nat)))) (let ((_let_21 (tptp.tc_fun tptp.tc_Lambda_OdB _let_19))) (let ((_let_22 (tptp.hAPP (tptp.c_COMBB _let_17 _let_21 _let_9) _let_20))) (let ((_let_23 (tptp.c_COMBS tptp.tc_Lambda_OdB _let_5 _let_5))) (let ((_let_24 (tptp.tc_fun _let_7 _let_7))) (let ((_let_25 (tptp.hAPP (tptp.c_COMBB _let_21 _let_24 _let_9) _let_23))) (let ((_let_26 (tptp.c_COMBC _let_9 _let_7 _let_7))) (let ((_let_27 (tptp.tc_fun _let_9 _let_7))) (let ((_let_28 (tptp.c_COMBB _let_7 _let_27 tptp.tc_Lambda_OdB))) (let ((_let_29 (tptp.c_COMBB _let_7 _let_7 _let_9))) (let ((_let_30 (tptp.c_COMBB _let_27 _let_27 tptp.tc_Lambda_OdB))) (let ((_let_31 (tptp.tc_fun tptp.tc_nat _let_9))) (let ((_let_32 (tptp.tc_fun tptp.tc_nat _let_12))) (let ((_let_33 (tptp.tc_fun tptp.tc_nat _let_3))) (let ((_let_34 (tptp.tc_fun tptp.tc_Type_Otype _let_5))) (let ((_let_35 (tptp.tc_fun _let_9 _let_34))) (let ((_let_36 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun _let_9 _let_33) _let_35 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_33 _let_34 _let_9) (tptp.c_COMBC tptp.tc_nat tptp.tc_Type_Otype tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC _let_9 tptp.tc_Lambda_OdB _let_33) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_32 (tptp.tc_fun tptp.tc_Lambda_OdB _let_33) _let_9) (tptp.c_COMBC tptp.tc_nat tptp.tc_Lambda_OdB _let_3)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_31 _let_32 _let_9) (tptp.hAPP (tptp.c_COMBB _let_9 _let_12 tptp.tc_nat) tptp.c_Type_Otyping)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_9 tptp.tc_Type_Otype _let_31) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_nat (tptp.tc_fun tptp.tc_Type_Otype _let_9)) (tptp.tc_fun tptp.tc_Type_Otype _let_31) _let_9) (tptp.c_COMBC tptp.tc_nat tptp.tc_Type_Otype _let_9)) _let_1)) tptp.v_T____))))))) (let ((_let_37 (tptp.c_COMBB tptp.tc_bool _let_14 tptp.tc_nat))) (let ((_let_38 (tptp.tc_fun tptp.tc_nat _let_14))) (let ((_let_39 (tptp.c_COMBB _let_5 _let_38 tptp.tc_Type_Otype))) (let ((_let_40 (tptp.tc_fun tptp.tc_Type_Otype _let_38))) (let ((_let_41 (tptp.c_COMBB _let_34 _let_40 _let_9))) (let ((_let_42 (tptp.tc_fun _let_9 _let_40))) (let ((_let_43 (tptp.c_COMBB _let_35 _let_42 tptp.tc_Lambda_OdB))) (let ((_let_44 (tptp.tc_fun tptp.tc_Type_Otype _let_19))) (let ((_let_45 (tptp.tc_fun _let_9 _let_44))) (let ((_let_46 (tptp.hAPP (tptp.c_COMBB _let_42 _let_45 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_40 _let_44 _let_9) (tptp.hAPP (tptp.c_COMBB _let_38 _let_19 tptp.tc_Type_Otype) (tptp.c_COMBS tptp.tc_nat tptp.tc_bool tptp.tc_bool)))))) (let ((_let_47 (tptp.tc_fun tptp.tc_Type_Otype _let_24))) (let ((_let_48 (tptp.tc_fun _let_9 _let_47))) (let ((_let_49 (tptp.hAPP (tptp.c_COMBB _let_45 _let_48 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_44 _let_47 _let_9) (tptp.hAPP (tptp.c_COMBB _let_19 _let_24 tptp.tc_Type_Otype) (tptp.c_COMBB _let_5 _let_5 tptp.tc_Lambda_OdB)))))) (let ((_let_50 (tptp.tc_fun tptp.tc_Type_Otype _let_7))) (let ((_let_51 (tptp.tc_fun _let_7 _let_50))) (let ((_let_52 (tptp.tc_fun _let_9 _let_51))) (let ((_let_53 (tptp.hAPP (tptp.c_COMBB _let_48 _let_52 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_47 _let_51 _let_9) (tptp.c_COMBC tptp.tc_Type_Otype _let_7 _let_7))))) (let ((_let_54 (tptp.tc_fun _let_9 _let_50))) (let ((_let_55 (tptp.hAPP (tptp.c_COMBB _let_52 (tptp.tc_fun _let_27 _let_54) tptp.tc_Lambda_OdB) (tptp.c_COMBS _let_9 _let_7 _let_50)))) (let ((_let_56 (tptp.c_COMBS tptp.tc_Lambda_OdB _let_27 _let_54))) (let ((_let_57 (tptp.tc_fun _let_9 _let_11))) (let ((_let_58 (tptp.hAPP (tptp.c_COMBB _let_54 _let_57 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_50 _let_11 _let_9) (tptp.hAPP (tptp.c_COMBB _let_7 _let_10 tptp.tc_Type_Otype) (tptp.hAPP (tptp.c_COMBB _let_5 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_All tptp.tc_nat))))))) (let ((_let_59 (tptp.tc_fun _let_9 _let_3))) (let ((_let_60 (tptp.hAPP (tptp.c_COMBB _let_57 _let_59 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_11 _let_3 _let_9) (tptp.hAPP (tptp.c_COMBB _let_10 tptp.tc_bool tptp.tc_Type_Otype) (tptp.c_All tptp.tc_Lambda_OdB)))))) (let ((_let_61 (tptp.tc_fun _let_9 tptp.tc_bool))) (let ((_let_62 (tptp.hAPP (tptp.c_COMBB _let_59 _let_61 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool _let_9) (tptp.c_All tptp.tc_Type_Otype))))) (let ((_let_63 (tptp.hAPP (tptp.c_COMBB _let_61 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_All _let_9)))) (let ((_let_64 (tptp.hAPP _let_63 (tptp.hAPP _let_62 (tptp.hAPP _let_60 (tptp.hAPP _let_58 (tptp.hAPP (tptp.hAPP _let_56 (tptp.hAPP _let_55 (tptp.hAPP _let_53 (tptp.hAPP _let_49 (tptp.hAPP _let_46 (tptp.hAPP (tptp.hAPP _let_43 (tptp.hAPP _let_41 (tptp.hAPP _let_39 (tptp.hAPP _let_37 tptp.c_implies)))) _let_36)))))) (tptp.hAPP (tptp.hAPP _let_30 (tptp.hAPP _let_29 (tptp.hAPP _let_23 (tptp.hAPP _let_20 (tptp.hAPP _let_16 tptp.c_InductTermi_OIT))))) (tptp.hAPP (tptp.hAPP _let_28 (tptp.hAPP _let_26 (tptp.hAPP _let_25 (tptp.hAPP _let_22 (tptp.hAPP (tptp.hAPP _let_18 _let_16) _let_13))))) _let_8))))))))) (let ((_let_65 (tptp.hAPP _let_15 tptp.c_and))) (let ((_let_66 (tptp.c_COMBS tptp.tc_Lambda_OdB tptp.tc_bool tptp.tc_bool))) (let ((_let_67 (not (tptp.hBOOL (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP _let_66 (tptp.hAPP _let_65 _let_64)) _let_4) tptp.v_rs____ tptp.tc_Lambda_OdB))))) (let ((_let_68 (tptp.hBOOL (tptp.c_List_Olistsp _let_64 tptp.v_rs____ tptp.tc_Lambda_OdB)))) (let ((_let_69 (tptp.hBOOL (tptp.c_List_Olistsp _let_4 tptp.v_rs____ tptp.tc_Lambda_OdB)))) (let ((_let_70 (tptp.tc_fun tptp.t_b tptp.tc_bool))) (let ((_let_71 (tptp.c_COMBB tptp.t_b _let_70 tptp.t_a))) (let ((_let_72 (tptp.c_COMBB tptp.t_b tptp.tc_bool tptp.t_a))) (let ((_let_73 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_74 (tptp.tc_fun tptp.t_a tptp.t_b))) (let ((_let_75 (tptp.tc_fun _let_74 _let_73))) (let ((_let_76 (tptp.hAPP (tptp.c_COMBB _let_70 _let_75 tptp.t_a) _let_72))) (let ((_let_77 (tptp.c_COMBC tptp.t_a _let_74 _let_73))) (let ((_let_78 (tptp.c_COMBB tptp.tc_bool _let_14 tptp.t_a))) (let ((_let_79 (tptp.hAPP _let_78 tptp.c_implies))) (let ((_let_80 (tptp.tc_fun tptp.t_a _let_14))) (let ((_let_81 (tptp.c_COMBB _let_73 _let_80 tptp.t_a))) (let ((_let_82 (tptp.hAPP _let_81 _let_79))) (let ((_let_83 (tptp.c_COMBS tptp.t_a tptp.tc_bool tptp.tc_bool))) (let ((_let_84 (tptp.hAPP (tptp.c_COMBB _let_80 (tptp.tc_fun _let_73 _let_73) tptp.t_a) _let_83))) (let ((_let_85 (tptp.c_COMBS tptp.t_a _let_73 _let_73))) (let ((_let_86 (tptp.c_All tptp.t_a))) (let ((_let_87 (tptp.hAPP (tptp.c_COMBB _let_73 tptp.tc_bool tptp.t_a) _let_86))) (let ((_let_88 (not (tptp.class_Orderings_Oorder tptp.t_b)))) (let ((_let_89 (not (tptp.class_Orderings_Oorder tptp.t_a)))) (let ((_let_90 (tptp.c_lessequals tptp.t_a))) (let ((_let_91 (tptp.c_COMBI tptp.t_b))) (let ((_let_92 (tptp.c_Fun_Oid tptp.t_a))) (let ((_let_93 (tptp.c_fequal tptp.t_b))) (let ((_let_94 (tptp.hAPP (tptp.c_COMBB tptp.t_b _let_70 tptp.t_b) _let_93))) (let ((_let_95 (tptp.c_COMBS tptp.t_b tptp.t_b tptp.tc_bool))) (let ((_let_96 (tptp.c_All tptp.t_b))) (let ((_let_97 (tptp.tc_fun tptp.t_b tptp.t_a))) (let ((_let_98 (tptp.tc_fun tptp.t_a tptp.t_a))) (let ((_let_99 (tptp.tc_fun tptp.t_b _let_98))) (let ((_let_100 (tptp.tc_fun tptp.t_b tptp.t_b))) (let ((_let_101 (tptp.tc_fun tptp.t_b _let_100))) (let ((_let_102 (tptp.tc_fun tptp.t_b _let_70))) (let ((_let_103 (tptp.c_fequal tptp.t_a))) (let ((_let_104 (tptp.hAPP (tptp.c_COMBC tptp.t_a tptp.t_a tptp.tc_bool) _let_103))) (let ((_let_105 (tptp.c_COMBB _let_73 _let_73 tptp.t_a))) (let ((_let_106 (tptp.hAPP _let_105 (tptp.hAPP _let_83 (tptp.hAPP _let_79 tptp.v_P))))) (let ((_let_107 (tptp.hAPP _let_78 tptp.c_and))) (let ((_let_108 (tptp.hAPP _let_83 (tptp.hAPP _let_107 tptp.v_P)))) (let ((_let_109 (tptp.c_Ex tptp.t_a))) (let ((_let_110 (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_P)) (tptp.hAPP _let_1 V_Q))))))) (let ((_let_111 (tptp.c_Pair tptp.t_a tptp.t_b))) (let ((_let_112 (tptp.tc_prod tptp.t_a tptp.t_b))) (let ((_let_113 (tptp.c_in _let_112))) (let ((_let_114 (tptp.tc_fun _let_112 tptp.tc_bool))) (let ((_let_115 (tptp.tc_fun _let_114 tptp.tc_bool))) (let ((_let_116 (tptp.tc_fun tptp.t_b _let_115))) (let ((_let_117 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_114 _let_70) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_116 (tptp.tc_fun _let_114 _let_70) tptp.t_a) (tptp.c_COMBC tptp.t_b _let_114 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.t_b _let_112) _let_116 tptp.t_a) (tptp.hAPP (tptp.c_COMBB _let_112 _let_115 tptp.t_b) _let_113)) _let_111))) tptp.v_r))) (let ((_let_118 (tptp.c_COMBB tptp.tc_bool _let_14 tptp.t_b))) (let ((_let_119 (tptp.tc_fun tptp.t_b _let_14))) (let ((_let_120 (tptp.c_COMBB _let_70 _let_119 tptp.t_a))) (let ((_let_121 (tptp.tc_fun _let_70 _let_70))) (let ((_let_122 (tptp.hAPP (tptp.c_COMBB _let_119 _let_121 tptp.t_a) (tptp.c_COMBS tptp.t_b tptp.tc_bool tptp.tc_bool)))) (let ((_let_123 (tptp.hAPP _let_122 (tptp.hAPP (tptp.hAPP _let_120 (tptp.hAPP _let_118 tptp.c_implies)) _let_117)))) (let ((_let_124 (tptp.c_Predicate_Oeval tptp.t_a))) (let ((_let_125 (tptp.hAPP _let_124 tptp.v_A))) (let ((_let_126 (tptp.c_COMBB _let_73 _let_73 tptp.t_b))) (let ((_let_127 (tptp.hAPP (tptp.c_COMBB _let_73 tptp.tc_bool tptp.t_b) _let_109))) (let ((_let_128 (tptp.c_in tptp.t_a))) (let ((_let_129 (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_73 tptp.tc_bool) _let_128))) (let ((_let_130 (tptp.hAPP _let_129 tptp.v_A))) (let ((_let_131 (tptp.c_Collect tptp.t_b))) (let ((_let_132 (tptp.hAPP (tptp.c_Set_Oimage tptp.v_f tptp.t_a tptp.t_b) tptp.v_A))) (let ((_let_133 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_l T_a)) (not (tptp.hBOOL (tptp.c_List_Olistsp V_B V_l T_a))) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A V_l T_a))))))) (let ((_let_134 (tptp.c_lessequals tptp.tc_bool))) (let ((_let_135 (= _let_134 tptp.c_implies))) (let ((_let_136 (tptp.c_Pair tptp.t_a tptp.t_a))) (let ((_let_137 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_138 (tptp.tc_fun _let_137 tptp.tc_bool))) (let ((_let_139 (tptp.tc_fun _let_138 tptp.tc_bool))) (let ((_let_140 (tptp.tc_fun tptp.t_a _let_139))) (let ((_let_141 (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.t_a _let_137) _let_140 tptp.t_a) (tptp.hAPP (tptp.c_COMBB _let_137 _let_139 tptp.t_a) (tptp.c_in _let_137))))) (let ((_let_142 (tptp.hAPP (tptp.c_COMBB _let_140 (tptp.tc_fun _let_138 _let_73) tptp.t_a) (tptp.c_COMBC tptp.t_a _let_138 tptp.tc_bool)))) (let ((_let_143 (tptp.c_COMBC tptp.t_a _let_138 _let_73))) (let ((_let_144 (tptp.hAPP (tptp.hAPP _let_143 (tptp.hAPP _let_142 (tptp.hAPP _let_141 _let_136))) tptp.v_r))) (let ((_let_145 (tptp.hAPP _let_84 (tptp.hAPP _let_82 _let_144)))) (let ((_let_146 (tptp.tc_fun tptp.t_a _let_73))) (let ((_let_147 (not (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.t_b)))) (let ((_let_148 (tptp.c_Orderings_Obot__class_Obot _let_73))) (let ((_let_149 (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_Collect T_a) V_P) V_P)))) (let ((_let_150 (tptp.tc_fun tptp.t_a _let_115))) (let ((_let_151 (tptp.hAPP _let_83 (tptp.hAPP _let_79 _let_130)))) (let ((_let_152 (tptp.tc_prod tptp.t_b tptp.t_c))) (let ((_let_153 (tptp.tc_fun _let_152 tptp.tc_bool))) (let ((_let_154 (tptp.tc_fun _let_153 tptp.tc_bool))) (let ((_let_155 (tptp.tc_fun tptp.t_b _let_154))) (let ((_let_156 (tptp.tc_fun tptp.t_c _let_70))) (let ((_let_157 (tptp.c_Collect tptp.tc_Lambda_OdB))) (let ((_let_158 (tptp.hAPP _let_157 _let_4))) (let ((_let_159 (tptp.hAPP _let_15 _let_134))) (let ((_let_160 (tptp.hAPP _let_63 (tptp.hAPP _let_62 (tptp.hAPP _let_60 (tptp.hAPP _let_58 (tptp.hAPP (tptp.hAPP _let_56 (tptp.hAPP _let_55 (tptp.hAPP _let_53 (tptp.hAPP _let_49 (tptp.hAPP _let_46 (tptp.hAPP 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_let_66 (tptp.hAPP _let_65 _let_160)) _let_4))) (let ((_let_170 (tptp.hAPP _let_157 _let_169))) (let ((_let_171 (= _let_169 _let_170))) (let ((_let_172 (= _let_170 _let_162))) (let ((_let_173 (tptp.hBOOL (tptp.c_List_Olistsp _let_169 tptp.v_rs____ tptp.tc_Lambda_OdB)))) (let ((_let_174 (not _let_163))) (let ((_let_175 (forall ((T_a $$unsorted) (V_P $$unsorted)) (= V_P (tptp.hAPP (tptp.c_Collect T_a) V_P))))) (let ((_let_176 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_177 (_let_175))) (let ((_let_178 (_let_110))) (let ((_let_179 (ASSUME :args _let_178))) (let ((_let_180 (SYMM (ASSUME :args (_let_135))))) (let ((_let_181 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO _let_180 :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_182 (not _let_173))) (let ((_let_183 (and _let_182 _let_172 _let_171))) (let ((_let_184 (APPLY_UF tptp.hBOOL))) (let ((_let_185 (APPLY_UF tptp.c_List_Olistsp))) (let ((_let_186 (REFL :args (tptp.tc_Lambda_OdB)))) (let ((_let_187 (REFL :args (tptp.v_rs____)))) (let ((_let_188 (ASSUME :args (_let_171)))) (let ((_let_189 (ASSUME :args (_let_172)))) (let ((_let_190 (_let_133))) (let ((_let_191 (ASSUME :args _let_190))) (let ((_let_192 (= _let_160 _let_161))) (let ((_let_193 (tptp.hBOOL (tptp.c_List_Olistsp _let_160 tptp.v_rs____ tptp.tc_Lambda_OdB)))) (let ((_let_194 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO _let_180 :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_195 (and _let_193 _let_192))) (let ((_let_196 (_let_193 _let_192))) (let ((_let_197 (ASSUME :args (_let_192)))) (let ((_let_198 (= _let_4 _let_158))) (let ((_let_199 (ASSUME :args (_let_69)))) (let ((_let_200 (and _let_69 _let_198))) (let ((_let_201 (_let_69 _let_198))) (let ((_let_202 (ASSUME :args (_let_198)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_163 _let_167 _let_165 (not _let_168)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_200)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_199 _let_202) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (SYMM _let_202) _let_187 _let_186 :args _let_185) :args _let_184) (TRUE_INTRO _let_199))) :args _let_201)) :args _let_201)) :args (true _let_200)) _let_199 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_176 :args (tptp.tc_Lambda_OdB _let_4 QUANTIFIERS_INST_CBQI_PROP)) :args _let_177)) _let_176 :args (_let_198 false _let_175)) :args (_let_166 false _let_69 false _let_198)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_195)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_194 _let_197) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (SYMM _let_197) _let_187 _let_186 :args _let_185) :args _let_184) (TRUE_INTRO _let_194))) :args _let_196)) :args _let_196)) :args (true _let_195)) _let_194 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_176 :args (tptp.tc_Lambda_OdB _let_160 QUANTIFIERS_INST_CBQI_PROP)) :args _let_177)) _let_176 :args (_let_192 false _let_175)) :args (_let_164 false _let_193 false _let_192)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_191 :args (tptp.tc_Lambda_OdB _let_161 _let_158 tptp.v_rs____ QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_190)) _let_191 :args (_let_168 false _let_133)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_183)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_181 _let_188 _let_189) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (TRANS (SYMM _let_189) (SYMM _let_188)) _let_187 _let_186 :args _let_185) :args _let_184) (FALSE_INTRO _let_181))) :args (_let_182 _let_171 _let_172))) :args (_let_182 _let_172 _let_171))) :args (true _let_183)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_182) _let_173))) (REFL :args ((not _let_172))) (REFL :args ((not _let_171))) (REFL :args (_let_174)) :args (or))) _let_181 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_179 :args (tptp.tc_Lambda_OdB _let_160 _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_14 T_a) tptp.c_and) V_P)) V_Q)))) :args _let_178)) _let_179 :args (_let_172 false _let_110)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_176 :args (tptp.tc_Lambda_OdB _let_169 QUANTIFIERS_INST_CBQI_PROP)) :args _let_177)) _let_176 :args (_let_171 false _let_175)) :args (_let_174 true _let_173 false _let_172 false _let_171)) :args (false false _let_166 false _let_164 false _let_168 true _let_163)) :args ((forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.hBOOL (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.c_Pair T_a T_a))) (let ((_let_3 (tptp.c_in (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_xa) V_x)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_xa)) V_r)) (= V_x V_xa) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.hBOOL (tptp.c_Relation_Ototal__on V_A V_r T_a)))))))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) _let_2) _let_2)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_f V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_split V_f T_a T_b tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_split V_f T_a T_b tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_f V_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) V_A))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_upd $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_acc $$unsorted) (V_va $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_upd (tptp.hAPP (tptp.c_COMBK T_a T_a) (tptp.hAPP V_f (tptp.hAPP V_acc V_va)))) V_va) (tptp.hAPP (tptp.hAPP V_upd V_f) V_va)) (not (tptp.hBOOL (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist V_upd V_acc T_a T_b))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_I $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_I) V_A))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_A V_k)) _let_2) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_k) V_I))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_A)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_B)) V_A))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_f T_a T_b))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b)))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f V_xs T_b T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage V_r T_b T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_B))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_bool)) V_I) V_A) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP V_A V_x) T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_I))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.hAPP (tptp.c_Set_Oimage V_f T_c T_b) V_A)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_c) V_B) V_f))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Owellorder T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_k) (tptp.c_Orderings_Oord__class_OLeast V_P T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x)) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset V_xs T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_xs V_ys) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_a T_b) (tptp.c_List_Omap V_f V_ys T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_xs V_ys))) (= (tptp.c_Relation_Orel__comp tptp.v_r tptp.v_s tptp.t_a tptp.t_b tptp.t_c) (tptp.hAPP (tptp.c_Collect (tptp.tc_prod tptp.t_a tptp.t_c)) (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_156 (tptp.tc_fun tptp.t_c tptp.tc_bool) tptp.t_a) (tptp.hAPP (tptp.c_COMBB _let_70 tptp.tc_bool tptp.t_c) (tptp.c_Ex tptp.t_b))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_156 _let_156) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_121 (tptp.tc_fun _let_156 _let_156) tptp.t_a) (tptp.c_COMBB _let_70 _let_70 tptp.t_c)) (tptp.hAPP _let_122 (tptp.hAPP (tptp.hAPP _let_120 (tptp.hAPP _let_118 tptp.c_and)) _let_117)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_c _let_153 _let_70) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_155 (tptp.tc_fun _let_153 _let_70) tptp.t_c) (tptp.c_COMBC tptp.t_b _let_153 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.t_b _let_152) _let_155 tptp.t_c) (tptp.hAPP (tptp.c_COMBB _let_152 _let_154 tptp.t_b) (tptp.c_in _let_152))) (tptp.hAPP (tptp.c_COMBC tptp.t_b tptp.t_c _let_152) (tptp.c_Pair tptp.t_b tptp.t_c))))) tptp.v_s))) tptp.t_a tptp.t_c tptp.tc_bool))) (= (tptp.c_Relation_Ototal__on tptp.v_A tptp.v_r tptp.t_a) (tptp.hAPP _let_86 (tptp.hAPP _let_151 (tptp.hAPP _let_87 (tptp.hAPP (tptp.hAPP _let_105 _let_151) (tptp.hAPP (tptp.hAPP _let_85 (tptp.hAPP _let_84 (tptp.hAPP _let_82 (tptp.hAPP (tptp.hAPP _let_105 (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool tptp.t_a) tptp.c_Not)) _let_103)))) (tptp.hAPP (tptp.hAPP _let_85 (tptp.hAPP _let_84 (tptp.hAPP (tptp.hAPP _let_81 (tptp.hAPP _let_78 tptp.c_or)) _let_144))) (tptp.hAPP (tptp.hAPP _let_143 (tptp.hAPP _let_142 (tptp.hAPP _let_141 (tptp.hAPP (tptp.c_COMBC tptp.t_a tptp.t_a _let_137) _let_136)))) tptp.v_r)))))))) (= (tptp.hAPP (tptp.c_Relation_OImage tptp.v_r tptp.t_a tptp.t_b) tptp.v_s) (tptp.hAPP _let_131 (tptp.hAPP _let_127 (tptp.hAPP (tptp.hAPP _let_126 (tptp.hAPP _let_83 (tptp.hAPP _let_107 (tptp.hAPP _let_129 tptp.v_s)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_b _let_114 _let_73) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_150 (tptp.tc_fun _let_114 _let_73) tptp.t_b) (tptp.c_COMBC tptp.t_a _let_114 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.t_a _let_112) _let_150 tptp.t_b) (tptp.hAPP (tptp.c_COMBB _let_112 _let_115 tptp.t_a) _let_113)) (tptp.hAPP (tptp.c_COMBC tptp.t_a tptp.t_b _let_112) _let_111)))) tptp.v_r))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) _let_1) _let_1)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k)) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_u) V_A)))))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_a T_b))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)) (= V_A V_B)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))) (= V_x V_y))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.c_List_Onth (tptp.c_List_Oappend V_xs V_ys T_a) T_a) V_n) (tptp.hAPP (tptp.c_List_Onth V_xs T_a) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) V_B) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP V_B V_x) T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Orel__comp V_R V_S T_a T_d T_c) V_T T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_Orel__comp V_S V_T T_d T_c T_b) T_a T_d T_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) (tptp.c_Finite__Set_Olattice__class_OInf__fin V_A T_a)) V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_COMBI T_a) V_A T_a T_a)) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Collect (tptp.tc_prod T_a T_b)) (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_2 T_a) tptp.c_and) V_P))) V_Q) T_a T_b tptp.tc_bool)) (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Collect T_a) V_P) (tptp.hAPP (tptp.c_COMBK _let_1 T_a) (tptp.hAPP (tptp.c_Collect T_b) V_Q)) T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_a T_b T_c) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_b T_c T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_b T_c) V_a) V_b)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_OSup__class_OSup T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_2) V_C))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) _let_1) V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((V_inf $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.c_Finite__Set_Olattice_OInf__fin V_inf V_A T_a) (tptp.hAPP V_Inf V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) _let_149 (forall ((T_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool))))) (let ((_let_3 (tptp.c_in tptp.t_a))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_1 tptp.tc_bool) _let_3)) V_r)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP _let_2 V_r))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) V_C))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) _let_1) V_B))))))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Ofoldl (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a) V_xs T_a T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_OInf__class_OInf T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) V_B)))))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp V_A V_xs T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.c_List_Osko__List__Xin__listsp__conv__set__1__1 V_A V_xs T_a)) (tptp.c_List_Oset V_xs T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_x))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_a))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_u) V_A)))))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_b T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_2 tptp.tc_bool) T_a) (tptp.c_in _let_1)) (tptp.hAPP (tptp.c_Pair T_b T_a) V_a))) V_r)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (or (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_bool) T_b) V_C))) (or (not (= (tptp.c_Product__Type_OSigma V_A _let_1 T_b T_a) (tptp.c_Product__Type_OSigma V_B _let_1 T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_C))) (= V_A V_B)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_COMBI T_a) T_a T_a) V_Y) V_Y)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_xs T_a) V_xs)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_List_Oset V_xs T_a)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Omono V_f T_a T_b)) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Ostrict__mono V_f T_a T_b))))) (forall ((T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_c T_b) V_f) V_g) T_b T_c) _let_1) T_c) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage V_g T_b T_a) _let_1) T_a))))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_M V_i)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a T_b) V_A) V_M))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) V_A))))) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_s) V_k) _let_1) (= V_i V_k) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_k) V_i))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_b)))) (forall ((V_xa $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_xa) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP (tptp.c_List_Onth V_xs T_a) V_xa)) (tptp.c_List_Oset V_xs T_a))))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP (tptp.c_List_Onth V_xs T_a) V_n)) (tptp.c_List_Oset V_xs T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.c_COMBK T_b T_a) V_c) T_a T_b) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_Sup $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Ofoldl V_sup V_bot V_xs T_a T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Ofoldl V_inf V_top V_xs T_a T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) (tptp.tc_fun T_b T_c) T_a) (tptp.hAPP (tptp.c_COMBB _let_1 T_c T_b) V_f)) (tptp.c_Pair T_a T_b)) T_a T_b T_c) V_f))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not) V_P)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_P) T_a))))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not) V_P)) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_P) T_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_a T_b) (tptp.c_List_Omap V_f V_ys T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Oset V_ys T_a)) T_a T_b)) (= V_xs V_ys))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_xs V_ys) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_List_Oset V_xs T_b)) (tptp.c_List_Oset V_ys T_b)) T_b T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Collect T_a) V_P))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A) (tptp.hAPP (tptp.c_COMBK _let_1 T_b) V_c)) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_xs $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_a) (tptp.c_List_Oset V_xs T_b)) V_f) (tptp.c_List_Ofoldl (tptp.hAPP (tptp.c_COMBC T_b T_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a)) V_f)) (tptp.c_Orderings_Obot__class_Obot T_a) V_xs T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_M $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b) V_A) (tptp.hAPP (tptp.c_COMBK T_b T_a) V_M)) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Hilbert__Choice_OEps V_P T_a))) (or (tptp.hBOOL (tptp.hAPP V_P _let_1)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (= _let_1 V_x)))) (forall ((V_uminus $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_uminus V_x) (tptp.hAPP V_uminus V_y))) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)) (= V_x V_y))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage V_R T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c T_a T_b) V_f) V_g) T_b T_a) _let_1) (tptp.hAPP (tptp.c_Set_Oimage V_f T_c T_a) (tptp.hAPP (tptp.c_Set_Oimage V_g T_b T_c) _let_1))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) T_a T_c)) (not (tptp.hBOOL (tptp.c_Relation_Osingle__valued V_s T_b T_c))) (not (tptp.hBOOL (tptp.c_Relation_Osingle__valued V_r T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2))) (let ((_let_4 (tptp.tc_fun T_c _let_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_4 _let_2) T_b) _let_3) V_B)) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) V_B)) V_C))))))) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_B $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c _let_1 T_b) V_B) V_f)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_c) V_A)) V_B)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) V_B))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_b))) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= (tptp.c_Nat_Osize__class_Osize V_xs _let_1) (tptp.c_Nat_Osize__class_Osize V_ys _let_1))))) (= (tptp.hAPP _let_92 tptp.v_x) tptp.v_x) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b) V_A) V_M)) (tptp.hAPP V_M V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_in tptp.t_a))) (let ((_let_4 (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_1 tptp.tc_bool) _let_3))) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R)) (tptp.hAPP _let_4 V_S)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 V_R) V_S)))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_A)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_B)) V_A))) (forall ((V_nat $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_a T_b))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oorder_Ostrict__mono V_less T_a T_b) V_f))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A) V_B))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Owellorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Oord__class_OLeast V_P T_a)) V_k)) (not (tptp.hBOOL (tptp.hAPP V_P V_k))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oorder_Omono V_less__eq T_a T_b) V_f))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.c_COMBK T_a T_b) V_c) T_b T_a) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_b) (tptp.c_Fun_Oid T_b)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_B))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_List_Oset V_xs T_a)))) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A V_xs T_a))))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Predicate_Oeval T_a))) (or (not (= (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y))) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_B $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c _let_1 T_b) V_B) V_f)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_c) V_A)) V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A))))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Oappend V_xs V_ys T_b) T_b T_a) (tptp.c_List_Oappend (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a) T_a))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Collect T_a) V_P) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (= V_m V_n)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_e) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (or (= V_T V_U) (not (tptp.hBOOL (tptp.hAPP _let_1 V_U))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_T)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Oset V_ys T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Ocut T_a T_b))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_f) V_r) V_x) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_g) V_r) V_x))) (= (tptp.hAPP V_f V_y) (tptp.hAPP V_g V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_a) V_y) V_x)) V_r)))))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_Fun_Oid T_a) V_A T_a T_a)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A)) V_B)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBK T_a T_b) V_P) V_Q) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Predicate_Opred_OPred (tptp.hAPP (tptp.c_Predicate_Oeval T_a) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_x)) V_s) V_x) V_s))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_f $$unsorted)) (= (tptp.hAPP (tptp.c_Predicate_Oeval T_a) (tptp.c_Predicate_Opred_OPred V_f T_a)) V_f)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2))) (let ((_let_4 (tptp.tc_fun T_c _let_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_4 _let_2) T_b) _let_3) V_B)) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_xa))) (let ((_let_4 (tptp.hAPP _let_2 V_x))) (= (tptp.hAPP _let_3 (tptp.hAPP _let_4 _let_1)) (tptp.hAPP _let_4 (tptp.hAPP _let_3 _let_1)))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_fun $$unsorted) (T_a $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Predicate_Opred_OPred V_fun T_a) (tptp.c_Predicate_Opred_OPred V_fun_H T_a))) (= V_fun V_fun_H))) (forall ((T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_b) _let_1) V_f)) V_A)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) (tptp.c_Finite__Set_Olattice__class_OSup__fin V_A T_a)) V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))))))) (forall ((T_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool))))) (let ((_let_3 (tptp.c_in tptp.t_a))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_1 tptp.tc_bool) _let_3)) V_r)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP _let_2 V_r))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A)) V_B)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (= V_a V_b))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_sup $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_inf V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_sup V_y) V_z)) (tptp.hAPP (tptp.hAPP V_sup (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a))))) (forall ((V_inf $$unsorted) (V_sup $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP (tptp.hAPP V_sup V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP V_sup (tptp.hAPP (tptp.hAPP V_inf V_y) V_x)) (tptp.hAPP (tptp.hAPP V_inf V_z) V_x))) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a)))) (forall ((V_sup $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_sup V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_inf V_y) V_z)) (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a))))) (forall ((V_sup $$unsorted) (V_inf $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_sup (tptp.hAPP (tptp.hAPP V_inf V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP (tptp.hAPP V_sup V_y) V_x)) (tptp.hAPP (tptp.hAPP V_sup V_z) V_x))) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a)))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) (tptp.c_in T_a)))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_Orderings_Oorder (tptp.hAPP _let_1 (tptp.c_lessequals T_a)) (tptp.hAPP _let_1 (tptp.c_HOL_Oord__class_Oless T_a)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Hilbert__Choice_OEps V_P T_a))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Hilbert__Choice_OEps V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1)) V_A)) V_B)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.c_COMBK T_a T_b) V_c) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.hAPP (tptp.c_Collect T_a) V_P))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.hAPP (tptp.c_Collect T_a) V_P)))))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) (tptp.hAPP (tptp.c_COMBK _let_1 T_b) V_c)) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_M $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a T_b) V_A) (tptp.hAPP (tptp.c_COMBK T_b T_a) V_M)) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) (tptp.hAPP V_f V_x)) _let_1) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (not (= (tptp.hAPP _let_2 V_A) (tptp.hAPP _let_2 V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_A V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Olattice__class_OInf__fin V_A T_a)) (tptp.c_Finite__Set_Olattice__class_OSup__fin V_A T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_b) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_B _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBK _let_1 T_b) V_c)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Relation_OImage V_r T_b T_a))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP _let_2 V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_3) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.c_Set_Oinsert T_b)) (tptp.c_Orderings_Obot__class_Obot _let_1))))))))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_List_Oset V_xs T_a)) (tptp.c_List_Ofoldl (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a) V_xs T_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) V_B)))))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1)) (= V_s _let_1)))) (forall ((V_h $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage V_h T_a T_b) V_F) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Type_Otyping V_env))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) V_U)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_T))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) (tptp.c_Type_Otype_OFun V_T V_U))))))) (forall ((V_sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.c_Finite__Set_Olattice_OSup__fin V_sup V_A T_a) (tptp.hAPP V_Sup V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_I))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_A))))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.c_List_Onth (tptp.c_List_Omap V_f V_xs T_a T_b) T_b) V_n) (tptp.hAPP V_f (tptp.hAPP (tptp.c_List_Onth V_xs T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a))))))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_in tptp.t_a))) (let ((_let_4 (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_1 tptp.tc_bool) _let_3))) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R)) (tptp.hAPP _let_4 V_S)) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_3 tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 V_R) V_S)))))))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i) V_t))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_a V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_a V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_b V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_b V_d))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (tptp.c_Lattices_Odistrib__lattice (tptp.hAPP _let_1 (tptp.c_lessequals T_a)) (tptp.hAPP _let_1 (tptp.c_HOL_Oord__class_Oless T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_b T_a) V_a) V_b)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_b T_a) V_a) V_b)) V_r))))) (= (tptp.hAPP _let_148 tptp.v_x) (tptp.hAPP (tptp.hAPP _let_128 tptp.v_x) _let_148)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_B V_a)) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_b T_a) V_x) V_b)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_upd $$unsorted) (T_a $$unsorted) (V_v $$unsorted) (V_acc $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_upd (tptp.c_Fun_Oid T_a)) V_v) V_v) (not (tptp.hBOOL (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist V_upd V_acc T_a T_b))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_List_Oset V_xs T_a)))))) (forall ((V_f $$unsorted) (V_acc $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_upd $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.hAPP V_acc V_x))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_f_H _let_1))) (not (tptp.hBOOL (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist V_upd V_acc T_a T_aa))) (= (tptp.hAPP (tptp.hAPP V_upd V_f) V_x) (tptp.hAPP (tptp.hAPP V_upd V_f_H) V_x))))) (forall ((V_f $$unsorted) (V_acc $$unsorted) (V_x $$unsorted) (V_upd $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP V_acc V_x))) (or (not (= (tptp.hAPP V_f _let_1) _let_1)) (not (tptp.hBOOL (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist V_upd V_acc T_a T_b))) (= (tptp.hAPP (tptp.hAPP V_upd V_f) V_x) V_x)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a)) V_B)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.hAPP V_f V_a)) (tptp.hAPP _let_1 V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_B)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Ofilter V_P V_xs T_a) _let_1)) (tptp.c_Nat_Osize__class_Osize V_xs _let_1))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_List_Oset V_xs T_a))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) V_B) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBK _let_1 T_b) V_c)) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Collect T_a) V_P))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_u) V_i) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_j) V_i)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) V_B) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A)) V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (tptp.class_Lattices_Oupper__semilattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_b) (tptp.hAPP V_f V_A)) (tptp.hAPP V_f V_B))) (tptp.hAPP V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B)))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Omono V_f T_a T_b))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_3) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_B))))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_List_Oset V_xs T_a) T_a)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_xs $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_a) (tptp.c_List_Oset V_xs T_b)) V_f) (tptp.c_List_Ofoldl (tptp.hAPP (tptp.c_COMBC T_b T_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a)) V_f)) (tptp.c_Orderings_Otop__class_Otop T_a) V_xs T_a T_b)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OFun V_type1 V_type2) (tptp.c_Type_Otype_OFun V_type1_H V_type2_H))) (= V_type2 V_type2_H))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OFun V_type1 V_type2) (tptp.c_Type_Otype_OFun V_type1_H V_type2_H))) (= V_type1 V_type1_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Pair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.c_in (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_b)) V_r))) (not (tptp.hBOOL (tptp.c_Relation_Otrans V_r T_a)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Pair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.c_in (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_y)) V_r))) (not (tptp.hBOOL (tptp.c_Relation_Otrans V_r T_a)))))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) (tptp.hAPP _let_2 V_A))) (tptp.hAPP _let_2 V_B))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) (tptp.hAPP (tptp.c_COMBK _let_1 T_b) _let_2)) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((V_sup $$unsorted) (V_x $$unsorted) (V_uminus $$unsorted) (V_top $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_sup V_x) (tptp.hAPP V_uminus V_x)) V_top) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_uminus $$unsorted) (V_bot $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf V_x) (tptp.hAPP V_uminus V_x)) V_bot) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_sup $$unsorted) (V_uminus $$unsorted) (V_x $$unsorted) (V_top $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_sup (tptp.hAPP V_uminus V_x)) V_x) V_top) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_inf $$unsorted) (V_uminus $$unsorted) (V_x $$unsorted) (V_bot $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP V_uminus V_x)) V_x) V_bot) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_uminus $$unsorted) (V_x $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_uminus (tptp.hAPP V_uminus V_x)) V_x) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_minus $$unsorted) (V_uminus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup (tptp.hAPP (tptp.hAPP V_inf V_x) V_y) (tptp.hAPP (tptp.hAPP V_sup V_x) V_y) T_a)) (= (tptp.hAPP V_uminus V_x) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) V_B) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A)) V_B))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_Set_Oinsert T_a)) V_f)) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) V_B)) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a))) V_B))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A) V_B) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s) (tptp.hAPP _let_1 V_t)) (not (tptp.c_Lambda_Obeta V_s V_t))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage (tptp.c_Fun_Oid T_a) T_a T_a) V_Y) V_Y)) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (let ((_let_4 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_3 _let_1) T_c) _let_2) V_B)) V_C)))))))) (forall ((T_a $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_c) V_a) V_c)) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_b T_c) V_b) V_c)) V_s))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) V_r))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) V_B) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A)) V_B))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Omono V_f T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (= (tptp.hAPP (tptp.c_COMBI tptp.t_a) tptp.v_P) tptp.v_P) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (= V_a V_b) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.c_List_Oset V_xs T_b)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Owellorder T_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Oord__class_OLeast V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Owellorder T_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Oord__class_OLeast V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_k))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Collect T_a) V_P)))))))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Olift _let_1 V_k) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_k)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift V_r V_i) (tptp.c_Lambda_Olift V_s V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_upd $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_acc $$unsorted)) (or (= (tptp.hAPP V_upd (tptp.c_Fun_Oid T_a)) (tptp.c_Fun_Oid T_b)) (not (tptp.hBOOL (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist V_upd V_acc T_a T_b))))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_A) V_B) V_x) V_y))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_A) V_B) V_x) V_y))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) (tptp.c_in T_a)) (tptp.c_List_Oset V_xs T_a)))) V_P)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1)) V_A)) V_B)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_in _let_1))) (tptp.c_Pair T_a T_b)))))) (or (not (= (tptp.hAPP _let_6 V_R) (tptp.hAPP _let_6 V_S))) (= V_R V_S))))))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (= (tptp.c_Transitive__Closure_Ortranclp _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Finite__Set_Olattice__class_OInf__fin V_A T_a) (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s) (tptp.c_Lambda_OdB_OAbs V_t)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Oid T_a) V_x) V_x)) (forall ((T_aa $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_aa T_a) V_A))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_b) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((T_b $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Predicate_Oeval T_b))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Predicate_Obind V_P V_Q T_a T_b)) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_Q V_x)) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oeval T_a) V_P) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a) T_a))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) (tptp.c_in T_a)) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP _let_2 V_A))) (tptp.hAPP _let_2 V_B))))))) (forall ((V_n $$unsorted) (V_rs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_rs tptp.tc_Lambda_OdB))))) (= (tptp.c_Predicate_OPowp tptp.v_A tptp.v_B tptp.t_a) (tptp.hAPP _let_86 (tptp.hAPP (tptp.hAPP _let_83 (tptp.hAPP _let_79 (tptp.hAPP _let_129 tptp.v_B))) tptp.v_A))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) (tptp.hAPP (tptp.c_Set_Oimage V_g T_c T_b) V_A)) (tptp.hAPP (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_f) V_g) T_c T_a) V_A))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_f)) V_r)) V_A)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_4 (tptp.tc_fun T_c tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c T_a) (tptp.tc_fun _let_4 T_a) T_b) _let_3) V_f)) V_B)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_2 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) (tptp.tc_fun _let_2 T_a) T_c) _let_1) (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_f))) V_A)) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Hilbert__Choice_OEps (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a) T_a) V_a)) (forall ((T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (tptp.c_Lattices_Odistrib__lattice (tptp.hAPP _let_1 V_less__eq) (tptp.hAPP _let_1 V_less) V_sup V_inf T_a) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a))))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.hAPP _let_1 V_less__eq) (tptp.hAPP _let_1 V_less) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (tptp.c_Orderings_Oorder (tptp.hAPP _let_1 V_less__eq) (tptp.hAPP _let_1 V_less) T_a) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_Q) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_P) T_a))))) (forall ((T_a $$unsorted) (V_Q $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_Q) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q)) T_a))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_P) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q)) T_a))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_P)) (tptp.hAPP _let_1 V_Q))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_a))) V_P)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_sup $$unsorted) (V_x $$unsorted) (V_inf $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP V_sup V_x))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olattice_OInf__fin V_inf V_A T_a)) (tptp.c_Finite__Set_Olattice_OInf__fin V_inf (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a))))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olattice__class_OSup__fin V_A T_a)) (tptp.c_Finite__Set_Olattice__class_OSup__fin (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olattice__class_OInf__fin V_A T_a)) (tptp.c_Finite__Set_Olattice__class_OInf__fin (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))))) (forall ((V_inf $$unsorted) (V_x $$unsorted) (V_sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP V_inf V_x))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olattice_OSup__fin V_sup V_A T_a)) (tptp.c_Finite__Set_Olattice_OSup__fin V_sup (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a))))))))) (forall ((V_uminus $$unsorted) (V_top $$unsorted) (V_bot $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_uminus V_top) V_bot) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_uminus $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_uminus V_bot) V_top) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_minus $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_inf $$unsorted) (V_uminus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_minus V_x) V_y) (tptp.hAPP (tptp.hAPP V_inf V_x) (tptp.hAPP V_uminus V_y))) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_uminus $$unsorted) (V_inf $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_sup $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_uminus (tptp.hAPP (tptp.hAPP V_inf V_x) V_y)) (tptp.hAPP (tptp.hAPP V_sup (tptp.hAPP V_uminus V_x)) (tptp.hAPP V_uminus V_y))) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_uminus $$unsorted) (V_sup $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_inf $$unsorted) (V_minus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_bot $$unsorted) (V_top $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_uminus (tptp.hAPP (tptp.hAPP V_sup V_x) V_y)) (tptp.hAPP (tptp.hAPP V_inf (tptp.hAPP V_uminus V_x)) (tptp.hAPP V_uminus V_y))) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_a) V_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_b))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_m V_n))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.hAPP (tptp.c_Set_Oimage V_f T_c T_b) V_A)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_c) V_B) V_f))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) V_B) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A)) V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_dB_H $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Finite__Set_Olattice__class_OSup__fin V_A T_a) (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) V_A)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_less $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oorder_Omono V_less__eq T_a T_b) V_f)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oorder_Ostrict__mono V_less T_a T_b) V_f))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) V_M) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_M)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_M)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Hilbert__Choice_OEps (tptp.hAPP (tptp.c_fequal T_a) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.c_Set_Oinsert T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Pair T_a T_b))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H))) (= V_a V_a_H)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Pair T_a T_b))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H))) (= V_b V_b_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OVar V_nat_H))) (= V_nat V_nat_H))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Collect T_a) V_P)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f) V_r) V_a) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_a) V_x) V_a)) V_r))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_R $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f) V_R) V_a) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_a) V_x) V_a)) V_R))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_I $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_I) V_A))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP V_A V_k)) _let_2) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_k) V_I))))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Pair T_a T_b) V_x))) (let ((_let_2 (tptp.c_in (tptp.tc_prod T_a T_b)))) (or (= V_y V_z) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) V_r))) (not (tptp.hBOOL (tptp.c_Relation_Osingle__valued V_r T_a T_b))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP _let_1 (tptp.c_lessequals T_a)) (tptp.hAPP _let_1 (tptp.c_HOL_Oord__class_Oless T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a) (tptp.c_Orderings_Obot__class_Obot T_a) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (let ((_let_4 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_3 _let_1) T_c) _let_2) V_B)) V_C)))))))) (or _let_147 (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI tptp.t_a tptp.t_b) tptp.v_A) tptp.v_f) (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf tptp.t_b) _let_132))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) V_M) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_M)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_M)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_fequal T_a) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) V_B)) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_g V_xs T_b T_a))) (= (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) (tptp.c_List_Oset V_xs T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_A) V_B) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_ONil T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.c_fequal T_a) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Set_Oimage V_f T_b T_a) V_A) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) _let_2) _let_2) _let_2)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oset V_xs T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (tptp.class_Lattices_Olower__semilattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_b) (tptp.hAPP V_f V_A)) (tptp.hAPP V_f V_B)))) (not (tptp.hBOOL (tptp.c_Orderings_Oorder__class_Omono V_f T_a T_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C))) (or (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP _let_1 V_A)) (tptp.hAPP _let_1 V_B))))) (or _let_147 (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tptp.t_a tptp.t_b) tptp.v_A) tptp.v_f) (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup tptp.t_b) _let_132))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP V_B V_a)) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) (tptp.c_in T_a)) V_A)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_plus $$unsorted) (V_k $$unsorted) (V_less__eq $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP V_plus V_k))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olinorder_OMax V_less__eq V_N T_a)) (tptp.c_Finite__Set_Olinorder_OMax V_less__eq (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_N)))) T_a)) (= V_N (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (not (tptp.c_OrderedGroup_Oordered__ab__semigroup__add V_plus V_less__eq V_less T_a))))))))) (forall ((V_plus $$unsorted) (V_k $$unsorted) (V_less__eq $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP V_plus V_k))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (or (= (tptp.hAPP _let_2 (tptp.c_Finite__Set_Olinorder_OMin V_less__eq V_N T_a)) (tptp.c_Finite__Set_Olinorder_OMin V_less__eq (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a))) _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_N)))) T_a)) (= V_N (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (not (tptp.c_OrderedGroup_Oordered__ab__semigroup__add V_plus V_less__eq V_less T_a))))))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun tptp.tc_nat T_a))) (let ((_let_3 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun tptp.tc_nat _let_3))) (= (tptp.c_List_Oset V_xs T_a) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBS tptp.tc_nat tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_4 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_3 tptp.tc_nat) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun _let_2 _let_1) T_a) (tptp.c_COMBB T_a tptp.tc_bool tptp.tc_nat)) (tptp.c_fequal T_a))) (tptp.c_List_Onth V_xs T_a))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.tc_nat tptp.tc_nat tptp.tc_bool) (tptp.c_HOL_Oord__class_Oless tptp.tc_nat)) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))))))))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Transitive__Closure_Ortranclp (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a _let_1)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not)) (tptp.c_fequal T_a))) T_a) (tptp.c_Transitive__Closure_Ortranclp V_r T_a)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) V_s) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_k)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_s) V_k)))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k)) V_u) V_k) V_u)) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) V_t) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k)) V_s) V_k) V_t)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A) V_B) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_a) (tptp.c_All T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_a) (tptp.hAPP (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_b) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_2 tptp.tc_bool) (tptp.c_in T_b)) V_A)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun _let_1 tptp.tc_bool) (tptp.tc_fun _let_3 _let_2) T_a) (tptp.c_COMBB _let_1 tptp.tc_bool T_b)) (tptp.c_in T_a))) V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) V_A) (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) (tptp.c_lessequals T_a))))))))) (forall ((V_A $$unsorted)) (= (tptp.c_Predicate_OPowp V_A tptp.v_B tptp.t_a) (tptp.hAPP (tptp.c_All tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.t_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) tptp.t_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_a (tptp.tc_fun tptp.t_a tptp.tc_bool) tptp.tc_bool) (tptp.c_in tptp.t_a)) tptp.v_B))) V_A)))) (= (tptp.c_Relation_Otrans tptp.v_r tptp.t_a) (tptp.hAPP _let_86 (tptp.hAPP _let_87 (tptp.hAPP (tptp.hAPP _let_85 _let_145) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_146 _let_73 tptp.t_a) _let_87) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_73 _let_146 tptp.t_a) (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_73 _let_73) _let_145)) _let_144)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.c_The (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_2 _let_2) T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_1 T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_x)))) (tptp.hAPP (tptp.c_fequal T_b) V_y)) T_a T_b tptp.tc_bool) (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_x) V_y))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.c_Hilbert__Choice_OEps (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_2 _let_2) T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_1 T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_x)))) (tptp.hAPP (tptp.c_fequal T_b) V_y)) T_a T_b tptp.tc_bool) (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Pair T_a T_b) V_x) V_y))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_I))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A)) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))) _let_135 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_c T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun T_c _let_3))) (let ((_let_5 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_6 (tptp.tc_prod T_a T_c))) (let ((_let_7 (tptp.tc_fun _let_6 tptp.tc_bool))) (let ((_let_8 (tptp.tc_fun _let_7 tptp.tc_bool))) (let ((_let_9 (tptp.tc_fun T_c _let_8))) (let ((_let_10 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_11 (tptp.tc_fun T_c _let_10))) (let ((_let_12 (tptp.tc_fun _let_5 _let_5))) (let ((_let_13 (tptp.tc_fun T_b _let_5))) (= (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.hAPP (tptp.c_Collect (tptp.tc_prod T_a T_b)) (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 (tptp.tc_fun T_b tptp.tc_bool) T_a) (tptp.hAPP (tptp.c_COMBB _let_5 tptp.tc_bool T_b) (tptp.c_Ex T_c))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_13 _let_13) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_12 (tptp.tc_fun _let_13 _let_13) T_a) (tptp.c_COMBB _let_5 _let_5 T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_11 _let_12 T_a) (tptp.c_COMBS T_c tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 _let_11 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_10 T_c) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_7 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 (tptp.tc_fun _let_7 _let_5) T_a) (tptp.c_COMBC T_c _let_7 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c _let_6) _let_9 T_a) (tptp.hAPP (tptp.c_COMBB _let_6 _let_8 T_c) (tptp.c_in _let_6))) (tptp.c_Pair T_a T_c)))) V_r))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_b) (tptp.c_COMBC T_c _let_2 tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c _let_1) _let_4 T_b) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_c) (tptp.c_in _let_1))) (tptp.hAPP (tptp.c_COMBC T_c T_b _let_1) (tptp.c_Pair T_c T_b))))) V_s))) T_a T_b tptp.tc_bool))))))))))))))))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______)) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____)) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t_H) V_T)) (not (tptp.c_Lambda_Obeta V_t V_t_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_T)))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_e) (tptp.c_Lambda_OdB_OVar V_i)) V_T))))) (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_env) (tptp.c_Lambda_OdB_OVar V_x)) (tptp.hAPP V_env V_x)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A V_ys T_a))) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A V_xs T_a))))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp V_A V_xs T_a)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.c_List_Osko__List__Xin__listsp__conv__set__1__1 V_A V_xs T_a)))))) _let_133 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_A $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp V_A V_ys T_a)) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a))))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp V_A V_xs T_a)) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_S $$unsorted) (T_c $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_COMBB _let_1 _let_1 T_c))) (let ((_let_3 (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_g))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.hAPP _let_3 V_S) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_c T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 T_b T_c) _let_3) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Collect T_a)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_S)))) (tptp.hAPP (tptp.c_COMBC T_a T_c tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c (tptp.tc_fun T_c tptp.tc_bool) T_a) (tptp.c_fequal T_c)) V_f)))))) (tptp.hAPP (tptp.c_Set_Oimage V_f T_a T_c) V_S))) (not (tptp.c_Finite__Set_Ofinite V_S T_a))))))) (= _let_132 (tptp.hAPP _let_131 (tptp.hAPP _let_127 (tptp.hAPP (tptp.hAPP _let_126 (tptp.hAPP _let_83 (tptp.hAPP _let_107 _let_130))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_b _let_74 _let_73) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_70 _let_75 tptp.t_b) _let_72) _let_93)) tptp.v_f))))) (= (tptp.c_Predicate_Obind tptp.v_P tptp.v_f tptp.t_a tptp.t_b) (tptp.c_Predicate_Opred_OPred (tptp.hAPP _let_127 (tptp.hAPP (tptp.hAPP _let_126 (tptp.hAPP _let_83 (tptp.hAPP _let_107 (tptp.hAPP _let_124 tptp.v_P)))) (tptp.hAPP (tptp.c_COMBC tptp.t_a tptp.t_b tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_Predicate_Opred tptp.t_b) _let_70 tptp.t_a) (tptp.c_Predicate_Oeval tptp.t_b)) tptp.v_f)))) tptp.t_b)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.hAPP (tptp.c_Collect (tptp.tc_prod T_b T_a)) (tptp.c_split V_P T_b T_a tptp.tc_bool)) T_b T_a) V_A) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_b) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 tptp.tc_bool) (tptp.c_in T_b)) V_A)))) (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) V_P))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) V_A) (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_lessequals T_a)))))))))) (forall ((T_a $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted) (V_j $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift T_a) V_e) V_i) V_T) V_j) (tptp.hAPP V_e V_j)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_j) V_i))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 tptp.tc_bool) _let_1) V_A)))) V_Q))) T_b) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 V_A V_Q T_a T_b)) V_A)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping tptp.v_ea______) tptp.v_ua______) tptp.v_T____)) (= (tptp.c_Predicate_Osingleton tptp.v_dfault tptp.v_A tptp.t_a) (tptp.c_HOL_OIf (tptp.hAPP _let_109 (tptp.hAPP (tptp.hAPP _let_83 (tptp.hAPP _let_107 _let_125)) (tptp.hAPP _let_87 (tptp.hAPP (tptp.hAPP _let_105 (tptp.hAPP _let_83 (tptp.hAPP _let_79 _let_125))) _let_104)))) (tptp.c_The _let_125 tptp.t_a) (tptp.hAPP tptp.v_dfault tptp.c_Product__Type_OUnity) tptp.t_a)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a))) V_P)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_F $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.tc_fun T_a _let_1))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (tptp.c_Recdef_Oadm__wf V_R (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_1) _let_1) (tptp.c_COMBS T_a T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 _let_1) (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) V_F)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool) _let_2) (tptp.c_Recdef_Ocut T_a T_b)) V_R)))) (tptp.c_COMBI T_a)) T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool T_a) (tptp.c_All T_b)) V_P)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) (tptp.c_Orderings_Otop__class_Otop _let_3)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) _let_1) (tptp.hAPP (tptp.c_COMBC T_a T_b tptp.tc_bool) V_P)))))))) (forall ((V_g $$unsorted) (V_h $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_s $$unsorted) (V_xs $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c T_a))) (let ((_let_2 (tptp.c_List_Osko__List__Xfoldl__apply__inv__1__1 V_g V_h T_b T_a))) (or (not (= (tptp.hAPP V_g (tptp.hAPP V_h _let_2)) _let_2)) (= (tptp.c_List_Ofoldl V_f (tptp.hAPP V_g V_s) V_xs T_a T_c) (tptp.hAPP V_g (tptp.c_List_Ofoldl (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun T_c T_b) T_b) (tptp.hAPP (tptp.c_COMBB T_a T_b T_c) V_h)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a _let_1 T_b) V_f) V_g)) V_s V_xs T_b T_c))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) V_Q))) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) V_Q) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 V_A V_Q T_a T_b))) T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_g $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c T_a))) (let ((_let_2 (tptp.tc_fun T_c T_b))) (= (tptp.c_List_Ofoldl V_g V_a (tptp.c_List_Omap V_f V_xs T_c T_b) T_a T_b) (tptp.c_List_Ofoldl (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) (tptp.tc_fun _let_2 _let_1) T_a) (tptp.c_COMBB T_b T_a T_c)) V_g)) V_f) V_a V_xs T_a T_c))))) (= (tptp.c_Relation_Osingle__valued tptp.v_r tptp.t_a tptp.t_b) (tptp.hAPP _let_86 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_70 tptp.tc_bool tptp.t_a) _let_96) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.t_a _let_70 _let_70) _let_123) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_102 _let_70 tptp.t_a) (tptp.hAPP (tptp.c_COMBB _let_70 tptp.tc_bool tptp.t_b) _let_96)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.t_a _let_102 _let_102) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_121 (tptp.tc_fun _let_102 _let_102) tptp.t_a) (tptp.c_COMBB _let_70 _let_70 tptp.t_b)) _let_123)) _let_93)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_a))) V_P)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP V_P V_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_Q) T_a))))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_P) T_a))))) _let_110 (forall ((V_Inf $$unsorted) (V_A $$unsorted) (V_Sup $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP V_Inf V_A) (tptp.hAPP V_Sup (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) V_less__eq))))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Collect (tptp.tc_prod T_a T_b)) (tptp.c_split (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_2 T_a) tptp.c_and) V_P))) V_Q) T_a T_b tptp.tc_bool)) (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Collect T_a) V_P) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.c_Collect T_b)) V_Q) T_a T_b))))) (forall ((T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_T $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_3 (tptp.c_COMBB _let_1 _let_1 T_b))) (let ((_let_4 (tptp.c_Finite__Set_Osetsum T_a T_c))) (let ((_let_5 (tptp.c_Finite__Set_Osetsum T_b T_c))) (let ((_let_6 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_7 (tptp.c_COMBB _let_6 _let_6 T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_c)) (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a _let_6 T_c) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_c) (tptp.tc_fun _let_6 T_c) T_a) _let_5) V_f)) (tptp.hAPP (tptp.hAPP _let_7 (tptp.c_Collect T_b)) (tptp.hAPP (tptp.hAPP _let_7 (tptp.hAPP (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_2 T_b) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_6 tptp.tc_bool) (tptp.c_in T_b)) V_T)))) V_R)))) V_S) (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b _let_1 T_c) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a T_c) (tptp.tc_fun _let_1 T_c) T_b) _let_4) (tptp.hAPP (tptp.c_COMBC T_a T_b T_c) V_f))) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Collect T_a)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_2 T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_S)))) (tptp.hAPP (tptp.c_COMBC T_a T_b tptp.tc_bool) V_R))))) V_T)) (not (tptp.c_Finite__Set_Ofinite V_T T_b)) (not (tptp.c_Finite__Set_Ofinite V_S T_a))))))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_g $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.tc_fun T_a T_a))) (let ((_let_3 (tptp.tc_fun T_c T_a))) (let ((_let_4 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_5 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_6 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_6 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_4 V_g) V_B)) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_5 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 (tptp.tc_fun _let_5 T_a) T_b) _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_3 _let_3) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_3) T_b) (tptp.c_COMBB T_a T_a T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a _let_2 T_b) _let_1) V_f))) V_g))) V_B)) V_A)))))))))) (forall ((V_P $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.c_Predicate_Obind V_P V_f T_b T_a) (tptp.c_Predicate_Opred_OPred (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_b) tptp.c_and) (tptp.hAPP (tptp.c_Predicate_Oeval T_b) V_P)))) (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_Predicate_Opred T_a) (tptp.tc_fun T_a tptp.tc_bool) T_b) (tptp.c_Predicate_Oeval T_a)) V_f)))) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Collect T_b))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) V_Q) V_x)) T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 tptp.tc_bool) _let_1) V_A)))) V_Q))) T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool T_a) (tptp.c_All T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_3 T_a) (tptp.hAPP (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_b) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_3 tptp.tc_bool) (tptp.c_in T_b)) V_A)))) V_P))) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) _let_1) (tptp.hAPP (tptp.c_COMBC T_a T_b tptp.tc_bool) V_P)))))))) (forall ((V_Sup $$unsorted) (V_A $$unsorted) (V_Inf $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP V_Sup V_A) (tptp.hAPP V_Inf (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) V_less__eq)))))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (or (not (tptp.class_HOL_Oord tptp.t_a)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.v_P tptp.t_a) (tptp.c_The (tptp.hAPP _let_108 (tptp.hAPP _let_87 (tptp.hAPP _let_106 _let_90))) tptp.t_a))) (= (tptp.c_FunDef_OTHE__default tptp.v_d tptp.v_P tptp.t_a) (tptp.c_HOL_OIf (tptp.hAPP _let_109 (tptp.hAPP _let_108 (tptp.hAPP _let_87 (tptp.hAPP _let_106 _let_104)))) (tptp.c_The tptp.v_P tptp.t_a) tptp.v_d tptp.t_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar tptp.v_n____) tptp.v_rs____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) tptp.v_T_H____)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a))) V_P)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP V_P V_a)))) (= (tptp.c_Record_Oiso__tuple__update__accessor__cong__assist tptp.v_upd tptp.v_acc tptp.t_a tptp.t_b) (tptp.hAPP (tptp.hAPP tptp.c_and (tptp.hAPP (tptp.c_All _let_98) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_70 tptp.tc_bool _let_98) _let_96) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS _let_98 _let_100 _let_70) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_102 (tptp.tc_fun _let_100 _let_70) _let_98) _let_95) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_100 _let_102 _let_98) _let_94) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_98 _let_100 _let_100) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_101 (tptp.tc_fun _let_100 _let_100) _let_98) (tptp.c_COMBS tptp.t_b tptp.t_b tptp.t_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_99 _let_101 _let_98) (tptp.hAPP (tptp.c_COMBB _let_98 _let_100 tptp.t_b) tptp.v_upd)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_97 _let_99 _let_98) (tptp.hAPP (tptp.c_COMBB tptp.t_a _let_98 tptp.t_b) (tptp.c_COMBK tptp.t_a tptp.t_a))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_98 _let_97 _let_97) (tptp.c_COMBB tptp.t_a tptp.t_a tptp.t_b)) tptp.v_acc))))) _let_91)))) tptp.v_upd)))) (tptp.hAPP _let_96 (tptp.hAPP (tptp.hAPP _let_95 (tptp.hAPP _let_94 (tptp.hAPP tptp.v_upd _let_92))) _let_91)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P))) V_Q))) T_b) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 V_P V_Q T_a T_b))) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_a) V_P) T_a))))) (not (= tptp.v_n____ tptp.v_i____)) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) (tptp.c_Lambda_OdB_OVar V_i)) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a T_b))) (let ((_let_3 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_4 T_b) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_3 T_a) tptp.c_and)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b tptp.tc_bool) (tptp.tc_fun _let_2 _let_1) T_b) (tptp.c_COMBB T_b tptp.tc_bool T_a)) (tptp.c_fequal T_b))) V_f)))) V_P))) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_a) V_P) T_a)))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_Collect T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P))) V_Q))) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) V_Q) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 V_P V_Q T_a T_b))) T_b)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_a) V_P) T_a)))))) (forall ((T_c $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_c))) (let ((_let_3 (tptp.tc_fun T_c T_c))) (let ((_let_4 (tptp.tc_fun T_b T_c))) (let ((_let_5 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_4 _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 (tptp.tc_fun _let_4 _let_4) T_a) (tptp.c_COMBB T_c T_c T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c _let_3 T_a) _let_2) V_f))) V_g))) (let ((_let_6 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_7 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_8 (tptp.tc_fun _let_1 _let_1))) (let ((_let_9 (tptp.tc_fun _let_4 _let_1))) (let ((_let_10 (tptp.tc_fun T_a _let_1))) (let ((_let_11 (tptp.tc_fun T_a _let_4))) (let ((_let_12 (tptp.tc_fun T_b _let_7))) (let ((_let_13 (tptp.tc_fun T_a _let_12))) (let ((_let_14 (tptp.tc_fun T_a _let_8))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_c)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_c) V_f) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_c) V_g) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_c T_c) (tptp.c_Fun_Oid T_c)) (tptp.hAPP (tptp.c_Collect T_c) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 tptp.tc_bool T_c) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_6 T_c) (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_b))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_10 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_14 (tptp.tc_fun _let_10 _let_10) T_c) (tptp.c_COMBS T_a _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 _let_14 T_c) (tptp.hAPP (tptp.c_COMBB _let_12 _let_8 T_a) (tptp.c_COMBS T_b tptp.tc_bool tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_13 T_c) (tptp.hAPP (tptp.c_COMBB _let_1 _let_12 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_7 T_b) tptp.c_and))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_11 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 (tptp.tc_fun _let_11 _let_10) T_c) (tptp.c_COMBB _let_4 _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c tptp.tc_bool) _let_9 T_c) (tptp.c_COMBB T_c tptp.tc_bool T_b)) (tptp.c_fequal T_c)))) _let_5))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_7 _let_8 T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_7 T_a) tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_6 tptp.tc_bool) (tptp.c_in T_a)) V_A)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 tptp.tc_bool) (tptp.c_in T_b)) V_B)))))))) (not (tptp.c_Fun_Oinj__on (tptp.c_split _let_5 T_a T_b T_c) (tptp.c_Product__Type_OSigma V_A (tptp.hAPP (tptp.c_COMBK _let_1 T_a) V_B) T_a T_b) (tptp.tc_prod T_a T_b) T_c)))))))))))))))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift tptp.tc_Type_Otype) V_e) V_i) V_U)) (tptp.c_Lambda_Olift V_t V_i)) V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_e) V_t) V_T))))) (forall ((V_less__eq $$unsorted)) (let ((_let_1 (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) tptp.t_a))) (let ((_let_2 (tptp.c_COMBS tptp.t_a tptp.tc_bool tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (= (tptp.c_Orderings_Oord_OLeast V_less__eq tptp.v_P tptp.t_a) (tptp.c_The (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.c_and) tptp.v_P)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool tptp.t_a) (tptp.c_All tptp.t_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_3 tptp.t_a) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.c_implies) tptp.v_P))) V_less__eq))) tptp.t_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_Collect T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.hAPP _let_1 V_P)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_implies) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_bool) (tptp.c_fequal T_a)) V_a)))) V_P))))) (forall ((T_b $$unsorted) (V_m $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_a T_b))) (let ((_let_4 (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a))) (let ((_let_5 (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (or (not (tptp.class_HOL_Oord T_b)) (= (tptp.c_Hilbert__Choice_OLeastM V_m V_P T_a T_b) (tptp.c_Hilbert__Choice_OEps (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 tptp.c_and) V_P)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_a) (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 tptp.c_implies) V_P))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_3 _let_2) T_a) (tptp.c_COMBB T_b tptp.tc_bool T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_a) (tptp.c_lessequals T_b)) V_m))) V_m)))) T_a))))))))) (forall ((V_inf $$unsorted) (V_sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and))) (let ((_let_6 (tptp.tc_fun _let_1 _let_1))) (let ((_let_7 (tptp.tc_fun T_a T_a))) (let ((_let_8 (tptp.tc_fun _let_7 _let_1))) (let ((_let_9 (tptp.tc_fun T_a _let_1))) (let ((_let_10 (tptp.tc_fun T_a _let_7))) (let ((_let_11 (tptp.tc_fun T_a _let_4))) (let ((_let_12 (tptp.tc_fun T_a _let_11))) (let ((_let_13 (tptp.tc_fun T_a _let_6))) (let ((_let_14 (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)))) (or (= (tptp.hAPP (tptp.hAPP V_inf (tptp.c_Finite__Set_Olattice_OSup__fin V_sup V_A T_a)) (tptp.c_Finite__Set_Olattice_OSup__fin V_sup V_B T_a)) (tptp.c_Finite__Set_Olattice_OSup__fin V_sup (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP _let_14 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 _let_1 T_a) _let_14) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_9 _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 (tptp.tc_fun _let_9 _let_9) T_a) (tptp.c_COMBS T_a _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_12 _let_13 T_a) (tptp.hAPP (tptp.c_COMBB _let_11 _let_6 T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 _let_12 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_11 T_a) _let_5)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_10 _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_10 _let_9) T_a) (tptp.c_COMBB _let_7 _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_8 T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a)))) V_inf))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_6 T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a)) (tptp.hAPP _let_5 (tptp.hAPP _let_3 V_A)))) (tptp.hAPP _let_3 V_B)))))) T_a)) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a)))))))))))))))))) (forall ((V_sup $$unsorted) (V_inf $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and))) (let ((_let_6 (tptp.tc_fun _let_1 _let_1))) (let ((_let_7 (tptp.tc_fun T_a T_a))) (let ((_let_8 (tptp.tc_fun _let_7 _let_1))) (let ((_let_9 (tptp.tc_fun T_a _let_1))) (let ((_let_10 (tptp.tc_fun T_a _let_7))) (let ((_let_11 (tptp.tc_fun T_a _let_4))) (let ((_let_12 (tptp.tc_fun T_a _let_11))) (let ((_let_13 (tptp.tc_fun T_a _let_6))) (let ((_let_14 (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)))) (or (= (tptp.hAPP (tptp.hAPP V_sup (tptp.c_Finite__Set_Olattice_OInf__fin V_inf V_A T_a)) (tptp.c_Finite__Set_Olattice_OInf__fin V_inf V_B T_a)) (tptp.c_Finite__Set_Olattice_OInf__fin V_inf (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP _let_14 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 _let_1 T_a) _let_14) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_9 _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 (tptp.tc_fun _let_9 _let_9) T_a) (tptp.c_COMBS T_a _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_12 _let_13 T_a) (tptp.hAPP (tptp.c_COMBB _let_11 _let_6 T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 _let_12 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_11 T_a) _let_5)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_10 _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_10 _let_9) T_a) (tptp.c_COMBB _let_7 _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_8 T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a)))) V_sup))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_6 T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a)) (tptp.hAPP _let_5 (tptp.hAPP _let_3 V_A)))) (tptp.hAPP _let_3 V_B)))))) T_a)) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Lattices_Odistrib__lattice V_less__eq V_less V_inf V_sup T_a)))))))))))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and))) (let ((_let_6 (tptp.tc_fun _let_1 _let_1))) (let ((_let_7 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_8 (tptp.tc_fun T_a T_a))) (let ((_let_9 (tptp.tc_fun _let_8 _let_1))) (let ((_let_10 (tptp.tc_fun T_a _let_1))) (let ((_let_11 (tptp.tc_fun T_a _let_8))) (let ((_let_12 (tptp.tc_fun T_a _let_4))) (let ((_let_13 (tptp.tc_fun T_a _let_12))) (let ((_let_14 (tptp.tc_fun T_a _let_6))) (let ((_let_15 (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_7 (tptp.c_Finite__Set_Olattice__class_OInf__fin V_A T_a)) (tptp.c_Finite__Set_Olattice__class_OInf__fin V_B T_a)) (tptp.c_Finite__Set_Olattice__class_OInf__fin (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP _let_15 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_1 T_a) _let_15) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_10 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_14 (tptp.tc_fun _let_10 _let_10) T_a) (tptp.c_COMBS T_a _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 _let_14 T_a) (tptp.hAPP (tptp.c_COMBB _let_12 _let_6 T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_13 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_12 T_a) _let_5)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_11 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 (tptp.tc_fun _let_11 _let_10) T_a) (tptp.c_COMBB _let_8 _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_9 T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a)))) _let_7))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_6 T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a)) (tptp.hAPP _let_5 (tptp.hAPP _let_3 V_A)))) (tptp.hAPP _let_3 V_B)))))) T_a)) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))))))))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_bool) (tptp.c_in T_a)))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 T_a) tptp.c_and))) (let ((_let_6 (tptp.tc_fun _let_1 _let_1))) (let ((_let_7 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_8 (tptp.tc_fun T_a T_a))) (let ((_let_9 (tptp.tc_fun _let_8 _let_1))) (let ((_let_10 (tptp.tc_fun T_a _let_1))) (let ((_let_11 (tptp.tc_fun T_a _let_8))) (let ((_let_12 (tptp.tc_fun T_a _let_4))) (let ((_let_13 (tptp.tc_fun T_a _let_12))) (let ((_let_14 (tptp.tc_fun T_a _let_6))) (let ((_let_15 (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_Ex T_a)))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_7 (tptp.c_Finite__Set_Olattice__class_OSup__fin V_A T_a)) (tptp.c_Finite__Set_Olattice__class_OSup__fin V_B T_a)) (tptp.c_Finite__Set_Olattice__class_OSup__fin (tptp.hAPP (tptp.c_Collect T_a) (tptp.hAPP _let_15 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_1 T_a) _let_15) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_10 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_14 (tptp.tc_fun _let_10 _let_10) T_a) (tptp.c_COMBS T_a _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_13 _let_14 T_a) (tptp.hAPP (tptp.c_COMBB _let_12 _let_6 T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_10 _let_13 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_12 T_a) _let_5)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_11 _let_10) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_9 (tptp.tc_fun _let_11 _let_10) T_a) (tptp.c_COMBB _let_8 _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_9 T_a) (tptp.c_COMBB T_a tptp.tc_bool T_a)) (tptp.c_fequal T_a)))) _let_7))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_6 T_a) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a)) (tptp.hAPP _let_5 (tptp.hAPP _let_3 V_A)))) (tptp.hAPP _let_3 V_B)))))) T_a)) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))))))))))))))) (or _let_89 _let_88 (= (tptp.c_Orderings_Oorder__class_Omono tptp.v_f tptp.t_a tptp.t_b) (tptp.hAPP _let_86 (tptp.hAPP _let_87 (tptp.hAPP (tptp.hAPP _let_85 (tptp.hAPP _let_84 (tptp.hAPP _let_82 _let_90))) (tptp.hAPP (tptp.hAPP _let_77 (tptp.hAPP _let_76 (tptp.hAPP (tptp.hAPP _let_71 (tptp.c_lessequals tptp.t_b)) tptp.v_f))) tptp.v_f)))))) (or _let_89 _let_88 (= (tptp.c_Orderings_Oorder__class_Ostrict__mono tptp.v_f tptp.t_a tptp.t_b) (tptp.hAPP _let_86 (tptp.hAPP _let_87 (tptp.hAPP (tptp.hAPP _let_85 (tptp.hAPP _let_84 (tptp.hAPP _let_82 (tptp.c_HOL_Oord__class_Oless tptp.t_a)))) (tptp.hAPP (tptp.hAPP _let_77 (tptp.hAPP _let_76 (tptp.hAPP (tptp.hAPP _let_71 (tptp.c_HOL_Oord__class_Oless tptp.t_b)) tptp.v_f))) tptp.v_f)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_J $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.tc_fun _let_1 _let_1))) (let ((_let_4 (tptp.tc_fun T_c _let_1))) (let ((_let_5 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_J))) (let ((_let_6 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_6 V_A)) (tptp.hAPP _let_5 V_B)) (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_1 T_b) _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 (tptp.tc_fun _let_4 _let_4) T_b) (tptp.c_COMBB _let_1 _let_1 T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) _let_2) V_A))) V_B))))))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_J $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.tc_fun _let_1 _let_1))) (let ((_let_4 (tptp.tc_fun T_c _let_1))) (let ((_let_5 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_J))) (let ((_let_6 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_I))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_6 V_A)) (tptp.hAPP _let_5 V_B)) (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_1 T_b) _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 (tptp.tc_fun _let_4 _let_4) T_b) (tptp.c_COMBB _let_1 _let_1 T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) _let_2) V_A))) V_B))))))))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Ofilter V_Q V_xs T_a) T_a) (tptp.c_List_Ofilter (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_Q)) V_P) V_xs T_a))) (forall ((T_b $$unsorted) (V_m $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a))) (let ((_let_3 (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool))) (or (not (tptp.class_HOL_Oord T_b)) (= (tptp.c_Hilbert__Choice_OGreatestM V_m V_P T_a T_b) (tptp.c_Hilbert__Choice_OEps (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.c_and) V_P)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.c_All T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.c_implies) V_P))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_a) (tptp.hAPP (tptp.c_COMBC T_a T_b tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b tptp.tc_bool) T_a) (tptp.c_lessequals T_b)) V_m))) V_m)))) T_a))))))) (forall ((T_b $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_1 _let_3))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (let ((_let_6 (tptp.tc_fun T_a _let_3))) (let ((_let_7 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_8 (tptp.tc_fun T_a _let_7))) (let ((_let_9 (tptp.c_All T_a))) (or (not (tptp.class_Orderings_Oorder T_b)) (= (tptp.c_Orderings_Oorder_Ostrict__mono V_less T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool _let_1) _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 _let_3 _let_1) (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool T_a) _let_9)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 _let_6 _let_1) (tptp.hAPP (tptp.c_COMBS T_a _let_3 _let_3) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_3 _let_3) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_8 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_7 T_a) tptp.c_implies)) V_less)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS _let_1 _let_1 _let_6) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_6) _let_1) (tptp.c_COMBC T_a _let_1 _let_3)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_2) _let_5 _let_1) (tptp.hAPP (tptp.c_COMBB _let_2 _let_4 T_a) (tptp.c_COMBB T_b tptp.tc_bool T_a))) (tptp.hAPP (tptp.c_COMBB T_b _let_2 T_a) (tptp.c_HOL_Oord__class_Oless T_b))))) (tptp.c_COMBI _let_1)))))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a))))))))))))) (forall ((T_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_1 _let_3))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (let ((_let_6 (tptp.tc_fun T_a _let_3))) (let ((_let_7 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_8 (tptp.tc_fun T_a _let_7))) (let ((_let_9 (tptp.c_All T_a))) (or (not (tptp.class_Orderings_Oorder T_b)) (= (tptp.c_Orderings_Oorder_Omono V_less__eq T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool _let_1) _let_9) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 _let_3 _let_1) (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_bool T_a) _let_9)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 _let_6 _let_1) (tptp.hAPP (tptp.c_COMBS T_a _let_3 _let_3) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_3 _let_3) T_a) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_8 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_7 T_a) tptp.c_implies)) V_less__eq)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS _let_1 _let_1 _let_6) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_1 _let_6) _let_1) (tptp.c_COMBC T_a _let_1 _let_3)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_2) _let_5 _let_1) (tptp.hAPP (tptp.c_COMBB _let_2 _let_4 T_a) (tptp.c_COMBB T_b tptp.tc_bool T_a))) (tptp.hAPP (tptp.c_COMBB T_b _let_2 T_a) (tptp.c_lessequals T_b))))) (tptp.c_COMBI _let_1)))))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a))))))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Collect T_b))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_a tptp.tc_bool) V_Q) V_x)) T_b) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P))) V_Q))) T_b)) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.c_Collect T_a) V_P) T_a)))))) (forall ((T_a $$unsorted) (V_sup $$unsorted) (V_uminus $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted) (V_minus $$unsorted)) (let ((_let_1 (tptp.c_COMBC T_a T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a T_a))) (or (tptp.c_Lattices_Oboolean__algebra (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_2 _let_2) T_a) (tptp.c_COMBB T_a T_a T_a)) V_sup)) V_uminus) V_uminus (tptp.hAPP _let_1 V_less__eq) (tptp.hAPP _let_1 V_less) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Lattices_Oboolean__algebra V_minus V_uminus V_less__eq V_less V_inf V_sup V_bot V_top T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (= (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.t_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) tptp.t_a) tptp.c_and) V_A)) V_B) tptp.v_x tptp.t_a) (tptp.hAPP (tptp.hAPP tptp.c_and (tptp.c_List_Olistsp V_A tptp.v_x tptp.t_a)) (tptp.c_List_Olistsp V_B tptp.v_x tptp.t_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping tptp.v_e____) tptp.v_u____) tptp.v_T____)) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.c_Type_Otype_OFun V_T1 V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_e) V_u) V_T2))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift tptp.tc_Type_Otype) V_e) V_i) V_T2)) V_t) V_Ta))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.c_Type_Otype_OFun V_T1 V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping V_e) V_u) V_T1))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift tptp.tc_Type_Otype) V_e) V_i) V_T1)) V_t) V_Ta))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Type_Otype tptp.tc_bool) tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_Ex tptp.tc_Type_Otype)) (tptp.hAPP tptp.c_Type_Otyping V_e)) V_ts tptp.tc_Lambda_OdB)) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)))) (tptp.hBOOL (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP _let_66 (tptp.hAPP _let_65 tptp.c_InductTermi_OIT)) _let_64) tptp.v_rs____ tptp.tc_Lambda_OdB)) (forall ((T_a $$unsorted) (V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift T_a) V_e) V_x) V_T) V_x) V_T)) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Type_Otyping V_e_H))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_u) V_U))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Type_Oshift tptp.tc_Type_Otype) V_e_H) V_i) V_U)) V_t) V_T))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i)) V_T))))) _let_69 _let_68 _let_67 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_prod T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Orderings_Owellorder tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_1 $$unsorted)) (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Lattices_Oupper__semilattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Lattices_Olower__semilattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Lattices_Odistrib__lattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Lattices_Obounded__lattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Opreorder (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Lattices_Olattice (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Oorder (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Otop (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Obot (tptp.tc_Predicate_Opred T_1))) (forall ((T_1 $$unsorted)) (tptp.class_HOL_Oord (tptp.tc_Predicate_Opred T_1))) (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 81.32/81.70  )
% 81.32/81.70  % SZS output end Proof for LCL823-1
% 81.32/81.71  % cvc5---1.0.5 exiting
% 81.32/81.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------