TPTP Problem File: SLH0335^1.p

%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Stalnaker_Logic/0000_Stalnaker_Logic/prob_00215_007008__6418828_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1667 ( 516 unt; 390 typ;   0 def)
%            Number of atoms       : 4643 ( 895 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives : 16207 ( 452   ~;  77   |; 315   &;13008   @)
%                                         (   0 <=>;2355  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   9 avg)
%            Number of types       :   47 (  46 usr)
%            Number of type conns  : 1916 (1916   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  347 ( 344 usr;  20 con; 0-5 aty)
%            Number of variables   : 4832 ( 489   ^;4206   !; 137   ?;4832   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:12:00.697
%------------------------------------------------------------------------------
% Could-be-implicit typings (46)
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thf(ty_n_t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(ty_n_t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
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thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
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thf(ty_n_t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
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thf(ty_n_t__Product____Type__Ounit,type,
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thf(ty_n_t__List__Olist_Itf__a_J,type,
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thf(ty_n_t__Set__Oset_Itf__a_J,type,
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thf(ty_n_t__Set__Oset_I_Eo_J,type,
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thf(ty_n_tf__a,type,
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% Explicit typings (344)
thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Epistemic____Logic__Ofm_Itf__a_J_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OFunc_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Epistemic____Logic__Ofm_Itf__a_J_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001tf__a,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001tf__a,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osuc_001tf__a,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osupr_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osupr_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Osupr_001tf__a,type,
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thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J,type,
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thf(sy_c_Complete__Lattices_OSup__class_OSup_001_Eo,type,
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thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_Epistemic__Logic_OAK_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_Ofilter_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    filter6053540574317342667c_fm_a: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a > set_Epistemic_fm_a ).

thf(sy_c_Set_Oimage_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    image_4449434806354059013c_fm_a: ( epistemic_fm_a > epistemic_fm_a ) > set_Epistemic_fm_a > set_Epistemic_fm_a ).

thf(sy_c_Set_Oimage_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    image_1263732536703906021c_fm_a: ( epistemic_fm_a > set_Epistemic_fm_a ) > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J,type,
    image_6902499629341727256fm_a_o: ( set_Epistemic_fm_a > epistemic_fm_a > $o ) > set_se5208064806568342746c_fm_a > set_Epistemic_fm_a_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001_Eo,type,
    image_3094577733827872675fm_a_o: ( set_Epistemic_fm_a > $o ) > set_se5208064806568342746c_fm_a > set_o ).

thf(sy_c_Set_Oinsert_001t__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    insert6916508371349555078c_fm_a: episte740340785640729014c_fm_a > set_Ep8485816078964734998c_fm_a > set_Ep8485816078964734998c_fm_a ).

thf(sy_c_Set_Oinsert_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    insert7817948963269374698c_fm_a: epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    insert4108635152042037623c_fm_a: produc2203834439629243303c_fm_a > set_Pr8948481099588399239c_fm_a > set_Pr8948481099588399239c_fm_a ).

thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    insert7129737658439086282c_fm_a: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a ).

thf(sy_c_Set_Oinsert_001tf__a,type,
    insert_a: a > set_a > set_a ).

thf(sy_c_Set_Othe__elem_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    the_el2173195877760541071c_fm_a: set_Epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Stalnaker__Logic_Oconjunct_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    stalna5968238273478151382c_fm_a: list_E5775909407618282812c_fm_a > episte740340785640729014c_fm_a ).

thf(sy_c_Stalnaker__Logic_Oconjunct_001tf__a,type,
    stalnaker_conjunct_a: list_Epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Wellorder__Constructions_Owo__rel_Oadm__woL_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    wellor8531372491315211020c_fm_a: set_Pr8948481099588399239c_fm_a > ( ( epistemic_fm_a > set_Epistemic_fm_a ) > epistemic_fm_a > set_Epistemic_fm_a ) > $o ).

thf(sy_c_Wellorder__Constructions_Owo__rel_OisLimOrd_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    wellor5744531135217078139c_fm_a: set_Pr8948481099588399239c_fm_a > $o ).

thf(sy_c_Wellorder__Constructions_Owo__rel_OworecZSL_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    wellor7234309849078405374c_fm_a: set_Pr8948481099588399239c_fm_a > set_Epistemic_fm_a > ( epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a ) > ( ( epistemic_fm_a > set_Epistemic_fm_a ) > epistemic_fm_a > set_Epistemic_fm_a ) > epistemic_fm_a > set_Epistemic_fm_a ).

thf(sy_c_member_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J,type,
    member4486839677911940090fm_a_o: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a_o > $o ).

thf(sy_c_member_001t__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    member1118567890201975263c_fm_a: episte740340785640729014c_fm_a > set_Ep8485816078964734998c_fm_a > $o ).

thf(sy_c_member_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    member6642669571620171971c_fm_a: epistemic_fm_a > set_Epistemic_fm_a > $o ).

thf(sy_c_member_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    member5906877432388582473c_fm_a: list_Epistemic_fm_a > set_li769143395467472256c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    member5029746173879296720c_fm_a: produc2203834439629243303c_fm_a > set_Pr8948481099588399239c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member7118756715807017744c_fm_a: produc3097728481292866791c_fm_a > set_Pr6593897923388255431c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member6846535391323571920c_fm_a: produc8009007716763201447c_fm_a > set_Pr4537461906582779015c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_M_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_J,type,
    member5250668776978656404c_fm_a: produc5398904771037890795c_fm_a > set_Pr1281480396656123467c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    member1426531477525435216od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).

thf(sy_c_member_001t__Set__Oset_It__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member7847018790254331967c_fm_a: set_Ep8485816078964734998c_fm_a > set_se8358038196042697334c_fm_a > $o ).

thf(sy_c_member_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    member536094252920883875c_fm_a: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
    member_set_a: set_a > set_set_a > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_v_A,type,
    a2: epistemic_fm_a > $o ).

thf(sy_v_V,type,
    v: set_Epistemic_fm_a ).

thf(sy_v_p,type,
    p: epistemic_fm_a ).

thf(sy_v_q,type,
    q: epistemic_fm_a ).

% Relevant facts (1276)
thf(fact_0_assms_I1_J,axiom,
    episte2285483198712856226tent_a @ a2 @ v ).

% assms(1)
thf(fact_1_assms_I2_J,axiom,
    maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ a2 ) @ v ).

% assms(2)
thf(fact_2__092_060open_062tautology_A_Ip_A_092_060_094bold_062_092_060longrightarrow_062_Aq_A_092_060_094bold_062_092_060longrightarrow_062_Ap_A_092_060_094bold_062_092_060and_062_Aq_J_092_060close_062,axiom,
    ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ p @ ( epistemic_Imp_a @ q @ ( epistemic_Con_a @ p @ q ) ) ) ) ).

% \<open>tautology (p \<^bold>\<longrightarrow> q \<^bold>\<longrightarrow> p \<^bold>\<and> q)\<close>
thf(fact_3_fm_Oinject_I3_J,axiom,
    ! [X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ( ( ( episte3685526487207141399c_fm_a @ X41 @ X42 )
        = ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) )
      = ( ( X41 = Y41 )
        & ( X42 = Y42 ) ) ) ).

% fm.inject(3)
thf(fact_4_fm_Oinject_I3_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( ( epistemic_Con_a @ X41 @ X42 )
        = ( epistemic_Con_a @ Y41 @ Y42 ) )
      = ( ( X41 = Y41 )
        & ( X42 = Y42 ) ) ) ).

% fm.inject(3)
thf(fact_5_fm_Oinject_I4_J,axiom,
    ! [X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ( ( ( episte260752218777527565c_fm_a @ X51 @ X52 )
        = ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) )
      = ( ( X51 = Y51 )
        & ( X52 = Y52 ) ) ) ).

% fm.inject(4)
thf(fact_6_fm_Oinject_I4_J,axiom,
    ! [X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( ( epistemic_Imp_a @ X51 @ X52 )
        = ( epistemic_Imp_a @ Y51 @ Y52 ) )
      = ( ( X51 = Y51 )
        & ( X52 = Y52 ) ) ) ).

% fm.inject(4)
thf(fact_7_K__imply__multi,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,A2: episte740340785640729014c_fm_a,B: episte740340785640729014c_fm_a,C: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ A2 @ B ) )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ A2 @ C ) )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ A2 @ ( episte3685526487207141399c_fm_a @ B @ C ) ) ) ) ) ).

% K_imply_multi
thf(fact_8_K__imply__multi,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ B ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ C ) )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Con_a @ B @ C ) ) ) ) ) ).

% K_imply_multi
thf(fact_9_K__multi__imply,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,A2: episte740340785640729014c_fm_a,B: episte740340785640729014c_fm_a,C: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ A2 @ ( episte260752218777527565c_fm_a @ B @ C ) ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ A2 @ B ) @ C ) ) ) ).

% K_multi_imply
thf(fact_10_K__multi__imply,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Imp_a @ B @ C ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ A2 @ B ) @ C ) ) ) ).

% K_multi_imply
thf(fact_11_fm_Odistinct_I25_J,axiom,
    ! [X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( ( episte3685526487207141399c_fm_a @ X41 @ X42 )
     != ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.distinct(25)
thf(fact_12_fm_Odistinct_I25_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Con_a @ X41 @ X42 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(25)
thf(fact_13_K__imp__trans,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,R: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ Q ) )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ Q @ R ) )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ R ) ) ) ) ).

% K_imp_trans
thf(fact_14_K__imp__trans,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans
thf(fact_15_K__imp__trans_H,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,Q: episte740340785640729014c_fm_a,R: episte740340785640729014c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ Q @ R ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ P @ Q ) @ ( episte260752218777527565c_fm_a @ P @ R ) ) ) ) ).

% K_imp_trans'
thf(fact_16_K__imp__trans_H,axiom,
    ! [A: epistemic_fm_a > $o,Q: epistemic_fm_a,R: epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans'
thf(fact_17_eval_Osimps_I4_J,axiom,
    ! [G2: list_char > $o,H2: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ ( episte3685526487207141399c_fm_a @ P @ Q ) )
      = ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ P )
        & ( episte6292435812075825844c_fm_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_18_eval_Osimps_I4_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
        & ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_19_eval_Osimps_I5_J,axiom,
    ! [G2: list_char > $o,H2: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ ( episte260752218777527565c_fm_a @ P @ Q ) )
      = ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ P )
       => ( episte6292435812075825844c_fm_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_20_eval_Osimps_I5_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
       => ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_21_K__conjunction__in,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte3685526487207141399c_fm_a @ P @ Q ) ) @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_22_K__conjunction__in,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_23_K__conjunction__out,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte3685526487207141399c_fm_a @ P @ Q ) ) ) ) ).

% K_conjunction_out
thf(fact_24_K__conjunction__out,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) ) ) ).

% K_conjunction_out
thf(fact_25_K__conj__imply__factor,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,R: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) @ R ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte3685526487207141399c_fm_a @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_26_K__conj__imply__factor,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) @ R ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_27_A1,axiom,
    ! [P: epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ P )
     => ( epistemic_AK_a @ A @ P ) ) ).

% A1
thf(fact_28_deriv__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
       => ( ( epistemic_AK_a @ A @ P )
         => ( member6642669571620171971c_fm_a @ P @ V ) ) ) ) ).

% deriv_in_maximal
thf(fact_29_fm_Oinject_I5_J,axiom,
    ! [X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ( ( ( epistemic_K_a @ X61 @ X62 )
        = ( epistemic_K_a @ Y61 @ Y62 ) )
      = ( ( X61 = Y61 )
        & ( X62 = Y62 ) ) ) ).

% fm.inject(5)
thf(fact_30_fm_Oinject_I5_J,axiom,
    ! [X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ( ( ( episte5657488632024175118c_fm_a @ X61 @ X62 )
        = ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) )
      = ( ( X61 = Y61 )
        & ( X62 = Y62 ) ) ) ).

% fm.inject(5)
thf(fact_31_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H2: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte6292435812075825844c_fm_a @ Ux @ H2 @ ( episte5657488632024175118c_fm_a @ I @ P ) )
      = ( H2 @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ).

% eval.simps(6)
thf(fact_32_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H2: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ Ux @ H2 @ ( epistemic_K_a @ I @ P ) )
      = ( H2 @ ( epistemic_K_a @ I @ P ) ) ) ).

% eval.simps(6)
thf(fact_33_Ax,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a] :
      ( ( A @ P )
     => ( epistemic_AK_a @ A @ P ) ) ).

% Ax
thf(fact_34_R2,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,I: epistemic_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ P )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ).

% R2
thf(fact_35_R2,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( epistemic_AK_a @ A @ P )
     => ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ P ) ) ) ).

% R2
thf(fact_36_ax__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
       => ( ( A @ P )
         => ( member6642669571620171971c_fm_a @ P @ V ) ) ) ) ).

% ax_in_maximal
thf(fact_37_K__map,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,I: epistemic_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ Q ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) ) ) ).

% K_map
thf(fact_38_K__map,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,I: a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_map
thf(fact_39_K__A2_H,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ Q ) ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) ) ) ).

% K_A2'
thf(fact_40_K__A2_H,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_A2'
thf(fact_41_fm_Odistinct_I29_J,axiom,
    ! [X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( ( episte260752218777527565c_fm_a @ X51 @ X52 )
     != ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ).

% fm.distinct(29)
thf(fact_42_fm_Odistinct_I29_J,axiom,
    ! [X51: epistemic_fm_a,X52: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Imp_a @ X51 @ X52 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(29)
thf(fact_43_fm_Odistinct_I27_J,axiom,
    ! [X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( ( episte3685526487207141399c_fm_a @ X41 @ X42 )
     != ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ).

% fm.distinct(27)
thf(fact_44_fm_Odistinct_I27_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Con_a @ X41 @ X42 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(27)
thf(fact_45_AK_Osimps,axiom,
    ( episte3601224840237526918c_fm_a
    = ( ^ [A3: episte740340785640729014c_fm_a > $o,A4: episte740340785640729014c_fm_a] :
          ( ? [P2: episte740340785640729014c_fm_a] :
              ( ( A4 = P2 )
              & ! [G4: list_char > $o,H4: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G4 @ H4 @ P2 ) )
          | ? [I2: epistemic_fm_a,P2: episte740340785640729014c_fm_a,Q2: episte740340785640729014c_fm_a] :
              ( A4
              = ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ P2 @ Q2 ) ) ) @ ( episte5657488632024175118c_fm_a @ I2 @ Q2 ) ) )
          | ? [P2: episte740340785640729014c_fm_a] :
              ( ( A4 = P2 )
              & ( A3 @ P2 ) )
          | ? [P2: episte740340785640729014c_fm_a,Q2: episte740340785640729014c_fm_a] :
              ( ( A4 = Q2 )
              & ( episte3601224840237526918c_fm_a @ A3 @ P2 )
              & ( episte3601224840237526918c_fm_a @ A3 @ ( episte260752218777527565c_fm_a @ P2 @ Q2 ) ) )
          | ? [P2: episte740340785640729014c_fm_a,I2: epistemic_fm_a] :
              ( ( A4
                = ( episte5657488632024175118c_fm_a @ I2 @ P2 ) )
              & ( episte3601224840237526918c_fm_a @ A3 @ P2 ) ) ) ) ) ).

% AK.simps
thf(fact_46_AK_Osimps,axiom,
    ( epistemic_AK_a
    = ( ^ [A3: epistemic_fm_a > $o,A4: epistemic_fm_a] :
          ( ? [P2: epistemic_fm_a] :
              ( ( A4 = P2 )
              & ! [G4: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G4 @ H4 @ P2 ) )
          | ? [I2: a,P2: epistemic_fm_a,Q2: epistemic_fm_a] :
              ( A4
              = ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I2 @ P2 ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ Q2 ) ) ) @ ( epistemic_K_a @ I2 @ Q2 ) ) )
          | ? [P2: epistemic_fm_a] :
              ( ( A4 = P2 )
              & ( A3 @ P2 ) )
          | ? [P2: epistemic_fm_a,Q2: epistemic_fm_a] :
              ( ( A4 = Q2 )
              & ( epistemic_AK_a @ A3 @ P2 )
              & ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P2 @ Q2 ) ) )
          | ? [P2: epistemic_fm_a,I2: a] :
              ( ( A4
                = ( epistemic_K_a @ I2 @ P2 ) )
              & ( epistemic_AK_a @ A3 @ P2 ) ) ) ) ) ).

% AK.simps
thf(fact_47_AK_Ocases,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,A2: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ A2 )
     => ( ~ ! [G: list_char > $o,H: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G @ H @ A2 )
       => ( ! [I3: epistemic_fm_a,P3: episte740340785640729014c_fm_a,Q3: episte740340785640729014c_fm_a] :
              ( A2
             != ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ P3 ) @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ P3 @ Q3 ) ) ) @ ( episte5657488632024175118c_fm_a @ I3 @ Q3 ) ) )
         => ( ~ ( A @ A2 )
           => ( ! [P3: episte740340785640729014c_fm_a] :
                  ( ( episte3601224840237526918c_fm_a @ A @ P3 )
                 => ~ ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P3 @ A2 ) ) )
             => ~ ! [P3: episte740340785640729014c_fm_a] :
                    ( ? [I3: epistemic_fm_a] :
                        ( A2
                        = ( episte5657488632024175118c_fm_a @ I3 @ P3 ) )
                   => ~ ( episte3601224840237526918c_fm_a @ A @ P3 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_48_AK_Ocases,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ A2 )
     => ( ~ ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ A2 )
       => ( ! [I3: a,P3: epistemic_fm_a,Q3: epistemic_fm_a] :
              ( A2
             != ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P3 ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ Q3 ) ) ) @ ( epistemic_K_a @ I3 @ Q3 ) ) )
         => ( ~ ( A @ A2 )
           => ( ! [P3: epistemic_fm_a] :
                  ( ( epistemic_AK_a @ A @ P3 )
                 => ~ ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P3 @ A2 ) ) )
             => ~ ! [P3: epistemic_fm_a] :
                    ( ? [I3: a] :
                        ( A2
                        = ( epistemic_K_a @ I3 @ P3 ) )
                   => ~ ( epistemic_AK_a @ A @ P3 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_49_A2,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ Q ) ) ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) ) ).

% A2
thf(fact_50_A2,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).

% A2
thf(fact_51_consequent__in__maximal,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
       => ( ( member1118567890201975263c_fm_a @ P @ V )
         => ( ( member1118567890201975263c_fm_a @ ( episte260752218777527565c_fm_a @ P @ Q ) @ V )
           => ( member1118567890201975263c_fm_a @ Q @ V ) ) ) ) ) ).

% consequent_in_maximal
thf(fact_52_consequent__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
       => ( ( member6642669571620171971c_fm_a @ P @ V )
         => ( ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ V )
           => ( member6642669571620171971c_fm_a @ Q @ V ) ) ) ) ) ).

% consequent_in_maximal
thf(fact_53_K__trans,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,R: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ P @ Q ) @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ Q @ R ) @ ( episte260752218777527565c_fm_a @ P @ R ) ) ) ) ).

% K_trans
thf(fact_54_K__trans,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ Q @ R ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_trans
thf(fact_55_R1,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ P )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ Q ) )
       => ( episte3601224840237526918c_fm_a @ A @ Q ) ) ) ).

% R1
thf(fact_56_R1,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ P )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
       => ( epistemic_AK_a @ A @ Q ) ) ) ).

% R1
thf(fact_57_K__thm,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ Q @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte3685526487207141399c_fm_a @ P @ Q ) @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ).

% K_thm
thf(fact_58_K__thm,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Con_a @ P @ Q ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ).

% K_thm
thf(fact_59_MCS_Omaximal_Ocong,axiom,
    maxima3264069584562520521c_fm_a = maxima3264069584562520521c_fm_a ).

% MCS.maximal.cong
thf(fact_60_distribution,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).

% distribution
thf(fact_61_distribution,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).

% distribution
thf(fact_62_exactly__one__in__maximal,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
       => ( ( member1118567890201975263c_fm_a @ P @ V )
          = ( ~ ( member1118567890201975263c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ V ) ) ) ) ) ).

% exactly_one_in_maximal
thf(fact_63_exactly__one__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
       => ( ( member6642669571620171971c_fm_a @ P @ V )
          = ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ V ) ) ) ) ) ).

% exactly_one_in_maximal
thf(fact_64_duality__taut,axiom,
    ! [I: epistemic_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,G: list_char > $o,H: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G @ H @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ Q @ episte5073044243917183961c_fm_a ) ) ) @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ Q @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ) ).

% duality_taut
thf(fact_65_duality__taut,axiom,
    ! [I: a,P: epistemic_fm_a,Q: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ).

% duality_taut
thf(fact_66_K__LK,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ).

% K_LK
thf(fact_67_K__LK,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ).

% K_LK
thf(fact_68_K__L__dual,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ).

% K_L_dual
thf(fact_69_K__L__dual,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ).

% K_L_dual
thf(fact_70_Ax4_Ocases,axiom,
    ! [A2: episte740340785640729014c_fm_a] :
      ( ( episte4964217022932375845c_fm_a @ A2 )
     => ~ ! [I3: epistemic_fm_a,P3: episte740340785640729014c_fm_a] :
            ( A2
           != ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ P3 ) @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte5657488632024175118c_fm_a @ I3 @ P3 ) ) ) ) ) ).

% Ax4.cases
thf(fact_71_Ax4_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_Ax4_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P3 ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P3 ) ) ) ) ) ).

% Ax4.cases
thf(fact_72_Ax4_Osimps,axiom,
    ( episte4964217022932375845c_fm_a
    = ( ^ [A4: episte740340785640729014c_fm_a] :
        ? [I2: epistemic_fm_a,P2: episte740340785640729014c_fm_a] :
          ( A4
          = ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_73_Ax4_Osimps,axiom,
    ( epistemic_Ax4_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P2 ) @ ( epistemic_K_a @ I2 @ ( epistemic_K_a @ I2 @ P2 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_74_Ax4_Ointros,axiom,
    ! [I: epistemic_fm_a,P: episte740340785640729014c_fm_a] : ( episte4964217022932375845c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% Ax4.intros
thf(fact_75_Ax4_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_Ax4_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% Ax4.intros
thf(fact_76_AxT_Ocases,axiom,
    ! [A2: episte740340785640729014c_fm_a] :
      ( ( episte4361910824569934085c_fm_a @ A2 )
     => ~ ! [I3: epistemic_fm_a,P3: episte740340785640729014c_fm_a] :
            ( A2
           != ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ P3 ) @ P3 ) ) ) ).

% AxT.cases
thf(fact_77_AxT_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_AxT_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P3 ) @ P3 ) ) ) ).

% AxT.cases
thf(fact_78_mem__Collect__eq,axiom,
    ! [A2: a,P4: a > $o] :
      ( ( member_a @ A2 @ ( collect_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_79_mem__Collect__eq,axiom,
    ! [A2: produc2203834439629243303c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( member5029746173879296720c_fm_a @ A2 @ ( collec7391038856303340306c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_80_mem__Collect__eq,axiom,
    ! [A2: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ A2 @ ( collec2519470961442302949c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_81_mem__Collect__eq,axiom,
    ! [A2: epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ A2 @ ( collec4904205152690461189c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_82_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X: a] : ( member_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_83_Collect__mem__eq,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a] :
      ( ( collec7391038856303340306c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_84_Collect__mem__eq,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_85_Collect__mem__eq,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_86_Collect__cong,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
          = ( Q4 @ X2 ) )
     => ( ( collec4904205152690461189c_fm_a @ P4 )
        = ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_87_Collect__cong,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( P4 @ X2 )
          = ( Q4 @ X2 ) )
     => ( ( collec2519470961442302949c_fm_a @ P4 )
        = ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_88_Imp__intro,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( ( episte5333283044364550848c_fm_a @ M @ W @ P )
       => ( episte5333283044364550848c_fm_a @ M @ W @ Q ) )
     => ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) ) ) ).

% Imp_intro
thf(fact_89_Imp__intro,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
       => ( episte7081087998767065248c_fm_a @ M @ W @ Q ) )
     => ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) ) ) ).

% Imp_intro
thf(fact_90_semantics_Osimps_I1_J,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ~ ( episte5333283044364550848c_fm_a @ M @ W @ epistemic_FF_a ) ).

% semantics.simps(1)
thf(fact_91_semantics_Osimps_I1_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ~ ( episte7081087998767065248c_fm_a @ M @ W @ epistemic_FF_a ) ).

% semantics.simps(1)
thf(fact_92_fm_Odistinct_I7_J,axiom,
    ! [X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( episte5073044243917183961c_fm_a
     != ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.distinct(7)
thf(fact_93_fm_Odistinct_I7_J,axiom,
    ! [X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(7)
thf(fact_94_fm_Odistinct_I9_J,axiom,
    ! [X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( episte5073044243917183961c_fm_a
     != ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_95_fm_Odistinct_I9_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_96_fm_Odistinct_I5_J,axiom,
    ! [X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ( episte5073044243917183961c_fm_a
     != ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.distinct(5)
thf(fact_97_fm_Odistinct_I5_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(5)
thf(fact_98_semantics_Osimps_I5_J,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( episte5333283044364550848c_fm_a @ M @ W @ P )
       => ( episte5333283044364550848c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(5)
thf(fact_99_semantics_Osimps_I5_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
       => ( episte7081087998767065248c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(5)
thf(fact_100_eval_Osimps_I1_J,axiom,
    ! [Uu: list_char > $o,Uv: epistemic_fm_a > $o] :
      ~ ( epistemic_eval_a @ Uu @ Uv @ epistemic_FF_a ) ).

% eval.simps(1)
thf(fact_101_semantics_Osimps_I4_J,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( episte5333283044364550848c_fm_a @ M @ W @ P )
        & ( episte5333283044364550848c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(4)
thf(fact_102_semantics_Osimps_I4_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
        & ( episte7081087998767065248c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(4)
thf(fact_103_tautology,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ P )
     => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ).

% tautology
thf(fact_104_tautology,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ P )
     => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ).

% tautology
thf(fact_105_AxT_Ointros,axiom,
    ! [I: epistemic_fm_a,P: episte740340785640729014c_fm_a] : ( episte4361910824569934085c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ P ) ) ).

% AxT.intros
thf(fact_106_AxT_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_AxT_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ).

% AxT.intros
thf(fact_107_AxT_Osimps,axiom,
    ( episte4361910824569934085c_fm_a
    = ( ^ [A4: episte740340785640729014c_fm_a] :
        ? [I2: epistemic_fm_a,P2: episte740340785640729014c_fm_a] :
          ( A4
          = ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ P2 ) ) ) ) ).

% AxT.simps
thf(fact_108_AxT_Osimps,axiom,
    ( epistemic_AxT_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P2 ) @ P2 ) ) ) ) ).

% AxT.simps
thf(fact_109_K4__L,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4964217022932375845c_fm_a @ A )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ).

% K4_L
thf(fact_110_K4__L,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% K4_L
thf(fact_111_T__L,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4361910824569934085c_fm_a @ A )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ).

% T_L
thf(fact_112_T__L,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% T_L
thf(fact_113_AxB_Ointros,axiom,
    ! [P: episte740340785640729014c_fm_a,I: epistemic_fm_a] : ( episte89022042721419671c_fm_a @ ( episte260752218777527565c_fm_a @ P @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ).

% AxB.intros
thf(fact_114_AxB_Ointros,axiom,
    ! [P: epistemic_fm_a,I: a] : ( epistemic_AxB_a @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% AxB.intros
thf(fact_115_AxB_Osimps,axiom,
    ( episte89022042721419671c_fm_a
    = ( ^ [A4: episte740340785640729014c_fm_a] :
        ? [P2: episte740340785640729014c_fm_a,I2: epistemic_fm_a] :
          ( A4
          = ( episte260752218777527565c_fm_a @ P2 @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ P2 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ).

% AxB.simps
thf(fact_116_AxB_Osimps,axiom,
    ( epistemic_AxB_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [P2: epistemic_fm_a,I2: a] :
          ( A4
          = ( epistemic_Imp_a @ P2 @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% AxB.simps
thf(fact_117_AxB_Ocases,axiom,
    ! [A2: episte740340785640729014c_fm_a] :
      ( ( episte89022042721419671c_fm_a @ A2 )
     => ~ ! [P3: episte740340785640729014c_fm_a,I3: epistemic_fm_a] :
            ( A2
           != ( episte260752218777527565c_fm_a @ P3 @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ P3 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ).

% AxB.cases
thf(fact_118_AxB_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_AxB_a @ A2 )
     => ~ ! [P3: epistemic_fm_a,I3: a] :
            ( A2
           != ( epistemic_Imp_a @ P3 @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% AxB.cases
thf(fact_119_Ax5_Ointros,axiom,
    ! [I: epistemic_fm_a,P: episte740340785640729014c_fm_a] : ( episte7251237963447243492c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ).

% Ax5.intros
thf(fact_120_Ax5_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_Ax5_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% Ax5.intros
thf(fact_121_Ax5_Osimps,axiom,
    ( episte7251237963447243492c_fm_a
    = ( ^ [A4: episte740340785640729014c_fm_a] :
        ? [I2: epistemic_fm_a,P2: episte740340785640729014c_fm_a] :
          ( A4
          = ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ P2 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ ( episte260752218777527565c_fm_a @ P2 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_122_Ax5_Osimps,axiom,
    ( epistemic_Ax5_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_123_Ax5_Ocases,axiom,
    ! [A2: episte740340785640729014c_fm_a] :
      ( ( episte7251237963447243492c_fm_a @ A2 )
     => ~ ! [I3: epistemic_fm_a,P3: episte740340785640729014c_fm_a] :
            ( A2
           != ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ P3 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I3 @ ( episte260752218777527565c_fm_a @ P3 @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ).

% Ax5.cases
thf(fact_124_Ax5_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_Ax5_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% Ax5.cases
thf(fact_125_KB4__5,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte89022042721419671c_fm_a @ A )
     => ( ( ord_le7240545311762076327fm_a_o @ episte4964217022932375845c_fm_a @ A )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ).

% KB4_5
thf(fact_126_KB4__5,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% KB4_5
thf(fact_127_K5__L,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte7251237963447243492c_fm_a @ A )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% K5_L
thf(fact_128_K5__L,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% K5_L
thf(fact_129_S5_H__4,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4361910824569934085c_fm_a @ A )
     => ( ( ord_le7240545311762076327fm_a_o @ episte7251237963447243492c_fm_a @ A )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_130_S5_H__4,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_131_S5_H__B,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4361910824569934085c_fm_a @ A )
     => ( ( ord_le7240545311762076327fm_a_o @ episte7251237963447243492c_fm_a @ A )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ).

% S5'_B
thf(fact_132_S5_H__B,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% S5'_B
thf(fact_133_predicate1I,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( Q4 @ X2 ) )
     => ( ord_le4043730696559282883fm_a_o @ P4 @ Q4 ) ) ).

% predicate1I
thf(fact_134_order__refl,axiom,
    ! [X3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X3 @ X3 ) ).

% order_refl
thf(fact_135_order__refl,axiom,
    ! [X3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X3 @ X3 ) ).

% order_refl
thf(fact_136_dual__order_Orefl,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ A2 ) ).

% dual_order.refl
thf(fact_137_dual__order_Orefl,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ A2 ) ).

% dual_order.refl
thf(fact_138_le__funD,axiom,
    ! [F: epistemic_fm_a > $o,G2: epistemic_fm_a > $o,X3: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ F @ G2 )
     => ( ord_less_eq_o @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ).

% le_funD
thf(fact_139_le__funE,axiom,
    ! [F: epistemic_fm_a > $o,G2: epistemic_fm_a > $o,X3: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ F @ G2 )
     => ( ord_less_eq_o @ ( F @ X3 ) @ ( G2 @ X3 ) ) ) ).

% le_funE
thf(fact_140_le__funI,axiom,
    ! [F: epistemic_fm_a > $o,G2: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a] : ( ord_less_eq_o @ ( F @ X2 ) @ ( G2 @ X2 ) )
     => ( ord_le4043730696559282883fm_a_o @ F @ G2 ) ) ).

% le_funI
thf(fact_141_le__fun__def,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [F2: epistemic_fm_a > $o,G4: epistemic_fm_a > $o] :
        ! [X: epistemic_fm_a] : ( ord_less_eq_o @ ( F2 @ X ) @ ( G4 @ X ) ) ) ) ).

% le_fun_def
thf(fact_142_predicate1D,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,X3: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ P4 @ Q4 )
     => ( ( P4 @ X3 )
       => ( Q4 @ X3 ) ) ) ).

% predicate1D
thf(fact_143_rev__predicate1D,axiom,
    ! [P4: epistemic_fm_a > $o,X3: epistemic_fm_a,Q4: epistemic_fm_a > $o] :
      ( ( P4 @ X3 )
     => ( ( ord_le4043730696559282883fm_a_o @ P4 @ Q4 )
       => ( Q4 @ X3 ) ) ) ).

% rev_predicate1D
thf(fact_144_verit__comp__simplify1_I2_J,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ A2 ) ).

% verit_comp_simplify1(2)
thf(fact_145_verit__comp__simplify1_I2_J,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ A2 ) ).

% verit_comp_simplify1(2)
thf(fact_146_consistent__hereditary,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,S2: set_Epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( ( ord_le3275665582123262618c_fm_a @ S2 @ S )
       => ( episte2285483198712856226tent_a @ A @ S2 ) ) ) ).

% consistent_hereditary
thf(fact_147_maximal__extension,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ~ ! [W2: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ V @ W2 )
           => ( ( episte2285483198712856226tent_a @ A @ W2 )
             => ~ ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W2 ) ) ) ) ).

% maximal_extension
thf(fact_148_order__antisym__conv,axiom,
    ! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
     => ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
        = ( X3 = Y ) ) ) ).

% order_antisym_conv
thf(fact_149_order__antisym__conv,axiom,
    ! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
     => ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
        = ( X3 = Y ) ) ) ).

% order_antisym_conv
thf(fact_150_ord__le__eq__subst,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_151_ord__le__eq__subst,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_152_ord__le__eq__subst,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_153_ord__le__eq__subst,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_154_ord__eq__le__subst,axiom,
    ! [A2: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_155_ord__eq__le__subst,axiom,
    ! [A2: set_Epistemic_fm_a,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_156_ord__eq__le__subst,axiom,
    ! [A2: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_157_ord__eq__le__subst,axiom,
    ! [A2: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( A2
        = ( F @ B ) )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_158_order__eq__refl,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
      ( ( X3 = Y )
     => ( ord_le4043730696559282883fm_a_o @ X3 @ Y ) ) ).

% order_eq_refl
thf(fact_159_order__eq__refl,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( X3 = Y )
     => ( ord_le3275665582123262618c_fm_a @ X3 @ Y ) ) ).

% order_eq_refl
thf(fact_160_order__subst2,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ord_le4043730696559282883fm_a_o @ ( F @ B ) @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_161_order__subst2,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ ( F @ B ) @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_162_order__subst2,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ord_le4043730696559282883fm_a_o @ ( F @ B ) @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_163_order__subst2,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ ( F @ B ) @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ A2 ) @ C ) ) ) ) ).

% order_subst2
thf(fact_164_order__subst1,axiom,
    ! [A2: epistemic_fm_a > $o,F: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ B ) )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_165_order__subst1,axiom,
    ! [A2: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ B ) )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le4043730696559282883fm_a_o @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_166_order__subst1,axiom,
    ! [A2: set_Epistemic_fm_a,F: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ B ) )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_167_order__subst1,axiom,
    ! [A2: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ B ) )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X2 @ Y2 )
             => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
         => ( ord_le3275665582123262618c_fm_a @ A2 @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_168_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: epistemic_fm_a > $o,Z: epistemic_fm_a > $o] : ( Y3 = Z ) )
    = ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
          ( ( ord_le4043730696559282883fm_a_o @ A4 @ B2 )
          & ( ord_le4043730696559282883fm_a_o @ B2 @ A4 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_169_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_Epistemic_fm_a,Z: set_Epistemic_fm_a] : ( Y3 = Z ) )
    = ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ A4 @ B2 )
          & ( ord_le3275665582123262618c_fm_a @ B2 @ A4 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_170_antisym,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_171_antisym,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% antisym
thf(fact_172_dual__order_Otrans,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
     => ( ( ord_le4043730696559282883fm_a_o @ C @ B )
       => ( ord_le4043730696559282883fm_a_o @ C @ A2 ) ) ) ).

% dual_order.trans
thf(fact_173_dual__order_Otrans,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
     => ( ( ord_le3275665582123262618c_fm_a @ C @ B )
       => ( ord_le3275665582123262618c_fm_a @ C @ A2 ) ) ) ).

% dual_order.trans
thf(fact_174_dual__order_Oantisym,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
     => ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
       => ( A2 = B ) ) ) ).

% dual_order.antisym
thf(fact_175_dual__order_Oantisym,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
     => ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
       => ( A2 = B ) ) ) ).

% dual_order.antisym
thf(fact_176_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: epistemic_fm_a > $o,Z: epistemic_fm_a > $o] : ( Y3 = Z ) )
    = ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
          ( ( ord_le4043730696559282883fm_a_o @ B2 @ A4 )
          & ( ord_le4043730696559282883fm_a_o @ A4 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_177_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_Epistemic_fm_a,Z: set_Epistemic_fm_a] : ( Y3 = Z ) )
    = ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ B2 @ A4 )
          & ( ord_le3275665582123262618c_fm_a @ A4 @ B2 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_178_order__trans,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
     => ( ( ord_le4043730696559282883fm_a_o @ Y @ Z2 )
       => ( ord_le4043730696559282883fm_a_o @ X3 @ Z2 ) ) ) ).

% order_trans
thf(fact_179_order__trans,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
     => ( ( ord_le3275665582123262618c_fm_a @ Y @ Z2 )
       => ( ord_le3275665582123262618c_fm_a @ X3 @ Z2 ) ) ) ).

% order_trans
thf(fact_180_order_Otrans,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).

% order.trans
thf(fact_181_order_Otrans,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).

% order.trans
thf(fact_182_order__antisym,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
     => ( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
       => ( X3 = Y ) ) ) ).

% order_antisym
thf(fact_183_order__antisym,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
     => ( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
       => ( X3 = Y ) ) ) ).

% order_antisym
thf(fact_184_ord__le__eq__trans,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( B = C )
       => ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_185_ord__le__eq__trans,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( B = C )
       => ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_186_ord__eq__le__trans,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( A2 = B )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ C )
       => ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_187_ord__eq__le__trans,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( A2 = B )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C )
       => ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_188_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: epistemic_fm_a > $o,Z: epistemic_fm_a > $o] : ( Y3 = Z ) )
    = ( ^ [X: epistemic_fm_a > $o,Y4: epistemic_fm_a > $o] :
          ( ( ord_le4043730696559282883fm_a_o @ X @ Y4 )
          & ( ord_le4043730696559282883fm_a_o @ Y4 @ X ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_189_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_Epistemic_fm_a,Z: set_Epistemic_fm_a] : ( Y3 = Z ) )
    = ( ^ [X: set_Epistemic_fm_a,Y4: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ X @ Y4 )
          & ( ord_le3275665582123262618c_fm_a @ Y4 @ X ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_190_Greatest__equality,axiom,
    ! [P4: ( epistemic_fm_a > $o ) > $o,X3: epistemic_fm_a > $o] :
      ( ( P4 @ X3 )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ( P4 @ Y2 )
           => ( ord_le4043730696559282883fm_a_o @ Y2 @ X3 ) )
       => ( ( order_253494837916242250fm_a_o @ P4 )
          = X3 ) ) ) ).

% Greatest_equality
thf(fact_191_Greatest__equality,axiom,
    ! [P4: set_Epistemic_fm_a > $o,X3: set_Epistemic_fm_a] :
      ( ( P4 @ X3 )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ( P4 @ Y2 )
           => ( ord_le3275665582123262618c_fm_a @ Y2 @ X3 ) )
       => ( ( order_4585748725732241747c_fm_a @ P4 )
          = X3 ) ) ) ).

% Greatest_equality
thf(fact_192_GreatestI2__order,axiom,
    ! [P4: ( epistemic_fm_a > $o ) > $o,X3: epistemic_fm_a > $o,Q4: ( epistemic_fm_a > $o ) > $o] :
      ( ( P4 @ X3 )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ( P4 @ Y2 )
           => ( ord_le4043730696559282883fm_a_o @ Y2 @ X3 ) )
       => ( ! [X2: epistemic_fm_a > $o] :
              ( ( P4 @ X2 )
             => ( ! [Y5: epistemic_fm_a > $o] :
                    ( ( P4 @ Y5 )
                   => ( ord_le4043730696559282883fm_a_o @ Y5 @ X2 ) )
               => ( Q4 @ X2 ) ) )
         => ( Q4 @ ( order_253494837916242250fm_a_o @ P4 ) ) ) ) ) ).

% GreatestI2_order
thf(fact_193_GreatestI2__order,axiom,
    ! [P4: set_Epistemic_fm_a > $o,X3: set_Epistemic_fm_a,Q4: set_Epistemic_fm_a > $o] :
      ( ( P4 @ X3 )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ( P4 @ Y2 )
           => ( ord_le3275665582123262618c_fm_a @ Y2 @ X3 ) )
       => ( ! [X2: set_Epistemic_fm_a] :
              ( ( P4 @ X2 )
             => ( ! [Y5: set_Epistemic_fm_a] :
                    ( ( P4 @ Y5 )
                   => ( ord_le3275665582123262618c_fm_a @ Y5 @ X2 ) )
               => ( Q4 @ X2 ) ) )
         => ( Q4 @ ( order_4585748725732241747c_fm_a @ P4 ) ) ) ) ) ).

% GreatestI2_order
thf(fact_194_le__rel__bool__arg__iff,axiom,
    ( ord_le2986116216980733324fm_a_o
    = ( ^ [X4: $o > epistemic_fm_a > $o,Y6: $o > epistemic_fm_a > $o] :
          ( ( ord_le4043730696559282883fm_a_o @ ( X4 @ $false ) @ ( Y6 @ $false ) )
          & ( ord_le4043730696559282883fm_a_o @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).

% le_rel_bool_arg_iff
thf(fact_195_le__rel__bool__arg__iff,axiom,
    ( ord_le1382570192702674727c_fm_a
    = ( ^ [X4: $o > set_Epistemic_fm_a,Y6: $o > set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( X4 @ $false ) @ ( Y6 @ $false ) )
          & ( ord_le3275665582123262618c_fm_a @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).

% le_rel_bool_arg_iff
thf(fact_196_fm_Opred__mono,axiom,
    ! [P4: a > $o,Pa: a > $o] :
      ( ( ord_less_eq_a_o @ P4 @ Pa )
     => ( ord_le4043730696559282883fm_a_o @ ( epistemic_pred_fm_a @ P4 ) @ ( epistemic_pred_fm_a @ Pa ) ) ) ).

% fm.pred_mono
thf(fact_197_fm_Opred__mono,axiom,
    ! [P4: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ P4 @ Pa )
     => ( ord_le7240545311762076327fm_a_o @ ( episte3114992851182798545c_fm_a @ P4 ) @ ( episte3114992851182798545c_fm_a @ Pa ) ) ) ).

% fm.pred_mono
thf(fact_198_S5_H__S5,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_Ax5_a @ P2 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_AxB_a @ P2 )
            | ( epistemic_Ax4_a @ P2 ) )
        @ P ) ) ).

% S5'_S5
thf(fact_199_S5__S5_H,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_AxB_a @ P2 )
            | ( epistemic_Ax4_a @ P2 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_Ax5_a @ P2 ) )
        @ P ) ) ).

% S5_S5'
thf(fact_200_AxB__symmetric_H,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,W3: set_Ep8485816078964734998c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte89022042721419671c_fm_a @ A )
     => ( ( episte704884124137261758c_fm_a @ A @ V )
       => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
         => ( ( episte704884124137261758c_fm_a @ A @ W3 )
           => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W3 )
             => ( ( member7847018790254331967c_fm_a @ W3
                  @ ( collec6235220954039818881c_fm_a
                    @ ( ord_le3671305448118956982c_fm_a
                      @ ( collec7281052159120012321c_fm_a
                        @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ V ) ) ) ) )
               => ( member7847018790254331967c_fm_a @ V
                  @ ( collec6235220954039818881c_fm_a
                    @ ( ord_le3671305448118956982c_fm_a
                      @ ( collec7281052159120012321c_fm_a
                        @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ W3 ) ) ) ) ) ) ) ) ) ) ) ).

% AxB_symmetric'
thf(fact_201_AxB__symmetric_H,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
         => ( ( episte2285483198712856226tent_a @ A @ W3 )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W3 )
             => ( ( member536094252920883875c_fm_a @ W3
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V ) ) ) ) )
               => ( member536094252920883875c_fm_a @ V
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ W3 ) ) ) ) ) ) ) ) ) ) ) ).

% AxB_symmetric'
thf(fact_202_Ax5__Euclidean,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,U: set_Ep8485816078964734998c_fm_a,V: set_Ep8485816078964734998c_fm_a,W3: set_Ep8485816078964734998c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte7251237963447243492c_fm_a @ A )
     => ( ( episte704884124137261758c_fm_a @ A @ U )
       => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ U )
         => ( ( episte704884124137261758c_fm_a @ A @ V )
           => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
             => ( ( episte704884124137261758c_fm_a @ A @ W3 )
               => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W3 )
                 => ( ( member7847018790254331967c_fm_a @ V
                      @ ( collec6235220954039818881c_fm_a
                        @ ( ord_le3671305448118956982c_fm_a
                          @ ( collec7281052159120012321c_fm_a
                            @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ U ) ) ) ) )
                   => ( ( member7847018790254331967c_fm_a @ W3
                        @ ( collec6235220954039818881c_fm_a
                          @ ( ord_le3671305448118956982c_fm_a
                            @ ( collec7281052159120012321c_fm_a
                              @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ U ) ) ) ) )
                     => ( member7847018790254331967c_fm_a @ W3
                        @ ( collec6235220954039818881c_fm_a
                          @ ( ord_le3671305448118956982c_fm_a
                            @ ( collec7281052159120012321c_fm_a
                              @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% Ax5_Euclidean
thf(fact_203_Ax5__Euclidean,axiom,
    ! [A: epistemic_fm_a > $o,U: set_Epistemic_fm_a,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ U )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ U )
         => ( ( episte2285483198712856226tent_a @ A @ V )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
             => ( ( episte2285483198712856226tent_a @ A @ W3 )
               => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W3 )
                 => ( ( member536094252920883875c_fm_a @ V
                      @ ( collec2519470961442302949c_fm_a
                        @ ( ord_le3275665582123262618c_fm_a
                          @ ( collec4904205152690461189c_fm_a
                            @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ U ) ) ) ) )
                   => ( ( member536094252920883875c_fm_a @ W3
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ U ) ) ) ) )
                     => ( member536094252920883875c_fm_a @ W3
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% Ax5_Euclidean
thf(fact_204_Ax4__transitive,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,W3: set_Ep8485816078964734998c_fm_a,I: epistemic_fm_a,U: set_Ep8485816078964734998c_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4964217022932375845c_fm_a @ A )
     => ( ( episte704884124137261758c_fm_a @ A @ V )
       => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
         => ( ( member7847018790254331967c_fm_a @ W3
              @ ( collec6235220954039818881c_fm_a
                @ ( ord_le3671305448118956982c_fm_a
                  @ ( collec7281052159120012321c_fm_a
                    @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ V ) ) ) ) )
           => ( ( member7847018790254331967c_fm_a @ U
                @ ( collec6235220954039818881c_fm_a
                  @ ( ord_le3671305448118956982c_fm_a
                    @ ( collec7281052159120012321c_fm_a
                      @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ W3 ) ) ) ) )
             => ( member7847018790254331967c_fm_a @ U
                @ ( collec6235220954039818881c_fm_a
                  @ ( ord_le3671305448118956982c_fm_a
                    @ ( collec7281052159120012321c_fm_a
                      @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ).

% Ax4_transitive
thf(fact_205_Ax4__transitive,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,W3: set_Epistemic_fm_a,I: a,U: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
         => ( ( member536094252920883875c_fm_a @ W3
              @ ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V ) ) ) ) )
           => ( ( member536094252920883875c_fm_a @ U
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ W3 ) ) ) ) )
             => ( member536094252920883875c_fm_a @ U
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ) ) ).

% Ax4_transitive
thf(fact_206_AxT__reflexive,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4361910824569934085c_fm_a @ A )
     => ( ( episte704884124137261758c_fm_a @ A @ V )
       => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
         => ( member7847018790254331967c_fm_a @ V
            @ ( collec6235220954039818881c_fm_a
              @ ( ord_le3671305448118956982c_fm_a
                @ ( collec7281052159120012321c_fm_a
                  @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ).

% AxT_reflexive
thf(fact_207_AxT__reflexive,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
         => ( member536094252920883875c_fm_a @ V
            @ ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V ) ) ) ) ) ) ) ) ).

% AxT_reflexive
thf(fact_208_fm_Opred__inject_I5_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: episte740340785640729014c_fm_a,Aa: episte740340785640729014c_fm_a] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ ( episte260752218777527565c_fm_a @ A2 @ Aa ) )
      = ( ( episte3114992851182798545c_fm_a @ P4 @ A2 )
        & ( episte3114992851182798545c_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(5)
thf(fact_209_fm_Opred__inject_I5_J,axiom,
    ! [P4: a > $o,A2: epistemic_fm_a,Aa: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Imp_a @ A2 @ Aa ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A2 )
        & ( epistemic_pred_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(5)
thf(fact_210_fm_Opred__inject_I6_J,axiom,
    ! [P4: a > $o,A2: a,Aa: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_K_a @ A2 @ Aa ) )
      = ( ( P4 @ A2 )
        & ( epistemic_pred_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(6)
thf(fact_211_fm_Opred__inject_I6_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: epistemic_fm_a,Aa: episte740340785640729014c_fm_a] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ ( episte5657488632024175118c_fm_a @ A2 @ Aa ) )
      = ( ( P4 @ A2 )
        & ( episte3114992851182798545c_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(6)
thf(fact_212_fm_Opred__inject_I4_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: episte740340785640729014c_fm_a,Aa: episte740340785640729014c_fm_a] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ ( episte3685526487207141399c_fm_a @ A2 @ Aa ) )
      = ( ( episte3114992851182798545c_fm_a @ P4 @ A2 )
        & ( episte3114992851182798545c_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(4)
thf(fact_213_fm_Opred__inject_I4_J,axiom,
    ! [P4: a > $o,A2: epistemic_fm_a,Aa: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Con_a @ A2 @ Aa ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A2 )
        & ( epistemic_pred_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(4)
thf(fact_214_fm_Opred__True,axiom,
    ( ( epistemic_pred_fm_a
      @ ^ [Uu2: a] : $true )
    = ( ^ [Uu2: epistemic_fm_a] : $true ) ) ).

% fm.pred_True
thf(fact_215_fm_Opred__True,axiom,
    ( ( episte3114992851182798545c_fm_a
      @ ^ [Uu2: epistemic_fm_a] : $true )
    = ( ^ [Uu2: episte740340785640729014c_fm_a] : $true ) ) ).

% fm.pred_True
thf(fact_216_fm_Opred__inject_I1_J,axiom,
    ! [P4: a > $o] : ( epistemic_pred_fm_a @ P4 @ epistemic_FF_a ) ).

% fm.pred_inject(1)
thf(fact_217_fm_Opred__inject_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] : ( episte3114992851182798545c_fm_a @ P4 @ episte5073044243917183961c_fm_a ) ).

% fm.pred_inject(1)
thf(fact_218_less__eq__set__def,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
          ( ord_le1568123225352354019fm_a_o
          @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A3 )
          @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_219_less__eq__set__def,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( ord_less_eq_a_o
          @ ^ [X: a] : ( member_a @ X @ A3 )
          @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_220_less__eq__set__def,axiom,
    ( ord_le8222437384497874983c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
          ( ord_le4942933042592423798fm_a_o
          @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A3 )
          @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_221_less__eq__set__def,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( ord_le4043730696559282883fm_a_o
          @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A3 )
          @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_222_pred__subset__eq,axiom,
    ! [R2: set_se5208064806568342746c_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( ord_le1568123225352354019fm_a_o
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ R2 )
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ S ) )
      = ( ord_le7112219575281605754c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_223_pred__subset__eq,axiom,
    ! [R2: set_a,S: set_a] :
      ( ( ord_less_eq_a_o
        @ ^ [X: a] : ( member_a @ X @ R2 )
        @ ^ [X: a] : ( member_a @ X @ S ) )
      = ( ord_less_eq_set_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_224_pred__subset__eq,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le4942933042592423798fm_a_o
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ R2 )
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ S ) )
      = ( ord_le8222437384497874983c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_225_pred__subset__eq,axiom,
    ! [R2: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ R2 )
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ S ) )
      = ( ord_le3275665582123262618c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_226_subsetI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( member536094252920883875c_fm_a @ X2 @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ A @ B4 ) ) ).

% subsetI
thf(fact_227_subsetI,axiom,
    ! [A: set_a,B4: set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ X2 @ B4 ) )
     => ( ord_less_eq_set_a @ A @ B4 ) ) ).

% subsetI
thf(fact_228_subsetI,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ! [X2: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X2 @ A )
         => ( member5029746173879296720c_fm_a @ X2 @ B4 ) )
     => ( ord_le8222437384497874983c_fm_a @ A @ B4 ) ) ).

% subsetI
thf(fact_229_subsetI,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ( member6642669571620171971c_fm_a @ X2 @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).

% subsetI
thf(fact_230_subset__antisym,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
       => ( A = B4 ) ) ) ).

% subset_antisym
thf(fact_231_Collect__subset,axiom,
    ! [A: set_a,P4: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ A )
            & ( P4 @ X ) ) )
      @ A ) ).

% Collect_subset
thf(fact_232_Collect__subset,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ord_le8222437384497874983c_fm_a
      @ ( collec7391038856303340306c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X @ A )
            & ( P4 @ X ) ) )
      @ A ) ).

% Collect_subset
thf(fact_233_Collect__subset,axiom,
    ! [A: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ord_le7112219575281605754c_fm_a
      @ ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ A )
            & ( P4 @ X ) ) )
      @ A ) ).

% Collect_subset
thf(fact_234_Collect__subset,axiom,
    ! [A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ord_le3275665582123262618c_fm_a
      @ ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ A )
            & ( P4 @ X ) ) )
      @ A ) ).

% Collect_subset
thf(fact_235_conj__subset__def,axiom,
    ! [A: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ A
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( P4 @ X )
              & ( Q4 @ X ) ) ) )
      = ( ( ord_le7112219575281605754c_fm_a @ A @ ( collec2519470961442302949c_fm_a @ P4 ) )
        & ( ord_le7112219575281605754c_fm_a @ A @ ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ) ).

% conj_subset_def
thf(fact_236_conj__subset__def,axiom,
    ! [A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( P4 @ X )
              & ( Q4 @ X ) ) ) )
      = ( ( ord_le3275665582123262618c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ P4 ) )
        & ( ord_le3275665582123262618c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ) ).

% conj_subset_def
thf(fact_237_prop__restrict,axiom,
    ! [X3: a,Z3: set_a,X5: set_a,P4: a > $o] :
      ( ( member_a @ X3 @ Z3 )
     => ( ( ord_less_eq_set_a @ Z3
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ X5 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_238_prop__restrict,axiom,
    ! [X3: produc2203834439629243303c_fm_a,Z3: set_Pr8948481099588399239c_fm_a,X5: set_Pr8948481099588399239c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( member5029746173879296720c_fm_a @ X3 @ Z3 )
     => ( ( ord_le8222437384497874983c_fm_a @ Z3
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ X5 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_239_prop__restrict,axiom,
    ! [X3: set_Epistemic_fm_a,Z3: set_se5208064806568342746c_fm_a,X5: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ X3 @ Z3 )
     => ( ( ord_le7112219575281605754c_fm_a @ Z3
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ X5 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_240_prop__restrict,axiom,
    ! [X3: epistemic_fm_a,Z3: set_Epistemic_fm_a,X5: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ X3 @ Z3 )
     => ( ( ord_le3275665582123262618c_fm_a @ Z3
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ X5 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_241_Collect__restrict,axiom,
    ! [X5: set_a,P4: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ X5 )
            & ( P4 @ X ) ) )
      @ X5 ) ).

% Collect_restrict
thf(fact_242_Collect__restrict,axiom,
    ! [X5: set_Pr8948481099588399239c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ord_le8222437384497874983c_fm_a
      @ ( collec7391038856303340306c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X @ X5 )
            & ( P4 @ X ) ) )
      @ X5 ) ).

% Collect_restrict
thf(fact_243_Collect__restrict,axiom,
    ! [X5: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ord_le7112219575281605754c_fm_a
      @ ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ X5 )
            & ( P4 @ X ) ) )
      @ X5 ) ).

% Collect_restrict
thf(fact_244_Collect__restrict,axiom,
    ! [X5: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ord_le3275665582123262618c_fm_a
      @ ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ X5 )
            & ( P4 @ X ) ) )
      @ X5 ) ).

% Collect_restrict
thf(fact_245_subset__CollectI,axiom,
    ! [B4: set_a,A: set_a,Q4: a > $o,P4: a > $o] :
      ( ( ord_less_eq_set_a @ B4 @ A )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ B4 )
           => ( ( Q4 @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_less_eq_set_a
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ B4 )
                & ( Q4 @ X ) ) )
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_246_subset__CollectI,axiom,
    ! [B4: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,Q4: produc2203834439629243303c_fm_a > $o,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( ord_le8222437384497874983c_fm_a @ B4 @ A )
     => ( ! [X2: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X2 @ B4 )
           => ( ( Q4 @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le8222437384497874983c_fm_a
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ B4 )
                & ( Q4 @ X ) ) )
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_247_subset__CollectI,axiom,
    ! [B4: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,Q4: set_Epistemic_fm_a > $o,P4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ B4 @ A )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ B4 )
           => ( ( Q4 @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le7112219575281605754c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ B4 )
                & ( Q4 @ X ) ) )
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_248_subset__CollectI,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a,Q4: epistemic_fm_a > $o,P4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ B4 )
           => ( ( Q4 @ X2 )
             => ( P4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ B4 )
                & ( Q4 @ X ) ) )
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_249_Collect__mono__iff,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q4 ) )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( P4 @ X )
           => ( Q4 @ X ) ) ) ) ).

% Collect_mono_iff
thf(fact_250_Collect__mono__iff,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q4 ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( P4 @ X )
           => ( Q4 @ X ) ) ) ) ).

% Collect_mono_iff
thf(fact_251_set__eq__subset,axiom,
    ( ( ^ [Y3: set_Epistemic_fm_a,Z: set_Epistemic_fm_a] : ( Y3 = Z ) )
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ A3 @ B3 )
          & ( ord_le3275665582123262618c_fm_a @ B3 @ A3 ) ) ) ) ).

% set_eq_subset
thf(fact_252_subset__trans,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ C2 )
       => ( ord_le3275665582123262618c_fm_a @ A @ C2 ) ) ) ).

% subset_trans
thf(fact_253_Collect__mono,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( Q4 @ X2 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ).

% Collect_mono
thf(fact_254_Collect__mono,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( Q4 @ X2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ).

% Collect_mono
thf(fact_255_subset__refl,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ A ) ).

% subset_refl
thf(fact_256_subset__iff,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
        ! [T: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ T @ A3 )
         => ( member536094252920883875c_fm_a @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_257_subset__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B3: set_a] :
        ! [T: a] :
          ( ( member_a @ T @ A3 )
         => ( member_a @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_258_subset__iff,axiom,
    ( ord_le8222437384497874983c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
        ! [T: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ T @ A3 )
         => ( member5029746173879296720c_fm_a @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_259_subset__iff,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
        ! [T: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ T @ A3 )
         => ( member6642669571620171971c_fm_a @ T @ B3 ) ) ) ) ).

% subset_iff
thf(fact_260_equalityD2,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A = B4 )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ).

% equalityD2
thf(fact_261_equalityD1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A = B4 )
     => ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).

% equalityD1
thf(fact_262_subset__eq,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
        ! [X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ A3 )
         => ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ).

% subset_eq
thf(fact_263_subset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B3: set_a] :
        ! [X: a] :
          ( ( member_a @ X @ A3 )
         => ( member_a @ X @ B3 ) ) ) ) ).

% subset_eq
thf(fact_264_subset__eq,axiom,
    ( ord_le8222437384497874983c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
        ! [X: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X @ A3 )
         => ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ).

% subset_eq
thf(fact_265_subset__eq,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
        ! [X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ A3 )
         => ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ).

% subset_eq
thf(fact_266_equalityE,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A = B4 )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
         => ~ ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ) ).

% equalityE
thf(fact_267_subsetD,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ( member536094252920883875c_fm_a @ C @ A )
       => ( member536094252920883875c_fm_a @ C @ B4 ) ) ) ).

% subsetD
thf(fact_268_subsetD,axiom,
    ! [A: set_a,B4: set_a,C: a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ( member_a @ C @ A )
       => ( member_a @ C @ B4 ) ) ) ).

% subsetD
thf(fact_269_subsetD,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a,C: produc2203834439629243303c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ A @ B4 )
     => ( ( member5029746173879296720c_fm_a @ C @ A )
       => ( member5029746173879296720c_fm_a @ C @ B4 ) ) ) ).

% subsetD
thf(fact_270_subsetD,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( member6642669571620171971c_fm_a @ C @ A )
       => ( member6642669571620171971c_fm_a @ C @ B4 ) ) ) ).

% subsetD
thf(fact_271_in__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ( member536094252920883875c_fm_a @ X3 @ A )
       => ( member536094252920883875c_fm_a @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_272_in__mono,axiom,
    ! [A: set_a,B4: set_a,X3: a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ( member_a @ X3 @ A )
       => ( member_a @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_273_in__mono,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a,X3: produc2203834439629243303c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ A @ B4 )
     => ( ( member5029746173879296720c_fm_a @ X3 @ A )
       => ( member5029746173879296720c_fm_a @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_274_in__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,X3: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( member6642669571620171971c_fm_a @ X3 @ A )
       => ( member6642669571620171971c_fm_a @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_275_subset__Collect__iff,axiom,
    ! [B4: set_a,A: set_a,P4: a > $o] :
      ( ( ord_less_eq_set_a @ B4 @ A )
     => ( ( ord_less_eq_set_a @ B4
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: a] :
              ( ( member_a @ X @ B4 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_276_subset__Collect__iff,axiom,
    ! [B4: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( ord_le8222437384497874983c_fm_a @ B4 @ A )
     => ( ( ord_le8222437384497874983c_fm_a @ B4
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X @ B4 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_277_subset__Collect__iff,axiom,
    ! [B4: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ B4 @ A )
     => ( ( ord_le7112219575281605754c_fm_a @ B4
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ B4 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_278_subset__Collect__iff,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ B4
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ B4 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_279_S5__S5_H__assms,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_AxB_a @ P2 )
                  | ( epistemic_Ax4_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_Ax5_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% S5_S5'_assms
thf(fact_280_Powp__mono,axiom,
    ! [A: epistemic_fm_a > $o,B4: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ B4 )
     => ( ord_le1568123225352354019fm_a_o @ ( powp_Epistemic_fm_a @ A ) @ ( powp_Epistemic_fm_a @ B4 ) ) ) ).

% Powp_mono
thf(fact_281_soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ! [M2: episte6182337868402532512t_unit,W4: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W4 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
           => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_282_soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte9194023259896155360t_unit > $o,P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ! [M2: episte9194023259896155360t_unit,W4: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member5029746173879296720c_fm_a @ W4 @ ( episte5714722596736476595t_unit @ M2 ) )
             => ( episte7505603015783396941c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
           => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_283_soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W4: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W4 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
           => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_284_soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte94448284482925344t_unit > $o,P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ! [M2: episte94448284482925344t_unit,W4: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W4 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
           => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_285_generalization,axiom,
    ! [P: epistemic_fm_a,W: a,M: episte6182337868402532512t_unit,I: a] :
      ( ! [M2: episte6182337868402532512t_unit,X2: a] :
          ( ( member_a @ X2 @ ( episte6926715892928323059t_unit @ M2 ) )
         => ( episte295617885132580260cs_a_a @ M2 @ X2 @ P ) )
     => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
       => ( episte295617885132580260cs_a_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_286_generalization,axiom,
    ! [P: epistemic_fm_a,W: produc2203834439629243303c_fm_a,M: episte9194023259896155360t_unit,I: a] :
      ( ! [M2: episte9194023259896155360t_unit,X2: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X2 @ ( episte5714722596736476595t_unit @ M2 ) )
         => ( episte7505603015783396941c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
       => ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_287_generalization,axiom,
    ! [P: episte740340785640729014c_fm_a,W: epistemic_fm_a,M: episte7841233106293114628t_unit,I: epistemic_fm_a] :
      ( ! [M2: episte7841233106293114628t_unit,X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ ( episte9016904500347944791t_unit @ M2 ) )
         => ( episte2906165861729879076c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte9016904500347944791t_unit @ M ) )
       => ( episte2906165861729879076c_fm_a @ M @ W @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_288_generalization,axiom,
    ! [P: episte740340785640729014c_fm_a,W: set_Epistemic_fm_a,M: episte540895788664713988t_unit,I: epistemic_fm_a] :
      ( ! [M2: episte540895788664713988t_unit,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte1037171729674672983t_unit @ M2 ) )
         => ( episte727306692928444932c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte1037171729674672983t_unit @ M ) )
       => ( episte727306692928444932c_fm_a @ M @ W @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_289_generalization,axiom,
    ! [P: episte740340785640729014c_fm_a,W: a,M: episte6869668086758133892t_unit,I: epistemic_fm_a] :
      ( ! [M2: episte6869668086758133892t_unit,X2: a] :
          ( ( member_a @ X2 @ ( episte5262195141974084311t_unit @ M2 ) )
         => ( episte1440391990539801864fm_a_a @ M2 @ X2 @ P ) )
     => ( ( member_a @ W @ ( episte5262195141974084311t_unit @ M ) )
       => ( episte1440391990539801864fm_a_a @ M @ W @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_290_generalization,axiom,
    ! [P: episte740340785640729014c_fm_a,W: produc2203834439629243303c_fm_a,M: episte692252130776546500t_unit,I: epistemic_fm_a] :
      ( ! [M2: episte692252130776546500t_unit,X2: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X2 @ ( episte5842432076962894487t_unit @ M2 ) )
         => ( episte7069945548607735217c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5842432076962894487t_unit @ M ) )
       => ( episte7069945548607735217c_fm_a @ M @ W @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_291_generalization,axiom,
    ! [P: epistemic_fm_a,W: epistemic_fm_a,M: episte94448284482925344t_unit,I: a] :
      ( ! [M2: episte94448284482925344t_unit,X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ ( episte6390737319716712051t_unit @ M2 ) )
         => ( episte5333283044364550848c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
       => ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_292_generalization,axiom,
    ! [P: epistemic_fm_a,W: set_Epistemic_fm_a,M: episte1560738328020401952t_unit,I: a] :
      ( ! [M2: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
         => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
       => ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% generalization
thf(fact_293_MCS__axioms,axiom,
    ! [A: epistemic_fm_a > $o] : ( maxima1924290459274269190c_fm_a @ ( episte2285483198712856226tent_a @ A ) ) ).

% MCS_axioms
thf(fact_294_dual__order_Opartial__preordering__axioms,axiom,
    ( partia8377733957543451565fm_a_o
    @ ^ [X: epistemic_fm_a > $o,Y4: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ Y4 @ X ) ) ).

% dual_order.partial_preordering_axioms
thf(fact_295_dual__order_Opartial__preordering__axioms,axiom,
    ( partia4735159733898207536c_fm_a
    @ ^ [X: set_Epistemic_fm_a,Y4: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ Y4 @ X ) ) ).

% dual_order.partial_preordering_axioms
thf(fact_296_inconsistent__finite,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ S )
     => ? [S3: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ S3 @ S )
          & ( finite3304564945125563331c_fm_a @ S3 )
          & ~ ( episte2285483198712856226tent_a @ A @ S3 ) ) ) ).

% inconsistent_finite
thf(fact_297_fm_Oexhaust,axiom,
    ! [Y: episte740340785640729014c_fm_a] :
      ( ( Y != episte5073044243917183961c_fm_a )
     => ( ! [X22: list_char] :
            ( Y
           != ( episte3759128466173231372c_fm_a @ X22 ) )
       => ( ! [X31: episte740340785640729014c_fm_a,X32: episte740340785640729014c_fm_a] :
              ( Y
             != ( episte6088726764479022859c_fm_a @ X31 @ X32 ) )
         => ( ! [X412: episte740340785640729014c_fm_a,X422: episte740340785640729014c_fm_a] :
                ( Y
               != ( episte3685526487207141399c_fm_a @ X412 @ X422 ) )
           => ( ! [X512: episte740340785640729014c_fm_a,X522: episte740340785640729014c_fm_a] :
                  ( Y
                 != ( episte260752218777527565c_fm_a @ X512 @ X522 ) )
             => ~ ! [X612: epistemic_fm_a,X622: episte740340785640729014c_fm_a] :
                    ( Y
                   != ( episte5657488632024175118c_fm_a @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_298_fm_Oexhaust,axiom,
    ! [Y: epistemic_fm_a] :
      ( ( Y != epistemic_FF_a )
     => ( ! [X22: list_char] :
            ( Y
           != ( epistemic_Pro_a @ X22 ) )
       => ( ! [X31: epistemic_fm_a,X32: epistemic_fm_a] :
              ( Y
             != ( epistemic_Dis_a @ X31 @ X32 ) )
         => ( ! [X412: epistemic_fm_a,X422: epistemic_fm_a] :
                ( Y
               != ( epistemic_Con_a @ X412 @ X422 ) )
           => ( ! [X512: epistemic_fm_a,X522: epistemic_fm_a] :
                  ( Y
                 != ( epistemic_Imp_a @ X512 @ X522 ) )
             => ~ ! [X612: a,X622: epistemic_fm_a] :
                    ( Y
                   != ( epistemic_K_a @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_299_fm_Oinject_I1_J,axiom,
    ! [X23: list_char,Y22: list_char] :
      ( ( ( epistemic_Pro_a @ X23 )
        = ( epistemic_Pro_a @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fm.inject(1)
thf(fact_300_fm_Oinject_I2_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( ( epistemic_Dis_a @ X312 @ X322 )
        = ( epistemic_Dis_a @ Y31 @ Y32 ) )
      = ( ( X312 = Y31 )
        & ( X322 = Y32 ) ) ) ).

% fm.inject(2)
thf(fact_301_fm_Oinject_I2_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ( ( ( episte6088726764479022859c_fm_a @ X312 @ X322 )
        = ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) )
      = ( ( X312 = Y31 )
        & ( X322 = Y32 ) ) ) ).

% fm.inject(2)
thf(fact_302_fm_Opred__inject_I3_J,axiom,
    ! [P4: a > $o,A2: epistemic_fm_a,Aa: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Dis_a @ A2 @ Aa ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A2 )
        & ( epistemic_pred_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(3)
thf(fact_303_fm_Opred__inject_I3_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: episte740340785640729014c_fm_a,Aa: episte740340785640729014c_fm_a] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ ( episte6088726764479022859c_fm_a @ A2 @ Aa ) )
      = ( ( episte3114992851182798545c_fm_a @ P4 @ A2 )
        & ( episte3114992851182798545c_fm_a @ P4 @ Aa ) ) ) ).

% fm.pred_inject(3)
thf(fact_304_fm_Odistinct_I11_J,axiom,
    ! [X23: list_char,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ( ( episte3759128466173231372c_fm_a @ X23 )
     != ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.distinct(11)
thf(fact_305_fm_Odistinct_I11_J,axiom,
    ! [X23: list_char,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X23 )
     != ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.distinct(11)
thf(fact_306_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte6182337868402532512t_unit,W4: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W4 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte6182337868402532512t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: a] :
                ( ( member_a @ X6 @ ( episte6926715892928323059t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte295617885132580260cs_a_a @ M3 @ X6 @ Xa ) )
                 => ( episte295617885132580260cs_a_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_307_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte9194023259896155360t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte9194023259896155360t_unit,W4: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member5029746173879296720c_fm_a @ W4 @ ( episte5714722596736476595t_unit @ M2 ) )
             => ( episte7505603015783396941c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte9194023259896155360t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X6 @ ( episte5714722596736476595t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte7505603015783396941c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte7505603015783396941c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_308_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W4: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W4 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte1560738328020401952t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_309_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte94448284482925344t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte94448284482925344t_unit,W4: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W4 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte94448284482925344t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_310_main_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit,X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
           => ( ! [Y4: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
             => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [Uu2: epistemic_fm_a] : $false
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>K
thf(fact_311_strong__completeness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
         => ( ! [Xa2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
           => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [Uu2: epistemic_fm_a] : $false
            @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>K
thf(fact_312_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte6182337868402532512t_unit,W4: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W4 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ? [Qs3: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
       => ! [M3: episte6182337868402532512t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: a] :
                ( ( member_a @ X6 @ ( episte6926715892928323059t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte295617885132580260cs_a_a @ M3 @ X6 @ Xa ) )
                 => ( episte295617885132580260cs_a_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_313_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte9194023259896155360t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte9194023259896155360t_unit,W4: produc2203834439629243303c_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member5029746173879296720c_fm_a @ W4 @ ( episte5714722596736476595t_unit @ M2 ) )
             => ( episte7505603015783396941c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ? [Qs3: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
       => ! [M3: episte9194023259896155360t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X6 @ ( episte5714722596736476595t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte7505603015783396941c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte7505603015783396941c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_314_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W4: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W4 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ? [Qs3: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
       => ! [M3: episte1560738328020401952t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_315_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte94448284482925344t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte94448284482925344t_unit,W4: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W4 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W4 @ P3 ) ) ) )
     => ( ? [Qs3: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) )
       => ! [M3: episte94448284482925344t_unit] :
            ( ( P4 @ M3 )
           => ! [X6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
                 => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_316_K__imply__weaken,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,Ps2: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
     => ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Ps2 ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps2 @ Q ) ) ) ) ).

% K_imply_weaken
thf(fact_317_strong__soundness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a,P4: episte94448284482925344t_unit > $o] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [Uu2: epistemic_fm_a] : $false
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( P4 @ M3 )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K
thf(fact_318_strong__soundness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a,P4: episte1560738328020401952t_unit > $o] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [Uu2: epistemic_fm_a] : $false
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( P4 @ M3 )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K
thf(fact_319_fm_Odistinct_I15_J,axiom,
    ! [X23: list_char,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( ( episte3759128466173231372c_fm_a @ X23 )
     != ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_320_fm_Odistinct_I15_J,axiom,
    ! [X23: list_char,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X23 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_321_fm_Odistinct_I21_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( ( episte6088726764479022859c_fm_a @ X312 @ X322 )
     != ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.distinct(21)
thf(fact_322_fm_Odistinct_I21_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X312 @ X322 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(21)
thf(fact_323_fm_Odistinct_I17_J,axiom,
    ! [X23: list_char,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( ( episte3759128466173231372c_fm_a @ X23 )
     != ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_324_fm_Odistinct_I17_J,axiom,
    ! [X23: list_char,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X23 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_325_fm_Odistinct_I23_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X312 @ X322 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(23)
thf(fact_326_fm_Odistinct_I23_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( ( episte6088726764479022859c_fm_a @ X312 @ X322 )
     != ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ).

% fm.distinct(23)
thf(fact_327_fm_Odistinct_I1_J,axiom,
    ! [X23: list_char] :
      ( epistemic_FF_a
     != ( epistemic_Pro_a @ X23 ) ) ).

% fm.distinct(1)
thf(fact_328_fm_Odistinct_I3_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.distinct(3)
thf(fact_329_fm_Odistinct_I3_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ( episte5073044243917183961c_fm_a
     != ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.distinct(3)
thf(fact_330_semantics_Osimps_I3_J,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( episte5333283044364550848c_fm_a @ M @ W @ P )
        | ( episte5333283044364550848c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(3)
thf(fact_331_semantics_Osimps_I3_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( episte7081087998767065248c_fm_a @ M @ W @ P )
        | ( episte7081087998767065248c_fm_a @ M @ W @ Q ) ) ) ).

% semantics.simps(3)
thf(fact_332_fm_Odistinct_I13_J,axiom,
    ! [X23: list_char,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ( ( episte3759128466173231372c_fm_a @ X23 )
     != ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_333_fm_Odistinct_I13_J,axiom,
    ! [X23: list_char,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X23 )
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_334_fm_Odistinct_I19_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ( ( episte6088726764479022859c_fm_a @ X312 @ X322 )
     != ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.distinct(19)
thf(fact_335_fm_Odistinct_I19_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X312 @ X322 )
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(19)
thf(fact_336_eval_Osimps_I2_J,axiom,
    ! [G2: list_char > $o,Uw: epistemic_fm_a > $o,X3: list_char] :
      ( ( epistemic_eval_a @ G2 @ Uw @ ( epistemic_Pro_a @ X3 ) )
      = ( G2 @ X3 ) ) ).

% eval.simps(2)
thf(fact_337_eval_Osimps_I3_J,axiom,
    ! [G2: list_char > $o,H2: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ ( episte6088726764479022859c_fm_a @ P @ Q ) )
      = ( ( episte6292435812075825844c_fm_a @ G2 @ H2 @ P )
        | ( episte6292435812075825844c_fm_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_338_eval_Osimps_I3_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
        | ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_339_tautology__imply__superset,axiom,
    ! [Ps: list_E5775909407618282812c_fm_a,Qs4: list_E5775909407618282812c_fm_a,R: episte740340785640729014c_fm_a] :
      ( ( ord_le3671305448118956982c_fm_a @ ( set_Ep2297100812554489931c_fm_a @ Ps ) @ ( set_Ep2297100812554489931c_fm_a @ Qs4 ) )
     => ! [G: list_char > $o,H: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G @ H @ ( episte260752218777527565c_fm_a @ ( episte1272216372155829993c_fm_a @ Ps @ R ) @ ( episte1272216372155829993c_fm_a @ Qs4 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_340_tautology__imply__superset,axiom,
    ! [Ps: list_Epistemic_fm_a,Qs4: list_Epistemic_fm_a,R: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Qs4 ) )
     => ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ Ps @ R ) @ ( epistemic_imply_a @ Qs4 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_341_order_Opartial__preordering__axioms,axiom,
    partia8377733957543451565fm_a_o @ ord_le4043730696559282883fm_a_o ).

% order.partial_preordering_axioms
thf(fact_342_order_Opartial__preordering__axioms,axiom,
    partia4735159733898207536c_fm_a @ ord_le3275665582123262618c_fm_a ).

% order.partial_preordering_axioms
thf(fact_343_consistent__def,axiom,
    ( episte2285483198712856226tent_a
    = ( ^ [A3: epistemic_fm_a > $o,S4: set_Epistemic_fm_a] :
          ~ ? [Qs: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ S4 )
              & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ epistemic_FF_a ) ) ) ) ) ).

% consistent_def
thf(fact_344_K__right__mp,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,Ps: list_E5775909407618282812c_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ Ps @ P ) )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ Ps @ ( episte260752218777527565c_fm_a @ P @ Q ) ) )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ Ps @ Q ) ) ) ) ).

% K_right_mp
thf(fact_345_K__right__mp,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ ( epistemic_Imp_a @ P @ Q ) ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) ) ) ) ).

% K_right_mp
thf(fact_346_finite__Collect__subsets,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [B3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ B3 @ A ) ) ) ) ).

% finite_Collect_subsets
thf(fact_347_strong__soundness_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( episte4583239219080210381t_unit @ M3 )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>5
thf(fact_348_strong__soundness_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte2449151000174023629t_unit @ M3 )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>5
thf(fact_349_strong__soundness_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( episte2438601301504999334t_unit @ M3 )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>B
thf(fact_350_strong__soundness_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte5478016696552465318t_unit @ M3 )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>B
thf(fact_351_strong__soundness_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( episte5633553332388074907t_unit @ M3 )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>T
thf(fact_352_strong__soundness_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte5648423998891577755t_unit @ M3 )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>T
thf(fact_353_strong__soundness_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte8364071018013720454t_unit @ M3 )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>4
thf(fact_354_strong__soundness_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( episte2264091934940175238t_unit @ M3 )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>4
thf(fact_355_finite__Collect__disjI,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( P4 @ X )
              | ( Q4 @ X ) ) ) )
      = ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
        & ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ) ).

% finite_Collect_disjI
thf(fact_356_finite__Collect__disjI,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( P4 @ X )
              | ( Q4 @ X ) ) ) )
      = ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
        & ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ) ).

% finite_Collect_disjI
thf(fact_357_finite__Collect__conjI,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
        | ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) ) )
     => ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( P4 @ X )
              & ( Q4 @ X ) ) ) ) ) ).

% finite_Collect_conjI
thf(fact_358_finite__Collect__conjI,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
        | ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) ) )
     => ( finite3304564945125563331c_fm_a
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( P4 @ X )
              & ( Q4 @ X ) ) ) ) ) ).

% finite_Collect_conjI
thf(fact_359_strong__completeness_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( episte2449151000174023629t_unit @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>5
thf(fact_360_main_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( episte2449151000174023629t_unit @ M4 )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>K\<^sub>5
thf(fact_361_refl__Euclid__equiv,axiom,
    ! [M: episte1560738328020401952t_unit] :
      ( ( episte5648423998891577755t_unit @ M )
     => ( ( episte2449151000174023629t_unit @ M )
       => ( ( episte5648423998891577755t_unit @ M )
          & ( episte5478016696552465318t_unit @ M )
          & ( episte8364071018013720454t_unit @ M ) ) ) ) ).

% refl_Euclid_equiv
thf(fact_362_refl__Euclid__equiv,axiom,
    ! [M: episte94448284482925344t_unit] :
      ( ( episte5633553332388074907t_unit @ M )
     => ( ( episte4583239219080210381t_unit @ M )
       => ( ( episte5633553332388074907t_unit @ M )
          & ( episte2438601301504999334t_unit @ M )
          & ( episte2264091934940175238t_unit @ M ) ) ) ) ).

% refl_Euclid_equiv
thf(fact_363_symm__trans__Euclid,axiom,
    ! [M: episte1560738328020401952t_unit] :
      ( ( episte5478016696552465318t_unit @ M )
     => ( ( episte8364071018013720454t_unit @ M )
       => ( episte2449151000174023629t_unit @ M ) ) ) ).

% symm_trans_Euclid
thf(fact_364_symm__trans__Euclid,axiom,
    ! [M: episte94448284482925344t_unit] :
      ( ( episte2438601301504999334t_unit @ M )
     => ( ( episte2264091934940175238t_unit @ M )
       => ( episte4583239219080210381t_unit @ M ) ) ) ).

% symm_trans_Euclid
thf(fact_365_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte8571156416534912283t_unit @ M )
          & ( episte820475350133869606t_unit @ M )
          & ( episte4939069199465351174t_unit @ M ) )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_366_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte3030712104470226139t_unit @ M )
          & ( episte2922248646238569446t_unit @ M )
          & ( episte9001638012126461894t_unit @ M ) )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_367_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte5648423998891577755t_unit @ M )
          & ( episte5478016696552465318t_unit @ M )
          & ( episte8364071018013720454t_unit @ M ) )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_368_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte5633553332388074907t_unit @ M )
          & ( episte2438601301504999334t_unit @ M )
          & ( episte2264091934940175238t_unit @ M ) )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_369_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte8571156416534912283t_unit @ M )
          & ( episte820475350133869606t_unit @ M )
          & ( episte4939069199465351174t_unit @ M ) )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_370_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte3030712104470226139t_unit @ M )
          & ( episte2922248646238569446t_unit @ M )
          & ( episte9001638012126461894t_unit @ M ) )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_371_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte5648423998891577755t_unit @ M )
          & ( episte5478016696552465318t_unit @ M )
          & ( episte8364071018013720454t_unit @ M ) )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_372_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte5633553332388074907t_unit @ M )
          & ( episte2438601301504999334t_unit @ M )
          & ( episte2264091934940175238t_unit @ M ) )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_373_strong__completeness_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M2 )
            & ( episte5478016696552465318t_unit @ M2 )
            & ( episte8364071018013720454t_unit @ M2 ) )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax5_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>5'
thf(fact_374_main_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( ( episte5648423998891577755t_unit @ M4 )
              & ( episte5478016696552465318t_unit @ M4 )
              & ( episte8364071018013720454t_unit @ M4 ) )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_Ax5_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>S\<^sub>5'
thf(fact_375_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte8571156416534912283t_unit @ M )
          & ( episte4939069199465351174t_unit @ M ) )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_376_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte3030712104470226139t_unit @ M )
          & ( episte9001638012126461894t_unit @ M ) )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_377_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte5648423998891577755t_unit @ M )
          & ( episte8364071018013720454t_unit @ M ) )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_378_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte5633553332388074907t_unit @ M )
          & ( episte2264091934940175238t_unit @ M ) )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_379_main_092_060_094sub_062S_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( ( episte5648423998891577755t_unit @ M4 )
              & ( episte5478016696552465318t_unit @ M4 )
              & ( episte8364071018013720454t_unit @ M4 ) )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_AxB_a @ P2 )
                  | ( epistemic_Ax4_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>S\<^sub>5
thf(fact_380_strong__completeness_092_060_094sub_062S_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M2 )
            & ( episte5478016696552465318t_unit @ M2 )
            & ( episte8364071018013720454t_unit @ M2 ) )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_AxB_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>5
thf(fact_381_neg__introspection,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I: a,P: epistemic_fm_a] :
      ( ( episte820475350133869606t_unit @ M )
     => ( ( episte4939069199465351174t_unit @ M )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_382_neg__introspection,axiom,
    ! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte2922248646238569446t_unit @ M )
     => ( ( episte9001638012126461894t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_383_neg__introspection,axiom,
    ! [M: episte7841233106293114628t_unit,W: epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte780273241712402954t_unit @ M )
     => ( ( episte7226253760293006826t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte9016904500347944791t_unit @ M ) )
         => ( episte2906165861729879076c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_384_neg__introspection,axiom,
    ! [M: episte540895788664713988t_unit,W: set_Epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte7189957130121897482t_unit @ M )
     => ( ( episte5721166466222043626t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte1037171729674672983t_unit @ M ) )
         => ( episte727306692928444932c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_385_neg__introspection,axiom,
    ! [M: episte6869668086758133892t_unit,W: a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte8385843561137097354t_unit @ M )
     => ( ( episte7620362419236157034t_unit @ M )
       => ( ( member_a @ W @ ( episte5262195141974084311t_unit @ M ) )
         => ( episte1440391990539801864fm_a_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_386_neg__introspection,axiom,
    ! [M: episte692252130776546500t_unit,W: produc2203834439629243303c_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte5368726661271454282t_unit @ M )
     => ( ( episte8989324696348716586t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5842432076962894487t_unit @ M ) )
         => ( episte7069945548607735217c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ episte5073044243917183961c_fm_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_387_neg__introspection,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte5478016696552465318t_unit @ M )
     => ( ( episte8364071018013720454t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_388_neg__introspection,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte2438601301504999334t_unit @ M )
     => ( ( episte2264091934940175238t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_389_not__finite__existsD,axiom,
    ! [P4: set_Epistemic_fm_a > $o] :
      ( ~ ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ? [X_1: set_Epistemic_fm_a] : ( P4 @ X_1 ) ) ).

% not_finite_existsD
thf(fact_390_not__finite__existsD,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ~ ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ? [X_1: epistemic_fm_a] : ( P4 @ X_1 ) ) ).

% not_finite_existsD
thf(fact_391_pigeonhole__infinite__rel,axiom,
    ! [A: set_a,B4: set_Epistemic_fm_a,R2: a > epistemic_fm_a > $o] :
      ( ~ ( finite_finite_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( ! [X2: a] :
              ( ( member_a @ X2 @ A )
             => ? [Xa2: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Xa2 @ B4 )
                  & ( R2 @ X2 @ Xa2 ) ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ B4 )
              & ~ ( finite_finite_a
                  @ ( collect_a
                    @ ^ [A4: a] :
                        ( ( member_a @ A4 @ A )
                        & ( R2 @ A4 @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite_rel
thf(fact_392_pigeonhole__infinite__rel,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,R2: produc2203834439629243303c_fm_a > epistemic_fm_a > $o] :
      ( ~ ( finite8252611493601906128c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( ! [X2: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X2 @ A )
             => ? [Xa2: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Xa2 @ B4 )
                  & ( R2 @ X2 @ Xa2 ) ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ B4 )
              & ~ ( finite8252611493601906128c_fm_a
                  @ ( collec7391038856303340306c_fm_a
                    @ ^ [A4: produc2203834439629243303c_fm_a] :
                        ( ( member5029746173879296720c_fm_a @ A4 @ A )
                        & ( R2 @ A4 @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite_rel
thf(fact_393_pigeonhole__infinite__rel,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a,R2: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ~ ( finite7364866884270929315c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ A )
             => ? [Xa2: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Xa2 @ B4 )
                  & ( R2 @ X2 @ Xa2 ) ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ B4 )
              & ~ ( finite7364866884270929315c_fm_a
                  @ ( collec2519470961442302949c_fm_a
                    @ ^ [A4: set_Epistemic_fm_a] :
                        ( ( member536094252920883875c_fm_a @ A4 @ A )
                        & ( R2 @ A4 @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite_rel
thf(fact_394_pigeonhole__infinite__rel,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,R2: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( ! [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ A )
             => ? [Xa2: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Xa2 @ B4 )
                  & ( R2 @ X2 @ Xa2 ) ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ B4 )
              & ~ ( finite3304564945125563331c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [A4: epistemic_fm_a] :
                        ( ( member6642669571620171971c_fm_a @ A4 @ A )
                        & ( R2 @ A4 @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite_rel
thf(fact_395_strong__completeness_092_060_094sub_062S_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M2 )
            & ( episte8364071018013720454t_unit @ M2 ) )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>4
thf(fact_396_main_092_060_094sub_062S_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( ( episte5648423998891577755t_unit @ M4 )
              & ( episte8364071018013720454t_unit @ M4 ) )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_Ax4_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>S\<^sub>4
thf(fact_397_strong__soundness_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax5_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte5478016696552465318t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5'
thf(fact_398_strong__soundness_092_060_094sub_062S_092_060_094sub_0625_H,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax5_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( ( episte5633553332388074907t_unit @ M3 )
            & ( episte2438601301504999334t_unit @ M3 )
            & ( episte2264091934940175238t_unit @ M3 ) )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5'
thf(fact_399_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte4939069199465351174t_unit @ M )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_400_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte9001638012126461894t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_401_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte8364071018013720454t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_402_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte2264091934940175238t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_403_strong__soundness_092_060_094sub_062S_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_AxB_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte5478016696552465318t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5
thf(fact_404_strong__soundness_092_060_094sub_062S_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_AxB_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( ( episte5633553332388074907t_unit @ M3 )
            & ( episte2438601301504999334t_unit @ M3 )
            & ( episte2264091934940175238t_unit @ M3 ) )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5
thf(fact_405_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte8571156416534912283t_unit @ M )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_406_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte3030712104470226139t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_407_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte5633553332388074907t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_408_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte5648423998891577755t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_409_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte820475350133869606t_unit @ M )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_410_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte2922248646238569446t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_411_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte2438601301504999334t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_412_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte5478016696552465318t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_413_finite__has__minimal2,axiom,
    ! [A: set_Epistemic_fm_a_o,A2: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( member4486839677911940090fm_a_o @ A2 @ A )
       => ? [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ A )
            & ( ord_le4043730696559282883fm_a_o @ X2 @ A2 )
            & ! [Xa2: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ Xa2 @ A )
               => ( ( ord_le4043730696559282883fm_a_o @ Xa2 @ X2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_minimal2
thf(fact_414_finite__has__minimal2,axiom,
    ! [A: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( member536094252920883875c_fm_a @ A2 @ A )
       => ? [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
            & ( ord_le3275665582123262618c_fm_a @ X2 @ A2 )
            & ! [Xa2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ Xa2 @ A )
               => ( ( ord_le3275665582123262618c_fm_a @ Xa2 @ X2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_minimal2
thf(fact_415_finite__has__maximal2,axiom,
    ! [A: set_Epistemic_fm_a_o,A2: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( member4486839677911940090fm_a_o @ A2 @ A )
       => ? [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ A )
            & ( ord_le4043730696559282883fm_a_o @ A2 @ X2 )
            & ! [Xa2: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ Xa2 @ A )
               => ( ( ord_le4043730696559282883fm_a_o @ X2 @ Xa2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_maximal2
thf(fact_416_finite__has__maximal2,axiom,
    ! [A: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( member536094252920883875c_fm_a @ A2 @ A )
       => ? [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
            & ( ord_le3275665582123262618c_fm_a @ A2 @ X2 )
            & ! [Xa2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ Xa2 @ A )
               => ( ( ord_le3275665582123262618c_fm_a @ X2 @ Xa2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_maximal2
thf(fact_417_finite__subset,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( finite3304564945125563331c_fm_a @ A ) ) ) ).

% finite_subset
thf(fact_418_infinite__super,axiom,
    ! [S: set_Epistemic_fm_a,T2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ S @ T2 )
     => ( ~ ( finite3304564945125563331c_fm_a @ S )
       => ~ ( finite3304564945125563331c_fm_a @ T2 ) ) ) ).

% infinite_super
thf(fact_419_rev__finite__subset,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ B4 )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
       => ( finite3304564945125563331c_fm_a @ A ) ) ) ).

% rev_finite_subset
thf(fact_420_pos__introspection,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I: a,P: epistemic_fm_a] :
      ( ( episte4939069199465351174t_unit @ M )
     => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
       => ( episte295617885132580260cs_a_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_421_pos__introspection,axiom,
    ! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte9001638012126461894t_unit @ M )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
       => ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_422_pos__introspection,axiom,
    ! [M: episte7841233106293114628t_unit,W: epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte7226253760293006826t_unit @ M )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte9016904500347944791t_unit @ M ) )
       => ( episte2906165861729879076c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_423_pos__introspection,axiom,
    ! [M: episte540895788664713988t_unit,W: set_Epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte5721166466222043626t_unit @ M )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte1037171729674672983t_unit @ M ) )
       => ( episte727306692928444932c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_424_pos__introspection,axiom,
    ! [M: episte6869668086758133892t_unit,W: a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte7620362419236157034t_unit @ M )
     => ( ( member_a @ W @ ( episte5262195141974084311t_unit @ M ) )
       => ( episte1440391990539801864fm_a_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_425_pos__introspection,axiom,
    ! [M: episte692252130776546500t_unit,W: produc2203834439629243303c_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte8989324696348716586t_unit @ M )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5842432076962894487t_unit @ M ) )
       => ( episte7069945548607735217c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ ( episte5657488632024175118c_fm_a @ I @ ( episte5657488632024175118c_fm_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_426_pos__introspection,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte8364071018013720454t_unit @ M )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
       => ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_427_pos__introspection,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte2264091934940175238t_unit @ M )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
       => ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_428_truth,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I: a,P: epistemic_fm_a] :
      ( ( episte8571156416534912283t_unit @ M )
     => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
       => ( episte295617885132580260cs_a_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_429_truth,axiom,
    ! [M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte3030712104470226139t_unit @ M )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
       => ( episte7505603015783396941c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_430_truth,axiom,
    ! [M: episte7841233106293114628t_unit,W: epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte2136517803509791359t_unit @ M )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte9016904500347944791t_unit @ M ) )
       => ( episte2906165861729879076c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_431_truth,axiom,
    ! [M: episte540895788664713988t_unit,W: set_Epistemic_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte7443042888565937791t_unit @ M )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte1037171729674672983t_unit @ M ) )
       => ( episte727306692928444932c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_432_truth,axiom,
    ! [M: episte6869668086758133892t_unit,W: a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte5208307268145159679t_unit @ M )
     => ( ( member_a @ W @ ( episte5262195141974084311t_unit @ M ) )
       => ( episte1440391990539801864fm_a_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_433_truth,axiom,
    ! [M: episte692252130776546500t_unit,W: produc2203834439629243303c_fm_a,I: epistemic_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte3499679942192063935t_unit @ M )
     => ( ( member5029746173879296720c_fm_a @ W @ ( episte5842432076962894487t_unit @ M ) )
       => ( episte7069945548607735217c_fm_a @ M @ W @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_434_truth,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte5648423998891577755t_unit @ M )
     => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
       => ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_435_truth,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,I: a,P: epistemic_fm_a] :
      ( ( episte5633553332388074907t_unit @ M )
     => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
       => ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ) ) ).

% truth
thf(fact_436_strong__soundness_092_060_094sub_062S_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X6 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>4
thf(fact_437_strong__soundness_092_060_094sub_062S_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ? [Qs3: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
          & ( epistemic_AK_a
            @ ^ [P2: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P2 )
                | ( epistemic_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs3 @ P ) ) )
     => ! [M3: episte94448284482925344t_unit] :
          ( ( ( episte5633553332388074907t_unit @ M3 )
            & ( episte2264091934940175238t_unit @ M3 ) )
         => ! [X6: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X6 @ ( episte6390737319716712051t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ Xa ) )
               => ( episte5333283044364550848c_fm_a @ M3 @ X6 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>4
thf(fact_438_main_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( episte8364071018013720454t_unit @ M4 )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>K\<^sub>4
thf(fact_439_strong__completeness_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( episte8364071018013720454t_unit @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>4
thf(fact_440_main_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( episte5648423998891577755t_unit @ M4 )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>T
thf(fact_441_strong__completeness_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( episte5648423998891577755t_unit @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>T
thf(fact_442_main_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M4: episte1560738328020401952t_unit] :
            ( ( episte5478016696552465318t_unit @ M4 )
           => ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Y4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y4 @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X @ Y4 ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X @ P ) ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% main\<^sub>K\<^sub>B
thf(fact_443_strong__completeness_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( episte5478016696552465318t_unit @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ? [Qs2: list_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
          & ( epistemic_AK_a @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>B
thf(fact_444_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte2339904321507024205t_unit @ M )
       => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
         => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_445_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte9194023259896155360t_unit,W: produc2203834439629243303c_fm_a] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte2443128549434688781t_unit @ M )
       => ( ( member5029746173879296720c_fm_a @ W @ ( episte5714722596736476595t_unit @ M ) )
         => ( episte7505603015783396941c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_446_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte94448284482925344t_unit,W: epistemic_fm_a] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte4583239219080210381t_unit @ M )
       => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
         => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_447_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte2449151000174023629t_unit @ M )
       => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
         => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_448_subset__code_I1_J,axiom,
    ! [Xs: list_s580375451141968640c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ ( set_se8855941934996405007c_fm_a @ Xs ) @ B4 )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
           => ( member536094252920883875c_fm_a @ X @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_449_subset__code_I1_J,axiom,
    ! [Xs: list_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ ( set_a2 @ Xs ) @ B4 )
      = ( ! [X: a] :
            ( ( member_a @ X @ ( set_a2 @ Xs ) )
           => ( member_a @ X @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_450_subset__code_I1_J,axiom,
    ! [Xs: list_P3099032918374241197c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ ( set_Pr6083076219314900284c_fm_a @ Xs ) @ B4 )
      = ( ! [X: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
           => ( member5029746173879296720c_fm_a @ X @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_451_subset__code_I1_J,axiom,
    ! [Xs: list_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) @ B4 )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
           => ( member6642669571620171971c_fm_a @ X @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_452_conjunct__imply,axiom,
    ! [G5: list_E5775909407618282812c_fm_a,P: episte740340785640729014c_fm_a,G: list_char > $o,H: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G @ H @ ( episte260752218777527565c_fm_a @ ( episte260752218777527565c_fm_a @ ( stalna5968238273478151382c_fm_a @ G5 ) @ P ) @ ( episte1272216372155829993c_fm_a @ G5 @ P ) ) ) ).

% conjunct_imply
thf(fact_453_conjunct__imply,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% conjunct_imply
thf(fact_454_imply__conjunct,axiom,
    ! [G5: list_E5775909407618282812c_fm_a,P: episte740340785640729014c_fm_a,G: list_char > $o,H: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G @ H @ ( episte260752218777527565c_fm_a @ ( episte1272216372155829993c_fm_a @ G5 @ P ) @ ( episte260752218777527565c_fm_a @ ( stalna5968238273478151382c_fm_a @ G5 ) @ P ) ) ) ).

% imply_conjunct
thf(fact_455_imply__conjunct,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ G5 @ P ) @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% imply_conjunct
thf(fact_456_fm_Orel__induct,axiom,
    ! [R2: epistemic_fm_a > a > $o,X3: episte740340785640729014c_fm_a,Y: epistemic_fm_a,Q4: episte740340785640729014c_fm_a > epistemic_fm_a > $o] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ X3 @ Y )
     => ( ( Q4 @ episte5073044243917183961c_fm_a @ epistemic_FF_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q4 @ ( episte3759128466173231372c_fm_a @ A22 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: episte740340785640729014c_fm_a,A32: episte740340785640729014c_fm_a,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q4 @ A31 @ B31 )
               => ( ( Q4 @ A32 @ B32 )
                 => ( Q4 @ ( episte6088726764479022859c_fm_a @ A31 @ A32 ) @ ( epistemic_Dis_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: episte740340785640729014c_fm_a,A42: episte740340785640729014c_fm_a,B41: epistemic_fm_a,B42: epistemic_fm_a] :
                  ( ( Q4 @ A41 @ B41 )
                 => ( ( Q4 @ A42 @ B42 )
                   => ( Q4 @ ( episte3685526487207141399c_fm_a @ A41 @ A42 ) @ ( epistemic_Con_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: episte740340785640729014c_fm_a,A52: episte740340785640729014c_fm_a,B51: epistemic_fm_a,B52: epistemic_fm_a] :
                    ( ( Q4 @ A51 @ B51 )
                   => ( ( Q4 @ A52 @ B52 )
                     => ( Q4 @ ( episte260752218777527565c_fm_a @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: epistemic_fm_a,A62: episte740340785640729014c_fm_a,B61: a,B62: epistemic_fm_a] :
                      ( ( R2 @ A61 @ B61 )
                     => ( ( Q4 @ A62 @ B62 )
                       => ( Q4 @ ( episte5657488632024175118c_fm_a @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q4 @ X3 @ Y ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_457_fm_Orel__induct,axiom,
    ! [R2: a > epistemic_fm_a > $o,X3: epistemic_fm_a,Y: episte740340785640729014c_fm_a,Q4: epistemic_fm_a > episte740340785640729014c_fm_a > $o] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ X3 @ Y )
     => ( ( Q4 @ epistemic_FF_a @ episte5073044243917183961c_fm_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q4 @ ( epistemic_Pro_a @ A22 ) @ ( episte3759128466173231372c_fm_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: episte740340785640729014c_fm_a,B32: episte740340785640729014c_fm_a] :
                ( ( Q4 @ A31 @ B31 )
               => ( ( Q4 @ A32 @ B32 )
                 => ( Q4 @ ( epistemic_Dis_a @ A31 @ A32 ) @ ( episte6088726764479022859c_fm_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_a,A42: epistemic_fm_a,B41: episte740340785640729014c_fm_a,B42: episte740340785640729014c_fm_a] :
                  ( ( Q4 @ A41 @ B41 )
                 => ( ( Q4 @ A42 @ B42 )
                   => ( Q4 @ ( epistemic_Con_a @ A41 @ A42 ) @ ( episte3685526487207141399c_fm_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_a,A52: epistemic_fm_a,B51: episte740340785640729014c_fm_a,B52: episte740340785640729014c_fm_a] :
                    ( ( Q4 @ A51 @ B51 )
                   => ( ( Q4 @ A52 @ B52 )
                     => ( Q4 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( episte260752218777527565c_fm_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: epistemic_fm_a,B62: episte740340785640729014c_fm_a] :
                      ( ( R2 @ A61 @ B61 )
                     => ( ( Q4 @ A62 @ B62 )
                       => ( Q4 @ ( epistemic_K_a @ A61 @ A62 ) @ ( episte5657488632024175118c_fm_a @ B61 @ B62 ) ) ) )
                 => ( Q4 @ X3 @ Y ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_458_fm_Orel__induct,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a,Y: episte740340785640729014c_fm_a,Q4: episte740340785640729014c_fm_a > episte740340785640729014c_fm_a > $o] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ X3 @ Y )
     => ( ( Q4 @ episte5073044243917183961c_fm_a @ episte5073044243917183961c_fm_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q4 @ ( episte3759128466173231372c_fm_a @ A22 ) @ ( episte3759128466173231372c_fm_a @ B22 ) ) )
         => ( ! [A31: episte740340785640729014c_fm_a,A32: episte740340785640729014c_fm_a,B31: episte740340785640729014c_fm_a,B32: episte740340785640729014c_fm_a] :
                ( ( Q4 @ A31 @ B31 )
               => ( ( Q4 @ A32 @ B32 )
                 => ( Q4 @ ( episte6088726764479022859c_fm_a @ A31 @ A32 ) @ ( episte6088726764479022859c_fm_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: episte740340785640729014c_fm_a,A42: episte740340785640729014c_fm_a,B41: episte740340785640729014c_fm_a,B42: episte740340785640729014c_fm_a] :
                  ( ( Q4 @ A41 @ B41 )
                 => ( ( Q4 @ A42 @ B42 )
                   => ( Q4 @ ( episte3685526487207141399c_fm_a @ A41 @ A42 ) @ ( episte3685526487207141399c_fm_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: episte740340785640729014c_fm_a,A52: episte740340785640729014c_fm_a,B51: episte740340785640729014c_fm_a,B52: episte740340785640729014c_fm_a] :
                    ( ( Q4 @ A51 @ B51 )
                   => ( ( Q4 @ A52 @ B52 )
                     => ( Q4 @ ( episte260752218777527565c_fm_a @ A51 @ A52 ) @ ( episte260752218777527565c_fm_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: epistemic_fm_a,A62: episte740340785640729014c_fm_a,B61: epistemic_fm_a,B62: episte740340785640729014c_fm_a] :
                      ( ( R2 @ A61 @ B61 )
                     => ( ( Q4 @ A62 @ B62 )
                       => ( Q4 @ ( episte5657488632024175118c_fm_a @ A61 @ A62 ) @ ( episte5657488632024175118c_fm_a @ B61 @ B62 ) ) ) )
                 => ( Q4 @ X3 @ Y ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_459_fm_Orel__induct,axiom,
    ! [R2: a > a > $o,X3: epistemic_fm_a,Y: epistemic_fm_a,Q4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X3 @ Y )
     => ( ( Q4 @ epistemic_FF_a @ epistemic_FF_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q4 @ ( epistemic_Pro_a @ A22 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q4 @ A31 @ B31 )
               => ( ( Q4 @ A32 @ B32 )
                 => ( Q4 @ ( epistemic_Dis_a @ A31 @ A32 ) @ ( epistemic_Dis_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_a,A42: epistemic_fm_a,B41: epistemic_fm_a,B42: epistemic_fm_a] :
                  ( ( Q4 @ A41 @ B41 )
                 => ( ( Q4 @ A42 @ B42 )
                   => ( Q4 @ ( epistemic_Con_a @ A41 @ A42 ) @ ( epistemic_Con_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_a,A52: epistemic_fm_a,B51: epistemic_fm_a,B52: epistemic_fm_a] :
                    ( ( Q4 @ A51 @ B51 )
                   => ( ( Q4 @ A52 @ B52 )
                     => ( Q4 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: a,B62: epistemic_fm_a] :
                      ( ( R2 @ A61 @ B61 )
                     => ( ( Q4 @ A62 @ B62 )
                       => ( Q4 @ ( epistemic_K_a @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q4 @ X3 @ Y ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_460_fm_Orel__cases,axiom,
    ! [R2: epistemic_fm_a > a > $o,A2: episte740340785640729014c_fm_a,B: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ A2 @ B )
     => ( ( ( A2 = episte5073044243917183961c_fm_a )
         => ( B != epistemic_FF_a ) )
       => ( ! [X2: list_char] :
              ( ( A2
                = ( episte3759128466173231372c_fm_a @ X2 ) )
             => ! [Y2: list_char] :
                  ( ( B
                    = ( epistemic_Pro_a @ Y2 ) )
                 => ( X2 != Y2 ) ) )
         => ( ! [X1: episte740340785640729014c_fm_a,X2a: episte740340785640729014c_fm_a] :
                ( ( A2
                  = ( episte6088726764479022859c_fm_a @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( episte4428145106359621316fm_a_a @ R2 @ X1 @ Y1 )
                     => ~ ( episte4428145106359621316fm_a_a @ R2 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: episte740340785640729014c_fm_a,X2b: episte740340785640729014c_fm_a] :
                  ( ( A2
                    = ( episte3685526487207141399c_fm_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( episte4428145106359621316fm_a_a @ R2 @ X1a @ Y1a )
                       => ~ ( episte4428145106359621316fm_a_a @ R2 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: episte740340785640729014c_fm_a,X2c: episte740340785640729014c_fm_a] :
                    ( ( A2
                      = ( episte260752218777527565c_fm_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( episte4428145106359621316fm_a_a @ R2 @ X1b @ Y1b )
                         => ~ ( episte4428145106359621316fm_a_a @ R2 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: epistemic_fm_a,X2d: episte740340785640729014c_fm_a] :
                      ( ( A2
                        = ( episte5657488632024175118c_fm_a @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R2 @ X1c @ Y1c )
                           => ~ ( episte4428145106359621316fm_a_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_461_fm_Orel__cases,axiom,
    ! [R2: a > epistemic_fm_a > $o,A2: epistemic_fm_a,B: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ A2 @ B )
     => ( ( ( A2 = epistemic_FF_a )
         => ( B != episte5073044243917183961c_fm_a ) )
       => ( ! [X2: list_char] :
              ( ( A2
                = ( epistemic_Pro_a @ X2 ) )
             => ! [Y2: list_char] :
                  ( ( B
                    = ( episte3759128466173231372c_fm_a @ Y2 ) )
                 => ( X2 != Y2 ) ) )
         => ( ! [X1: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A2
                  = ( epistemic_Dis_a @ X1 @ X2a ) )
               => ! [Y1: episte740340785640729014c_fm_a,Y2a: episte740340785640729014c_fm_a] :
                    ( ( B
                      = ( episte6088726764479022859c_fm_a @ Y1 @ Y2a ) )
                   => ( ( episte8321036160184370300c_fm_a @ R2 @ X1 @ Y1 )
                     => ~ ( episte8321036160184370300c_fm_a @ R2 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A2
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: episte740340785640729014c_fm_a,Y2b: episte740340785640729014c_fm_a] :
                      ( ( B
                        = ( episte3685526487207141399c_fm_a @ Y1a @ Y2b ) )
                     => ( ( episte8321036160184370300c_fm_a @ R2 @ X1a @ Y1a )
                       => ~ ( episte8321036160184370300c_fm_a @ R2 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A2
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: episte740340785640729014c_fm_a,Y2c: episte740340785640729014c_fm_a] :
                        ( ( B
                          = ( episte260752218777527565c_fm_a @ Y1b @ Y2c ) )
                       => ( ( episte8321036160184370300c_fm_a @ R2 @ X1b @ Y1b )
                         => ~ ( episte8321036160184370300c_fm_a @ R2 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A2
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: epistemic_fm_a,Y2d: episte740340785640729014c_fm_a] :
                          ( ( B
                            = ( episte5657488632024175118c_fm_a @ Y1c @ Y2d ) )
                         => ( ( R2 @ X1c @ Y1c )
                           => ~ ( episte8321036160184370300c_fm_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_462_fm_Orel__cases,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,A2: episte740340785640729014c_fm_a,B: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ A2 @ B )
     => ( ( ( A2 = episte5073044243917183961c_fm_a )
         => ( B != episte5073044243917183961c_fm_a ) )
       => ( ! [X2: list_char] :
              ( ( A2
                = ( episte3759128466173231372c_fm_a @ X2 ) )
             => ! [Y2: list_char] :
                  ( ( B
                    = ( episte3759128466173231372c_fm_a @ Y2 ) )
                 => ( X2 != Y2 ) ) )
         => ( ! [X1: episte740340785640729014c_fm_a,X2a: episte740340785640729014c_fm_a] :
                ( ( A2
                  = ( episte6088726764479022859c_fm_a @ X1 @ X2a ) )
               => ! [Y1: episte740340785640729014c_fm_a,Y2a: episte740340785640729014c_fm_a] :
                    ( ( B
                      = ( episte6088726764479022859c_fm_a @ Y1 @ Y2a ) )
                   => ( ( episte7774795710028497888c_fm_a @ R2 @ X1 @ Y1 )
                     => ~ ( episte7774795710028497888c_fm_a @ R2 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: episte740340785640729014c_fm_a,X2b: episte740340785640729014c_fm_a] :
                  ( ( A2
                    = ( episte3685526487207141399c_fm_a @ X1a @ X2b ) )
                 => ! [Y1a: episte740340785640729014c_fm_a,Y2b: episte740340785640729014c_fm_a] :
                      ( ( B
                        = ( episte3685526487207141399c_fm_a @ Y1a @ Y2b ) )
                     => ( ( episte7774795710028497888c_fm_a @ R2 @ X1a @ Y1a )
                       => ~ ( episte7774795710028497888c_fm_a @ R2 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: episte740340785640729014c_fm_a,X2c: episte740340785640729014c_fm_a] :
                    ( ( A2
                      = ( episte260752218777527565c_fm_a @ X1b @ X2c ) )
                   => ! [Y1b: episte740340785640729014c_fm_a,Y2c: episte740340785640729014c_fm_a] :
                        ( ( B
                          = ( episte260752218777527565c_fm_a @ Y1b @ Y2c ) )
                       => ( ( episte7774795710028497888c_fm_a @ R2 @ X1b @ Y1b )
                         => ~ ( episte7774795710028497888c_fm_a @ R2 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: epistemic_fm_a,X2d: episte740340785640729014c_fm_a] :
                      ( ( A2
                        = ( episte5657488632024175118c_fm_a @ X1c @ X2d ) )
                     => ! [Y1c: epistemic_fm_a,Y2d: episte740340785640729014c_fm_a] :
                          ( ( B
                            = ( episte5657488632024175118c_fm_a @ Y1c @ Y2d ) )
                         => ( ( R2 @ X1c @ Y1c )
                           => ~ ( episte7774795710028497888c_fm_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_463_fm_Orel__cases,axiom,
    ! [R2: a > a > $o,A2: epistemic_fm_a,B: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ A2 @ B )
     => ( ( ( A2 = epistemic_FF_a )
         => ( B != epistemic_FF_a ) )
       => ( ! [X2: list_char] :
              ( ( A2
                = ( epistemic_Pro_a @ X2 ) )
             => ! [Y2: list_char] :
                  ( ( B
                    = ( epistemic_Pro_a @ Y2 ) )
                 => ( X2 != Y2 ) ) )
         => ( ! [X1: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A2
                  = ( epistemic_Dis_a @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_a_a @ R2 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_a_a @ R2 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A2
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_a_a @ R2 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_a_a @ R2 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A2
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_a_a @ R2 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_a_a @ R2 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A2
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R2 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_a_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_464_K__conjunct__imply,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,G5: list_E5775909407618282812c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( stalna5968238273478151382c_fm_a @ G5 ) @ P ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ P ) ) ) ).

% K_conjunct_imply
thf(fact_465_K__conjunct__imply,axiom,
    ! [A: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_conjunct_imply
thf(fact_466_K__imply__conjunct,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,G5: list_E5775909407618282812c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ P ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( stalna5968238273478151382c_fm_a @ G5 ) @ P ) ) ) ).

% K_imply_conjunct
thf(fact_467_K__imply__conjunct,axiom,
    ! [A: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% K_imply_conjunct
thf(fact_468_semantics_Osimps_I2_J,axiom,
    ! [M: episte94448284482925344t_unit,W: epistemic_fm_a,X3: list_char] :
      ( ( episte5333283044364550848c_fm_a @ M @ W @ ( epistemic_Pro_a @ X3 ) )
      = ( episte5680354956628169428t_unit @ M @ W @ X3 ) ) ).

% semantics.simps(2)
thf(fact_469_semantics_Osimps_I2_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,X3: list_char] :
      ( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Pro_a @ X3 ) )
      = ( episte2398645135750866164t_unit @ M @ W @ X3 ) ) ).

% semantics.simps(2)
thf(fact_470_fm_Orel__refl,axiom,
    ! [Ra: a > a > $o,X3: epistemic_fm_a] :
      ( ! [X2: a] : ( Ra @ X2 @ X2 )
     => ( epistemic_rel_fm_a_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl
thf(fact_471_fm_Orel__refl,axiom,
    ! [Ra: epistemic_fm_a > epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a] :
      ( ! [X2: epistemic_fm_a] : ( Ra @ X2 @ X2 )
     => ( episte7774795710028497888c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl
thf(fact_472_fm_Orel__eq,axiom,
    ( ( epistemic_rel_fm_a_a
      @ ^ [Y3: a,Z: a] : ( Y3 = Z ) )
    = ( ^ [Y3: epistemic_fm_a,Z: epistemic_fm_a] : ( Y3 = Z ) ) ) ).

% fm.rel_eq
thf(fact_473_fm_Orel__eq,axiom,
    ( ( episte7774795710028497888c_fm_a
      @ ^ [Y3: epistemic_fm_a,Z: epistemic_fm_a] : ( Y3 = Z ) )
    = ( ^ [Y3: episte740340785640729014c_fm_a,Z: episte740340785640729014c_fm_a] : ( Y3 = Z ) ) ) ).

% fm.rel_eq
thf(fact_474_fm_Orel__mono,axiom,
    ! [R2: a > a > $o,Ra: a > a > $o] :
      ( ( ord_less_eq_a_a_o @ R2 @ Ra )
     => ( ord_le3934200179093585166fm_a_o @ ( epistemic_rel_fm_a_a @ R2 ) @ ( epistemic_rel_fm_a_a @ Ra ) ) ) ).

% fm.rel_mono
thf(fact_475_fm_Orel__mono,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Ra: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( ord_le3934200179093585166fm_a_o @ R2 @ Ra )
     => ( ord_le6583030472306871822fm_a_o @ ( episte7774795710028497888c_fm_a @ R2 ) @ ( episte7774795710028497888c_fm_a @ Ra ) ) ) ).

% fm.rel_mono
thf(fact_476_fm_Orel__intros_I5_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X51: epistemic_fm_a,Y51: episte740340785640729014c_fm_a,X52: epistemic_fm_a,Y52: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ X51 @ Y51 )
     => ( ( episte8321036160184370300c_fm_a @ R2 @ X52 @ Y52 )
       => ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_477_fm_Orel__intros_I5_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X51: episte740340785640729014c_fm_a,Y51: epistemic_fm_a,X52: episte740340785640729014c_fm_a,Y52: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ X51 @ Y51 )
     => ( ( episte4428145106359621316fm_a_a @ R2 @ X52 @ Y52 )
       => ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_478_fm_Orel__intros_I5_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X51: episte740340785640729014c_fm_a,Y51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ X51 @ Y51 )
     => ( ( episte7774795710028497888c_fm_a @ R2 @ X52 @ Y52 )
       => ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_479_fm_Orel__intros_I5_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,Y51: epistemic_fm_a,X52: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_480_fm_Orel__inject_I5_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) )
      = ( ( episte8321036160184370300c_fm_a @ R2 @ X51 @ Y51 )
        & ( episte8321036160184370300c_fm_a @ R2 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_481_fm_Orel__inject_I5_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) )
      = ( ( episte4428145106359621316fm_a_a @ R2 @ X51 @ Y51 )
        & ( episte4428145106359621316fm_a_a @ R2 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_482_fm_Orel__inject_I5_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) )
      = ( ( episte7774795710028497888c_fm_a @ R2 @ X51 @ Y51 )
        & ( episte7774795710028497888c_fm_a @ R2 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_483_fm_Orel__inject_I5_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
        & ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_484_fm_Orel__inject_I6_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X61: a,X62: epistemic_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) )
      = ( ( R2 @ X61 @ Y61 )
        & ( episte8321036160184370300c_fm_a @ R2 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_485_fm_Orel__inject_I6_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) )
      = ( ( R2 @ X61 @ Y61 )
        & ( episte4428145106359621316fm_a_a @ R2 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_486_fm_Orel__inject_I6_J,axiom,
    ! [R2: a > a > $o,X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) )
      = ( ( R2 @ X61 @ Y61 )
        & ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_487_fm_Orel__inject_I6_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) )
      = ( ( R2 @ X61 @ Y61 )
        & ( episte7774795710028497888c_fm_a @ R2 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_488_fm_Orel__intros_I6_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X61: a,Y61: epistemic_fm_a,X62: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ( ( R2 @ X61 @ Y61 )
     => ( ( episte8321036160184370300c_fm_a @ R2 @ X62 @ Y62 )
       => ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_489_fm_Orel__intros_I6_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X61: epistemic_fm_a,Y61: a,X62: episte740340785640729014c_fm_a,Y62: epistemic_fm_a] :
      ( ( R2 @ X61 @ Y61 )
     => ( ( episte4428145106359621316fm_a_a @ R2 @ X62 @ Y62 )
       => ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_490_fm_Orel__intros_I6_J,axiom,
    ! [R2: a > a > $o,X61: a,Y61: a,X62: epistemic_fm_a,Y62: epistemic_fm_a] :
      ( ( R2 @ X61 @ Y61 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_491_fm_Orel__intros_I6_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X61: epistemic_fm_a,Y61: epistemic_fm_a,X62: episte740340785640729014c_fm_a,Y62: episte740340785640729014c_fm_a] :
      ( ( R2 @ X61 @ Y61 )
     => ( ( episte7774795710028497888c_fm_a @ R2 @ X62 @ Y62 )
       => ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_492_fm_Octr__transfer_I1_J,axiom,
    ! [R2: a > a > $o] : ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ epistemic_FF_a ) ).

% fm.ctr_transfer(1)
thf(fact_493_fm_Octr__transfer_I1_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o] : ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ episte5073044243917183961c_fm_a ) ).

% fm.ctr_transfer(1)
thf(fact_494_fm_Orel__intros_I4_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X41: epistemic_fm_a,Y41: episte740340785640729014c_fm_a,X42: epistemic_fm_a,Y42: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ X41 @ Y41 )
     => ( ( episte8321036160184370300c_fm_a @ R2 @ X42 @ Y42 )
       => ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ) ) ).

% fm.rel_intros(4)
thf(fact_495_fm_Orel__intros_I4_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X41: episte740340785640729014c_fm_a,Y41: epistemic_fm_a,X42: episte740340785640729014c_fm_a,Y42: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ X41 @ Y41 )
     => ( ( episte4428145106359621316fm_a_a @ R2 @ X42 @ Y42 )
       => ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ) ) ).

% fm.rel_intros(4)
thf(fact_496_fm_Orel__intros_I4_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X41: episte740340785640729014c_fm_a,Y41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ X41 @ Y41 )
     => ( ( episte7774795710028497888c_fm_a @ R2 @ X42 @ Y42 )
       => ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ) ) ).

% fm.rel_intros(4)
thf(fact_497_fm_Orel__intros_I4_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,Y41: epistemic_fm_a,X42: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X41 @ Y41 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X42 @ Y42 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ) ) ).

% fm.rel_intros(4)
thf(fact_498_fm_Orel__inject_I4_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) )
      = ( ( episte8321036160184370300c_fm_a @ R2 @ X41 @ Y41 )
        & ( episte8321036160184370300c_fm_a @ R2 @ X42 @ Y42 ) ) ) ).

% fm.rel_inject(4)
thf(fact_499_fm_Orel__inject_I4_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) )
      = ( ( episte4428145106359621316fm_a_a @ R2 @ X41 @ Y41 )
        & ( episte4428145106359621316fm_a_a @ R2 @ X42 @ Y42 ) ) ) ).

% fm.rel_inject(4)
thf(fact_500_fm_Orel__inject_I4_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) )
      = ( ( episte7774795710028497888c_fm_a @ R2 @ X41 @ Y41 )
        & ( episte7774795710028497888c_fm_a @ R2 @ X42 @ Y42 ) ) ) ).

% fm.rel_inject(4)
thf(fact_501_fm_Orel__inject_I4_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X41 @ Y41 )
        & ( epistemic_rel_fm_a_a @ R2 @ X42 @ Y42 ) ) ) ).

% fm.rel_inject(4)
thf(fact_502_fm_Orel__intros_I2_J,axiom,
    ! [X23: list_char,Y22: list_char,R2: a > a > $o] :
      ( ( X23 = Y22 )
     => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_Pro_a @ Y22 ) ) ) ).

% fm.rel_intros(2)
thf(fact_503_fm_Orel__intros_I2_J,axiom,
    ! [X23: list_char,Y22: list_char,R2: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( X23 = Y22 )
     => ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte3759128466173231372c_fm_a @ Y22 ) ) ) ).

% fm.rel_intros(2)
thf(fact_504_fm_Orel__inject_I2_J,axiom,
    ! [R2: a > a > $o,X23: list_char,Y22: list_char] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_Pro_a @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fm.rel_inject(2)
thf(fact_505_fm_Orel__inject_I2_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X23: list_char,Y22: list_char] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte3759128466173231372c_fm_a @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fm.rel_inject(2)
thf(fact_506_fm_Orel__intros_I3_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X312: epistemic_fm_a,Y31: episte740340785640729014c_fm_a,X322: epistemic_fm_a,Y32: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ X312 @ Y31 )
     => ( ( episte8321036160184370300c_fm_a @ R2 @ X322 @ Y32 )
       => ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ) ) ).

% fm.rel_intros(3)
thf(fact_507_fm_Orel__intros_I3_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X312: episte740340785640729014c_fm_a,Y31: epistemic_fm_a,X322: episte740340785640729014c_fm_a,Y32: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ X312 @ Y31 )
     => ( ( episte4428145106359621316fm_a_a @ R2 @ X322 @ Y32 )
       => ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) ) ) ) ).

% fm.rel_intros(3)
thf(fact_508_fm_Orel__intros_I3_J,axiom,
    ! [R2: a > a > $o,X312: epistemic_fm_a,Y31: epistemic_fm_a,X322: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X312 @ Y31 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X322 @ Y32 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) ) ) ) ).

% fm.rel_intros(3)
thf(fact_509_fm_Orel__intros_I3_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X312: episte740340785640729014c_fm_a,Y31: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ X312 @ Y31 )
     => ( ( episte7774795710028497888c_fm_a @ R2 @ X322 @ Y32 )
       => ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ) ) ).

% fm.rel_intros(3)
thf(fact_510_fm_Orel__inject_I3_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) )
      = ( ( episte8321036160184370300c_fm_a @ R2 @ X312 @ Y31 )
        & ( episte8321036160184370300c_fm_a @ R2 @ X322 @ Y32 ) ) ) ).

% fm.rel_inject(3)
thf(fact_511_fm_Orel__inject_I3_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) )
      = ( ( episte4428145106359621316fm_a_a @ R2 @ X312 @ Y31 )
        & ( episte4428145106359621316fm_a_a @ R2 @ X322 @ Y32 ) ) ) ).

% fm.rel_inject(3)
thf(fact_512_fm_Orel__inject_I3_J,axiom,
    ! [R2: a > a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X312 @ Y31 )
        & ( epistemic_rel_fm_a_a @ R2 @ X322 @ Y32 ) ) ) ).

% fm.rel_inject(3)
thf(fact_513_fm_Orel__inject_I3_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) )
      = ( ( episte7774795710028497888c_fm_a @ R2 @ X312 @ Y31 )
        & ( episte7774795710028497888c_fm_a @ R2 @ X322 @ Y32 ) ) ) ).

% fm.rel_inject(3)
thf(fact_514_fm_Orel__distinct_I30_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_515_fm_Orel__distinct_I30_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y61: a,Y62: epistemic_fm_a,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_516_fm_Orel__distinct_I30_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_517_fm_Orel__distinct_I30_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_518_fm_Orel__distinct_I29_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_519_fm_Orel__distinct_I29_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_520_fm_Orel__distinct_I29_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_521_fm_Orel__distinct_I29_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_522_fm_Orel__distinct_I8_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(8)
thf(fact_523_fm_Orel__distinct_I8_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(8)
thf(fact_524_fm_Orel__distinct_I8_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ episte5073044243917183961c_fm_a ) ).

% fm.rel_distinct(8)
thf(fact_525_fm_Orel__distinct_I7_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ epistemic_FF_a @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(7)
thf(fact_526_fm_Orel__distinct_I7_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(7)
thf(fact_527_fm_Orel__distinct_I7_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(7)
thf(fact_528_fm_Orel__distinct_I10_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(10)
thf(fact_529_fm_Orel__distinct_I10_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(10)
thf(fact_530_fm_Orel__distinct_I10_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ episte5073044243917183961c_fm_a ) ).

% fm.rel_distinct(10)
thf(fact_531_fm_Orel__distinct_I9_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ epistemic_FF_a @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(9)
thf(fact_532_fm_Orel__distinct_I9_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(9)
thf(fact_533_fm_Orel__distinct_I9_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(9)
thf(fact_534_fm_Orel__distinct_I25_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(25)
thf(fact_535_fm_Orel__distinct_I25_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(25)
thf(fact_536_fm_Orel__distinct_I25_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(25)
thf(fact_537_fm_Orel__distinct_I25_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(25)
thf(fact_538_fm_Orel__distinct_I26_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(26)
thf(fact_539_fm_Orel__distinct_I26_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(26)
thf(fact_540_fm_Orel__distinct_I26_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(26)
thf(fact_541_fm_Orel__distinct_I26_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(26)
thf(fact_542_fm_Orel__distinct_I28_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(28)
thf(fact_543_fm_Orel__distinct_I28_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y61: a,Y62: epistemic_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(28)
thf(fact_544_fm_Orel__distinct_I28_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(28)
thf(fact_545_fm_Orel__distinct_I28_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(28)
thf(fact_546_fm_Orel__distinct_I27_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(27)
thf(fact_547_fm_Orel__distinct_I27_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(27)
thf(fact_548_fm_Orel__distinct_I27_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(27)
thf(fact_549_fm_Orel__distinct_I27_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(27)
thf(fact_550_fm_Orel__distinct_I15_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X23: list_char,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(15)
thf(fact_551_fm_Orel__distinct_I15_J,axiom,
    ! [R2: a > a > $o,X23: list_char,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(15)
thf(fact_552_fm_Orel__distinct_I15_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X23: list_char,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(15)
thf(fact_553_fm_Orel__distinct_I16_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(16)
thf(fact_554_fm_Orel__distinct_I16_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X23: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(16)
thf(fact_555_fm_Orel__distinct_I16_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( episte3759128466173231372c_fm_a @ X23 ) ) ).

% fm.rel_distinct(16)
thf(fact_556_fm_Orel__distinct_I21_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(21)
thf(fact_557_fm_Orel__distinct_I21_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(21)
thf(fact_558_fm_Orel__distinct_I21_J,axiom,
    ! [R2: a > a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(21)
thf(fact_559_fm_Orel__distinct_I21_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(21)
thf(fact_560_fm_Orel__distinct_I22_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(22)
thf(fact_561_fm_Orel__distinct_I22_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(22)
thf(fact_562_fm_Orel__distinct_I22_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(22)
thf(fact_563_fm_Orel__distinct_I22_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y51: episte740340785640729014c_fm_a,Y52: episte740340785640729014c_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte260752218777527565c_fm_a @ Y51 @ Y52 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(22)
thf(fact_564_fm_Orel__distinct_I17_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X23: list_char,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(17)
thf(fact_565_fm_Orel__distinct_I17_J,axiom,
    ! [R2: a > a > $o,X23: list_char,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(17)
thf(fact_566_fm_Orel__distinct_I17_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X23: list_char,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(17)
thf(fact_567_fm_Orel__distinct_I18_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(18)
thf(fact_568_fm_Orel__distinct_I18_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X23: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(18)
thf(fact_569_fm_Orel__distinct_I18_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( episte3759128466173231372c_fm_a @ X23 ) ) ).

% fm.rel_distinct(18)
thf(fact_570_fm_Orel__distinct_I23_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(23)
thf(fact_571_fm_Orel__distinct_I23_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(23)
thf(fact_572_fm_Orel__distinct_I23_J,axiom,
    ! [R2: a > a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(23)
thf(fact_573_fm_Orel__distinct_I23_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(23)
thf(fact_574_fm_Orel__distinct_I24_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(24)
thf(fact_575_fm_Orel__distinct_I24_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y61: a,Y62: epistemic_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(24)
thf(fact_576_fm_Orel__distinct_I24_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(24)
thf(fact_577_fm_Orel__distinct_I24_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y61: epistemic_fm_a,Y62: episte740340785640729014c_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte5657488632024175118c_fm_a @ Y61 @ Y62 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(24)
thf(fact_578_fm_Orel__distinct_I6_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(6)
thf(fact_579_fm_Orel__distinct_I6_J,axiom,
    ! [R2: a > a > $o,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ Y41 @ Y42 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(6)
thf(fact_580_fm_Orel__distinct_I6_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ episte5073044243917183961c_fm_a ) ).

% fm.rel_distinct(6)
thf(fact_581_fm_Orel__distinct_I5_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ epistemic_FF_a @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(5)
thf(fact_582_fm_Orel__distinct_I5_J,axiom,
    ! [R2: a > a > $o,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(5)
thf(fact_583_fm_Orel__distinct_I5_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(5)
thf(fact_584_fm_Orel__distinct_I2_J,axiom,
    ! [R2: a > a > $o,Y22: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ Y22 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(2)
thf(fact_585_fm_Orel__distinct_I2_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y22: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ Y22 ) @ episte5073044243917183961c_fm_a ) ).

% fm.rel_distinct(2)
thf(fact_586_fm_Orel__distinct_I1_J,axiom,
    ! [R2: a > a > $o,Y22: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_Pro_a @ Y22 ) ) ).

% fm.rel_distinct(1)
thf(fact_587_fm_Orel__distinct_I1_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y22: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ ( episte3759128466173231372c_fm_a @ Y22 ) ) ).

% fm.rel_distinct(1)
thf(fact_588_fm_Orel__distinct_I4_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(4)
thf(fact_589_fm_Orel__distinct_I4_J,axiom,
    ! [R2: a > a > $o,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ Y31 @ Y32 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(4)
thf(fact_590_fm_Orel__distinct_I4_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) @ episte5073044243917183961c_fm_a ) ).

% fm.rel_distinct(4)
thf(fact_591_fm_Orel__distinct_I3_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ epistemic_FF_a @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(3)
thf(fact_592_fm_Orel__distinct_I3_J,axiom,
    ! [R2: a > a > $o,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_Dis_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(3)
thf(fact_593_fm_Orel__distinct_I3_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ episte5073044243917183961c_fm_a @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(3)
thf(fact_594_fm_Orel__distinct_I13_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X23: list_char,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(13)
thf(fact_595_fm_Orel__distinct_I13_J,axiom,
    ! [R2: a > a > $o,X23: list_char,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(13)
thf(fact_596_fm_Orel__distinct_I13_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X23: list_char,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(13)
thf(fact_597_fm_Orel__distinct_I14_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(14)
thf(fact_598_fm_Orel__distinct_I14_J,axiom,
    ! [R2: a > a > $o,Y41: epistemic_fm_a,Y42: epistemic_fm_a,X23: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ Y41 @ Y42 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(14)
thf(fact_599_fm_Orel__distinct_I14_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ ( episte3759128466173231372c_fm_a @ X23 ) ) ).

% fm.rel_distinct(14)
thf(fact_600_fm_Orel__distinct_I19_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(19)
thf(fact_601_fm_Orel__distinct_I19_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(19)
thf(fact_602_fm_Orel__distinct_I19_J,axiom,
    ! [R2: a > a > $o,X312: epistemic_fm_a,X322: epistemic_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X312 @ X322 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(19)
thf(fact_603_fm_Orel__distinct_I19_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) ) ).

% fm.rel_distinct(19)
thf(fact_604_fm_Orel__distinct_I20_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(20)
thf(fact_605_fm_Orel__distinct_I20_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,Y41: epistemic_fm_a,Y42: epistemic_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Con_a @ Y41 @ Y42 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(20)
thf(fact_606_fm_Orel__distinct_I20_J,axiom,
    ! [R2: a > a > $o,Y41: epistemic_fm_a,Y42: epistemic_fm_a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ Y41 @ Y42 ) @ ( epistemic_Dis_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(20)
thf(fact_607_fm_Orel__distinct_I20_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y41: episte740340785640729014c_fm_a,Y42: episte740340785640729014c_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3685526487207141399c_fm_a @ Y41 @ Y42 ) @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ).

% fm.rel_distinct(20)
thf(fact_608_fm_Orel__distinct_I11_J,axiom,
    ! [R2: a > epistemic_fm_a > $o,X23: list_char,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte8321036160184370300c_fm_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(11)
thf(fact_609_fm_Orel__distinct_I11_J,axiom,
    ! [R2: a > a > $o,X23: list_char,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X23 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(11)
thf(fact_610_fm_Orel__distinct_I11_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X23: list_char,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte3759128466173231372c_fm_a @ X23 ) @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) ) ).

% fm.rel_distinct(11)
thf(fact_611_fm_Orel__distinct_I12_J,axiom,
    ! [R2: epistemic_fm_a > a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte4428145106359621316fm_a_a @ R2 @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(12)
thf(fact_612_fm_Orel__distinct_I12_J,axiom,
    ! [R2: a > a > $o,Y31: epistemic_fm_a,Y32: epistemic_fm_a,X23: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ Y31 @ Y32 ) @ ( epistemic_Pro_a @ X23 ) ) ).

% fm.rel_distinct(12)
thf(fact_613_fm_Orel__distinct_I12_J,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,Y31: episte740340785640729014c_fm_a,Y32: episte740340785640729014c_fm_a,X23: list_char] :
      ~ ( episte7774795710028497888c_fm_a @ R2 @ ( episte6088726764479022859c_fm_a @ Y31 @ Y32 ) @ ( episte3759128466173231372c_fm_a @ X23 ) ) ).

% fm.rel_distinct(12)
thf(fact_614_fm_Oset__cases,axiom,
    ! [E: set_Epistemic_fm_a,A2: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ A2 ) )
     => ( ! [Z1: episte5999154429349999510c_fm_a] :
            ( ? [Z22: episte5999154429349999510c_fm_a] :
                ( A2
                = ( episte9190102072588321003c_fm_a @ Z1 @ Z22 ) )
           => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
       => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
              ( ( A2
                = ( episte9190102072588321003c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
         => ( ! [Z1: episte5999154429349999510c_fm_a] :
                ( ? [Z22: episte5999154429349999510c_fm_a] :
                    ( A2
                    = ( episte8719284489194433015c_fm_a @ Z1 @ Z22 ) )
               => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
           => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
                  ( ( A2
                    = ( episte8719284489194433015c_fm_a @ Z1 @ Z22 ) )
                 => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
             => ( ! [Z1: episte5999154429349999510c_fm_a] :
                    ( ? [Z22: episte5999154429349999510c_fm_a] :
                        ( A2
                        = ( episte5200161025749276397c_fm_a @ Z1 @ Z22 ) )
                   => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
               => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
                      ( ( A2
                        = ( episte5200161025749276397c_fm_a @ Z1 @ Z22 ) )
                     => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
                 => ( ! [Z22: episte5999154429349999510c_fm_a] :
                        ( A2
                       != ( episte3013695276341575662c_fm_a @ E @ Z22 ) )
                   => ~ ! [Z1: set_Epistemic_fm_a,Z22: episte5999154429349999510c_fm_a] :
                          ( ( A2
                            = ( episte3013695276341575662c_fm_a @ Z1 @ Z22 ) )
                         => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_615_fm_Oset__cases,axiom,
    ! [E: produc2203834439629243303c_fm_a,A2: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ A2 ) )
     => ( ! [Z1: episte5084476396027969859c_fm_a] :
            ( ? [Z22: episte5084476396027969859c_fm_a] :
                ( A2
                = ( episte7929989809337111832c_fm_a @ Z1 @ Z22 ) )
           => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z1 ) ) )
       => ( ! [Z1: episte5084476396027969859c_fm_a,Z22: episte5084476396027969859c_fm_a] :
              ( ( A2
                = ( episte7929989809337111832c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z22 ) ) )
         => ( ! [Z1: episte5084476396027969859c_fm_a] :
                ( ? [Z22: episte5084476396027969859c_fm_a] :
                    ( A2
                    = ( episte4221383773983074340c_fm_a @ Z1 @ Z22 ) )
               => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z1 ) ) )
           => ( ! [Z1: episte5084476396027969859c_fm_a,Z22: episte5084476396027969859c_fm_a] :
                  ( ( A2
                    = ( episte4221383773983074340c_fm_a @ Z1 @ Z22 ) )
                 => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z22 ) ) )
             => ( ! [Z1: episte5084476396027969859c_fm_a] :
                    ( ? [Z22: episte5084476396027969859c_fm_a] :
                        ( A2
                        = ( episte1929166352076780058c_fm_a @ Z1 @ Z22 ) )
                   => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z1 ) ) )
               => ( ! [Z1: episte5084476396027969859c_fm_a,Z22: episte5084476396027969859c_fm_a] :
                      ( ( A2
                        = ( episte1929166352076780058c_fm_a @ Z1 @ Z22 ) )
                     => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z22 ) ) )
                 => ( ! [Z22: episte5084476396027969859c_fm_a] :
                        ( A2
                       != ( episte8827083141269495451c_fm_a @ E @ Z22 ) )
                   => ~ ! [Z1: produc2203834439629243303c_fm_a,Z22: episte5084476396027969859c_fm_a] :
                          ( ( A2
                            = ( episte8827083141269495451c_fm_a @ Z1 @ Z22 ) )
                         => ~ ( member5029746173879296720c_fm_a @ E @ ( episte3354128426494757597c_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_616_fm_Oset__cases,axiom,
    ! [E: epistemic_fm_a,A2: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ A2 ) )
     => ( ! [Z1: episte740340785640729014c_fm_a] :
            ( ? [Z22: episte740340785640729014c_fm_a] :
                ( A2
                = ( episte6088726764479022859c_fm_a @ Z1 @ Z22 ) )
           => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z1 ) ) )
       => ( ! [Z1: episte740340785640729014c_fm_a,Z22: episte740340785640729014c_fm_a] :
              ( ( A2
                = ( episte6088726764479022859c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z22 ) ) )
         => ( ! [Z1: episte740340785640729014c_fm_a] :
                ( ? [Z22: episte740340785640729014c_fm_a] :
                    ( A2
                    = ( episte3685526487207141399c_fm_a @ Z1 @ Z22 ) )
               => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z1 ) ) )
           => ( ! [Z1: episte740340785640729014c_fm_a,Z22: episte740340785640729014c_fm_a] :
                  ( ( A2
                    = ( episte3685526487207141399c_fm_a @ Z1 @ Z22 ) )
                 => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z22 ) ) )
             => ( ! [Z1: episte740340785640729014c_fm_a] :
                    ( ? [Z22: episte740340785640729014c_fm_a] :
                        ( A2
                        = ( episte260752218777527565c_fm_a @ Z1 @ Z22 ) )
                   => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z1 ) ) )
               => ( ! [Z1: episte740340785640729014c_fm_a,Z22: episte740340785640729014c_fm_a] :
                      ( ( A2
                        = ( episte260752218777527565c_fm_a @ Z1 @ Z22 ) )
                     => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z22 ) ) )
                 => ( ! [Z22: episte740340785640729014c_fm_a] :
                        ( A2
                       != ( episte5657488632024175118c_fm_a @ E @ Z22 ) )
                   => ~ ! [Z1: epistemic_fm_a,Z22: episte740340785640729014c_fm_a] :
                          ( ( A2
                            = ( episte5657488632024175118c_fm_a @ Z1 @ Z22 ) )
                         => ~ ( member6642669571620171971c_fm_a @ E @ ( episte9089240958480457552c_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_617_fm_Oset__cases,axiom,
    ! [E: a,A2: epistemic_fm_a] :
      ( ( member_a @ E @ ( epistemic_set_fm_a @ A2 ) )
     => ( ! [Z1: epistemic_fm_a] :
            ( ? [Z22: epistemic_fm_a] :
                ( A2
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
           => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
              ( ( A2
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_a] :
                ( ? [Z22: epistemic_fm_a] :
                    ( A2
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
               => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                  ( ( A2
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
                 => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_a] :
                    ( ? [Z22: epistemic_fm_a] :
                        ( A2
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                   => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                      ( ( A2
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                     => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_a] :
                        ( A2
                       != ( epistemic_K_a @ E @ Z22 ) )
                   => ~ ! [Z1: a,Z22: epistemic_fm_a] :
                          ( ( A2
                            = ( epistemic_K_a @ Z1 @ Z22 ) )
                         => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_618_K__Boole,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,G5: list_E5775909407618282812c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ G5 ) @ episte5073044243917183961c_fm_a ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ P ) ) ) ).

% K_Boole
thf(fact_619_K__Boole,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ G5 ) @ epistemic_FF_a ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_Boole
thf(fact_620_strong__completeness,axiom,
    ! [P4: episte3877084617698231684t_unit > $o,G5: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a,A: episte740340785640729014c_fm_a > $o] :
      ( ! [M2: episte3877084617698231684t_unit] :
          ( ( P4 @ M2 )
         => ! [X2: set_Ep8485816078964734998c_fm_a] :
              ( ( member7847018790254331967c_fm_a @ X2 @ ( episte1339899947425360855t_unit @ M2 ) )
             => ( ! [Xa2: episte740340785640729014c_fm_a] :
                    ( ( member1118567890201975263c_fm_a @ Xa2 @ G5 )
                   => ( episte7132408285163024416c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7132408285163024416c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ( ( P4
          @ ( episte880584267092070412t_unit
            @ ( collec6235220954039818881c_fm_a
              @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                  ( ( episte704884124137261758c_fm_a @ A @ W5 )
                  & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
            @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
                ( collec6235220954039818881c_fm_a
                @ ( ord_le3671305448118956982c_fm_a
                  @ ( collec7281052159120012321c_fm_a
                    @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte9009970336799620271t_unit
              @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
              @ product_Unity ) ) )
       => ? [Qs2: list_E5775909407618282812c_fm_a] :
            ( ( ord_le3671305448118956982c_fm_a @ ( set_Ep2297100812554489931c_fm_a @ Qs2 ) @ G5 )
            & ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ Qs2 @ P ) ) ) ) ) ).

% strong_completeness
thf(fact_621_strong__completeness,axiom,
    ! [P4: episte1560738328020401952t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( P4 @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ( ( P4
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W5: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A @ W5 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
            @ ^ [I2: a,V2: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
              @ product_Unity ) ) )
       => ? [Qs2: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ) ).

% strong_completeness
thf(fact_622_K__conjunction__in__mult,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,G5: list_E5775909407618282812c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( episte5657488632024175118c_fm_a @ I @ ( stalna5968238273478151382c_fm_a @ G5 ) ) @ ( stalna5968238273478151382c_fm_a @ ( map_Ep5770154533994987716c_fm_a @ ( episte5657488632024175118c_fm_a @ I ) @ G5 ) ) ) ) ).

% K_conjunction_in_mult
thf(fact_623_K__conjunction__in__mult,axiom,
    ! [A: epistemic_fm_a > $o,I: a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( stalnaker_conjunct_a @ G5 ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G5 ) ) ) ) ).

% K_conjunction_in_mult
thf(fact_624_K__conjunction__out__mult,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,G5: list_E5775909407618282812c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ ( stalna5968238273478151382c_fm_a @ ( map_Ep5770154533994987716c_fm_a @ ( episte5657488632024175118c_fm_a @ I ) @ G5 ) ) @ ( episte5657488632024175118c_fm_a @ I @ ( stalna5968238273478151382c_fm_a @ G5 ) ) ) ) ).

% K_conjunction_out_mult
thf(fact_625_K__conjunction__out__mult,axiom,
    ! [A: epistemic_fm_a > $o,I: a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G5 ) ) @ ( epistemic_K_a @ I @ ( stalnaker_conjunct_a @ G5 ) ) ) ) ).

% K_conjunction_out_mult
thf(fact_626_Euclidean__def,axiom,
    ( episte4583239219080210381t_unit
    = ( ^ [M4: episte94448284482925344t_unit] :
        ! [I2: a,X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ ( episte6390737319716712051t_unit @ M4 ) )
         => ! [Y4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Y4 @ ( episte6390737319716712051t_unit @ M4 ) )
             => ! [Z4: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte6390737319716712051t_unit @ M4 ) )
                 => ( ( member6642669571620171971c_fm_a @ Y4 @ ( episte1446228887608813159t_unit @ M4 @ I2 @ X ) )
                   => ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte1446228887608813159t_unit @ M4 @ I2 @ X ) )
                     => ( member6642669571620171971c_fm_a @ Z4 @ ( episte1446228887608813159t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ) ).

% Euclidean_def
thf(fact_627_Euclidean__def,axiom,
    ( episte2449151000174023629t_unit
    = ( ^ [M4: episte1560738328020401952t_unit] :
        ! [I2: a,X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
         => ! [Y4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ! [Z4: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z4 @ ( episte8072386903178013299t_unit @ M4 ) )
                 => ( ( member536094252920883875c_fm_a @ Y4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) )
                   => ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) )
                     => ( member536094252920883875c_fm_a @ Z4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ) ).

% Euclidean_def
thf(fact_628_symmetric__def,axiom,
    ( episte2438601301504999334t_unit
    = ( ^ [M4: episte94448284482925344t_unit] :
        ! [I2: a,X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ ( episte6390737319716712051t_unit @ M4 ) )
         => ! [Y4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Y4 @ ( episte6390737319716712051t_unit @ M4 ) )
             => ( ( member6642669571620171971c_fm_a @ X @ ( episte1446228887608813159t_unit @ M4 @ I2 @ Y4 ) )
                = ( member6642669571620171971c_fm_a @ Y4 @ ( episte1446228887608813159t_unit @ M4 @ I2 @ X ) ) ) ) ) ) ) ).

% symmetric_def
thf(fact_629_symmetric__def,axiom,
    ( episte5478016696552465318t_unit
    = ( ^ [M4: episte1560738328020401952t_unit] :
        ! [I2: a,X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
         => ! [Y4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ( ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) )
                = ( member536094252920883875c_fm_a @ Y4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) ) ) ) ) ) ) ).

% symmetric_def
thf(fact_630_frame_Oext__inject,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit,W7: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More2: episte1193835314949844379t_unit] :
      ( ( ( episte2888590659910966568t_unit @ W6 @ K @ More )
        = ( episte2888590659910966568t_unit @ W7 @ K2 @ More2 ) )
      = ( ( W6 = W7 )
        & ( K = K2 )
        & ( More = More2 ) ) ) ).

% frame.ext_inject
thf(fact_631_kripke_Oext__inject,axiom,
    ! [Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit,Pi2: set_Epistemic_fm_a > list_char > $o,More2: product_unit] :
      ( ( ( episte8239586592105053771t_unit @ Pi @ More )
        = ( episte8239586592105053771t_unit @ Pi2 @ More2 ) )
      = ( ( Pi = Pi2 )
        & ( More = More2 ) ) ) ).

% kripke.ext_inject
thf(fact_632_map__ident,axiom,
    ( ( map_Ep7084560364594560580c_fm_a
      @ ^ [X: epistemic_fm_a] : X )
    = ( ^ [Xs2: list_Epistemic_fm_a] : Xs2 ) ) ).

% map_ident
thf(fact_633_list_Omap__ident,axiom,
    ! [T3: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a
        @ ^ [X: epistemic_fm_a] : X
        @ T3 )
      = T3 ) ).

% list.map_ident
thf(fact_634_frame_Oselect__convs_I2_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte6250069432388174439t_unit @ ( episte2888590659910966568t_unit @ W6 @ K @ More ) )
      = K ) ).

% frame.select_convs(2)
thf(fact_635_kripke_Ocases,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K3 @ ( episte8239586592105053771t_unit @ Pi3 @ product_Unity ) ) ) ).

% kripke.cases
thf(fact_636_kripke_Oext__induct,axiom,
    ! [P4: episte1193835314949844379t_unit > $o,R: episte1193835314949844379t_unit] :
      ( ! [Pi3: set_Epistemic_fm_a > list_char > $o,More3: product_unit] : ( P4 @ ( episte8239586592105053771t_unit @ Pi3 @ More3 ) )
     => ( P4 @ R ) ) ).

% kripke.ext_induct
thf(fact_637_frame_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More3: episte1193835314949844379t_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K3 @ More3 ) ) ).

% frame.cases_scheme
thf(fact_638_kripke_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o,More3: product_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K3 @ ( episte8239586592105053771t_unit @ Pi3 @ More3 ) ) ) ).

% kripke.cases_scheme
thf(fact_639_eval__semantics,axiom,
    ! [Pi4: epistemic_fm_a > list_char > $o,W: epistemic_fm_a,W3: set_Epistemic_fm_a,R: a > epistemic_fm_a > set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ ( Pi4 @ W ) @ ( episte5333283044364550848c_fm_a @ ( episte1317669246615791848t_unit @ W3 @ R @ ( episte8033297913184815147t_unit @ Pi4 @ product_Unity ) ) @ W ) @ P )
      = ( episte5333283044364550848c_fm_a @ ( episte1317669246615791848t_unit @ W3 @ R @ ( episte8033297913184815147t_unit @ Pi4 @ product_Unity ) ) @ W @ P ) ) ).

% eval_semantics
thf(fact_640_eval__semantics,axiom,
    ! [Pi4: set_Epistemic_fm_a > list_char > $o,W: set_Epistemic_fm_a,W3: set_se5208064806568342746c_fm_a,R: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ ( Pi4 @ W ) @ ( episte7081087998767065248c_fm_a @ ( episte2888590659910966568t_unit @ W3 @ R @ ( episte8239586592105053771t_unit @ Pi4 @ product_Unity ) ) @ W ) @ P )
      = ( episte7081087998767065248c_fm_a @ ( episte2888590659910966568t_unit @ W3 @ R @ ( episte8239586592105053771t_unit @ Pi4 @ product_Unity ) ) @ W @ P ) ) ).

% eval_semantics
thf(fact_641_kripke_Oselect__convs_I1_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte2398645135750866164t_unit @ ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = Pi ) ).

% kripke.select_convs(1)
thf(fact_642_fm_Oset__intros_I6_J,axiom,
    ! [Yf: set_Epistemic_fm_a,X52: episte5999154429349999510c_fm_a,X51: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Yf @ ( episte6227279731293865264c_fm_a @ X52 ) )
     => ( member536094252920883875c_fm_a @ Yf @ ( episte6227279731293865264c_fm_a @ ( episte5200161025749276397c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(6)
thf(fact_643_fm_Oset__intros_I6_J,axiom,
    ! [Yf: produc2203834439629243303c_fm_a,X52: episte5084476396027969859c_fm_a,X51: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Yf @ ( episte3354128426494757597c_fm_a @ X52 ) )
     => ( member5029746173879296720c_fm_a @ Yf @ ( episte3354128426494757597c_fm_a @ ( episte1929166352076780058c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(6)
thf(fact_644_fm_Oset__intros_I6_J,axiom,
    ! [Yf: epistemic_fm_a,X52: episte740340785640729014c_fm_a,X51: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Yf @ ( episte9089240958480457552c_fm_a @ X52 ) )
     => ( member6642669571620171971c_fm_a @ Yf @ ( episte9089240958480457552c_fm_a @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(6)
thf(fact_645_fm_Oset__intros_I6_J,axiom,
    ! [Yf: a,X52: epistemic_fm_a,X51: epistemic_fm_a] :
      ( ( member_a @ Yf @ ( epistemic_set_fm_a @ X52 ) )
     => ( member_a @ Yf @ ( epistemic_set_fm_a @ ( epistemic_Imp_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(6)
thf(fact_646_fm_Oset__intros_I5_J,axiom,
    ! [Ye: set_Epistemic_fm_a,X51: episte5999154429349999510c_fm_a,X52: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Ye @ ( episte6227279731293865264c_fm_a @ X51 ) )
     => ( member536094252920883875c_fm_a @ Ye @ ( episte6227279731293865264c_fm_a @ ( episte5200161025749276397c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(5)
thf(fact_647_fm_Oset__intros_I5_J,axiom,
    ! [Ye: produc2203834439629243303c_fm_a,X51: episte5084476396027969859c_fm_a,X52: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Ye @ ( episte3354128426494757597c_fm_a @ X51 ) )
     => ( member5029746173879296720c_fm_a @ Ye @ ( episte3354128426494757597c_fm_a @ ( episte1929166352076780058c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(5)
thf(fact_648_fm_Oset__intros_I5_J,axiom,
    ! [Ye: epistemic_fm_a,X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Ye @ ( episte9089240958480457552c_fm_a @ X51 ) )
     => ( member6642669571620171971c_fm_a @ Ye @ ( episte9089240958480457552c_fm_a @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(5)
thf(fact_649_fm_Oset__intros_I5_J,axiom,
    ! [Ye: a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( member_a @ Ye @ ( epistemic_set_fm_a @ X51 ) )
     => ( member_a @ Ye @ ( epistemic_set_fm_a @ ( epistemic_Imp_a @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(5)
thf(fact_650_fm_Oset__intros_I7_J,axiom,
    ! [X61: set_Epistemic_fm_a,X62: episte5999154429349999510c_fm_a] : ( member536094252920883875c_fm_a @ X61 @ ( episte6227279731293865264c_fm_a @ ( episte3013695276341575662c_fm_a @ X61 @ X62 ) ) ) ).

% fm.set_intros(7)
thf(fact_651_fm_Oset__intros_I7_J,axiom,
    ! [X61: produc2203834439629243303c_fm_a,X62: episte5084476396027969859c_fm_a] : ( member5029746173879296720c_fm_a @ X61 @ ( episte3354128426494757597c_fm_a @ ( episte8827083141269495451c_fm_a @ X61 @ X62 ) ) ) ).

% fm.set_intros(7)
thf(fact_652_fm_Oset__intros_I7_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] : ( member_a @ X61 @ ( epistemic_set_fm_a @ ( epistemic_K_a @ X61 @ X62 ) ) ) ).

% fm.set_intros(7)
thf(fact_653_fm_Oset__intros_I7_J,axiom,
    ! [X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] : ( member6642669571620171971c_fm_a @ X61 @ ( episte9089240958480457552c_fm_a @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ) ).

% fm.set_intros(7)
thf(fact_654_fm_Oset__intros_I8_J,axiom,
    ! [Yg: set_Epistemic_fm_a,X62: episte5999154429349999510c_fm_a,X61: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ Yg @ ( episte6227279731293865264c_fm_a @ X62 ) )
     => ( member536094252920883875c_fm_a @ Yg @ ( episte6227279731293865264c_fm_a @ ( episte3013695276341575662c_fm_a @ X61 @ X62 ) ) ) ) ).

% fm.set_intros(8)
thf(fact_655_fm_Oset__intros_I8_J,axiom,
    ! [Yg: produc2203834439629243303c_fm_a,X62: episte5084476396027969859c_fm_a,X61: produc2203834439629243303c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Yg @ ( episte3354128426494757597c_fm_a @ X62 ) )
     => ( member5029746173879296720c_fm_a @ Yg @ ( episte3354128426494757597c_fm_a @ ( episte8827083141269495451c_fm_a @ X61 @ X62 ) ) ) ) ).

% fm.set_intros(8)
thf(fact_656_fm_Oset__intros_I8_J,axiom,
    ! [Yg: a,X62: epistemic_fm_a,X61: a] :
      ( ( member_a @ Yg @ ( epistemic_set_fm_a @ X62 ) )
     => ( member_a @ Yg @ ( epistemic_set_fm_a @ ( epistemic_K_a @ X61 @ X62 ) ) ) ) ).

% fm.set_intros(8)
thf(fact_657_fm_Oset__intros_I8_J,axiom,
    ! [Yg: epistemic_fm_a,X62: episte740340785640729014c_fm_a,X61: epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Yg @ ( episte9089240958480457552c_fm_a @ X62 ) )
     => ( member6642669571620171971c_fm_a @ Yg @ ( episte9089240958480457552c_fm_a @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) ) ) ) ).

% fm.set_intros(8)
thf(fact_658_fm_Orel__cong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ya: episte740340785640729014c_fm_a,Y: episte740340785640729014c_fm_a,Xa3: episte740340785640729014c_fm_a,R2: epistemic_fm_a > epistemic_fm_a > $o,Ra: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: epistemic_fm_a,Yb: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte7774795710028497888c_fm_a @ R2 @ X3 @ Y )
            = ( episte7774795710028497888c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_659_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y: epistemic_fm_a,Xa3: epistemic_fm_a,R2: a > a > $o,Ra: a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: a,Yb: a] :
              ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_a_a @ R2 @ X3 @ Y )
            = ( epistemic_rel_fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_660_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y: episte740340785640729014c_fm_a,Xa3: episte740340785640729014c_fm_a,R2: a > epistemic_fm_a > $o,Ra: a > epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: a,Yb: epistemic_fm_a] :
              ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte8321036160184370300c_fm_a @ R2 @ X3 @ Y )
            = ( episte8321036160184370300c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_661_fm_Orel__cong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ya: episte740340785640729014c_fm_a,Y: epistemic_fm_a,Xa3: epistemic_fm_a,R2: epistemic_fm_a > a > $o,Ra: epistemic_fm_a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: epistemic_fm_a,Yb: a] :
              ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte4428145106359621316fm_a_a @ R2 @ X3 @ Y )
            = ( episte4428145106359621316fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_662_fm_Orel__cong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ya: episte5999154429349999510c_fm_a,Y: epistemic_fm_a,Xa3: epistemic_fm_a,R2: set_Epistemic_fm_a > a > $o,Ra: set_Epistemic_fm_a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: set_Epistemic_fm_a,Yb: a] :
              ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte7682788968413056228fm_a_a @ R2 @ X3 @ Y )
            = ( episte7682788968413056228fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_663_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y: episte5999154429349999510c_fm_a,Xa3: episte5999154429349999510c_fm_a,R2: a > set_Epistemic_fm_a > $o,Ra: a > set_Epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: a,Yb: set_Epistemic_fm_a] :
              ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte6665775379439401564c_fm_a @ R2 @ X3 @ Y )
            = ( episte6665775379439401564c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_664_fm_Orel__cong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ya: episte5999154429349999510c_fm_a,Y: episte740340785640729014c_fm_a,Xa3: episte740340785640729014c_fm_a,R2: set_Epistemic_fm_a > epistemic_fm_a > $o,Ra: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: set_Epistemic_fm_a,Yb: epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte6543039790609369600c_fm_a @ R2 @ X3 @ Y )
            = ( episte6543039790609369600c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_665_fm_Orel__cong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ya: episte740340785640729014c_fm_a,Y: episte5999154429349999510c_fm_a,Xa3: episte5999154429349999510c_fm_a,R2: epistemic_fm_a > set_Epistemic_fm_a > $o,Ra: epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: epistemic_fm_a,Yb: set_Epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte4430291480098810304c_fm_a @ R2 @ X3 @ Y )
            = ( episte4430291480098810304c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_666_fm_Orel__cong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ya: episte5999154429349999510c_fm_a,Y: episte5999154429349999510c_fm_a,Xa3: episte5999154429349999510c_fm_a,R2: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,Ra: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: set_Epistemic_fm_a,Yb: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte8246226516352692192c_fm_a @ R2 @ X3 @ Y )
            = ( episte8246226516352692192c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_667_fm_Orel__cong,axiom,
    ! [X3: episte5084476396027969859c_fm_a,Ya: episte5084476396027969859c_fm_a,Y: epistemic_fm_a,Xa3: epistemic_fm_a,R2: produc2203834439629243303c_fm_a > a > $o,Ra: produc2203834439629243303c_fm_a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa3 )
       => ( ! [Z5: produc2203834439629243303c_fm_a,Yb: a] :
              ( ( member5029746173879296720c_fm_a @ Z5 @ ( episte3354128426494757597c_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z5 @ Yb )
                  = ( Ra @ Z5 @ Yb ) ) ) )
         => ( ( episte7846634331556293879fm_a_a @ R2 @ X3 @ Y )
            = ( episte7846634331556293879fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_668_fm_Orel__mono__strong,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a,Y: episte740340785640729014c_fm_a,Ra: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( episte7774795710028497888c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: epistemic_fm_a,Yb: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte7774795710028497888c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_669_fm_Orel__mono__strong,axiom,
    ! [R2: a > a > $o,X3: epistemic_fm_a,Y: epistemic_fm_a,Ra: a > a > $o] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X3 @ Y )
     => ( ! [Z5: a,Yb: a] :
            ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( epistemic_rel_fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_670_fm_Orel__mono__strong,axiom,
    ! [R2: a > epistemic_fm_a > $o,X3: epistemic_fm_a,Y: episte740340785640729014c_fm_a,Ra: a > epistemic_fm_a > $o] :
      ( ( episte8321036160184370300c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: a,Yb: epistemic_fm_a] :
            ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte8321036160184370300c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_671_fm_Orel__mono__strong,axiom,
    ! [R2: epistemic_fm_a > a > $o,X3: episte740340785640729014c_fm_a,Y: epistemic_fm_a,Ra: epistemic_fm_a > a > $o] :
      ( ( episte4428145106359621316fm_a_a @ R2 @ X3 @ Y )
     => ( ! [Z5: epistemic_fm_a,Yb: a] :
            ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte4428145106359621316fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_672_fm_Orel__mono__strong,axiom,
    ! [R2: set_Epistemic_fm_a > a > $o,X3: episte5999154429349999510c_fm_a,Y: epistemic_fm_a,Ra: set_Epistemic_fm_a > a > $o] :
      ( ( episte7682788968413056228fm_a_a @ R2 @ X3 @ Y )
     => ( ! [Z5: set_Epistemic_fm_a,Yb: a] :
            ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte7682788968413056228fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_673_fm_Orel__mono__strong,axiom,
    ! [R2: a > set_Epistemic_fm_a > $o,X3: epistemic_fm_a,Y: episte5999154429349999510c_fm_a,Ra: a > set_Epistemic_fm_a > $o] :
      ( ( episte6665775379439401564c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: a,Yb: set_Epistemic_fm_a] :
            ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte6665775379439401564c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_674_fm_Orel__mono__strong,axiom,
    ! [R2: set_Epistemic_fm_a > epistemic_fm_a > $o,X3: episte5999154429349999510c_fm_a,Y: episte740340785640729014c_fm_a,Ra: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( episte6543039790609369600c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: set_Epistemic_fm_a,Yb: epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte6543039790609369600c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_675_fm_Orel__mono__strong,axiom,
    ! [R2: epistemic_fm_a > set_Epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a,Y: episte5999154429349999510c_fm_a,Ra: epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( episte4430291480098810304c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: epistemic_fm_a,Yb: set_Epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte4430291480098810304c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_676_fm_Orel__mono__strong,axiom,
    ! [R2: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,X3: episte5999154429349999510c_fm_a,Y: episte5999154429349999510c_fm_a,Ra: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( episte8246226516352692192c_fm_a @ R2 @ X3 @ Y )
     => ( ! [Z5: set_Epistemic_fm_a,Yb: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte8246226516352692192c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_677_fm_Orel__mono__strong,axiom,
    ! [R2: produc2203834439629243303c_fm_a > a > $o,X3: episte5084476396027969859c_fm_a,Y: epistemic_fm_a,Ra: produc2203834439629243303c_fm_a > a > $o] :
      ( ( episte7846634331556293879fm_a_a @ R2 @ X3 @ Y )
     => ( ! [Z5: produc2203834439629243303c_fm_a,Yb: a] :
            ( ( member5029746173879296720c_fm_a @ Z5 @ ( episte3354128426494757597c_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z5 @ Yb )
               => ( Ra @ Z5 @ Yb ) ) ) )
       => ( episte7846634331556293879fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_678_fm_Orel__refl__strong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ra: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ! [Z5: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ X3 ) )
         => ( Ra @ Z5 @ Z5 ) )
     => ( episte8246226516352692192c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_679_fm_Orel__refl__strong,axiom,
    ! [X3: episte5084476396027969859c_fm_a,Ra: produc2203834439629243303c_fm_a > produc2203834439629243303c_fm_a > $o] :
      ( ! [Z5: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ Z5 @ ( episte3354128426494757597c_fm_a @ X3 ) )
         => ( Ra @ Z5 @ Z5 ) )
     => ( episte3465247737680606624c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_680_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_a,Ra: a > a > $o] :
      ( ! [Z5: a] :
          ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ X3 ) )
         => ( Ra @ Z5 @ Z5 ) )
     => ( epistemic_rel_fm_a_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_681_fm_Orel__refl__strong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ra: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ! [Z5: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ X3 ) )
         => ( Ra @ Z5 @ Z5 ) )
     => ( episte7774795710028497888c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_682_fm_Oset__intros_I4_J,axiom,
    ! [Yd: set_Epistemic_fm_a,X42: episte5999154429349999510c_fm_a,X41: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Yd @ ( episte6227279731293865264c_fm_a @ X42 ) )
     => ( member536094252920883875c_fm_a @ Yd @ ( episte6227279731293865264c_fm_a @ ( episte8719284489194433015c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_683_fm_Oset__intros_I4_J,axiom,
    ! [Yd: produc2203834439629243303c_fm_a,X42: episte5084476396027969859c_fm_a,X41: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Yd @ ( episte3354128426494757597c_fm_a @ X42 ) )
     => ( member5029746173879296720c_fm_a @ Yd @ ( episte3354128426494757597c_fm_a @ ( episte4221383773983074340c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_684_fm_Oset__intros_I4_J,axiom,
    ! [Yd: epistemic_fm_a,X42: episte740340785640729014c_fm_a,X41: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Yd @ ( episte9089240958480457552c_fm_a @ X42 ) )
     => ( member6642669571620171971c_fm_a @ Yd @ ( episte9089240958480457552c_fm_a @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_685_fm_Oset__intros_I4_J,axiom,
    ! [Yd: a,X42: epistemic_fm_a,X41: epistemic_fm_a] :
      ( ( member_a @ Yd @ ( epistemic_set_fm_a @ X42 ) )
     => ( member_a @ Yd @ ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_686_fm_Oset__intros_I3_J,axiom,
    ! [Yc: set_Epistemic_fm_a,X41: episte5999154429349999510c_fm_a,X42: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Yc @ ( episte6227279731293865264c_fm_a @ X41 ) )
     => ( member536094252920883875c_fm_a @ Yc @ ( episte6227279731293865264c_fm_a @ ( episte8719284489194433015c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_687_fm_Oset__intros_I3_J,axiom,
    ! [Yc: produc2203834439629243303c_fm_a,X41: episte5084476396027969859c_fm_a,X42: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Yc @ ( episte3354128426494757597c_fm_a @ X41 ) )
     => ( member5029746173879296720c_fm_a @ Yc @ ( episte3354128426494757597c_fm_a @ ( episte4221383773983074340c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_688_fm_Oset__intros_I3_J,axiom,
    ! [Yc: epistemic_fm_a,X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Yc @ ( episte9089240958480457552c_fm_a @ X41 ) )
     => ( member6642669571620171971c_fm_a @ Yc @ ( episte9089240958480457552c_fm_a @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_689_fm_Oset__intros_I3_J,axiom,
    ! [Yc: a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( member_a @ Yc @ ( epistemic_set_fm_a @ X41 ) )
     => ( member_a @ Yc @ ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_690_fm_Oset__intros_I2_J,axiom,
    ! [Yb2: set_Epistemic_fm_a,X322: episte5999154429349999510c_fm_a,X312: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Yb2 @ ( episte6227279731293865264c_fm_a @ X322 ) )
     => ( member536094252920883875c_fm_a @ Yb2 @ ( episte6227279731293865264c_fm_a @ ( episte9190102072588321003c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(2)
thf(fact_691_fm_Oset__intros_I2_J,axiom,
    ! [Yb2: produc2203834439629243303c_fm_a,X322: episte5084476396027969859c_fm_a,X312: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Yb2 @ ( episte3354128426494757597c_fm_a @ X322 ) )
     => ( member5029746173879296720c_fm_a @ Yb2 @ ( episte3354128426494757597c_fm_a @ ( episte7929989809337111832c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(2)
thf(fact_692_fm_Oset__intros_I2_J,axiom,
    ! [Yb2: a,X322: epistemic_fm_a,X312: epistemic_fm_a] :
      ( ( member_a @ Yb2 @ ( epistemic_set_fm_a @ X322 ) )
     => ( member_a @ Yb2 @ ( epistemic_set_fm_a @ ( epistemic_Dis_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(2)
thf(fact_693_fm_Oset__intros_I2_J,axiom,
    ! [Yb2: epistemic_fm_a,X322: episte740340785640729014c_fm_a,X312: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Yb2 @ ( episte9089240958480457552c_fm_a @ X322 ) )
     => ( member6642669571620171971c_fm_a @ Yb2 @ ( episte9089240958480457552c_fm_a @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(2)
thf(fact_694_fm_Oset__intros_I1_J,axiom,
    ! [Ya: set_Epistemic_fm_a,X312: episte5999154429349999510c_fm_a,X322: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Ya @ ( episte6227279731293865264c_fm_a @ X312 ) )
     => ( member536094252920883875c_fm_a @ Ya @ ( episte6227279731293865264c_fm_a @ ( episte9190102072588321003c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(1)
thf(fact_695_fm_Oset__intros_I1_J,axiom,
    ! [Ya: produc2203834439629243303c_fm_a,X312: episte5084476396027969859c_fm_a,X322: episte5084476396027969859c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Ya @ ( episte3354128426494757597c_fm_a @ X312 ) )
     => ( member5029746173879296720c_fm_a @ Ya @ ( episte3354128426494757597c_fm_a @ ( episte7929989809337111832c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(1)
thf(fact_696_fm_Oset__intros_I1_J,axiom,
    ! [Ya: a,X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ( ( member_a @ Ya @ ( epistemic_set_fm_a @ X312 ) )
     => ( member_a @ Ya @ ( epistemic_set_fm_a @ ( epistemic_Dis_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(1)
thf(fact_697_fm_Oset__intros_I1_J,axiom,
    ! [Ya: epistemic_fm_a,X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Ya @ ( episte9089240958480457552c_fm_a @ X312 ) )
     => ( member6642669571620171971c_fm_a @ Ya @ ( episte9089240958480457552c_fm_a @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) ) ) ) ).

% fm.set_intros(1)
thf(fact_698_fm_Opred__cong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ya: episte5999154429349999510c_fm_a,P4: set_Epistemic_fm_a > $o,Pa: set_Epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z5: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ Ya ) )
           => ( ( P4 @ Z5 )
              = ( Pa @ Z5 ) ) )
       => ( ( episte1367365995573110961c_fm_a @ P4 @ X3 )
          = ( episte1367365995573110961c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_699_fm_Opred__cong,axiom,
    ! [X3: episte5084476396027969859c_fm_a,Ya: episte5084476396027969859c_fm_a,P4: produc2203834439629243303c_fm_a > $o,Pa: produc2203834439629243303c_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z5: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ Z5 @ ( episte3354128426494757597c_fm_a @ Ya ) )
           => ( ( P4 @ Z5 )
              = ( Pa @ Z5 ) ) )
       => ( ( episte221682106247147998c_fm_a @ P4 @ X3 )
          = ( episte221682106247147998c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_700_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,P4: a > $o,Pa: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z5: a] :
            ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ Ya ) )
           => ( ( P4 @ Z5 )
              = ( Pa @ Z5 ) ) )
       => ( ( epistemic_pred_fm_a @ P4 @ X3 )
          = ( epistemic_pred_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_701_fm_Opred__cong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ya: episte740340785640729014c_fm_a,P4: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z5: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ Ya ) )
           => ( ( P4 @ Z5 )
              = ( Pa @ Z5 ) ) )
       => ( ( episte3114992851182798545c_fm_a @ P4 @ X3 )
          = ( episte3114992851182798545c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_702_fm_Opred__mono__strong,axiom,
    ! [P4: set_Epistemic_fm_a > $o,X3: episte5999154429349999510c_fm_a,Pa: set_Epistemic_fm_a > $o] :
      ( ( episte1367365995573110961c_fm_a @ P4 @ X3 )
     => ( ! [Z5: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( P4 @ Z5 )
             => ( Pa @ Z5 ) ) )
       => ( episte1367365995573110961c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_703_fm_Opred__mono__strong,axiom,
    ! [P4: produc2203834439629243303c_fm_a > $o,X3: episte5084476396027969859c_fm_a,Pa: produc2203834439629243303c_fm_a > $o] :
      ( ( episte221682106247147998c_fm_a @ P4 @ X3 )
     => ( ! [Z5: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ Z5 @ ( episte3354128426494757597c_fm_a @ X3 ) )
           => ( ( P4 @ Z5 )
             => ( Pa @ Z5 ) ) )
       => ( episte221682106247147998c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_704_fm_Opred__mono__strong,axiom,
    ! [P4: a > $o,X3: epistemic_fm_a,Pa: a > $o] :
      ( ( epistemic_pred_fm_a @ P4 @ X3 )
     => ( ! [Z5: a] :
            ( ( member_a @ Z5 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( P4 @ Z5 )
             => ( Pa @ Z5 ) ) )
       => ( epistemic_pred_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_705_fm_Opred__mono__strong,axiom,
    ! [P4: epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a,Pa: epistemic_fm_a > $o] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ X3 )
     => ( ! [Z5: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z5 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( P4 @ Z5 )
             => ( Pa @ Z5 ) ) )
       => ( episte3114992851182798545c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_706_frame_Oselect__convs_I1_J,axiom,
    ! [W6: set_Epistemic_fm_a,K: a > epistemic_fm_a > set_Epistemic_fm_a,More: episte907100752178756475t_unit] :
      ( ( episte6390737319716712051t_unit @ ( episte1317669246615791848t_unit @ W6 @ K @ More ) )
      = W6 ) ).

% frame.select_convs(1)
thf(fact_707_frame_Oselect__convs_I1_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte8072386903178013299t_unit @ ( episte2888590659910966568t_unit @ W6 @ K @ More ) )
      = W6 ) ).

% frame.select_convs(1)
thf(fact_708_set__subset__Cons,axiom,
    ! [Xs: list_Epistemic_fm_a,X3: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X3 @ Xs ) ) ) ).

% set_subset_Cons
thf(fact_709_imply_Osimps_I2_J,axiom,
    ! [P: episte740340785640729014c_fm_a,Ps: list_E5775909407618282812c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ Ps ) @ Q )
      = ( episte260752218777527565c_fm_a @ P @ ( episte1272216372155829993c_fm_a @ Ps @ Q ) ) ) ).

% imply.simps(2)
thf(fact_710_imply_Osimps_I2_J,axiom,
    ! [P: epistemic_fm_a,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q )
      = ( epistemic_Imp_a @ P @ ( epistemic_imply_a @ Ps @ Q ) ) ) ).

% imply.simps(2)
thf(fact_711_K__swap,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G5: list_Epistemic_fm_a,R: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ Q @ G5 ) ) @ R ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ ( cons_Epistemic_fm_a @ P @ G5 ) ) @ R ) ) ) ).

% K_swap
thf(fact_712_K__imply__Cons,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) ) ) ).

% K_imply_Cons
thf(fact_713_K__imply__head,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ P ) ) ).

% K_imply_head
thf(fact_714_truth__lemma,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ V )
       => ( ( member1118567890201975263c_fm_a @ P @ V )
          = ( episte7132408285163024416c_fm_a
            @ ( episte880584267092070412t_unit
              @ ( collec6235220954039818881c_fm_a
                @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                    ( ( episte704884124137261758c_fm_a @ A @ W5 )
                    & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
              @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
                  ( collec6235220954039818881c_fm_a
                  @ ( ord_le3671305448118956982c_fm_a
                    @ ( collec7281052159120012321c_fm_a
                      @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
              @ ( episte9009970336799620271t_unit
                @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
                @ product_Unity ) )
            @ V
            @ P ) ) ) ) ).

% truth_lemma
thf(fact_715_truth__lemma,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V )
       => ( ( member6642669571620171971c_fm_a @ P @ V )
          = ( episte7081087998767065248c_fm_a
            @ ( episte2888590659910966568t_unit
              @ ( collec2519470961442302949c_fm_a
                @ ^ [W5: set_Epistemic_fm_a] :
                    ( ( episte2285483198712856226tent_a @ A @ W5 )
                    & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
              @ ^ [I2: a,V2: set_Epistemic_fm_a] :
                  ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
              @ ( episte8239586592105053771t_unit
                @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
                @ product_Unity ) )
            @ V
            @ P ) ) ) ) ).

% truth_lemma
thf(fact_716_conjunct_Osimps_I2_J,axiom,
    ! [P: episte740340785640729014c_fm_a,Ps: list_E5775909407618282812c_fm_a] :
      ( ( stalna5968238273478151382c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ Ps ) )
      = ( episte3685526487207141399c_fm_a @ P @ ( stalna5968238273478151382c_fm_a @ Ps ) ) ) ).

% conjunct.simps(2)
thf(fact_717_conjunct_Osimps_I2_J,axiom,
    ! [P: epistemic_fm_a,Ps: list_Epistemic_fm_a] :
      ( ( stalnaker_conjunct_a @ ( cons_Epistemic_fm_a @ P @ Ps ) )
      = ( epistemic_Con_a @ P @ ( stalnaker_conjunct_a @ Ps ) ) ) ).

% conjunct.simps(2)
thf(fact_718_K__distrib__K__imp,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,I: epistemic_fm_a,G5: list_E5775909407618282812c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte5657488632024175118c_fm_a @ I @ ( episte1272216372155829993c_fm_a @ G5 @ Q ) ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( map_Ep5770154533994987716c_fm_a @ ( episte5657488632024175118c_fm_a @ I ) @ G5 ) @ ( episte5657488632024175118c_fm_a @ I @ Q ) ) ) ) ).

% K_distrib_K_imp
thf(fact_719_K__distrib__K__imp,axiom,
    ! [A: epistemic_fm_a > $o,I: a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ ( epistemic_imply_a @ G5 @ Q ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G5 ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_distrib_K_imp
thf(fact_720_K__ImpI,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,G5: list_E5775909407618282812c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ G5 ) @ Q ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ ( episte260752218777527565c_fm_a @ P @ Q ) ) ) ) ).

% K_ImpI
thf(fact_721_K__ImpI,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G5 ) @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ ( epistemic_Imp_a @ P @ Q ) ) ) ) ).

% K_ImpI
thf(fact_722_K__mp,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a,G5: list_E5775909407618282812c_fm_a] : ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ ( cons_E3009779368504322924c_fm_a @ ( episte260752218777527565c_fm_a @ P @ Q ) @ G5 ) ) @ Q ) ) ).

% K_mp
thf(fact_723_K__mp,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ G5 ) ) @ Q ) ) ).

% K_mp
thf(fact_724_K__DisE,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,G5: list_E5775909407618282812c_fm_a,R: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ G5 ) @ R ) )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ Q @ G5 ) @ R ) )
       => ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ ( episte6088726764479022859c_fm_a @ P @ Q ) ) )
         => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ R ) ) ) ) ) ).

% K_DisE
thf(fact_725_K__DisE,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a,R: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G5 ) @ R ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ G5 ) @ R ) )
       => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ ( epistemic_Dis_a @ P @ Q ) ) )
         => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ R ) ) ) ) ) ).

% K_DisE
thf(fact_726_K__DisL,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,Ps: list_E5775909407618282812c_fm_a,Q: episte740340785640729014c_fm_a,P5: episte740340785640729014c_fm_a] :
      ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P @ Ps ) @ Q ) )
     => ( ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ P5 @ Ps ) @ Q ) )
       => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ ( cons_E3009779368504322924c_fm_a @ ( episte6088726764479022859c_fm_a @ P @ P5 ) @ Ps ) @ Q ) ) ) ) ).

% K_DisL
thf(fact_727_K__DisL,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P5: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P5 @ Ps ) @ Q ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Dis_a @ P @ P5 ) @ Ps ) @ Q ) ) ) ) ).

% K_DisL
thf(fact_728_reflexive_092_060_094sub_062T,axiom,
    ! [A: episte740340785640729014c_fm_a > $o] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4361910824569934085c_fm_a @ A )
     => ( episte3804094267682344703t_unit
        @ ( episte880584267092070412t_unit
          @ ( collec6235220954039818881c_fm_a
            @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                ( ( episte704884124137261758c_fm_a @ A @ W5 )
                & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
          @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
              ( collec6235220954039818881c_fm_a
              @ ( ord_le3671305448118956982c_fm_a
                @ ( collec7281052159120012321c_fm_a
                  @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte9009970336799620271t_unit
            @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% reflexive\<^sub>T
thf(fact_729_reflexive_092_060_094sub_062T,axiom,
    ! [A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( episte5648423998891577755t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W5: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A @ W5 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
          @ ^ [I2: a,V2: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% reflexive\<^sub>T
thf(fact_730_transitive_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [A: episte740340785640729014c_fm_a > $o] :
      ( ( ord_le7240545311762076327fm_a_o @ episte4964217022932375845c_fm_a @ A )
     => ( episte7636020103745521002t_unit
        @ ( episte880584267092070412t_unit
          @ ( collec6235220954039818881c_fm_a
            @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                ( ( episte704884124137261758c_fm_a @ A @ W5 )
                & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
          @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
              ( collec6235220954039818881c_fm_a
              @ ( ord_le3671305448118956982c_fm_a
                @ ( collec7281052159120012321c_fm_a
                  @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte9009970336799620271t_unit
            @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% transitive\<^sub>K\<^sub>4
thf(fact_731_transitive_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
     => ( episte8364071018013720454t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W5: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A @ W5 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
          @ ^ [I2: a,V2: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% transitive\<^sub>K\<^sub>4
thf(fact_732_symmetric_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [A: episte740340785640729014c_fm_a > $o] :
      ( ( ord_le7240545311762076327fm_a_o @ episte89022042721419671c_fm_a @ A )
     => ( episte1684026544603634058t_unit
        @ ( episte880584267092070412t_unit
          @ ( collec6235220954039818881c_fm_a
            @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                ( ( episte704884124137261758c_fm_a @ A @ W5 )
                & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
          @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
              ( collec6235220954039818881c_fm_a
              @ ( ord_le3671305448118956982c_fm_a
                @ ( collec7281052159120012321c_fm_a
                  @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte9009970336799620271t_unit
            @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% symmetric\<^sub>K\<^sub>B
thf(fact_733_symmetric_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
     => ( episte5478016696552465318t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W5: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A @ W5 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
          @ ^ [I2: a,V2: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% symmetric\<^sub>K\<^sub>B
thf(fact_734_Euclidean_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [A: episte740340785640729014c_fm_a > $o] :
      ( ( ord_le7240545311762076327fm_a_o @ episte7251237963447243492c_fm_a @ A )
     => ( episte105443737378589745t_unit
        @ ( episte880584267092070412t_unit
          @ ( collec6235220954039818881c_fm_a
            @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                ( ( episte704884124137261758c_fm_a @ A @ W5 )
                & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
          @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
              ( collec6235220954039818881c_fm_a
              @ ( ord_le3671305448118956982c_fm_a
                @ ( collec7281052159120012321c_fm_a
                  @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte9009970336799620271t_unit
            @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% Euclidean\<^sub>K\<^sub>5
thf(fact_735_Euclidean_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
     => ( episte2449151000174023629t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W5: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A @ W5 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
          @ ^ [I2: a,V2: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
            @ product_Unity ) ) ) ) ).

% Euclidean\<^sub>K\<^sub>5
thf(fact_736_transitive__def,axiom,
    ( episte8364071018013720454t_unit
    = ( ^ [M4: episte1560738328020401952t_unit] :
        ! [I2: a,X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
         => ! [Y4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ! [Z4: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z4 @ ( episte8072386903178013299t_unit @ M4 ) )
                 => ( ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) )
                      & ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Z4 ) ) )
                   => ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ).

% transitive_def
thf(fact_737_transitive__def,axiom,
    ( episte2264091934940175238t_unit
    = ( ^ [M4: episte94448284482925344t_unit] :
        ! [I2: a,X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ ( episte6390737319716712051t_unit @ M4 ) )
         => ! [Y4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Y4 @ ( episte6390737319716712051t_unit @ M4 ) )
             => ! [Z4: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte6390737319716712051t_unit @ M4 ) )
                 => ( ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte1446228887608813159t_unit @ M4 @ I2 @ Y4 ) )
                      & ( member6642669571620171971c_fm_a @ X @ ( episte1446228887608813159t_unit @ M4 @ I2 @ Z4 ) ) )
                   => ( member6642669571620171971c_fm_a @ X @ ( episte1446228887608813159t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ).

% transitive_def
thf(fact_738_reflexive__def,axiom,
    ( episte5633553332388074907t_unit
    = ( ^ [M4: episte94448284482925344t_unit] :
        ! [I2: a,X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ ( episte6390737319716712051t_unit @ M4 ) )
         => ( member6642669571620171971c_fm_a @ X @ ( episte1446228887608813159t_unit @ M4 @ I2 @ X ) ) ) ) ) ).

% reflexive_def
thf(fact_739_reflexive__def,axiom,
    ( episte5648423998891577755t_unit
    = ( ^ [M4: episte1560738328020401952t_unit] :
        ! [I2: a,X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M4 ) )
         => ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) ) ) ) ) ).

% reflexive_def
thf(fact_740_completeness,axiom,
    ! [P4: episte3877084617698231684t_unit > $o,P: episte740340785640729014c_fm_a,A: episte740340785640729014c_fm_a > $o] :
      ( ! [M2: episte3877084617698231684t_unit] :
          ( ( P4 @ M2 )
         => ! [X2: set_Ep8485816078964734998c_fm_a] :
              ( ( member7847018790254331967c_fm_a @ X2 @ ( episte1339899947425360855t_unit @ M2 ) )
             => ( ! [Xa2: episte740340785640729014c_fm_a] :
                    ( ( member1118567890201975263c_fm_a @ Xa2 @ bot_bo2004111608301611650c_fm_a )
                   => ( episte7132408285163024416c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7132408285163024416c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ( ( P4
          @ ( episte880584267092070412t_unit
            @ ( collec6235220954039818881c_fm_a
              @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                  ( ( episte704884124137261758c_fm_a @ A @ W5 )
                  & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
            @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
                ( collec6235220954039818881c_fm_a
                @ ( ord_le3671305448118956982c_fm_a
                  @ ( collec7281052159120012321c_fm_a
                    @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte9009970336799620271t_unit
              @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
              @ product_Unity ) ) )
       => ( episte3601224840237526918c_fm_a @ A @ P ) ) ) ).

% completeness
thf(fact_741_completeness,axiom,
    ! [P4: episte1560738328020401952t_unit > $o,P: epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( P4 @ M2 )
         => ! [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ bot_bo3626323581529592678c_fm_a )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) ) )
     => ( ( P4
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W5: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A @ W5 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
            @ ^ [I2: a,V2: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
              @ product_Unity ) ) )
       => ( epistemic_AK_a @ A @ P ) ) ) ).

% completeness
thf(fact_742_kripke_Osurjective,axiom,
    ! [R: episte94448284482925344t_unit] :
      ( R
      = ( episte1317669246615791848t_unit @ ( episte6390737319716712051t_unit @ R ) @ ( episte1446228887608813159t_unit @ R ) @ ( episte8033297913184815147t_unit @ ( episte5680354956628169428t_unit @ R ) @ ( episte5592780975282114042t_unit @ R ) ) ) ) ).

% kripke.surjective
thf(fact_743_kripke_Osurjective,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ( R
      = ( episte2888590659910966568t_unit @ ( episte8072386903178013299t_unit @ R ) @ ( episte6250069432388174439t_unit @ R ) @ ( episte8239586592105053771t_unit @ ( episte2398645135750866164t_unit @ R ) @ ( episte5479201149095757850t_unit @ R ) ) ) ) ).

% kripke.surjective
thf(fact_744_frame_Osurjective,axiom,
    ! [R: episte94448284482925344t_unit] :
      ( R
      = ( episte1317669246615791848t_unit @ ( episte6390737319716712051t_unit @ R ) @ ( episte1446228887608813159t_unit @ R ) @ ( episte6697046293004816513t_unit @ R ) ) ) ).

% frame.surjective
thf(fact_745_frame_Osurjective,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ( R
      = ( episte2888590659910966568t_unit @ ( episte8072386903178013299t_unit @ R ) @ ( episte6250069432388174439t_unit @ R ) @ ( episte3309513806868946049t_unit @ R ) ) ) ).

% frame.surjective
thf(fact_746_kripke_Oequality,axiom,
    ! [R: episte94448284482925344t_unit,R3: episte94448284482925344t_unit] :
      ( ( ( episte6390737319716712051t_unit @ R )
        = ( episte6390737319716712051t_unit @ R3 ) )
     => ( ( ( episte1446228887608813159t_unit @ R )
          = ( episte1446228887608813159t_unit @ R3 ) )
       => ( ( ( episte5680354956628169428t_unit @ R )
            = ( episte5680354956628169428t_unit @ R3 ) )
         => ( ( ( episte5592780975282114042t_unit @ R )
              = ( episte5592780975282114042t_unit @ R3 ) )
           => ( R = R3 ) ) ) ) ) ).

% kripke.equality
thf(fact_747_kripke_Oequality,axiom,
    ! [R: episte1560738328020401952t_unit,R3: episte1560738328020401952t_unit] :
      ( ( ( episte8072386903178013299t_unit @ R )
        = ( episte8072386903178013299t_unit @ R3 ) )
     => ( ( ( episte6250069432388174439t_unit @ R )
          = ( episte6250069432388174439t_unit @ R3 ) )
       => ( ( ( episte2398645135750866164t_unit @ R )
            = ( episte2398645135750866164t_unit @ R3 ) )
         => ( ( ( episte5479201149095757850t_unit @ R )
              = ( episte5479201149095757850t_unit @ R3 ) )
           => ( R = R3 ) ) ) ) ) ).

% kripke.equality
thf(fact_748_kripke_Oupdate__convs_I2_J,axiom,
    ! [More2: product_unit > product_unit,W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte9120385895580347753c_fm_a @ More2 @ ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ Pi @ ( More2 @ More ) ) ) ) ).

% kripke.update_convs(2)
thf(fact_749_subset__empty,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ bot_bo3626323581529592678c_fm_a )
      = ( A = bot_bo3626323581529592678c_fm_a ) ) ).

% subset_empty
thf(fact_750_empty__subsetI,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ bot_bo3626323581529592678c_fm_a @ A ) ).

% empty_subsetI
thf(fact_751_empty__def,axiom,
    ( bot_bo1868452413526482246c_fm_a
    = ( collec2519470961442302949c_fm_a
      @ ^ [X: set_Epistemic_fm_a] : $false ) ) ).

% empty_def
thf(fact_752_empty__def,axiom,
    ( bot_bo3626323581529592678c_fm_a
    = ( collec4904205152690461189c_fm_a
      @ ^ [X: epistemic_fm_a] : $false ) ) ).

% empty_def
thf(fact_753_bot_Oextremum,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ bot_bo6433428028861825271fm_a_o @ A2 ) ).

% bot.extremum
thf(fact_754_bot_Oextremum,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ bot_bo3626323581529592678c_fm_a @ A2 ) ).

% bot.extremum
thf(fact_755_bot_Oextremum__unique,axiom,
    ! [A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ bot_bo6433428028861825271fm_a_o )
      = ( A2 = bot_bo6433428028861825271fm_a_o ) ) ).

% bot.extremum_unique
thf(fact_756_bot_Oextremum__unique,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a )
      = ( A2 = bot_bo3626323581529592678c_fm_a ) ) ).

% bot.extremum_unique
thf(fact_757_bot_Oextremum__uniqueI,axiom,
    ! [A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ bot_bo6433428028861825271fm_a_o )
     => ( A2 = bot_bo6433428028861825271fm_a_o ) ) ).

% bot.extremum_uniqueI
thf(fact_758_bot_Oextremum__uniqueI,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a )
     => ( A2 = bot_bo3626323581529592678c_fm_a ) ) ).

% bot.extremum_uniqueI
thf(fact_759_subset__emptyI,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ~ ( member536094252920883875c_fm_a @ X2 @ A )
     => ( ord_le7112219575281605754c_fm_a @ A @ bot_bo1868452413526482246c_fm_a ) ) ).

% subset_emptyI
thf(fact_760_subset__emptyI,axiom,
    ! [A: set_a] :
      ( ! [X2: a] :
          ~ ( member_a @ X2 @ A )
     => ( ord_less_eq_set_a @ A @ bot_bot_set_a ) ) ).

% subset_emptyI
thf(fact_761_subset__emptyI,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a] :
      ( ! [X2: produc2203834439629243303c_fm_a] :
          ~ ( member5029746173879296720c_fm_a @ X2 @ A )
     => ( ord_le8222437384497874983c_fm_a @ A @ bot_bo7958537672377389811c_fm_a ) ) ).

% subset_emptyI
thf(fact_762_subset__emptyI,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ~ ( member6642669571620171971c_fm_a @ X2 @ A )
     => ( ord_le3275665582123262618c_fm_a @ A @ bot_bo3626323581529592678c_fm_a ) ) ).

% subset_emptyI
thf(fact_763_finite__has__maximal,axiom,
    ! [A: set_Epistemic_fm_a_o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ? [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ A )
            & ! [Xa2: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ Xa2 @ A )
               => ( ( ord_le4043730696559282883fm_a_o @ X2 @ Xa2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_maximal
thf(fact_764_finite__has__maximal,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ? [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
            & ! [Xa2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ Xa2 @ A )
               => ( ( ord_le3275665582123262618c_fm_a @ X2 @ Xa2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_maximal
thf(fact_765_finite__has__minimal,axiom,
    ! [A: set_Epistemic_fm_a_o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ? [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ A )
            & ! [Xa2: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ Xa2 @ A )
               => ( ( ord_le4043730696559282883fm_a_o @ Xa2 @ X2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_minimal
thf(fact_766_finite__has__minimal,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ? [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
            & ! [Xa2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ Xa2 @ A )
               => ( ( ord_le3275665582123262618c_fm_a @ Xa2 @ X2 )
                 => ( X2 = Xa2 ) ) ) ) ) ) ).

% finite_has_minimal
thf(fact_767_fm_Osimps_I90_J,axiom,
    ( ( epistemic_set_fm_a @ epistemic_FF_a )
    = bot_bot_set_a ) ).

% fm.simps(90)
thf(fact_768_fm_Osimps_I90_J,axiom,
    ( ( episte9089240958480457552c_fm_a @ episte5073044243917183961c_fm_a )
    = bot_bo3626323581529592678c_fm_a ) ).

% fm.simps(90)
thf(fact_769_fm_Osimps_I91_J,axiom,
    ! [X23: list_char] :
      ( ( epistemic_set_fm_a @ ( epistemic_Pro_a @ X23 ) )
      = bot_bot_set_a ) ).

% fm.simps(91)
thf(fact_770_fm_Osimps_I91_J,axiom,
    ! [X23: list_char] :
      ( ( episte9089240958480457552c_fm_a @ ( episte3759128466173231372c_fm_a @ X23 ) )
      = bot_bo3626323581529592678c_fm_a ) ).

% fm.simps(91)
thf(fact_771_frame_Oselect__convs_I3_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte3309513806868946049t_unit @ ( episte2888590659910966568t_unit @ W6 @ K @ More ) )
      = More ) ).

% frame.select_convs(3)
thf(fact_772_completeness_092_060_094sub_062A,axiom,
    ! [P: epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ! [M2: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M2 ) )
         => ( ! [Xa2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ Xa2 @ bot_bo3626323581529592678c_fm_a )
               => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ Xa2 ) )
           => ( episte7081087998767065248c_fm_a @ M2 @ X2 @ P ) ) )
     => ( epistemic_AK_a @ A @ P ) ) ).

% completeness\<^sub>A
thf(fact_773_frame_Oequality,axiom,
    ! [R: episte94448284482925344t_unit,R3: episte94448284482925344t_unit] :
      ( ( ( episte6390737319716712051t_unit @ R )
        = ( episte6390737319716712051t_unit @ R3 ) )
     => ( ( ( episte1446228887608813159t_unit @ R )
          = ( episte1446228887608813159t_unit @ R3 ) )
       => ( ( ( episte6697046293004816513t_unit @ R )
            = ( episte6697046293004816513t_unit @ R3 ) )
         => ( R = R3 ) ) ) ) ).

% frame.equality
thf(fact_774_frame_Oequality,axiom,
    ! [R: episte1560738328020401952t_unit,R3: episte1560738328020401952t_unit] :
      ( ( ( episte8072386903178013299t_unit @ R )
        = ( episte8072386903178013299t_unit @ R3 ) )
     => ( ( ( episte6250069432388174439t_unit @ R )
          = ( episte6250069432388174439t_unit @ R3 ) )
       => ( ( ( episte3309513806868946049t_unit @ R )
            = ( episte3309513806868946049t_unit @ R3 ) )
         => ( R = R3 ) ) ) ) ).

% frame.equality
thf(fact_775_kripke_Oselect__convs_I2_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte5479201149095757850t_unit @ ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = More ) ).

% kripke.select_convs(2)
thf(fact_776_kripke_Oupdate__convs_I1_J,axiom,
    ! [Pi2: ( set_Epistemic_fm_a > list_char > $o ) > set_Epistemic_fm_a > list_char > $o,W6: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte1857908288096881731t_unit @ Pi2 @ ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W6 @ K @ ( episte8239586592105053771t_unit @ ( Pi2 @ Pi ) @ More ) ) ) ).

% kripke.update_convs(1)
thf(fact_777_inconsistent__subset,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P @ bot_bo3626323581529592678c_fm_a ) @ V ) )
       => ~ ! [V3: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ V3 ) @ V )
             => ~ ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ V3 ) @ epistemic_FF_a ) ) ) ) ) ).

% inconsistent_subset
thf(fact_778_Shift__def,axiom,
    ( bNF_Gr8437504134799245625c_fm_a
    = ( ^ [Kl: set_li769143395467472256c_fm_a,K4: epistemic_fm_a] :
          ( collec5191077796991884427c_fm_a
          @ ^ [Kl2: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ K4 @ Kl2 ) @ Kl ) ) ) ) ).

% Shift_def
thf(fact_779_canonical__model_I1_J,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,S: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ S )
     => ( ( member1118567890201975263c_fm_a @ P @ S )
       => ( episte7132408285163024416c_fm_a
          @ ( episte880584267092070412t_unit
            @ ( collec6235220954039818881c_fm_a
              @ ^ [W5: set_Ep8485816078964734998c_fm_a] :
                  ( ( episte704884124137261758c_fm_a @ A @ W5 )
                  & ( maxima1560535778301255141c_fm_a @ ( episte704884124137261758c_fm_a @ A ) @ W5 ) ) )
            @ ^ [I2: epistemic_fm_a,V2: set_Ep8485816078964734998c_fm_a] :
                ( collec6235220954039818881c_fm_a
                @ ( ord_le3671305448118956982c_fm_a
                  @ ( collec7281052159120012321c_fm_a
                    @ ^ [P2: episte740340785640729014c_fm_a] : ( member1118567890201975263c_fm_a @ ( episte5657488632024175118c_fm_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte9009970336799620271t_unit
              @ ^ [V2: set_Ep8485816078964734998c_fm_a,X: list_char] : ( member1118567890201975263c_fm_a @ ( episte3759128466173231372c_fm_a @ X ) @ V2 )
              @ product_Unity ) )
          @ ( maxima7880383203592540967c_fm_a @ ( bNF_Ca3821065485395942930c_fm_a @ top_to4668791042291726694c_fm_a ) @ ( episte704884124137261758c_fm_a @ A ) @ S )
          @ P ) ) ) ).

% canonical_model(1)
thf(fact_780_canonical__model_I1_J,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( ( member6642669571620171971c_fm_a @ P @ S )
       => ( episte7081087998767065248c_fm_a
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W5: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A @ W5 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W5 ) ) )
            @ ^ [I2: a,V2: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P2 ) @ V2 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V2: set_Epistemic_fm_a,X: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X ) @ V2 )
              @ product_Unity ) )
          @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S )
          @ P ) ) ) ).

% canonical_model(1)
thf(fact_781_insert__subset,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ ( insert7129737658439086282c_fm_a @ X3 @ A ) @ B4 )
      = ( ( member536094252920883875c_fm_a @ X3 @ B4 )
        & ( ord_le7112219575281605754c_fm_a @ A @ B4 ) ) ) ).

% insert_subset
thf(fact_782_insert__subset,axiom,
    ! [X3: a,A: set_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ ( insert_a @ X3 @ A ) @ B4 )
      = ( ( member_a @ X3 @ B4 )
        & ( ord_less_eq_set_a @ A @ B4 ) ) ) ).

% insert_subset
thf(fact_783_insert__subset,axiom,
    ! [X3: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ ( insert4108635152042037623c_fm_a @ X3 @ A ) @ B4 )
      = ( ( member5029746173879296720c_fm_a @ X3 @ B4 )
        & ( ord_le8222437384497874983c_fm_a @ A @ B4 ) ) ) ).

% insert_subset
thf(fact_784_insert__subset,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ X3 @ A ) @ B4 )
      = ( ( member6642669571620171971c_fm_a @ X3 @ B4 )
        & ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ) ).

% insert_subset
thf(fact_785_Un__subset__iff,axiom,
    ! [A: set_a,B4: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B4 ) @ C2 )
      = ( ( ord_less_eq_set_a @ A @ C2 )
        & ( ord_less_eq_set_a @ B4 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_786_Un__subset__iff,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) @ C2 )
      = ( ( ord_le3275665582123262618c_fm_a @ A @ C2 )
        & ( ord_le3275665582123262618c_fm_a @ B4 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_787_Collect__const,axiom,
    ! [P4: $o] :
      ( ( P4
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [S5: set_Epistemic_fm_a] : P4 )
          = top_to5398033090887092778c_fm_a ) )
      & ( ~ P4
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [S5: set_Epistemic_fm_a] : P4 )
          = bot_bo1868452413526482246c_fm_a ) ) ) ).

% Collect_const
thf(fact_788_Collect__const,axiom,
    ! [P4: $o] :
      ( ( P4
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [S5: epistemic_fm_a] : P4 )
          = top_to7796028867103199306c_fm_a ) )
      & ( ~ P4
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [S5: epistemic_fm_a] : P4 )
          = bot_bo3626323581529592678c_fm_a ) ) ) ).

% Collect_const
thf(fact_789_finite__Collect__not,axiom,
    ! [P4: set_Epistemic_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ~ ( P4 @ X ) ) )
        = ( finite7364866884270929315c_fm_a @ top_to5398033090887092778c_fm_a ) ) ) ).

% finite_Collect_not
thf(fact_790_finite__Collect__not,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ~ ( P4 @ X ) ) )
        = ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a ) ) ) ).

% finite_Collect_not
thf(fact_791_singleton__conv2,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ( ^ [Y3: set_Epistemic_fm_a,Z: set_Epistemic_fm_a] : ( Y3 = Z )
          @ A2 ) )
      = ( insert7129737658439086282c_fm_a @ A2 @ bot_bo1868452413526482246c_fm_a ) ) ).

% singleton_conv2
thf(fact_792_singleton__conv2,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ( ^ [Y3: epistemic_fm_a,Z: epistemic_fm_a] : ( Y3 = Z )
          @ A2 ) )
      = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) ).

% singleton_conv2
thf(fact_793_singleton__conv,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] : ( X = A2 ) )
      = ( insert7129737658439086282c_fm_a @ A2 @ bot_bo1868452413526482246c_fm_a ) ) ).

% singleton_conv
thf(fact_794_singleton__conv,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] : ( X = A2 ) )
      = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) ).

% singleton_conv
thf(fact_795_singleton__insert__inj__eq_H,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( ( insert7817948963269374698c_fm_a @ A2 @ A )
        = ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a ) )
      = ( ( A2 = B )
        & ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_796_singleton__insert__inj__eq,axiom,
    ! [B: epistemic_fm_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a )
        = ( insert7817948963269374698c_fm_a @ A2 @ A ) )
      = ( ( A2 = B )
        & ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_797_fm_Osimps_I95_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_K_a @ X61 @ X62 ) )
      = ( insert_a @ X61 @ ( epistemic_set_fm_a @ X62 ) ) ) ).

% fm.simps(95)
thf(fact_798_fm_Osimps_I95_J,axiom,
    ! [X61: epistemic_fm_a,X62: episte740340785640729014c_fm_a] :
      ( ( episte9089240958480457552c_fm_a @ ( episte5657488632024175118c_fm_a @ X61 @ X62 ) )
      = ( insert7817948963269374698c_fm_a @ X61 @ ( episte9089240958480457552c_fm_a @ X62 ) ) ) ).

% fm.simps(95)
thf(fact_799_MCS_OExtend__subset,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima1924290459274269190c_fm_a @ Consistent )
     => ( ord_le3275665582123262618c_fm_a @ S @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ Consistent @ S ) ) ) ).

% MCS.Extend_subset
thf(fact_800_MCS_Omaximal__Extend,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima1924290459274269190c_fm_a @ Consistent )
     => ( maxima3264069584562520521c_fm_a @ Consistent @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ Consistent @ S ) ) ) ).

% MCS.maximal_Extend
thf(fact_801_UNIV__def,axiom,
    ( top_to5398033090887092778c_fm_a
    = ( collec2519470961442302949c_fm_a
      @ ^ [X: set_Epistemic_fm_a] : $true ) ) ).

% UNIV_def
thf(fact_802_UNIV__def,axiom,
    ( top_to7796028867103199306c_fm_a
    = ( collec4904205152690461189c_fm_a
      @ ^ [X: epistemic_fm_a] : $true ) ) ).

% UNIV_def
thf(fact_803_MCS__Lim__Ord_OExtend_Ocong,axiom,
    maxima2580775624958445067c_fm_a = maxima2580775624958445067c_fm_a ).

% MCS_Lim_Ord.Extend.cong
thf(fact_804_consistent__Extend,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( episte2285483198712856226tent_a @ A @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ) ).

% consistent_Extend
thf(fact_805_canonical__model_I2_J,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( ( member6642669571620171971c_fm_a @ P @ S )
       => ( episte2285483198712856226tent_a @ A @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ) ) ).

% canonical_model(2)
thf(fact_806_Collect__disj__eq,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( P4 @ X )
            | ( Q4 @ X ) ) )
      = ( sup_su4305657963326700718c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ).

% Collect_disj_eq
thf(fact_807_Collect__disj__eq,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( P4 @ X )
            | ( Q4 @ X ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ).

% Collect_disj_eq
thf(fact_808_Collect__disj__eq,axiom,
    ! [P4: a > $o,Q4: a > $o] :
      ( ( collect_a
        @ ^ [X: a] :
            ( ( P4 @ X )
            | ( Q4 @ X ) ) )
      = ( sup_sup_set_a @ ( collect_a @ P4 ) @ ( collect_a @ Q4 ) ) ) ).

% Collect_disj_eq
thf(fact_809_insert__Collect,axiom,
    ! [A2: epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( insert7817948963269374698c_fm_a @ A2 @ ( collec4904205152690461189c_fm_a @ P4 ) )
      = ( collec4904205152690461189c_fm_a
        @ ^ [U2: epistemic_fm_a] :
            ( ( U2 != A2 )
           => ( P4 @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_810_insert__Collect,axiom,
    ! [A2: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( insert7129737658439086282c_fm_a @ A2 @ ( collec2519470961442302949c_fm_a @ P4 ) )
      = ( collec2519470961442302949c_fm_a
        @ ^ [U2: set_Epistemic_fm_a] :
            ( ( U2 != A2 )
           => ( P4 @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_811_insert__compr,axiom,
    ( insert_a
    = ( ^ [A4: a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( X = A4 )
              | ( member_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_812_insert__compr,axiom,
    ( insert4108635152042037623c_fm_a
    = ( ^ [A4: produc2203834439629243303c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
          ( collec7391038856303340306c_fm_a
          @ ^ [X: produc2203834439629243303c_fm_a] :
              ( ( X = A4 )
              | ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_813_insert__compr,axiom,
    ( insert7129737658439086282c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B3: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( X = A4 )
              | ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_814_insert__compr,axiom,
    ( insert7817948963269374698c_fm_a
    = ( ^ [A4: epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( X = A4 )
              | ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_815_insert__def,axiom,
    ( insert7129737658439086282c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a] :
          ( sup_su4305657963326700718c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_816_insert__def,axiom,
    ( insert7817948963269374698c_fm_a
    = ( ^ [A4: epistemic_fm_a] :
          ( sup_su1367922730591523534c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_817_insert__def,axiom,
    ( insert_a
    = ( ^ [A4: a] :
          ( sup_sup_set_a
          @ ( collect_a
            @ ^ [X: a] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_818_Un__def,axiom,
    ( sup_su6976870698533002843c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
          ( collec7391038856303340306c_fm_a
          @ ^ [X: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X @ A3 )
              | ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_819_Un__def,axiom,
    ( sup_su4305657963326700718c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ A3 )
              | ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_820_Un__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A3 )
              | ( member_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_821_Un__def,axiom,
    ( sup_su1367922730591523534c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A3 )
              | ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_822_canonical__model_I3_J,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( ( member6642669571620171971c_fm_a @ P @ S )
       => ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ) ) ).

% canonical_model(3)
thf(fact_823_maximal__Extend,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] : ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ).

% maximal_Extend
thf(fact_824_Extend__subset,axiom,
    ! [S: set_Epistemic_fm_a,A: epistemic_fm_a > $o] : ( ord_le3275665582123262618c_fm_a @ S @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ).

% Extend_subset
thf(fact_825_top_Oextremum__uniqueI,axiom,
    ! [A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ top_to6710954824118802707fm_a_o @ A2 )
     => ( A2 = top_to6710954824118802707fm_a_o ) ) ).

% top.extremum_uniqueI
thf(fact_826_top_Oextremum__uniqueI,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ top_to7796028867103199306c_fm_a @ A2 )
     => ( A2 = top_to7796028867103199306c_fm_a ) ) ).

% top.extremum_uniqueI
thf(fact_827_top_Oextremum__unique,axiom,
    ! [A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ top_to6710954824118802707fm_a_o @ A2 )
      = ( A2 = top_to6710954824118802707fm_a_o ) ) ).

% top.extremum_unique
thf(fact_828_top_Oextremum__unique,axiom,
    ! [A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ top_to7796028867103199306c_fm_a @ A2 )
      = ( A2 = top_to7796028867103199306c_fm_a ) ) ).

% top.extremum_unique
thf(fact_829_top__greatest,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ top_to6710954824118802707fm_a_o ) ).

% top_greatest
thf(fact_830_top__greatest,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ top_to7796028867103199306c_fm_a ) ).

% top_greatest
thf(fact_831_subset__Un__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( ( sup_sup_set_a @ A3 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_832_subset__Un__eq,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( ( sup_su1367922730591523534c_fm_a @ A3 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_833_subset__UnE,axiom,
    ! [C2: set_a,A: set_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ C2 @ ( sup_sup_set_a @ A @ B4 ) )
     => ~ ! [A5: set_a] :
            ( ( ord_less_eq_set_a @ A5 @ A )
           => ! [B5: set_a] :
                ( ( ord_less_eq_set_a @ B5 @ B4 )
               => ( C2
                 != ( sup_sup_set_a @ A5 @ B5 ) ) ) ) ) ).

% subset_UnE
thf(fact_834_subset__UnE,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C2 @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) )
     => ~ ! [A5: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ A5 @ A )
           => ! [B5: set_Epistemic_fm_a] :
                ( ( ord_le3275665582123262618c_fm_a @ B5 @ B4 )
               => ( C2
                 != ( sup_su1367922730591523534c_fm_a @ A5 @ B5 ) ) ) ) ) ).

% subset_UnE
thf(fact_835_Un__absorb2,axiom,
    ! [B4: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ B4 @ A )
     => ( ( sup_sup_set_a @ A @ B4 )
        = A ) ) ).

% Un_absorb2
thf(fact_836_Un__absorb2,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ A )
     => ( ( sup_su1367922730591523534c_fm_a @ A @ B4 )
        = A ) ) ).

% Un_absorb2
thf(fact_837_Un__absorb1,axiom,
    ! [A: set_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ( sup_sup_set_a @ A @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_838_Un__absorb1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ( sup_su1367922730591523534c_fm_a @ A @ B4 )
        = B4 ) ) ).

% Un_absorb1
thf(fact_839_Un__upper2,axiom,
    ! [B4: set_a,A: set_a] : ( ord_less_eq_set_a @ B4 @ ( sup_sup_set_a @ A @ B4 ) ) ).

% Un_upper2
thf(fact_840_Un__upper2,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ B4 @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) ).

% Un_upper2
thf(fact_841_Un__upper1,axiom,
    ! [A: set_a,B4: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B4 ) ) ).

% Un_upper1
thf(fact_842_Un__upper1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) ).

% Un_upper1
thf(fact_843_Un__least,axiom,
    ! [A: set_a,C2: set_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ A @ C2 )
     => ( ( ord_less_eq_set_a @ B4 @ C2 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B4 ) @ C2 ) ) ) ).

% Un_least
thf(fact_844_Un__least,axiom,
    ! [A: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ C2 )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ C2 )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) @ C2 ) ) ) ).

% Un_least
thf(fact_845_Un__mono,axiom,
    ! [A: set_a,C2: set_a,B4: set_a,D: set_a] :
      ( ( ord_less_eq_set_a @ A @ C2 )
     => ( ( ord_less_eq_set_a @ B4 @ D )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B4 ) @ ( sup_sup_set_a @ C2 @ D ) ) ) ) ).

% Un_mono
thf(fact_846_Un__mono,axiom,
    ! [A: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ C2 )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ D )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) @ ( sup_su1367922730591523534c_fm_a @ C2 @ D ) ) ) ) ).

% Un_mono
thf(fact_847_insert__subsetI,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,X5: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ( ord_le7112219575281605754c_fm_a @ X5 @ A )
       => ( ord_le7112219575281605754c_fm_a @ ( insert7129737658439086282c_fm_a @ X3 @ X5 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_848_insert__subsetI,axiom,
    ! [X3: a,A: set_a,X5: set_a] :
      ( ( member_a @ X3 @ A )
     => ( ( ord_less_eq_set_a @ X5 @ A )
       => ( ord_less_eq_set_a @ ( insert_a @ X3 @ X5 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_849_insert__subsetI,axiom,
    ! [X3: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,X5: set_Pr8948481099588399239c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X3 @ A )
     => ( ( ord_le8222437384497874983c_fm_a @ X5 @ A )
       => ( ord_le8222437384497874983c_fm_a @ ( insert4108635152042037623c_fm_a @ X3 @ X5 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_850_insert__subsetI,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,X5: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X3 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ X5 @ A )
       => ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ X3 @ X5 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_851_subset__insertI2,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ B @ B4 ) ) ) ).

% subset_insertI2
thf(fact_852_subset__insertI,axiom,
    ! [B4: set_Epistemic_fm_a,A2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ B4 @ ( insert7817948963269374698c_fm_a @ A2 @ B4 ) ) ).

% subset_insertI
thf(fact_853_subset__insert,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ~ ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ( ord_le7112219575281605754c_fm_a @ A @ ( insert7129737658439086282c_fm_a @ X3 @ B4 ) )
        = ( ord_le7112219575281605754c_fm_a @ A @ B4 ) ) ) ).

% subset_insert
thf(fact_854_subset__insert,axiom,
    ! [X3: a,A: set_a,B4: set_a] :
      ( ~ ( member_a @ X3 @ A )
     => ( ( ord_less_eq_set_a @ A @ ( insert_a @ X3 @ B4 ) )
        = ( ord_less_eq_set_a @ A @ B4 ) ) ) ).

% subset_insert
thf(fact_855_subset__insert,axiom,
    ! [X3: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ~ ( member5029746173879296720c_fm_a @ X3 @ A )
     => ( ( ord_le8222437384497874983c_fm_a @ A @ ( insert4108635152042037623c_fm_a @ X3 @ B4 ) )
        = ( ord_le8222437384497874983c_fm_a @ A @ B4 ) ) ) ).

% subset_insert
thf(fact_856_subset__insert,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( member6642669571620171971c_fm_a @ X3 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ X3 @ B4 ) )
        = ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ) ).

% subset_insert
thf(fact_857_insert__mono,axiom,
    ! [C2: set_Epistemic_fm_a,D: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C2 @ D )
     => ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ A2 @ C2 ) @ ( insert7817948963269374698c_fm_a @ A2 @ D ) ) ) ).

% insert_mono
thf(fact_858_subset__UNIV,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ top_to7796028867103199306c_fm_a ) ).

% subset_UNIV
thf(fact_859_Collect__conv__if2,axiom,
    ! [P4: set_Epistemic_fm_a > $o,A2: set_Epistemic_fm_a] :
      ( ( ( P4 @ A2 )
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = ( insert7129737658439086282c_fm_a @ A2 @ bot_bo1868452413526482246c_fm_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = bot_bo1868452413526482246c_fm_a ) ) ) ).

% Collect_conv_if2
thf(fact_860_Collect__conv__if2,axiom,
    ! [P4: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( ( P4 @ A2 )
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = bot_bo3626323581529592678c_fm_a ) ) ) ).

% Collect_conv_if2
thf(fact_861_Collect__conv__if,axiom,
    ! [P4: set_Epistemic_fm_a > $o,A2: set_Epistemic_fm_a] :
      ( ( ( P4 @ A2 )
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = ( insert7129737658439086282c_fm_a @ A2 @ bot_bo1868452413526482246c_fm_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = bot_bo1868452413526482246c_fm_a ) ) ) ).

% Collect_conv_if
thf(fact_862_Collect__conv__if,axiom,
    ! [P4: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( ( P4 @ A2 )
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = bot_bo3626323581529592678c_fm_a ) ) ) ).

% Collect_conv_if
thf(fact_863_consistent__disjuncts,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( member1118567890201975263c_fm_a @ ( episte6088726764479022859c_fm_a @ P @ Q ) @ V )
       => ( ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ P @ bot_bo2004111608301611650c_fm_a ) @ V ) )
          | ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ Q @ bot_bo2004111608301611650c_fm_a ) @ V ) ) ) ) ) ).

% consistent_disjuncts
thf(fact_864_consistent__disjuncts,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( member6642669571620171971c_fm_a @ ( epistemic_Dis_a @ P @ Q ) @ V )
       => ( ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P @ bot_bo3626323581529592678c_fm_a ) @ V ) )
          | ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V ) ) ) ) ) ).

% consistent_disjuncts
thf(fact_865_maximal__def,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ S )
      = ( ! [P2: epistemic_fm_a] :
            ( ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P2 @ bot_bo3626323581529592678c_fm_a ) @ S ) )
           => ( member6642669571620171971c_fm_a @ P2 @ S ) ) ) ) ).

% maximal_def
thf(fact_866_MCS_Omaximal__def,axiom,
    ! [Consistent: set_se5208064806568342746c_fm_a > $o,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima4972129789629145062c_fm_a @ Consistent )
     => ( ( maxima7173642526191862697c_fm_a @ Consistent @ S )
        = ( ! [P2: set_Epistemic_fm_a] :
              ( ( Consistent @ ( sup_su4305657963326700718c_fm_a @ ( insert7129737658439086282c_fm_a @ P2 @ bot_bo1868452413526482246c_fm_a ) @ S ) )
             => ( member536094252920883875c_fm_a @ P2 @ S ) ) ) ) ) ).

% MCS.maximal_def
thf(fact_867_MCS_Omaximal__def,axiom,
    ! [Consistent: set_Pr8948481099588399239c_fm_a > $o,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima6892556003377668755c_fm_a @ Consistent )
     => ( ( maxima2158090237565087958c_fm_a @ Consistent @ S )
        = ( ! [P2: produc2203834439629243303c_fm_a] :
              ( ( Consistent @ ( sup_su6976870698533002843c_fm_a @ ( insert4108635152042037623c_fm_a @ P2 @ bot_bo7958537672377389811c_fm_a ) @ S ) )
             => ( member5029746173879296720c_fm_a @ P2 @ S ) ) ) ) ) ).

% MCS.maximal_def
thf(fact_868_MCS_Omaximal__def,axiom,
    ! [Consistent: set_a > $o,S: set_a] :
      ( ( maxima4369210283088814570_MCS_a @ Consistent )
     => ( ( maxima1626912167156234285imal_a @ Consistent @ S )
        = ( ! [P2: a] :
              ( ( Consistent @ ( sup_sup_set_a @ ( insert_a @ P2 @ bot_bot_set_a ) @ S ) )
             => ( member_a @ P2 @ S ) ) ) ) ) ).

% MCS.maximal_def
thf(fact_869_MCS_Omaximal__def,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima1924290459274269190c_fm_a @ Consistent )
     => ( ( maxima3264069584562520521c_fm_a @ Consistent @ S )
        = ( ! [P2: epistemic_fm_a] :
              ( ( Consistent @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P2 @ bot_bo3626323581529592678c_fm_a ) @ S ) )
             => ( member6642669571620171971c_fm_a @ P2 @ S ) ) ) ) ) ).

% MCS.maximal_def
thf(fact_870_subset__singleton__iff,axiom,
    ! [X5: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X5 @ ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) )
      = ( ( X5 = bot_bo3626323581529592678c_fm_a )
        | ( X5
          = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% subset_singleton_iff
thf(fact_871_subset__singletonD,axiom,
    ! [A: set_Epistemic_fm_a,X3: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ X3 @ bot_bo3626323581529592678c_fm_a ) )
     => ( ( A = bot_bo3626323581529592678c_fm_a )
        | ( A
          = ( insert7817948963269374698c_fm_a @ X3 @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% subset_singletonD
thf(fact_872_infinite__UNIV__fm,axiom,
    ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% infinite_UNIV_fm
thf(fact_873_consistent__consequent,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( member1118567890201975263c_fm_a @ P @ V )
       => ( ( episte3601224840237526918c_fm_a @ A @ ( episte260752218777527565c_fm_a @ P @ Q ) )
         => ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ Q @ bot_bo2004111608301611650c_fm_a ) @ V ) ) ) ) ) ).

% consistent_consequent
thf(fact_874_consistent__consequent,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( member6642669571620171971c_fm_a @ P @ V )
       => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V ) ) ) ) ) ).

% consistent_consequent
thf(fact_875_consistent__consequent_H,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,V: set_Ep8485816078964734998c_fm_a,P: episte740340785640729014c_fm_a,Q: episte740340785640729014c_fm_a] :
      ( ( episte704884124137261758c_fm_a @ A @ V )
     => ( ( member1118567890201975263c_fm_a @ P @ V )
       => ( ! [G3: list_char > $o,H3: episte740340785640729014c_fm_a > $o] : ( episte6292435812075825844c_fm_a @ G3 @ H3 @ ( episte260752218777527565c_fm_a @ P @ Q ) )
         => ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ Q @ bot_bo2004111608301611650c_fm_a ) @ V ) ) ) ) ) ).

% consistent_consequent'
thf(fact_876_consistent__consequent_H,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ( ( member6642669571620171971c_fm_a @ P @ V )
       => ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V ) ) ) ) ) ).

% consistent_consequent'
thf(fact_877_fm_Osimps_I94_J,axiom,
    ! [X51: episte740340785640729014c_fm_a,X52: episte740340785640729014c_fm_a] :
      ( ( episte9089240958480457552c_fm_a @ ( episte260752218777527565c_fm_a @ X51 @ X52 ) )
      = ( sup_su1367922730591523534c_fm_a @ ( episte9089240958480457552c_fm_a @ X51 ) @ ( episte9089240958480457552c_fm_a @ X52 ) ) ) ).

% fm.simps(94)
thf(fact_878_fm_Osimps_I94_J,axiom,
    ! [X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_Imp_a @ X51 @ X52 ) )
      = ( sup_sup_set_a @ ( epistemic_set_fm_a @ X51 ) @ ( epistemic_set_fm_a @ X52 ) ) ) ).

% fm.simps(94)
thf(fact_879_fm_Osimps_I93_J,axiom,
    ! [X41: episte740340785640729014c_fm_a,X42: episte740340785640729014c_fm_a] :
      ( ( episte9089240958480457552c_fm_a @ ( episte3685526487207141399c_fm_a @ X41 @ X42 ) )
      = ( sup_su1367922730591523534c_fm_a @ ( episte9089240958480457552c_fm_a @ X41 ) @ ( episte9089240958480457552c_fm_a @ X42 ) ) ) ).

% fm.simps(93)
thf(fact_880_fm_Osimps_I93_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) )
      = ( sup_sup_set_a @ ( epistemic_set_fm_a @ X41 ) @ ( epistemic_set_fm_a @ X42 ) ) ) ).

% fm.simps(93)
thf(fact_881_fm_Osimps_I92_J,axiom,
    ! [X312: epistemic_fm_a,X322: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_Dis_a @ X312 @ X322 ) )
      = ( sup_sup_set_a @ ( epistemic_set_fm_a @ X312 ) @ ( epistemic_set_fm_a @ X322 ) ) ) ).

% fm.simps(92)
thf(fact_882_fm_Osimps_I92_J,axiom,
    ! [X312: episte740340785640729014c_fm_a,X322: episte740340785640729014c_fm_a] :
      ( ( episte9089240958480457552c_fm_a @ ( episte6088726764479022859c_fm_a @ X312 @ X322 ) )
      = ( sup_su1367922730591523534c_fm_a @ ( episte9089240958480457552c_fm_a @ X312 ) @ ( episte9089240958480457552c_fm_a @ X322 ) ) ) ).

% fm.simps(92)
thf(fact_883_MCS_Oinfinite__UNIV,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o] :
      ( ( maxima1924290459274269190c_fm_a @ Consistent )
     => ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a ) ) ).

% MCS.infinite_UNIV
thf(fact_884_finite__subset__induct_H,axiom,
    ! [F3: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,P4: set_se5208064806568342746c_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a @ F3 )
     => ( ( ord_le7112219575281605754c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo1868452413526482246c_fm_a )
         => ( ! [A6: set_Epistemic_fm_a,F4: set_se5208064806568342746c_fm_a] :
                ( ( finite7364866884270929315c_fm_a @ F4 )
               => ( ( member536094252920883875c_fm_a @ A6 @ A )
                 => ( ( ord_le7112219575281605754c_fm_a @ F4 @ A )
                   => ( ~ ( member536094252920883875c_fm_a @ A6 @ F4 )
                     => ( ( P4 @ F4 )
                       => ( P4 @ ( insert7129737658439086282c_fm_a @ A6 @ F4 ) ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_885_finite__subset__induct_H,axiom,
    ! [F3: set_a,A: set_a,P4: set_a > $o] :
      ( ( finite_finite_a @ F3 )
     => ( ( ord_less_eq_set_a @ F3 @ A )
       => ( ( P4 @ bot_bot_set_a )
         => ( ! [A6: a,F4: set_a] :
                ( ( finite_finite_a @ F4 )
               => ( ( member_a @ A6 @ A )
                 => ( ( ord_less_eq_set_a @ F4 @ A )
                   => ( ~ ( member_a @ A6 @ F4 )
                     => ( ( P4 @ F4 )
                       => ( P4 @ ( insert_a @ A6 @ F4 ) ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_886_finite__subset__induct_H,axiom,
    ! [F3: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,P4: set_Pr8948481099588399239c_fm_a > $o] :
      ( ( finite8252611493601906128c_fm_a @ F3 )
     => ( ( ord_le8222437384497874983c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo7958537672377389811c_fm_a )
         => ( ! [A6: produc2203834439629243303c_fm_a,F4: set_Pr8948481099588399239c_fm_a] :
                ( ( finite8252611493601906128c_fm_a @ F4 )
               => ( ( member5029746173879296720c_fm_a @ A6 @ A )
                 => ( ( ord_le8222437384497874983c_fm_a @ F4 @ A )
                   => ( ~ ( member5029746173879296720c_fm_a @ A6 @ F4 )
                     => ( ( P4 @ F4 )
                       => ( P4 @ ( insert4108635152042037623c_fm_a @ A6 @ F4 ) ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_887_finite__subset__induct_H,axiom,
    ! [F3: set_Epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ F3 )
     => ( ( ord_le3275665582123262618c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo3626323581529592678c_fm_a )
         => ( ! [A6: epistemic_fm_a,F4: set_Epistemic_fm_a] :
                ( ( finite3304564945125563331c_fm_a @ F4 )
               => ( ( member6642669571620171971c_fm_a @ A6 @ A )
                 => ( ( ord_le3275665582123262618c_fm_a @ F4 @ A )
                   => ( ~ ( member6642669571620171971c_fm_a @ A6 @ F4 )
                     => ( ( P4 @ F4 )
                       => ( P4 @ ( insert7817948963269374698c_fm_a @ A6 @ F4 ) ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_888_finite__subset__induct,axiom,
    ! [F3: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,P4: set_se5208064806568342746c_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a @ F3 )
     => ( ( ord_le7112219575281605754c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo1868452413526482246c_fm_a )
         => ( ! [A6: set_Epistemic_fm_a,F4: set_se5208064806568342746c_fm_a] :
                ( ( finite7364866884270929315c_fm_a @ F4 )
               => ( ( member536094252920883875c_fm_a @ A6 @ A )
                 => ( ~ ( member536094252920883875c_fm_a @ A6 @ F4 )
                   => ( ( P4 @ F4 )
                     => ( P4 @ ( insert7129737658439086282c_fm_a @ A6 @ F4 ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_889_finite__subset__induct,axiom,
    ! [F3: set_a,A: set_a,P4: set_a > $o] :
      ( ( finite_finite_a @ F3 )
     => ( ( ord_less_eq_set_a @ F3 @ A )
       => ( ( P4 @ bot_bot_set_a )
         => ( ! [A6: a,F4: set_a] :
                ( ( finite_finite_a @ F4 )
               => ( ( member_a @ A6 @ A )
                 => ( ~ ( member_a @ A6 @ F4 )
                   => ( ( P4 @ F4 )
                     => ( P4 @ ( insert_a @ A6 @ F4 ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_890_finite__subset__induct,axiom,
    ! [F3: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,P4: set_Pr8948481099588399239c_fm_a > $o] :
      ( ( finite8252611493601906128c_fm_a @ F3 )
     => ( ( ord_le8222437384497874983c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo7958537672377389811c_fm_a )
         => ( ! [A6: produc2203834439629243303c_fm_a,F4: set_Pr8948481099588399239c_fm_a] :
                ( ( finite8252611493601906128c_fm_a @ F4 )
               => ( ( member5029746173879296720c_fm_a @ A6 @ A )
                 => ( ~ ( member5029746173879296720c_fm_a @ A6 @ F4 )
                   => ( ( P4 @ F4 )
                     => ( P4 @ ( insert4108635152042037623c_fm_a @ A6 @ F4 ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_891_finite__subset__induct,axiom,
    ! [F3: set_Epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ F3 )
     => ( ( ord_le3275665582123262618c_fm_a @ F3 @ A )
       => ( ( P4 @ bot_bo3626323581529592678c_fm_a )
         => ( ! [A6: epistemic_fm_a,F4: set_Epistemic_fm_a] :
                ( ( finite3304564945125563331c_fm_a @ F4 )
               => ( ( member6642669571620171971c_fm_a @ A6 @ A )
                 => ( ~ ( member6642669571620171971c_fm_a @ A6 @ F4 )
                   => ( ( P4 @ F4 )
                     => ( P4 @ ( insert7817948963269374698c_fm_a @ A6 @ F4 ) ) ) ) ) )
           => ( P4 @ F3 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_892_exists__finite__inconsistent,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,V: set_Ep8485816078964734998c_fm_a] :
      ( ~ ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ bot_bo2004111608301611650c_fm_a ) @ V ) )
     => ~ ! [W2: set_Ep8485816078964734998c_fm_a] :
            ( ( ord_le3671305448118956982c_fm_a @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ bot_bo2004111608301611650c_fm_a ) @ W2 ) @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ bot_bo2004111608301611650c_fm_a ) @ V ) )
           => ( ~ ( member1118567890201975263c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ W2 )
             => ( ( finite2437329807571584223c_fm_a @ W2 )
               => ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ bot_bo2004111608301611650c_fm_a ) @ W2 ) ) ) ) ) ) ).

% exists_finite_inconsistent
thf(fact_893_exists__finite__inconsistent,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,V: set_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V ) )
     => ~ ! [W2: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W2 ) @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V ) )
           => ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ W2 )
             => ( ( finite3304564945125563331c_fm_a @ W2 )
               => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W2 ) ) ) ) ) ) ).

% exists_finite_inconsistent
thf(fact_894_MCS_Ointro,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o] :
      ( ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a )
     => ( ! [S6: set_Epistemic_fm_a,S3: set_Epistemic_fm_a] :
            ( ( Consistent @ S6 )
           => ( ( ord_le3275665582123262618c_fm_a @ S3 @ S6 )
             => ( Consistent @ S3 ) ) )
       => ( ! [S6: set_Epistemic_fm_a] :
              ( ~ ( Consistent @ S6 )
             => ? [S7: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S7 @ S6 )
                  & ( finite3304564945125563331c_fm_a @ S7 )
                  & ~ ( Consistent @ S7 ) ) )
         => ( maxima1924290459274269190c_fm_a @ Consistent ) ) ) ) ).

% MCS.intro
thf(fact_895_MCS__def,axiom,
    ( maxima1924290459274269190c_fm_a
    = ( ^ [Consistent2: set_Epistemic_fm_a > $o] :
          ( ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a )
          & ! [S4: set_Epistemic_fm_a,S8: set_Epistemic_fm_a] :
              ( ( Consistent2 @ S4 )
             => ( ( ord_le3275665582123262618c_fm_a @ S8 @ S4 )
               => ( Consistent2 @ S8 ) ) )
          & ! [S4: set_Epistemic_fm_a] :
              ( ~ ( Consistent2 @ S4 )
             => ? [S8: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S8 @ S4 )
                  & ( finite3304564945125563331c_fm_a @ S8 )
                  & ~ ( Consistent2 @ S8 ) ) ) ) ) ) ).

% MCS_def
thf(fact_896_inconsistent__imply,axiom,
    ! [A: episte740340785640729014c_fm_a > $o,P: episte740340785640729014c_fm_a,G5: list_E5775909407618282812c_fm_a] :
      ( ~ ( episte704884124137261758c_fm_a @ A @ ( sup_su8115892239007440362c_fm_a @ ( insert6916508371349555078c_fm_a @ ( episte260752218777527565c_fm_a @ P @ episte5073044243917183961c_fm_a ) @ bot_bo2004111608301611650c_fm_a ) @ ( set_Ep2297100812554489931c_fm_a @ G5 ) ) )
     => ( episte3601224840237526918c_fm_a @ A @ ( episte1272216372155829993c_fm_a @ G5 @ P ) ) ) ).

% inconsistent_imply
thf(fact_897_inconsistent__imply,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ ( set_Epistemic_fm_a2 @ G5 ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% inconsistent_imply
thf(fact_898_sup_Obounded__iff,axiom,
    ! [B: set_a,C: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A2 )
      = ( ( ord_less_eq_set_a @ B @ A2 )
        & ( ord_less_eq_set_a @ C @ A2 ) ) ) ).

% sup.bounded_iff
thf(fact_899_sup_Obounded__iff,axiom,
    ! [B: epistemic_fm_a > $o,C: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ B @ C ) @ A2 )
      = ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
        & ( ord_le4043730696559282883fm_a_o @ C @ A2 ) ) ) ).

% sup.bounded_iff
thf(fact_900_sup_Obounded__iff,axiom,
    ! [B: set_Epistemic_fm_a,C: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ B @ C ) @ A2 )
      = ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
        & ( ord_le3275665582123262618c_fm_a @ C @ A2 ) ) ) ).

% sup.bounded_iff
thf(fact_901_le__sup__iff,axiom,
    ! [X3: set_a,Y: set_a,Z2: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z2 )
      = ( ( ord_less_eq_set_a @ X3 @ Z2 )
        & ( ord_less_eq_set_a @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_902_le__sup__iff,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ X3 @ Y ) @ Z2 )
      = ( ( ord_le4043730696559282883fm_a_o @ X3 @ Z2 )
        & ( ord_le4043730696559282883fm_a_o @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_903_le__sup__iff,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ X3 @ Y ) @ Z2 )
      = ( ( ord_le3275665582123262618c_fm_a @ X3 @ Z2 )
        & ( ord_le3275665582123262618c_fm_a @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_904_MCS_Omaximal__maximal_H,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima1924290459274269190c_fm_a @ Consistent )
     => ( ( maxima3264069584562520521c_fm_a @ Consistent @ S )
        = ( maxima2621630783216038545c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ Consistent @ S ) ) ) ).

% MCS.maximal_maximal'
thf(fact_905_extendS__def,axiom,
    ! [A: epistemic_fm_a > $o,N: epistemic_fm_a,Prev: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) )
       => ( ( maxima5458213586468375476c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ S @ N @ Prev )
          = ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) ) )
      & ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) )
       => ( ( maxima5458213586468375476c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ S @ N @ Prev )
          = Prev ) ) ) ).

% extendS_def
thf(fact_906_fm_Opred__inject_I2_J,axiom,
    ! [P4: a > $o,A2: list_char] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Pro_a @ A2 ) )
      = ( top_top_list_char_o @ A2 ) ) ).

% fm.pred_inject(2)
thf(fact_907_fm_Opred__inject_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: list_char] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ ( episte3759128466173231372c_fm_a @ A2 ) )
      = ( top_top_list_char_o @ A2 ) ) ).

% fm.pred_inject(2)
thf(fact_908_MCS__Lim__Ord_Omaximal_H_Ocong,axiom,
    maxima2621630783216038545c_fm_a = maxima2621630783216038545c_fm_a ).

% MCS_Lim_Ord.maximal'.cong
thf(fact_909_MCS__Lim__Ord_OextendS_Ocong,axiom,
    maxima5458213586468375476c_fm_a = maxima5458213586468375476c_fm_a ).

% MCS_Lim_Ord.extendS.cong
thf(fact_910_sup__set__def,axiom,
    ( sup_su6976870698533002843c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
          ( collec7391038856303340306c_fm_a
          @ ( sup_su2056381551999066690fm_a_o
            @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A3 )
            @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_911_sup__set__def,axiom,
    ( sup_su4305657963326700718c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ( sup_su2585399871592001967fm_a_o
            @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A3 )
            @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_912_sup__set__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( collect_a
          @ ( sup_sup_a_o
            @ ^ [X: a] : ( member_a @ X @ A3 )
            @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_913_sup__set__def,axiom,
    ( sup_su1367922730591523534c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ( sup_su6697315146409554831fm_a_o
            @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A3 )
            @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_914_sup__Un__eq,axiom,
    ! [R2: set_se5208064806568342746c_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( sup_su2585399871592001967fm_a_o
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ R2 )
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ S ) )
      = ( ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ ( sup_su4305657963326700718c_fm_a @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_915_sup__Un__eq,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( sup_su2056381551999066690fm_a_o
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ R2 )
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ S ) )
      = ( ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ ( sup_su6976870698533002843c_fm_a @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_916_sup__Un__eq,axiom,
    ! [R2: set_a,S: set_a] :
      ( ( sup_sup_a_o
        @ ^ [X: a] : ( member_a @ X @ R2 )
        @ ^ [X: a] : ( member_a @ X @ S ) )
      = ( ^ [X: a] : ( member_a @ X @ ( sup_sup_set_a @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_917_sup__Un__eq,axiom,
    ! [R2: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( sup_su6697315146409554831fm_a_o
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ R2 )
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ S ) )
      = ( ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ ( sup_su1367922730591523534c_fm_a @ R2 @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_918_inf__sup__ord_I4_J,axiom,
    ! [Y: set_a,X3: set_a] : ( ord_less_eq_set_a @ Y @ ( sup_sup_set_a @ X3 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_919_inf__sup__ord_I4_J,axiom,
    ! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ Y @ ( sup_su6697315146409554831fm_a_o @ X3 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_920_inf__sup__ord_I4_J,axiom,
    ! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ Y @ ( sup_su1367922730591523534c_fm_a @ X3 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_921_inf__sup__ord_I3_J,axiom,
    ! [X3: set_a,Y: set_a] : ( ord_less_eq_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_922_inf__sup__ord_I3_J,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X3 @ ( sup_su6697315146409554831fm_a_o @ X3 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_923_inf__sup__ord_I3_J,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X3 @ ( sup_su1367922730591523534c_fm_a @ X3 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_924_le__supE,axiom,
    ! [A2: set_a,B: set_a,X3: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ X3 )
     => ~ ( ( ord_less_eq_set_a @ A2 @ X3 )
         => ~ ( ord_less_eq_set_a @ B @ X3 ) ) ) ).

% le_supE
thf(fact_925_le__supE,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) @ X3 )
     => ~ ( ( ord_le4043730696559282883fm_a_o @ A2 @ X3 )
         => ~ ( ord_le4043730696559282883fm_a_o @ B @ X3 ) ) ) ).

% le_supE
thf(fact_926_le__supE,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) @ X3 )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ A2 @ X3 )
         => ~ ( ord_le3275665582123262618c_fm_a @ B @ X3 ) ) ) ).

% le_supE
thf(fact_927_le__supI,axiom,
    ! [A2: set_a,X3: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ X3 )
     => ( ( ord_less_eq_set_a @ B @ X3 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ X3 ) ) ) ).

% le_supI
thf(fact_928_le__supI,axiom,
    ! [A2: epistemic_fm_a > $o,X3: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ X3 )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ X3 )
       => ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) @ X3 ) ) ) ).

% le_supI
thf(fact_929_le__supI,axiom,
    ! [A2: set_Epistemic_fm_a,X3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ X3 )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ X3 )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) @ X3 ) ) ) ).

% le_supI
thf(fact_930_sup__ge1,axiom,
    ! [X3: set_a,Y: set_a] : ( ord_less_eq_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) ) ).

% sup_ge1
thf(fact_931_sup__ge1,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X3 @ ( sup_su6697315146409554831fm_a_o @ X3 @ Y ) ) ).

% sup_ge1
thf(fact_932_sup__ge1,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X3 @ ( sup_su1367922730591523534c_fm_a @ X3 @ Y ) ) ).

% sup_ge1
thf(fact_933_sup__ge2,axiom,
    ! [Y: set_a,X3: set_a] : ( ord_less_eq_set_a @ Y @ ( sup_sup_set_a @ X3 @ Y ) ) ).

% sup_ge2
thf(fact_934_sup__ge2,axiom,
    ! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ Y @ ( sup_su6697315146409554831fm_a_o @ X3 @ Y ) ) ).

% sup_ge2
thf(fact_935_sup__ge2,axiom,
    ! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ Y @ ( sup_su1367922730591523534c_fm_a @ X3 @ Y ) ) ).

% sup_ge2
thf(fact_936_le__supI1,axiom,
    ! [X3: set_a,A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ X3 @ A2 )
     => ( ord_less_eq_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% le_supI1
thf(fact_937_le__supI1,axiom,
    ! [X3: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ A2 )
     => ( ord_le4043730696559282883fm_a_o @ X3 @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ).

% le_supI1
thf(fact_938_le__supI1,axiom,
    ! [X3: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ A2 )
     => ( ord_le3275665582123262618c_fm_a @ X3 @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ).

% le_supI1
thf(fact_939_le__supI2,axiom,
    ! [X3: set_a,B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ X3 @ B )
     => ( ord_less_eq_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% le_supI2
thf(fact_940_le__supI2,axiom,
    ! [X3: epistemic_fm_a > $o,B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ B )
     => ( ord_le4043730696559282883fm_a_o @ X3 @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ).

% le_supI2
thf(fact_941_le__supI2,axiom,
    ! [X3: set_Epistemic_fm_a,B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ B )
     => ( ord_le3275665582123262618c_fm_a @ X3 @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ).

% le_supI2
thf(fact_942_sup_Omono,axiom,
    ! [C: set_a,A2: set_a,D2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ C @ A2 )
     => ( ( ord_less_eq_set_a @ D2 @ B )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ C @ D2 ) @ ( sup_sup_set_a @ A2 @ B ) ) ) ) ).

% sup.mono
thf(fact_943_sup_Omono,axiom,
    ! [C: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,D2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ C @ A2 )
     => ( ( ord_le4043730696559282883fm_a_o @ D2 @ B )
       => ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ C @ D2 ) @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ) ).

% sup.mono
thf(fact_944_sup_Omono,axiom,
    ! [C: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,D2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C @ A2 )
     => ( ( ord_le3275665582123262618c_fm_a @ D2 @ B )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ C @ D2 ) @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ) ).

% sup.mono
thf(fact_945_sup__mono,axiom,
    ! [A2: set_a,C: set_a,B: set_a,D2: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ C )
     => ( ( ord_less_eq_set_a @ B @ D2 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ ( sup_sup_set_a @ C @ D2 ) ) ) ) ).

% sup_mono
thf(fact_946_sup__mono,axiom,
    ! [A2: epistemic_fm_a > $o,C: epistemic_fm_a > $o,B: epistemic_fm_a > $o,D2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ C )
     => ( ( ord_le4043730696559282883fm_a_o @ B @ D2 )
       => ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) @ ( sup_su6697315146409554831fm_a_o @ C @ D2 ) ) ) ) ).

% sup_mono
thf(fact_947_sup__mono,axiom,
    ! [A2: set_Epistemic_fm_a,C: set_Epistemic_fm_a,B: set_Epistemic_fm_a,D2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ C )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ D2 )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) @ ( sup_su1367922730591523534c_fm_a @ C @ D2 ) ) ) ) ).

% sup_mono
thf(fact_948_sup__least,axiom,
    ! [Y: set_a,X3: set_a,Z2: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X3 )
     => ( ( ord_less_eq_set_a @ Z2 @ X3 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ Y @ Z2 ) @ X3 ) ) ) ).

% sup_least
thf(fact_949_sup__least,axiom,
    ! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
     => ( ( ord_le4043730696559282883fm_a_o @ Z2 @ X3 )
       => ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ Y @ Z2 ) @ X3 ) ) ) ).

% sup_least
thf(fact_950_sup__least,axiom,
    ! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
     => ( ( ord_le3275665582123262618c_fm_a @ Z2 @ X3 )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ Y @ Z2 ) @ X3 ) ) ) ).

% sup_least
thf(fact_951_le__iff__sup,axiom,
    ( ord_less_eq_set_a
    = ( ^ [X: set_a,Y4: set_a] :
          ( ( sup_sup_set_a @ X @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_952_le__iff__sup,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [X: epistemic_fm_a > $o,Y4: epistemic_fm_a > $o] :
          ( ( sup_su6697315146409554831fm_a_o @ X @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_953_le__iff__sup,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [X: set_Epistemic_fm_a,Y4: set_Epistemic_fm_a] :
          ( ( sup_su1367922730591523534c_fm_a @ X @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_954_sup_OorderE,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( A2
        = ( sup_sup_set_a @ A2 @ B ) ) ) ).

% sup.orderE
thf(fact_955_sup_OorderE,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
     => ( A2
        = ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ).

% sup.orderE
thf(fact_956_sup_OorderE,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
     => ( A2
        = ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ).

% sup.orderE
thf(fact_957_sup_OorderI,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( A2
        = ( sup_sup_set_a @ A2 @ B ) )
     => ( ord_less_eq_set_a @ B @ A2 ) ) ).

% sup.orderI
thf(fact_958_sup_OorderI,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( A2
        = ( sup_su6697315146409554831fm_a_o @ A2 @ B ) )
     => ( ord_le4043730696559282883fm_a_o @ B @ A2 ) ) ).

% sup.orderI
thf(fact_959_sup_OorderI,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( A2
        = ( sup_su1367922730591523534c_fm_a @ A2 @ B ) )
     => ( ord_le3275665582123262618c_fm_a @ B @ A2 ) ) ).

% sup.orderI
thf(fact_960_sup__unique,axiom,
    ! [F: set_a > set_a > set_a,X3: set_a,Y: set_a] :
      ( ! [X2: set_a,Y2: set_a] : ( ord_less_eq_set_a @ X2 @ ( F @ X2 @ Y2 ) )
     => ( ! [X2: set_a,Y2: set_a] : ( ord_less_eq_set_a @ Y2 @ ( F @ X2 @ Y2 ) )
       => ( ! [X2: set_a,Y2: set_a,Z5: set_a] :
              ( ( ord_less_eq_set_a @ Y2 @ X2 )
             => ( ( ord_less_eq_set_a @ Z5 @ X2 )
               => ( ord_less_eq_set_a @ ( F @ Y2 @ Z5 ) @ X2 ) ) )
         => ( ( sup_sup_set_a @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_961_sup__unique,axiom,
    ! [F: ( epistemic_fm_a > $o ) > ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X2 @ ( F @ X2 @ Y2 ) )
     => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ Y2 @ ( F @ X2 @ Y2 ) )
       => ( ! [X2: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o,Z5: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ Y2 @ X2 )
             => ( ( ord_le4043730696559282883fm_a_o @ Z5 @ X2 )
               => ( ord_le4043730696559282883fm_a_o @ ( F @ Y2 @ Z5 ) @ X2 ) ) )
         => ( ( sup_su6697315146409554831fm_a_o @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_962_sup__unique,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X2 @ ( F @ X2 @ Y2 ) )
     => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ Y2 @ ( F @ X2 @ Y2 ) )
       => ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Z5: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ Y2 @ X2 )
             => ( ( ord_le3275665582123262618c_fm_a @ Z5 @ X2 )
               => ( ord_le3275665582123262618c_fm_a @ ( F @ Y2 @ Z5 ) @ X2 ) ) )
         => ( ( sup_su1367922730591523534c_fm_a @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_963_sup_Oabsorb1,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( sup_sup_set_a @ A2 @ B )
        = A2 ) ) ).

% sup.absorb1
thf(fact_964_sup_Oabsorb1,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
     => ( ( sup_su6697315146409554831fm_a_o @ A2 @ B )
        = A2 ) ) ).

% sup.absorb1
thf(fact_965_sup_Oabsorb1,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
     => ( ( sup_su1367922730591523534c_fm_a @ A2 @ B )
        = A2 ) ) ).

% sup.absorb1
thf(fact_966_sup_Oabsorb2,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( sup_sup_set_a @ A2 @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_967_sup_Oabsorb2,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
     => ( ( sup_su6697315146409554831fm_a_o @ A2 @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_968_sup_Oabsorb2,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
     => ( ( sup_su1367922730591523534c_fm_a @ A2 @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_969_sup__absorb1,axiom,
    ! [Y: set_a,X3: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X3 )
     => ( ( sup_sup_set_a @ X3 @ Y )
        = X3 ) ) ).

% sup_absorb1
thf(fact_970_sup__absorb1,axiom,
    ! [Y: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ Y @ X3 )
     => ( ( sup_su6697315146409554831fm_a_o @ X3 @ Y )
        = X3 ) ) ).

% sup_absorb1
thf(fact_971_sup__absorb1,axiom,
    ! [Y: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ Y @ X3 )
     => ( ( sup_su1367922730591523534c_fm_a @ X3 @ Y )
        = X3 ) ) ).

% sup_absorb1
thf(fact_972_sup__absorb2,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X3 @ Y )
     => ( ( sup_sup_set_a @ X3 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_973_sup__absorb2,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
     => ( ( sup_su6697315146409554831fm_a_o @ X3 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_974_sup__absorb2,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
     => ( ( sup_su1367922730591523534c_fm_a @ X3 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_975_sup_OboundedE,axiom,
    ! [B: set_a,C: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A2 )
     => ~ ( ( ord_less_eq_set_a @ B @ A2 )
         => ~ ( ord_less_eq_set_a @ C @ A2 ) ) ) ).

% sup.boundedE
thf(fact_976_sup_OboundedE,axiom,
    ! [B: epistemic_fm_a > $o,C: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ B @ C ) @ A2 )
     => ~ ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
         => ~ ( ord_le4043730696559282883fm_a_o @ C @ A2 ) ) ) ).

% sup.boundedE
thf(fact_977_sup_OboundedE,axiom,
    ! [B: set_Epistemic_fm_a,C: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ B @ C ) @ A2 )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
         => ~ ( ord_le3275665582123262618c_fm_a @ C @ A2 ) ) ) ).

% sup.boundedE
thf(fact_978_sup_OboundedI,axiom,
    ! [B: set_a,A2: set_a,C: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( ord_less_eq_set_a @ C @ A2 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ B @ C ) @ A2 ) ) ) ).

% sup.boundedI
thf(fact_979_sup_OboundedI,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ A2 )
     => ( ( ord_le4043730696559282883fm_a_o @ C @ A2 )
       => ( ord_le4043730696559282883fm_a_o @ ( sup_su6697315146409554831fm_a_o @ B @ C ) @ A2 ) ) ) ).

% sup.boundedI
thf(fact_980_sup_OboundedI,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ A2 )
     => ( ( ord_le3275665582123262618c_fm_a @ C @ A2 )
       => ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ B @ C ) @ A2 ) ) ) ).

% sup.boundedI
thf(fact_981_sup_Oorder__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [B2: set_a,A4: set_a] :
          ( A4
          = ( sup_sup_set_a @ A4 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_982_sup_Oorder__iff,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [B2: epistemic_fm_a > $o,A4: epistemic_fm_a > $o] :
          ( A4
          = ( sup_su6697315146409554831fm_a_o @ A4 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_983_sup_Oorder__iff,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [B2: set_Epistemic_fm_a,A4: set_Epistemic_fm_a] :
          ( A4
          = ( sup_su1367922730591523534c_fm_a @ A4 @ B2 ) ) ) ) ).

% sup.order_iff
thf(fact_984_sup_Ocobounded1,axiom,
    ! [A2: set_a,B: set_a] : ( ord_less_eq_set_a @ A2 @ ( sup_sup_set_a @ A2 @ B ) ) ).

% sup.cobounded1
thf(fact_985_sup_Ocobounded1,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ).

% sup.cobounded1
thf(fact_986_sup_Ocobounded1,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ).

% sup.cobounded1
thf(fact_987_sup_Ocobounded2,axiom,
    ! [B: set_a,A2: set_a] : ( ord_less_eq_set_a @ B @ ( sup_sup_set_a @ A2 @ B ) ) ).

% sup.cobounded2
thf(fact_988_sup_Ocobounded2,axiom,
    ! [B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ B @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ).

% sup.cobounded2
thf(fact_989_sup_Ocobounded2,axiom,
    ! [B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ B @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ).

% sup.cobounded2
thf(fact_990_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_a
    = ( ^ [B2: set_a,A4: set_a] :
          ( ( sup_sup_set_a @ A4 @ B2 )
          = A4 ) ) ) ).

% sup.absorb_iff1
thf(fact_991_sup_Oabsorb__iff1,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [B2: epistemic_fm_a > $o,A4: epistemic_fm_a > $o] :
          ( ( sup_su6697315146409554831fm_a_o @ A4 @ B2 )
          = A4 ) ) ) ).

% sup.absorb_iff1
thf(fact_992_sup_Oabsorb__iff1,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [B2: set_Epistemic_fm_a,A4: set_Epistemic_fm_a] :
          ( ( sup_su1367922730591523534c_fm_a @ A4 @ B2 )
          = A4 ) ) ) ).

% sup.absorb_iff1
thf(fact_993_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B2: set_a] :
          ( ( sup_sup_set_a @ A4 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_994_sup_Oabsorb__iff2,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
          ( ( sup_su6697315146409554831fm_a_o @ A4 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_995_sup_Oabsorb__iff2,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
          ( ( sup_su1367922730591523534c_fm_a @ A4 @ B2 )
          = B2 ) ) ) ).

% sup.absorb_iff2
thf(fact_996_sup_OcoboundedI1,axiom,
    ! [C: set_a,A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ C @ A2 )
     => ( ord_less_eq_set_a @ C @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% sup.coboundedI1
thf(fact_997_sup_OcoboundedI1,axiom,
    ! [C: epistemic_fm_a > $o,A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ C @ A2 )
     => ( ord_le4043730696559282883fm_a_o @ C @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ).

% sup.coboundedI1
thf(fact_998_sup_OcoboundedI1,axiom,
    ! [C: set_Epistemic_fm_a,A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C @ A2 )
     => ( ord_le3275665582123262618c_fm_a @ C @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ).

% sup.coboundedI1
thf(fact_999_sup_OcoboundedI2,axiom,
    ! [C: set_a,B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ C @ B )
     => ( ord_less_eq_set_a @ C @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% sup.coboundedI2
thf(fact_1000_sup_OcoboundedI2,axiom,
    ! [C: epistemic_fm_a > $o,B: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ C @ B )
     => ( ord_le4043730696559282883fm_a_o @ C @ ( sup_su6697315146409554831fm_a_o @ A2 @ B ) ) ) ).

% sup.coboundedI2
thf(fact_1001_sup_OcoboundedI2,axiom,
    ! [C: set_Epistemic_fm_a,B: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C @ B )
     => ( ord_le3275665582123262618c_fm_a @ C @ ( sup_su1367922730591523534c_fm_a @ A2 @ B ) ) ) ).

% sup.coboundedI2
thf(fact_1002_maximal__maximal_H,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ S )
      = ( maxima2621630783216038545c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ).

% maximal_maximal'
thf(fact_1003_maximal_H__Extend,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] : ( maxima2621630783216038545c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ).

% maximal'_Extend
thf(fact_1004_maximal_H__def,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima2621630783216038545c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) )
           => ( ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ X @ bot_bo3626323581529592678c_fm_a ) @ S ) )
             => ( member6642669571620171971c_fm_a @ X @ S ) ) ) ) ) ).

% maximal'_def
thf(fact_1005_Extend__subset_H,axiom,
    ! [S: set_Epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ( ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) )
       != bot_bo3626323581529592678c_fm_a )
     => ( ord_le3275665582123262618c_fm_a @ S @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ) ).

% Extend_subset'
thf(fact_1006_MCS__Lim__Ord_OextendS__def,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,N: a,Prev: set_a,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( ( Consistent @ ( sup_sup_set_a @ ( insert_a @ N @ bot_bot_set_a ) @ Prev ) )
         => ( ( maxima3849362494499116184endS_a @ Consistent @ S @ N @ Prev )
            = ( sup_sup_set_a @ ( insert_a @ N @ bot_bot_set_a ) @ Prev ) ) )
        & ( ~ ( Consistent @ ( sup_sup_set_a @ ( insert_a @ N @ bot_bot_set_a ) @ Prev ) )
         => ( ( maxima3849362494499116184endS_a @ Consistent @ S @ N @ Prev )
            = Prev ) ) ) ) ).

% MCS_Lim_Ord.extendS_def
thf(fact_1007_MCS__Lim__Ord_OextendS__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,N: epistemic_fm_a,Prev: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( ( Consistent @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) )
         => ( ( maxima5458213586468375476c_fm_a @ Consistent @ S @ N @ Prev )
            = ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) ) )
        & ( ~ ( Consistent @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ N @ bot_bo3626323581529592678c_fm_a ) @ Prev ) )
         => ( ( maxima5458213586468375476c_fm_a @ Consistent @ S @ N @ Prev )
            = Prev ) ) ) ) ).

% MCS_Lim_Ord.extendS_def
thf(fact_1008_set__rec,axiom,
    ( set_Epistemic_fm_a2
    = ( rec_li8401250755714504918c_fm_a @ bot_bo3626323581529592678c_fm_a
      @ ^ [X: epistemic_fm_a,Uu2: list_Epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ X ) ) ) ).

% set_rec
thf(fact_1009_mono__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,S9: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ R @ S9 )
     => ( ord_le3275665582123262618c_fm_a @ ( field_Epistemic_fm_a @ R ) @ ( field_Epistemic_fm_a @ S9 ) ) ) ).

% mono_Field
thf(fact_1010_MCS__Lim__Ord_Oconsistent__hereditary,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a,S2: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( Consistent @ S )
       => ( ( ord_le3275665582123262618c_fm_a @ S2 @ S )
         => ( Consistent @ S2 ) ) ) ) ).

% MCS_Lim_Ord.consistent_hereditary
thf(fact_1011_MCS__Lim__Ord_OExtend__subset_H,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( ( field_Epistemic_fm_a @ R )
         != bot_bo3626323581529592678c_fm_a )
       => ( ord_le3275665582123262618c_fm_a @ S @ ( maxima2580775624958445067c_fm_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.Extend_subset'
thf(fact_1012_MCS__Lim__Ord_Oconsistent__Extend,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( Consistent @ S )
       => ( Consistent @ ( maxima2580775624958445067c_fm_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.consistent_Extend
thf(fact_1013_MCS__Lim__Ord_Omaximal_H__def,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,Consistent: set_se5208064806568342746c_fm_a > $o,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima8505690773950114933c_fm_a @ R @ Consistent )
     => ( ( maxima2311692462071403633c_fm_a @ R @ Consistent @ S )
        = ( ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( field_3462791820427926727c_fm_a @ R ) )
             => ( ( Consistent @ ( sup_su4305657963326700718c_fm_a @ ( insert7129737658439086282c_fm_a @ X @ bot_bo1868452413526482246c_fm_a ) @ S ) )
               => ( member536094252920883875c_fm_a @ X @ S ) ) ) ) ) ) ).

% MCS_Lim_Ord.maximal'_def
thf(fact_1014_MCS__Lim__Ord_Omaximal_H__def,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,Consistent: set_Pr8948481099588399239c_fm_a > $o,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima8093661031691903906c_fm_a @ R @ Consistent )
     => ( ( maxima4614831103992561054c_fm_a @ R @ Consistent @ S )
        = ( ! [X: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X @ ( field_4566226324314649332c_fm_a @ R ) )
             => ( ( Consistent @ ( sup_su6976870698533002843c_fm_a @ ( insert4108635152042037623c_fm_a @ X @ bot_bo7958537672377389811c_fm_a ) @ S ) )
               => ( member5029746173879296720c_fm_a @ X @ S ) ) ) ) ) ) ).

% MCS_Lim_Ord.maximal'_def
thf(fact_1015_MCS__Lim__Ord_Omaximal_H__def,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( maxima5282053167310095605imal_a @ R @ Consistent @ S )
        = ( ! [X: a] :
              ( ( member_a @ X @ ( field_a @ R ) )
             => ( ( Consistent @ ( sup_sup_set_a @ ( insert_a @ X @ bot_bot_set_a ) @ S ) )
               => ( member_a @ X @ S ) ) ) ) ) ) ).

% MCS_Lim_Ord.maximal'_def
thf(fact_1016_MCS__Lim__Ord_Omaximal_H__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( maxima2621630783216038545c_fm_a @ R @ Consistent @ S )
        = ( ! [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ ( field_Epistemic_fm_a @ R ) )
             => ( ( Consistent @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ X @ bot_bo3626323581529592678c_fm_a ) @ S ) )
               => ( member6642669571620171971c_fm_a @ X @ S ) ) ) ) ) ) ).

% MCS_Lim_Ord.maximal'_def
thf(fact_1017_MCS__Lim__Ord_Oinconsistent__finite,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ~ ( Consistent @ S )
       => ? [S3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ S3 @ S )
            & ( finite3304564945125563331c_fm_a @ S3 )
            & ~ ( Consistent @ S3 ) ) ) ) ).

% MCS_Lim_Ord.inconsistent_finite
thf(fact_1018_MCS__Lim__Ord_Omaximal_H__Extend,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( maxima2621630783216038545c_fm_a @ R @ Consistent @ ( maxima2580775624958445067c_fm_a @ R @ Consistent @ S ) ) ) ).

% MCS_Lim_Ord.maximal'_Extend
thf(fact_1019_MCS__Lim__Ord__axioms,axiom,
    ! [A: epistemic_fm_a > $o] : ( maxima8116622252184345237c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) ) ).

% MCS_Lim_Ord_axioms
thf(fact_1020_Extend__bound,axiom,
    ! [N: epistemic_fm_a,A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ N @ ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) )
     => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N ) @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) ) ) ).

% Extend_bound
thf(fact_1021_extend__subset,axiom,
    ! [N: epistemic_fm_a,S: set_Epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ N @ ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) )
     => ( ord_le3275665582123262618c_fm_a @ S @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N ) ) ) ).

% extend_subset
thf(fact_1022_MCS__Lim__Ord_OExtend__bound,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,Consistent: set_se5208064806568342746c_fm_a > $o,N: set_Epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima8505690773950114933c_fm_a @ R @ Consistent )
     => ( ( member536094252920883875c_fm_a @ N @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ord_le7112219575281605754c_fm_a @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ N ) @ ( maxima2136919731711262699c_fm_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.Extend_bound
thf(fact_1023_MCS__Lim__Ord_OExtend__bound,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,N: a,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( member_a @ N @ ( field_a @ R ) )
       => ( ord_less_eq_set_a @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ N ) @ ( maxima2486273825106742127tend_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.Extend_bound
thf(fact_1024_MCS__Lim__Ord_OExtend__bound,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,Consistent: set_Pr8948481099588399239c_fm_a > $o,N: produc2203834439629243303c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima8093661031691903906c_fm_a @ R @ Consistent )
     => ( ( member5029746173879296720c_fm_a @ N @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ord_le8222437384497874983c_fm_a @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ N ) @ ( maxima1206778815090856984c_fm_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.Extend_bound
thf(fact_1025_MCS__Lim__Ord_OExtend__bound,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,N: epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( member6642669571620171971c_fm_a @ N @ ( field_Epistemic_fm_a @ R ) )
       => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N ) @ ( maxima2580775624958445067c_fm_a @ R @ Consistent @ S ) ) ) ) ).

% MCS_Lim_Ord.Extend_bound
thf(fact_1026_MCS__Lim__Ord_Oextend__subset,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,Consistent: set_se5208064806568342746c_fm_a > $o,N: set_Epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima8505690773950114933c_fm_a @ R @ Consistent )
     => ( ( member536094252920883875c_fm_a @ N @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ord_le7112219575281605754c_fm_a @ S @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_subset
thf(fact_1027_MCS__Lim__Ord_Oextend__subset,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,N: a,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( member_a @ N @ ( field_a @ R ) )
       => ( ord_less_eq_set_a @ S @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_subset
thf(fact_1028_MCS__Lim__Ord_Oextend__subset,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,Consistent: set_Pr8948481099588399239c_fm_a > $o,N: produc2203834439629243303c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima8093661031691903906c_fm_a @ R @ Consistent )
     => ( ( member5029746173879296720c_fm_a @ N @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ord_le8222437384497874983c_fm_a @ S @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_subset
thf(fact_1029_MCS__Lim__Ord_Oextend__subset,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,N: epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( member6642669571620171971c_fm_a @ N @ ( field_Epistemic_fm_a @ R ) )
       => ( ord_le3275665582123262618c_fm_a @ S @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_subset
thf(fact_1030_MCS__Lim__Ord_Oextend_Ocong,axiom,
    maxima1168816336865142315c_fm_a = maxima1168816336865142315c_fm_a ).

% MCS_Lim_Ord.extend.cong
thf(fact_1031_MCS__Lim__Ord_Oconsistent__extend,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( Consistent @ S )
       => ( Consistent @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.consistent_extend
thf(fact_1032_consistent__extend,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( episte2285483198712856226tent_a @ A @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N ) ) ) ).

% consistent_extend
thf(fact_1033_Epistemic__Logic_Oextend__def,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N )
      = ( wellor7234309849078405374c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ S @ ( maxima5458213586468375476c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ S ) @ ( maxima7895811076573853563c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) @ N ) ) ).

% Epistemic_Logic.extend_def
thf(fact_1034_extend__under,axiom,
    ! [M5: epistemic_fm_a,N: epistemic_fm_a,A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ M5 @ ( order_1815523470270482687c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ N ) )
     => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ M5 ) @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N ) ) ) ).

% extend_under
thf(fact_1035_extend__underS,axiom,
    ! [M5: epistemic_fm_a,N: epistemic_fm_a,A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ M5 @ ( order_1288088311422721504c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ N ) )
     => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ M5 ) @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S @ N ) ) ) ).

% extend_underS
thf(fact_1036_subset__singleton__iff__Uniq,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( ? [A4: set_Epistemic_fm_a] : ( ord_le7112219575281605754c_fm_a @ A @ ( insert7129737658439086282c_fm_a @ A4 @ bot_bo1868452413526482246c_fm_a ) ) )
      = ( uniq_s5323624820373029887c_fm_a
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1037_subset__singleton__iff__Uniq,axiom,
    ! [A: set_a] :
      ( ( ? [A4: a] : ( ord_less_eq_set_a @ A @ ( insert_a @ A4 @ bot_bot_set_a ) ) )
      = ( uniq_a
        @ ^ [X: a] : ( member_a @ X @ A ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1038_subset__singleton__iff__Uniq,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a] :
      ( ( ? [A4: produc2203834439629243303c_fm_a] : ( ord_le8222437384497874983c_fm_a @ A @ ( insert4108635152042037623c_fm_a @ A4 @ bot_bo7958537672377389811c_fm_a ) ) )
      = ( uniq_P7718672049783348780c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1039_subset__singleton__iff__Uniq,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( ? [A4: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ ( insert7817948963269374698c_fm_a @ A4 @ bot_bo3626323581529592678c_fm_a ) ) )
      = ( uniq_Epistemic_fm_a
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1040_MCS__Lim__Ord_OextendL_Ocong,axiom,
    maxima7895811076573853563c_fm_a = maxima7895811076573853563c_fm_a ).

% MCS_Lim_Ord.extendL.cong
thf(fact_1041_MCS__Lim__Ord_Oextend__underS,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,Consistent: set_se5208064806568342746c_fm_a > $o,M5: set_Epistemic_fm_a,N: set_Epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima8505690773950114933c_fm_a @ R @ Consistent )
     => ( ( member536094252920883875c_fm_a @ M5 @ ( order_7871341057202914240c_fm_a @ R @ N ) )
       => ( ord_le7112219575281605754c_fm_a @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_underS
thf(fact_1042_MCS__Lim__Ord_Oextend__underS,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,M5: a,N: a,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( member_a @ M5 @ ( order_underS_a @ R @ N ) )
       => ( ord_less_eq_set_a @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ M5 ) @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_underS
thf(fact_1043_MCS__Lim__Ord_Oextend__underS,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,Consistent: set_Pr8948481099588399239c_fm_a > $o,M5: produc2203834439629243303c_fm_a,N: produc2203834439629243303c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima8093661031691903906c_fm_a @ R @ Consistent )
     => ( ( member5029746173879296720c_fm_a @ M5 @ ( order_7711974919420625261c_fm_a @ R @ N ) )
       => ( ord_le8222437384497874983c_fm_a @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_underS
thf(fact_1044_MCS__Lim__Ord_Oextend__underS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,M5: epistemic_fm_a,N: epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( member6642669571620171971c_fm_a @ M5 @ ( order_1288088311422721504c_fm_a @ R @ N ) )
       => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_underS
thf(fact_1045_MCS__Lim__Ord_Oextend__under,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,Consistent: set_se5208064806568342746c_fm_a > $o,M5: set_Epistemic_fm_a,N: set_Epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( maxima8505690773950114933c_fm_a @ R @ Consistent )
     => ( ( member536094252920883875c_fm_a @ M5 @ ( order_4320674923736412895c_fm_a @ R @ N ) )
       => ( ord_le7112219575281605754c_fm_a @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima2942051681900060683c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_under
thf(fact_1046_MCS__Lim__Ord_Oextend__under,axiom,
    ! [R: set_Product_prod_a_a,Consistent: set_a > $o,M5: a,N: a,S: set_a] :
      ( ( maxima3603147619815099129_Ord_a @ R @ Consistent )
     => ( ( member_a @ M5 @ ( order_under_a @ R @ N ) )
       => ( ord_less_eq_set_a @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ M5 ) @ ( maxima2937105246822620047tend_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_under
thf(fact_1047_MCS__Lim__Ord_Oextend__under,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,Consistent: set_Pr8948481099588399239c_fm_a > $o,M5: produc2203834439629243303c_fm_a,N: produc2203834439629243303c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( maxima8093661031691903906c_fm_a @ R @ Consistent )
     => ( ( member5029746173879296720c_fm_a @ M5 @ ( order_5358731147316321548c_fm_a @ R @ N ) )
       => ( ord_le8222437384497874983c_fm_a @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima5651364120436909112c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_under
thf(fact_1048_MCS__Lim__Ord_Oextend__under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,M5: epistemic_fm_a,N: epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( member6642669571620171971c_fm_a @ M5 @ ( order_1815523470270482687c_fm_a @ R @ N ) )
       => ( ord_le3275665582123262618c_fm_a @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ M5 ) @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N ) ) ) ) ).

% MCS_Lim_Ord.extend_under
thf(fact_1049_MCS__Lim__Ord_Oextend__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S @ N )
        = ( wellor7234309849078405374c_fm_a @ R @ S @ ( maxima5458213586468375476c_fm_a @ Consistent @ S ) @ ( maxima7895811076573853563c_fm_a @ R ) @ N ) ) ) ).

% MCS_Lim_Ord.extend_def
thf(fact_1050_underS__subset__under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_1288088311422721504c_fm_a @ R @ A2 ) @ ( order_1815523470270482687c_fm_a @ R @ A2 ) ) ).

% underS_subset_under
thf(fact_1051_under__incr2,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,R3: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ R @ R3 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_1815523470270482687c_fm_a @ R @ A2 ) @ ( order_1815523470270482687c_fm_a @ R3 @ A2 ) ) ) ).

% under_incr2
thf(fact_1052_underS__incr2,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,R3: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ R @ R3 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_1288088311422721504c_fm_a @ R @ A2 ) @ ( order_1288088311422721504c_fm_a @ R3 @ A2 ) ) ) ).

% underS_incr2
thf(fact_1053_under__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_1815523470270482687c_fm_a @ R @ A2 ) @ ( field_Epistemic_fm_a @ R ) ) ).

% under_Field
thf(fact_1054_Order__Relation_OunderS__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_1288088311422721504c_fm_a @ R @ A2 ) @ ( field_Epistemic_fm_a @ R ) ) ).

% Order_Relation.underS_Field
thf(fact_1055_adm__woL__extendL,axiom,
    wellor8531372491315211020c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( maxima7895811076573853563c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) ).

% adm_woL_extendL
thf(fact_1056_ex1__iff__ex__Uniq,axiom,
    ( ex1_Epistemic_fm_a
    = ( ^ [P6: epistemic_fm_a > $o] :
          ( ? [X4: epistemic_fm_a] : ( P6 @ X4 )
          & ( uniq_Epistemic_fm_a @ P6 ) ) ) ) ).

% ex1_iff_ex_Uniq
thf(fact_1057_alt__ex1E_H,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ? [X6: epistemic_fm_a] :
          ( ( P4 @ X6 )
          & ! [Y2: epistemic_fm_a] :
              ( ( P4 @ Y2 )
             => ( Y2 = X6 ) ) )
     => ~ ( ? [X_1: epistemic_fm_a] : ( P4 @ X_1 )
         => ~ ( uniq_Epistemic_fm_a @ P4 ) ) ) ).

% alt_ex1E'
thf(fact_1058_MCS__Lim__Ord_Oadm__woL__extendL,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( wellor8531372491315211020c_fm_a @ R @ ( maxima7895811076573853563c_fm_a @ R ) ) ) ).

% MCS_Lim_Ord.adm_woL_extendL
thf(fact_1059_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,X5: set_se5208064806568342746c_fm_a,N: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( finite7364866884270929315c_fm_a @ X5 )
       => ( ( ord_le7112219575281605754c_fm_a @ X5 @ ( order_7871341057202914240c_fm_a @ R @ N ) )
         => ( ( X5 != bot_bo1868452413526482246c_fm_a )
           => ? [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ X5 )
                & ! [Xa2: set_Epistemic_fm_a] :
                    ( ( member536094252920883875c_fm_a @ Xa2 @ X5 )
                   => ( member536094252920883875c_fm_a @ Xa2 @ ( order_4320674923736412895c_fm_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_1060_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Product_prod_a_a,X5: set_a,N: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( finite_finite_a @ X5 )
       => ( ( ord_less_eq_set_a @ X5 @ ( order_underS_a @ R @ N ) )
         => ( ( X5 != bot_bot_set_a )
           => ? [X2: a] :
                ( ( member_a @ X2 @ X5 )
                & ! [Xa2: a] :
                    ( ( member_a @ Xa2 @ X5 )
                   => ( member_a @ Xa2 @ ( order_under_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_1061_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,X5: set_Pr8948481099588399239c_fm_a,N: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( finite8252611493601906128c_fm_a @ X5 )
       => ( ( ord_le8222437384497874983c_fm_a @ X5 @ ( order_7711974919420625261c_fm_a @ R @ N ) )
         => ( ( X5 != bot_bo7958537672377389811c_fm_a )
           => ? [X2: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X2 @ X5 )
                & ! [Xa2: produc2203834439629243303c_fm_a] :
                    ( ( member5029746173879296720c_fm_a @ Xa2 @ X5 )
                   => ( member5029746173879296720c_fm_a @ Xa2 @ ( order_5358731147316321548c_fm_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_1062_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,X5: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( finite3304564945125563331c_fm_a @ X5 )
       => ( ( ord_le3275665582123262618c_fm_a @ X5 @ ( order_1288088311422721504c_fm_a @ R @ N ) )
         => ( ( X5 != bot_bo3626323581529592678c_fm_a )
           => ? [X2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X2 @ X5 )
                & ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ X5 )
                   => ( member6642669571620171971c_fm_a @ Xa2 @ ( order_1815523470270482687c_fm_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_1063_Sup__fin_Osubset,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( B4 != bot_bo1868452413526482246c_fm_a )
       => ( ( ord_le7112219575281605754c_fm_a @ B4 @ A )
         => ( ( sup_su1367922730591523534c_fm_a @ ( lattic3176627891459829297c_fm_a @ B4 ) @ ( lattic3176627891459829297c_fm_a @ A ) )
            = ( lattic3176627891459829297c_fm_a @ A ) ) ) ) ) ).

% Sup_fin.subset
thf(fact_1064_Sup__fin_Osubset,axiom,
    ! [A: set_set_a,B4: set_set_a] :
      ( ( finite_finite_set_a @ A )
     => ( ( B4 != bot_bot_set_set_a )
       => ( ( ord_le3724670747650509150_set_a @ B4 @ A )
         => ( ( sup_sup_set_a @ ( lattic2918178356826803221_set_a @ B4 ) @ ( lattic2918178356826803221_set_a @ A ) )
            = ( lattic2918178356826803221_set_a @ A ) ) ) ) ) ).

% Sup_fin.subset
thf(fact_1065_Sup__fin_Osubset,axiom,
    ! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( B4 != bot_bo4908879468608929837fm_a_o )
       => ( ( ord_le4525777775358908921fm_a_o @ B4 @ A )
         => ( ( sup_su6697315146409554831fm_a_o @ ( lattic18181228415053292fm_a_o @ B4 ) @ ( lattic18181228415053292fm_a_o @ A ) )
            = ( lattic18181228415053292fm_a_o @ A ) ) ) ) ) ).

% Sup_fin.subset
thf(fact_1066_Sup__fin_Osubset__imp,axiom,
    ! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
      ( ( ord_le4525777775358908921fm_a_o @ A @ B4 )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( finite5407549452671652090fm_a_o @ B4 )
         => ( ord_le4043730696559282883fm_a_o @ ( lattic18181228415053292fm_a_o @ A ) @ ( lattic18181228415053292fm_a_o @ B4 ) ) ) ) ) ).

% Sup_fin.subset_imp
thf(fact_1067_Sup__fin_Osubset__imp,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( finite7364866884270929315c_fm_a @ B4 )
         => ( ord_le3275665582123262618c_fm_a @ ( lattic3176627891459829297c_fm_a @ A ) @ ( lattic3176627891459829297c_fm_a @ B4 ) ) ) ) ) ).

% Sup_fin.subset_imp
thf(fact_1068_MCS__Lim__Ord_Owo__rel__r,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( bNF_We8255954830765735686c_fm_a @ R ) ) ).

% MCS_Lim_Ord.wo_rel_r
thf(fact_1069_wo__rel_OunderS__bound,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,A2: set_Epistemic_fm_a,N: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( member536094252920883875c_fm_a @ A2 @ ( order_7871341057202914240c_fm_a @ R @ N ) )
       => ( ( member536094252920883875c_fm_a @ B @ ( order_7871341057202914240c_fm_a @ R @ N ) )
         => ( ( member536094252920883875c_fm_a @ A2 @ ( order_4320674923736412895c_fm_a @ R @ B ) )
            | ( member536094252920883875c_fm_a @ B @ ( order_4320674923736412895c_fm_a @ R @ A2 ) ) ) ) ) ) ).

% wo_rel.underS_bound
thf(fact_1070_wo__rel_OunderS__bound,axiom,
    ! [R: set_Product_prod_a_a,A2: a,N: a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ A2 @ ( order_underS_a @ R @ N ) )
       => ( ( member_a @ B @ ( order_underS_a @ R @ N ) )
         => ( ( member_a @ A2 @ ( order_under_a @ R @ B ) )
            | ( member_a @ B @ ( order_under_a @ R @ A2 ) ) ) ) ) ) ).

% wo_rel.underS_bound
thf(fact_1071_wo__rel_OunderS__bound,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,A2: produc2203834439629243303c_fm_a,N: produc2203834439629243303c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_7711974919420625261c_fm_a @ R @ N ) )
       => ( ( member5029746173879296720c_fm_a @ B @ ( order_7711974919420625261c_fm_a @ R @ N ) )
         => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_5358731147316321548c_fm_a @ R @ B ) )
            | ( member5029746173879296720c_fm_a @ B @ ( order_5358731147316321548c_fm_a @ R @ A2 ) ) ) ) ) ) ).

% wo_rel.underS_bound
thf(fact_1072_wo__rel_OunderS__bound,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a,N: epistemic_fm_a,B: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_1288088311422721504c_fm_a @ R @ N ) )
       => ( ( member6642669571620171971c_fm_a @ B @ ( order_1288088311422721504c_fm_a @ R @ N ) )
         => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_1815523470270482687c_fm_a @ R @ B ) )
            | ( member6642669571620171971c_fm_a @ B @ ( order_1815523470270482687c_fm_a @ R @ A2 ) ) ) ) ) ) ).

% wo_rel.underS_bound
thf(fact_1073_wo__rel__r,axiom,
    bNF_We8255954830765735686c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% wo_rel_r
thf(fact_1074_Sup__fin_OcoboundedI,axiom,
    ! [A: set_Epistemic_fm_a_o,A2: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( member4486839677911940090fm_a_o @ A2 @ A )
       => ( ord_le4043730696559282883fm_a_o @ A2 @ ( lattic18181228415053292fm_a_o @ A ) ) ) ) ).

% Sup_fin.coboundedI
thf(fact_1075_Sup__fin_OcoboundedI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( member536094252920883875c_fm_a @ A2 @ A )
       => ( ord_le3275665582123262618c_fm_a @ A2 @ ( lattic3176627891459829297c_fm_a @ A ) ) ) ) ).

% Sup_fin.coboundedI
thf(fact_1076_Sup__fin_OboundedE,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( ord_le4043730696559282883fm_a_o @ ( lattic18181228415053292fm_a_o @ A ) @ X3 )
         => ! [A7: epistemic_fm_a > $o] :
              ( ( member4486839677911940090fm_a_o @ A7 @ A )
             => ( ord_le4043730696559282883fm_a_o @ A7 @ X3 ) ) ) ) ) ).

% Sup_fin.boundedE
thf(fact_1077_Sup__fin_OboundedE,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ ( lattic3176627891459829297c_fm_a @ A ) @ X3 )
         => ! [A7: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ A7 @ A )
             => ( ord_le3275665582123262618c_fm_a @ A7 @ X3 ) ) ) ) ) ).

% Sup_fin.boundedE
thf(fact_1078_Sup__fin_OboundedI,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ! [A6: epistemic_fm_a > $o] :
              ( ( member4486839677911940090fm_a_o @ A6 @ A )
             => ( ord_le4043730696559282883fm_a_o @ A6 @ X3 ) )
         => ( ord_le4043730696559282883fm_a_o @ ( lattic18181228415053292fm_a_o @ A ) @ X3 ) ) ) ) ).

% Sup_fin.boundedI
thf(fact_1079_Sup__fin_OboundedI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ! [A6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ A6 @ A )
             => ( ord_le3275665582123262618c_fm_a @ A6 @ X3 ) )
         => ( ord_le3275665582123262618c_fm_a @ ( lattic3176627891459829297c_fm_a @ A ) @ X3 ) ) ) ) ).

% Sup_fin.boundedI
thf(fact_1080_Sup__fin_Obounded__iff,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( ord_le4043730696559282883fm_a_o @ ( lattic18181228415053292fm_a_o @ A ) @ X3 )
          = ( ! [X: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ X @ A )
               => ( ord_le4043730696559282883fm_a_o @ X @ X3 ) ) ) ) ) ) ).

% Sup_fin.bounded_iff
thf(fact_1081_Sup__fin_Obounded__iff,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ ( lattic3176627891459829297c_fm_a @ A ) @ X3 )
          = ( ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
               => ( ord_le3275665582123262618c_fm_a @ X @ X3 ) ) ) ) ) ) ).

% Sup_fin.bounded_iff
thf(fact_1082_wo__rel_OWell__order__isMinim__exists,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ? [X_1: epistemic_fm_a] : ( bNF_We541765430379730896c_fm_a @ R @ B4 @ X_1 ) ) ) ) ).

% wo_rel.Well_order_isMinim_exists
thf(fact_1083_Inf__fin__le__Sup__fin,axiom,
    ! [A: set_Epistemic_fm_a_o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ord_le4043730696559282883fm_a_o @ ( lattic8370817070757793286fm_a_o @ A ) @ ( lattic18181228415053292fm_a_o @ A ) ) ) ) ).

% Inf_fin_le_Sup_fin
thf(fact_1084_Inf__fin__le__Sup__fin,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ord_le3275665582123262618c_fm_a @ ( lattic7927669795667837335c_fm_a @ A ) @ ( lattic3176627891459829297c_fm_a @ A ) ) ) ) ).

% Inf_fin_le_Sup_fin
thf(fact_1085_wo__rel_OunderS__suc,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( member536094252920883875c_fm_a @ B @ ( order_7871341057202914240c_fm_a @ R @ ( bNF_We1342240761504683227c_fm_a @ R @ A ) ) )
       => ( ( ord_le7112219575281605754c_fm_a @ A @ ( field_3462791820427926727c_fm_a @ R ) )
         => ? [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ A )
              & ( member536094252920883875c_fm_a @ B @ ( order_4320674923736412895c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_suc
thf(fact_1086_wo__rel_OunderS__suc,axiom,
    ! [R: set_Product_prod_a_a,B: a,A: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ B @ ( order_underS_a @ R @ ( bNF_We6154283375207884895_suc_a @ R @ A ) ) )
       => ( ( ord_less_eq_set_a @ A @ ( field_a @ R ) )
         => ? [X2: a] :
              ( ( member_a @ X2 @ A )
              & ( member_a @ B @ ( order_under_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_suc
thf(fact_1087_wo__rel_OunderS__suc,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( member5029746173879296720c_fm_a @ B @ ( order_7711974919420625261c_fm_a @ R @ ( bNF_We66005243949969672c_fm_a @ R @ A ) ) )
       => ( ( ord_le8222437384497874983c_fm_a @ A @ ( field_4566226324314649332c_fm_a @ R ) )
         => ? [X2: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X2 @ A )
              & ( member5029746173879296720c_fm_a @ B @ ( order_5358731147316321548c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_suc
thf(fact_1088_wo__rel_OunderS__suc,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( member6642669571620171971c_fm_a @ B @ ( order_1288088311422721504c_fm_a @ R @ ( bNF_We6750397625931619067c_fm_a @ R @ A ) ) )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ A )
              & ( member6642669571620171971c_fm_a @ B @ ( order_1815523470270482687c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_suc
thf(fact_1089_Inf__fin_Osubset__imp,axiom,
    ! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
      ( ( ord_le4525777775358908921fm_a_o @ A @ B4 )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( finite5407549452671652090fm_a_o @ B4 )
         => ( ord_le4043730696559282883fm_a_o @ ( lattic8370817070757793286fm_a_o @ B4 ) @ ( lattic8370817070757793286fm_a_o @ A ) ) ) ) ) ).

% Inf_fin.subset_imp
thf(fact_1090_Inf__fin_Osubset__imp,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( finite7364866884270929315c_fm_a @ B4 )
         => ( ord_le3275665582123262618c_fm_a @ ( lattic7927669795667837335c_fm_a @ B4 ) @ ( lattic7927669795667837335c_fm_a @ A ) ) ) ) ) ).

% Inf_fin.subset_imp
thf(fact_1091_Inf__fin_OcoboundedI,axiom,
    ! [A: set_Epistemic_fm_a_o,A2: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( member4486839677911940090fm_a_o @ A2 @ A )
       => ( ord_le4043730696559282883fm_a_o @ ( lattic8370817070757793286fm_a_o @ A ) @ A2 ) ) ) ).

% Inf_fin.coboundedI
thf(fact_1092_Inf__fin_OcoboundedI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( member536094252920883875c_fm_a @ A2 @ A )
       => ( ord_le3275665582123262618c_fm_a @ ( lattic7927669795667837335c_fm_a @ A ) @ A2 ) ) ) ).

% Inf_fin.coboundedI
thf(fact_1093_Inf__fin_Obounded__iff,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( ord_le4043730696559282883fm_a_o @ X3 @ ( lattic8370817070757793286fm_a_o @ A ) )
          = ( ! [X: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ X @ A )
               => ( ord_le4043730696559282883fm_a_o @ X3 @ X ) ) ) ) ) ) ).

% Inf_fin.bounded_iff
thf(fact_1094_Inf__fin_Obounded__iff,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ X3 @ ( lattic7927669795667837335c_fm_a @ A ) )
          = ( ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
               => ( ord_le3275665582123262618c_fm_a @ X3 @ X ) ) ) ) ) ) ).

% Inf_fin.bounded_iff
thf(fact_1095_Inf__fin_OboundedI,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ! [A6: epistemic_fm_a > $o] :
              ( ( member4486839677911940090fm_a_o @ A6 @ A )
             => ( ord_le4043730696559282883fm_a_o @ X3 @ A6 ) )
         => ( ord_le4043730696559282883fm_a_o @ X3 @ ( lattic8370817070757793286fm_a_o @ A ) ) ) ) ) ).

% Inf_fin.boundedI
thf(fact_1096_Inf__fin_OboundedI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ! [A6: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ A6 @ A )
             => ( ord_le3275665582123262618c_fm_a @ X3 @ A6 ) )
         => ( ord_le3275665582123262618c_fm_a @ X3 @ ( lattic7927669795667837335c_fm_a @ A ) ) ) ) ) ).

% Inf_fin.boundedI
thf(fact_1097_Inf__fin_OboundedE,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( ord_le4043730696559282883fm_a_o @ X3 @ ( lattic8370817070757793286fm_a_o @ A ) )
         => ! [A7: epistemic_fm_a > $o] :
              ( ( member4486839677911940090fm_a_o @ A7 @ A )
             => ( ord_le4043730696559282883fm_a_o @ X3 @ A7 ) ) ) ) ) ).

% Inf_fin.boundedE
thf(fact_1098_Inf__fin_OboundedE,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ X3 @ ( lattic7927669795667837335c_fm_a @ A ) )
         => ! [A7: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ A7 @ A )
             => ( ord_le3275665582123262618c_fm_a @ X3 @ A7 ) ) ) ) ) ).

% Inf_fin.boundedE
thf(fact_1099_wo__rel_Ominim__isMinim,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ( bNF_We541765430379730896c_fm_a @ R @ B4 @ ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.minim_isMinim
thf(fact_1100_Wellorder__Constructions_Owo__rel_Osuc__underS,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_6674880131641743173c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( ( member536094252920883875c_fm_a @ B @ B4 )
           => ( member536094252920883875c_fm_a @ B @ ( order_7871341057202914240c_fm_a @ R @ ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% Wellorder_Constructions.wo_rel.suc_underS
thf(fact_1101_Wellorder__Constructions_Owo__rel_Osuc__underS,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_AboveS_a @ R @ B4 )
           != bot_bot_set_a )
         => ( ( member_a @ B @ B4 )
           => ( member_a @ B @ ( order_underS_a @ R @ ( bNF_We6154283375207884895_suc_a @ R @ B4 ) ) ) ) ) ) ) ).

% Wellorder_Constructions.wo_rel.suc_underS
thf(fact_1102_Wellorder__Constructions_Owo__rel_Osuc__underS,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_4222029354439091826c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( ( member5029746173879296720c_fm_a @ B @ B4 )
           => ( member5029746173879296720c_fm_a @ B @ ( order_7711974919420625261c_fm_a @ R @ ( bNF_We66005243949969672c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% Wellorder_Constructions.wo_rel.suc_underS
thf(fact_1103_Wellorder__Constructions_Owo__rel_Osuc__underS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_225095655763363173c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( member6642669571620171971c_fm_a @ B @ B4 )
           => ( member6642669571620171971c_fm_a @ B @ ( order_1288088311422721504c_fm_a @ R @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% Wellorder_Constructions.wo_rel.suc_underS
thf(fact_1104_wo__rel_Osuc__inField,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_6674880131641743173c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) @ ( field_3462791820427926727c_fm_a @ R ) ) ) ) ) ).

% wo_rel.suc_inField
thf(fact_1105_wo__rel_Osuc__inField,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_AboveS_a @ R @ B4 )
           != bot_bot_set_a )
         => ( member_a @ ( bNF_We6154283375207884895_suc_a @ R @ B4 ) @ ( field_a @ R ) ) ) ) ) ).

% wo_rel.suc_inField
thf(fact_1106_wo__rel_Osuc__inField,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_4222029354439091826c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We66005243949969672c_fm_a @ R @ B4 ) @ ( field_4566226324314649332c_fm_a @ R ) ) ) ) ) ).

% wo_rel.suc_inField
thf(fact_1107_wo__rel_Osuc__inField,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_225095655763363173c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) @ ( field_Epistemic_fm_a @ R ) ) ) ) ) ).

% wo_rel.suc_inField
thf(fact_1108_wo__rel_Osuc__AboveS,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_6674880131641743173c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) @ ( order_6674880131641743173c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.suc_AboveS
thf(fact_1109_wo__rel_Osuc__AboveS,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_AboveS_a @ R @ B4 )
           != bot_bot_set_a )
         => ( member_a @ ( bNF_We6154283375207884895_suc_a @ R @ B4 ) @ ( order_AboveS_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.suc_AboveS
thf(fact_1110_wo__rel_Osuc__AboveS,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_4222029354439091826c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We66005243949969672c_fm_a @ R @ B4 ) @ ( order_4222029354439091826c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.suc_AboveS
thf(fact_1111_wo__rel_Osuc__AboveS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_225095655763363173c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) @ ( order_225095655763363173c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.suc_AboveS
thf(fact_1112_AboveS__decr,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_225095655763363173c_fm_a @ R @ B4 ) @ ( order_225095655763363173c_fm_a @ R @ A ) ) ) ).

% AboveS_decr
thf(fact_1113_AboveS__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_225095655763363173c_fm_a @ R @ A ) @ ( field_Epistemic_fm_a @ R ) ) ).

% AboveS_Field
thf(fact_1114_wo__rel_Ominim__in,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( B4 != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) @ B4 ) ) ) ) ).

% wo_rel.minim_in
thf(fact_1115_wo__rel_Ominim__in,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( B4 != bot_bot_set_a )
         => ( member_a @ ( bNF_We5615626441682584778inim_a @ R @ B4 ) @ B4 ) ) ) ) ).

% wo_rel.minim_in
thf(fact_1116_wo__rel_Ominim__in,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( B4 != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) @ B4 ) ) ) ) ).

% wo_rel.minim_in
thf(fact_1117_wo__rel_Ominim__in,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) @ B4 ) ) ) ) ).

% wo_rel.minim_in
thf(fact_1118_wo__rel_Ominim__inField,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( B4 != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) @ ( field_3462791820427926727c_fm_a @ R ) ) ) ) ) ).

% wo_rel.minim_inField
thf(fact_1119_wo__rel_Ominim__inField,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( B4 != bot_bot_set_a )
         => ( member_a @ ( bNF_We5615626441682584778inim_a @ R @ B4 ) @ ( field_a @ R ) ) ) ) ) ).

% wo_rel.minim_inField
thf(fact_1120_wo__rel_Ominim__inField,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( B4 != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) @ ( field_4566226324314649332c_fm_a @ R ) ) ) ) ) ).

% wo_rel.minim_inField
thf(fact_1121_wo__rel_Ominim__inField,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) @ ( field_Epistemic_fm_a @ R ) ) ) ) ) ).

% wo_rel.minim_inField
thf(fact_1122_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_6674880131641743173c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( ( member536094252920883875c_fm_a @ B @ B4 )
           => ( ( ( bNF_We1342240761504683227c_fm_a @ R @ B4 )
               != B )
              & ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B @ ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_1123_wo__rel_Osuc__greater,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_AboveS_a @ R @ B4 )
           != bot_bot_set_a )
         => ( ( member_a @ B @ B4 )
           => ( ( ( bNF_We6154283375207884895_suc_a @ R @ B4 )
               != B )
              & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We6154283375207884895_suc_a @ R @ B4 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_1124_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_4222029354439091826c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( ( member5029746173879296720c_fm_a @ B @ B4 )
           => ( ( ( bNF_We66005243949969672c_fm_a @ R @ B4 )
               != B )
              & ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B @ ( bNF_We66005243949969672c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_1125_wo__rel_Osuc__greater,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_225095655763363173c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( member6642669571620171971c_fm_a @ B @ B4 )
           => ( ( ( bNF_We6750397625931619067c_fm_a @ R @ B4 )
               != B )
              & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ) ).

% wo_rel.suc_greater
thf(fact_1126_wo__rel_OunderS__supr,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( member536094252920883875c_fm_a @ B @ ( order_7871341057202914240c_fm_a @ R @ ( bNF_We2920625255559816434c_fm_a @ R @ A ) ) )
       => ( ( ord_le7112219575281605754c_fm_a @ A @ ( field_3462791820427926727c_fm_a @ R ) )
         => ? [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ A )
              & ( member536094252920883875c_fm_a @ B @ ( order_7871341057202914240c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_supr
thf(fact_1127_wo__rel_OunderS__supr,axiom,
    ! [R: set_Product_prod_a_a,B: a,A: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ B @ ( order_underS_a @ R @ ( bNF_We1039243157376381174supr_a @ R @ A ) ) )
       => ( ( ord_less_eq_set_a @ A @ ( field_a @ R ) )
         => ? [X2: a] :
              ( ( member_a @ X2 @ A )
              & ( member_a @ B @ ( order_underS_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_supr
thf(fact_1128_wo__rel_OunderS__supr,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( member5029746173879296720c_fm_a @ B @ ( order_7711974919420625261c_fm_a @ R @ ( bNF_We8469788483847803295c_fm_a @ R @ A ) ) )
       => ( ( ord_le8222437384497874983c_fm_a @ A @ ( field_4566226324314649332c_fm_a @ R ) )
         => ? [X2: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X2 @ A )
              & ( member5029746173879296720c_fm_a @ B @ ( order_7711974919420625261c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_supr
thf(fact_1129_wo__rel_OunderS__supr,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( member6642669571620171971c_fm_a @ B @ ( order_1288088311422721504c_fm_a @ R @ ( bNF_We3666122547472320274c_fm_a @ R @ A ) ) )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ A )
              & ( member6642669571620171971c_fm_a @ B @ ( order_1288088311422721504c_fm_a @ R @ X2 ) ) ) ) ) ) ).

% wo_rel.underS_supr
thf(fact_1130_wo__rel_Ominim__UnderS__underS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
         => ( ( order_2700047599516024256c_fm_a @ R @ A )
            = ( order_1288088311422721504c_fm_a @ R @ ( bNF_We6247850539267499238c_fm_a @ R @ A ) ) ) ) ) ) ).

% wo_rel.minim_UnderS_underS
thf(fact_1131_wo__rel_Ominim__Under__under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
         => ( ( order_2859517270982914335c_fm_a @ R @ A )
            = ( order_1815523470270482687c_fm_a @ R @ ( bNF_We6247850539267499238c_fm_a @ R @ A ) ) ) ) ) ) ).

% wo_rel.minim_Under_under
thf(fact_1132_UnderS__subset__Under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_2700047599516024256c_fm_a @ R @ A ) @ ( order_2859517270982914335c_fm_a @ R @ A ) ) ).

% UnderS_subset_Under
thf(fact_1133_top__empty__eq2,axiom,
    ( top_to8092407255657902782fm_a_o
    = ( ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ top_to4207332589035249111c_fm_a ) ) ) ).

% top_empty_eq2
thf(fact_1134_subrelI,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,S9: set_Pr8948481099588399239c_fm_a] :
      ( ! [X2: epistemic_fm_a,Y2: epistemic_fm_a] :
          ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y2 ) @ R )
         => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y2 ) @ S9 ) )
     => ( ord_le8222437384497874983c_fm_a @ R @ S9 ) ) ).

% subrelI
thf(fact_1135_pred__equals__eq2,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( ( ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R2 ) )
        = ( ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ S ) ) )
      = ( R2 = S ) ) ).

% pred_equals_eq2
thf(fact_1136_bot__empty__eq2,axiom,
    ( bot_bo8256154652621639642fm_a_o
    = ( ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ bot_bo7958537672377389811c_fm_a ) ) ) ).

% bot_empty_eq2
thf(fact_1137_sup__Un__eq2,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( sup_su5518344886633089858fm_a_o
        @ ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R2 )
        @ ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ S ) )
      = ( ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ ( sup_su6976870698533002843c_fm_a @ R2 @ S ) ) ) ) ).

% sup_Un_eq2
thf(fact_1138_wo__rel_Oequals__supr,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( field_3462791820427926727c_fm_a @ R ) )
         => ( ! [B6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ B6 @ B4 )
               => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B6 @ A2 ) @ R ) )
           => ( ! [A8: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ A8 @ ( field_3462791820427926727c_fm_a @ R ) )
                 => ( ! [B7: set_Epistemic_fm_a] :
                        ( ( member536094252920883875c_fm_a @ B7 @ B4 )
                       => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B7 @ A8 ) @ R ) )
                   => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_supr
thf(fact_1139_wo__rel_Oequals__supr,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( field_a @ R ) )
         => ( ! [B6: a] :
                ( ( member_a @ B6 @ B4 )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B6 @ A2 ) @ R ) )
           => ( ! [A8: a] :
                  ( ( member_a @ A8 @ ( field_a @ R ) )
                 => ( ! [B7: a] :
                        ( ( member_a @ B7 @ B4 )
                       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B7 @ A8 ) @ R ) )
                   => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We1039243157376381174supr_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_supr
thf(fact_1140_wo__rel_Oequals__supr,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( field_4566226324314649332c_fm_a @ R ) )
         => ( ! [B6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ B6 @ B4 )
               => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B6 @ A2 ) @ R ) )
           => ( ! [A8: produc2203834439629243303c_fm_a] :
                  ( ( member5029746173879296720c_fm_a @ A8 @ ( field_4566226324314649332c_fm_a @ R ) )
                 => ( ! [B7: produc2203834439629243303c_fm_a] :
                        ( ( member5029746173879296720c_fm_a @ B7 @ B4 )
                       => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B7 @ A8 ) @ R ) )
                   => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_supr
thf(fact_1141_wo__rel_Oequals__supr,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( field_Epistemic_fm_a @ R ) )
         => ( ! [B6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ B6 @ B4 )
               => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B6 @ A2 ) @ R ) )
           => ( ! [A8: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ A8 @ ( field_Epistemic_fm_a @ R ) )
                 => ( ! [B7: epistemic_fm_a] :
                        ( ( member6642669571620171971c_fm_a @ B7 @ B4 )
                       => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B7 @ A8 ) @ R ) )
                   => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_supr
thf(fact_1142_wo__rel_Osupr__least,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( field_3462791820427926727c_fm_a @ R ) )
         => ( ! [B6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ B6 @ B4 )
               => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B6 @ A2 ) @ R ) )
           => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.supr_least
thf(fact_1143_wo__rel_Osupr__least,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( field_a @ R ) )
         => ( ! [B6: a] :
                ( ( member_a @ B6 @ B4 )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B6 @ A2 ) @ R ) )
           => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We1039243157376381174supr_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.supr_least
thf(fact_1144_wo__rel_Osupr__least,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( field_4566226324314649332c_fm_a @ R ) )
         => ( ! [B6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ B6 @ B4 )
               => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B6 @ A2 ) @ R ) )
           => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.supr_least
thf(fact_1145_wo__rel_Osupr__least,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( field_Epistemic_fm_a @ R ) )
         => ( ! [B6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ B6 @ B4 )
               => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B6 @ A2 ) @ R ) )
           => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.supr_least
thf(fact_1146_Under__decr,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_2859517270982914335c_fm_a @ R @ B4 ) @ ( order_2859517270982914335c_fm_a @ R @ A ) ) ) ).

% Under_decr
thf(fact_1147_underS__def,axiom,
    ( order_7871341057202914240c_fm_a
    = ( ^ [R4: set_Pr4537461906582779015c_fm_a,A4: set_Epistemic_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [B2: set_Epistemic_fm_a] :
              ( ( B2 != A4 )
              & ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B2 @ A4 ) @ R4 ) ) ) ) ) ).

% underS_def
thf(fact_1148_underS__def,axiom,
    ( order_1288088311422721504c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,A4: epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [B2: epistemic_fm_a] :
              ( ( B2 != A4 )
              & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B2 @ A4 ) @ R4 ) ) ) ) ) ).

% underS_def
thf(fact_1149_under__def,axiom,
    ( order_4320674923736412895c_fm_a
    = ( ^ [R4: set_Pr4537461906582779015c_fm_a,A4: set_Epistemic_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [B2: set_Epistemic_fm_a] : ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B2 @ A4 ) @ R4 ) ) ) ) ).

% under_def
thf(fact_1150_under__def,axiom,
    ( order_1815523470270482687c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,A4: epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [B2: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B2 @ A4 ) @ R4 ) ) ) ) ).

% under_def
thf(fact_1151_UnderS__decr,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_2700047599516024256c_fm_a @ R @ B4 ) @ ( order_2700047599516024256c_fm_a @ R @ A ) ) ) ).

% UnderS_decr
thf(fact_1152_pred__subset__eq2,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3934200179093585166fm_a_o
        @ ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R2 )
        @ ^ [X: epistemic_fm_a,Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ S ) )
      = ( ord_le8222437384497874983c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq2
thf(fact_1153_Under__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_2859517270982914335c_fm_a @ R @ A ) @ ( field_Epistemic_fm_a @ R ) ) ).

% Under_Field
thf(fact_1154_UnderS__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_2700047599516024256c_fm_a @ R @ A ) @ ( field_Epistemic_fm_a @ R ) ) ).

% UnderS_Field
thf(fact_1155_wo__rel_Osuc__least,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( field_3462791820427926727c_fm_a @ R ) )
         => ( ! [B6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.suc_least
thf(fact_1156_wo__rel_Osuc__least,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( field_a @ R ) )
         => ( ! [B6: a] :
                ( ( member_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B6 @ A2 ) @ R ) ) )
           => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We6154283375207884895_suc_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.suc_least
thf(fact_1157_wo__rel_Osuc__least,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( field_4566226324314649332c_fm_a @ R ) )
         => ( ! [B6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ ( bNF_We66005243949969672c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.suc_least
thf(fact_1158_wo__rel_Osuc__least,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( field_Epistemic_fm_a @ R ) )
         => ( ! [B6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ) ).

% wo_rel.suc_least
thf(fact_1159_wo__rel_Oequals__suc,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( field_3462791820427926727c_fm_a @ R ) )
         => ( ! [B6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( ! [A8: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ A8 @ ( field_3462791820427926727c_fm_a @ R ) )
                 => ( ! [B7: set_Epistemic_fm_a] :
                        ( ( member536094252920883875c_fm_a @ B7 @ B4 )
                       => ( ( A8 != B7 )
                          & ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B7 @ A8 ) @ R ) ) )
                   => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_suc
thf(fact_1160_wo__rel_Oequals__suc,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( field_a @ R ) )
         => ( ! [B6: a] :
                ( ( member_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B6 @ A2 ) @ R ) ) )
           => ( ! [A8: a] :
                  ( ( member_a @ A8 @ ( field_a @ R ) )
                 => ( ! [B7: a] :
                        ( ( member_a @ B7 @ B4 )
                       => ( ( A8 != B7 )
                          & ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B7 @ A8 ) @ R ) ) )
                   => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We6154283375207884895_suc_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_suc
thf(fact_1161_wo__rel_Oequals__suc,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( field_4566226324314649332c_fm_a @ R ) )
         => ( ! [B6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( ! [A8: produc2203834439629243303c_fm_a] :
                  ( ( member5029746173879296720c_fm_a @ A8 @ ( field_4566226324314649332c_fm_a @ R ) )
                 => ( ! [B7: produc2203834439629243303c_fm_a] :
                        ( ( member5029746173879296720c_fm_a @ B7 @ B4 )
                       => ( ( A8 != B7 )
                          & ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B7 @ A8 ) @ R ) ) )
                   => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We66005243949969672c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_suc
thf(fact_1162_wo__rel_Oequals__suc,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( field_Epistemic_fm_a @ R ) )
         => ( ! [B6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ B6 @ B4 )
               => ( ( A2 != B6 )
                  & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B6 @ A2 ) @ R ) ) )
           => ( ! [A8: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ A8 @ ( field_Epistemic_fm_a @ R ) )
                 => ( ! [B7: epistemic_fm_a] :
                        ( ( member6642669571620171971c_fm_a @ B7 @ B4 )
                       => ( ( A8 != B7 )
                          & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B7 @ A8 ) @ R ) ) )
                   => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ A8 ) @ R ) ) )
             => ( A2
                = ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.equals_suc
thf(fact_1163_wo__rel_OTrans__Under__regressive,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
         => ( ord_le3275665582123262618c_fm_a @ ( order_2859517270982914335c_fm_a @ R @ ( order_2859517270982914335c_fm_a @ R @ A ) ) @ ( order_2859517270982914335c_fm_a @ R @ A ) ) ) ) ) ).

% wo_rel.Trans_Under_regressive
thf(fact_1164_wo__rel_Oequals__minim__Under,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ B4 )
         => ( ( member536094252920883875c_fm_a @ A2 @ ( order_2458666036161633023c_fm_a @ R @ B4 ) )
           => ( A2
              = ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim_Under
thf(fact_1165_wo__rel_Oequals__minim__Under,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ B4 )
         => ( ( member_a @ A2 @ ( order_Under_a @ R @ B4 ) )
           => ( A2
              = ( bNF_We5615626441682584778inim_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim_Under
thf(fact_1166_wo__rel_Oequals__minim__Under,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ B4 )
         => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_2581767438827058476c_fm_a @ R @ B4 ) )
           => ( A2
              = ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim_Under
thf(fact_1167_wo__rel_Oequals__minim__Under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ B4 )
         => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_2859517270982914335c_fm_a @ R @ B4 ) )
           => ( A2
              = ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim_Under
thf(fact_1168_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ B @ B4 )
         => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_1169_wo__rel_Ominim__least,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ B @ B4 )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We5615626441682584778inim_a @ R @ B4 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_1170_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ B @ B4 )
         => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_1171_wo__rel_Ominim__least,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ B @ B4 )
         => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) @ B ) @ R ) ) ) ) ).

% wo_rel.minim_least
thf(fact_1172_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ B4 )
         => ( ! [B6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ B6 @ B4 )
               => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ B6 ) @ R ) )
           => ( A2
              = ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_1173_wo__rel_Oequals__minim,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ B4 )
         => ( ! [B6: a] :
                ( ( member_a @ B6 @ B4 )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ B6 ) @ R ) )
           => ( A2
              = ( bNF_We5615626441682584778inim_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_1174_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ B4 )
         => ( ! [B6: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ B6 @ B4 )
               => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ B6 ) @ R ) )
           => ( A2
              = ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_1175_wo__rel_Oequals__minim,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ B4 )
         => ( ! [B6: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ B6 @ B4 )
               => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B6 ) @ R ) )
           => ( A2
              = ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_minim
thf(fact_1176_UnderS__AboveS__Galois,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,C2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ( ord_le3275665582123262618c_fm_a @ C2 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_225095655763363173c_fm_a @ R @ C2 ) )
          = ( ord_le3275665582123262618c_fm_a @ C2 @ ( order_2700047599516024256c_fm_a @ R @ B4 ) ) ) ) ) ).

% UnderS_AboveS_Galois
thf(fact_1177_subset__AboveS__UnderS,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_225095655763363173c_fm_a @ R @ ( order_2700047599516024256c_fm_a @ R @ B4 ) ) ) ) ).

% subset_AboveS_UnderS
thf(fact_1178_subset__UnderS__AboveS,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_2700047599516024256c_fm_a @ R @ ( order_225095655763363173c_fm_a @ R @ B4 ) ) ) ) ).

% subset_UnderS_AboveS
thf(fact_1179_wo__rel_Ominim__iff__In__Under,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( B4 != bot_bo1868452413526482246c_fm_a )
         => ( ( A2
              = ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) )
            = ( ( member536094252920883875c_fm_a @ A2 @ B4 )
              & ( member536094252920883875c_fm_a @ A2 @ ( order_2458666036161633023c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.minim_iff_In_Under
thf(fact_1180_wo__rel_Ominim__iff__In__Under,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( B4 != bot_bot_set_a )
         => ( ( A2
              = ( bNF_We5615626441682584778inim_a @ R @ B4 ) )
            = ( ( member_a @ A2 @ B4 )
              & ( member_a @ A2 @ ( order_Under_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.minim_iff_In_Under
thf(fact_1181_wo__rel_Ominim__iff__In__Under,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( B4 != bot_bo7958537672377389811c_fm_a )
         => ( ( A2
              = ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) )
            = ( ( member5029746173879296720c_fm_a @ A2 @ B4 )
              & ( member5029746173879296720c_fm_a @ A2 @ ( order_2581767438827058476c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.minim_iff_In_Under
thf(fact_1182_wo__rel_Ominim__iff__In__Under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ( ( A2
              = ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) )
            = ( ( member6642669571620171971c_fm_a @ A2 @ B4 )
              & ( member6642669571620171971c_fm_a @ A2 @ ( order_2859517270982914335c_fm_a @ R @ B4 ) ) ) ) ) ) ) ).

% wo_rel.minim_iff_In_Under
thf(fact_1183_wo__rel_Ominim__Under,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( B4 != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We5423793456056005318c_fm_a @ R @ B4 ) @ ( order_2458666036161633023c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.minim_Under
thf(fact_1184_wo__rel_Ominim__Under,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( B4 != bot_bot_set_a )
         => ( member_a @ ( bNF_We5615626441682584778inim_a @ R @ B4 ) @ ( order_Under_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.minim_Under
thf(fact_1185_wo__rel_Ominim__Under,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( B4 != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We5629211394675361139c_fm_a @ R @ B4 ) @ ( order_2581767438827058476c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.minim_Under
thf(fact_1186_wo__rel_Ominim__Under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( B4 != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We6247850539267499238c_fm_a @ R @ B4 ) @ ( order_2859517270982914335c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.minim_Under
thf(fact_1187_wo__rel_Ocases__Total,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a,B: epistemic_fm_a,Phi: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ A2 @ ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a ) ) @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B ) @ R )
           => ( Phi @ A2 @ B ) )
         => ( ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B @ A2 ) @ R )
             => ( Phi @ A2 @ B ) )
           => ( Phi @ A2 @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_1188_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( order_6674880131641743173c_fm_a @ R @ B4 ) )
         => ( ! [A8: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ A8 @ ( order_6674880131641743173c_fm_a @ R @ B4 ) )
               => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We1342240761504683227c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_1189_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( order_AboveS_a @ R @ B4 ) )
         => ( ! [A8: a] :
                ( ( member_a @ A8 @ ( order_AboveS_a @ R @ B4 ) )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We6154283375207884895_suc_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_1190_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_4222029354439091826c_fm_a @ R @ B4 ) )
         => ( ! [A8: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ A8 @ ( order_4222029354439091826c_fm_a @ R @ B4 ) )
               => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We66005243949969672c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_1191_wo__rel_Oequals__suc__AboveS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_225095655763363173c_fm_a @ R @ B4 ) )
         => ( ! [A8: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ A8 @ ( order_225095655763363173c_fm_a @ R @ B4 ) )
               => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_suc_AboveS
thf(fact_1192_wo__rel_Osuc__above__AboveS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_225095655763363173c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( order_225095655763363173c_fm_a @ R @ B4 )
            = ( order_1596567918915635226c_fm_a @ R @ ( bNF_We6750397625931619067c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.suc_above_AboveS
thf(fact_1193_wo__rel_Oin__underS__supr,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,J: set_Epistemic_fm_a,I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( member536094252920883875c_fm_a @ J @ ( order_7871341057202914240c_fm_a @ R @ I ) )
       => ( ( member536094252920883875c_fm_a @ I @ A )
         => ( ( ord_le7112219575281605754c_fm_a @ A @ ( field_3462791820427926727c_fm_a @ R ) )
           => ( ( ( order_606786824185998874c_fm_a @ R @ A )
               != bot_bo1868452413526482246c_fm_a )
             => ( member536094252920883875c_fm_a @ J @ ( order_7871341057202914240c_fm_a @ R @ ( bNF_We2920625255559816434c_fm_a @ R @ A ) ) ) ) ) ) ) ) ).

% wo_rel.in_underS_supr
thf(fact_1194_wo__rel_Oin__underS__supr,axiom,
    ! [R: set_Product_prod_a_a,J: a,I: a,A: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( member_a @ J @ ( order_underS_a @ R @ I ) )
       => ( ( member_a @ I @ A )
         => ( ( ord_less_eq_set_a @ A @ ( field_a @ R ) )
           => ( ( ( order_Above_a @ R @ A )
               != bot_bot_set_a )
             => ( member_a @ J @ ( order_underS_a @ R @ ( bNF_We1039243157376381174supr_a @ R @ A ) ) ) ) ) ) ) ) ).

% wo_rel.in_underS_supr
thf(fact_1195_wo__rel_Oin__underS__supr,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,J: produc2203834439629243303c_fm_a,I: produc2203834439629243303c_fm_a,A: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( member5029746173879296720c_fm_a @ J @ ( order_7711974919420625261c_fm_a @ R @ I ) )
       => ( ( member5029746173879296720c_fm_a @ I @ A )
         => ( ( ord_le8222437384497874983c_fm_a @ A @ ( field_4566226324314649332c_fm_a @ R ) )
           => ( ( ( order_2949878883090327239c_fm_a @ R @ A )
               != bot_bo7958537672377389811c_fm_a )
             => ( member5029746173879296720c_fm_a @ J @ ( order_7711974919420625261c_fm_a @ R @ ( bNF_We8469788483847803295c_fm_a @ R @ A ) ) ) ) ) ) ) ) ).

% wo_rel.in_underS_supr
thf(fact_1196_wo__rel_Oin__underS__supr,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,J: epistemic_fm_a,I: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( member6642669571620171971c_fm_a @ J @ ( order_1288088311422721504c_fm_a @ R @ I ) )
       => ( ( member6642669571620171971c_fm_a @ I @ A )
         => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
           => ( ( ( order_2640561719628066874c_fm_a @ R @ A )
               != bot_bo3626323581529592678c_fm_a )
             => ( member6642669571620171971c_fm_a @ J @ ( order_1288088311422721504c_fm_a @ R @ ( bNF_We3666122547472320274c_fm_a @ R @ A ) ) ) ) ) ) ) ) ).

% wo_rel.in_underS_supr
thf(fact_1197_wo__rel_Osupr__greater,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_606786824185998874c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( ( member536094252920883875c_fm_a @ B @ B4 )
           => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ B @ ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ).

% wo_rel.supr_greater
thf(fact_1198_wo__rel_Osupr__greater,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,B: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_Above_a @ R @ B4 )
           != bot_bot_set_a )
         => ( ( member_a @ B @ B4 )
           => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ ( bNF_We1039243157376381174supr_a @ R @ B4 ) ) @ R ) ) ) ) ) ).

% wo_rel.supr_greater
thf(fact_1199_wo__rel_Osupr__greater,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_2949878883090327239c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( ( member5029746173879296720c_fm_a @ B @ B4 )
           => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ B @ ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ).

% wo_rel.supr_greater
thf(fact_1200_wo__rel_Osupr__greater,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_2640561719628066874c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( member6642669571620171971c_fm_a @ B @ B4 )
           => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ B @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) ) @ R ) ) ) ) ) ).

% wo_rel.supr_greater
thf(fact_1201_wo__rel_Osupr__inField,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_606786824185998874c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) @ ( field_3462791820427926727c_fm_a @ R ) ) ) ) ) ).

% wo_rel.supr_inField
thf(fact_1202_wo__rel_Osupr__inField,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_Above_a @ R @ B4 )
           != bot_bot_set_a )
         => ( member_a @ ( bNF_We1039243157376381174supr_a @ R @ B4 ) @ ( field_a @ R ) ) ) ) ) ).

% wo_rel.supr_inField
thf(fact_1203_wo__rel_Osupr__inField,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_2949878883090327239c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) @ ( field_4566226324314649332c_fm_a @ R ) ) ) ) ) ).

% wo_rel.supr_inField
thf(fact_1204_wo__rel_Osupr__inField,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_2640561719628066874c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) @ ( field_Epistemic_fm_a @ R ) ) ) ) ) ).

% wo_rel.supr_inField
thf(fact_1205_Above__decr,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_2640561719628066874c_fm_a @ R @ B4 ) @ ( order_2640561719628066874c_fm_a @ R @ A ) ) ) ).

% Above_decr
thf(fact_1206_above__def,axiom,
    ( order_2468795711760778746c_fm_a
    = ( ^ [R4: set_Pr4537461906582779015c_fm_a,A4: set_Epistemic_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [B2: set_Epistemic_fm_a] : ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A4 @ B2 ) @ R4 ) ) ) ) ).

% above_def
thf(fact_1207_above__def,axiom,
    ( order_1596567918915635226c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,A4: epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [B2: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A4 @ B2 ) @ R4 ) ) ) ) ).

% above_def
thf(fact_1208_Above__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_2640561719628066874c_fm_a @ R @ A ) @ ( field_Epistemic_fm_a @ R ) ) ).

% Above_Field
thf(fact_1209_above__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_1596567918915635226c_fm_a @ R @ A2 ) @ ( field_Epistemic_fm_a @ R ) ) ).

% above_Field
thf(fact_1210_above__incr2,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,R3: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ R @ R3 )
     => ( ord_le3275665582123262618c_fm_a @ ( order_1596567918915635226c_fm_a @ R @ A2 ) @ ( order_1596567918915635226c_fm_a @ R3 @ A2 ) ) ) ).

% above_incr2
thf(fact_1211_AboveS__subset__Above,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( order_225095655763363173c_fm_a @ R @ A ) @ ( order_2640561719628066874c_fm_a @ R @ A ) ) ).

% AboveS_subset_Above
thf(fact_1212_wo__rel_Osupr__above__Above,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_2640561719628066874c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( order_2640561719628066874c_fm_a @ R @ B4 )
            = ( order_1596567918915635226c_fm_a @ R @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.supr_above_Above
thf(fact_1213_subset__Under__Above,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_2859517270982914335c_fm_a @ R @ ( order_2640561719628066874c_fm_a @ R @ B4 ) ) ) ) ).

% subset_Under_Above
thf(fact_1214_subset__Above__Under,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_2640561719628066874c_fm_a @ R @ ( order_2859517270982914335c_fm_a @ R @ B4 ) ) ) ) ).

% subset_Above_Under
thf(fact_1215_Under__Above__Galois,axiom,
    ! [B4: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,C2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
     => ( ( ord_le3275665582123262618c_fm_a @ C2 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( order_2640561719628066874c_fm_a @ R @ C2 ) )
          = ( ord_le3275665582123262618c_fm_a @ C2 @ ( order_2859517270982914335c_fm_a @ R @ B4 ) ) ) ) ) ).

% Under_Above_Galois
thf(fact_1216_wo__rel_Osupr__least__Above,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( order_606786824185998874c_fm_a @ R @ B4 ) )
         => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ).

% wo_rel.supr_least_Above
thf(fact_1217_wo__rel_Osupr__least__Above,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( order_Above_a @ R @ B4 ) )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ ( bNF_We1039243157376381174supr_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ).

% wo_rel.supr_least_Above
thf(fact_1218_wo__rel_Osupr__least__Above,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_2949878883090327239c_fm_a @ R @ B4 ) )
         => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ).

% wo_rel.supr_least_Above
thf(fact_1219_wo__rel_Osupr__least__Above,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_2640561719628066874c_fm_a @ R @ B4 ) )
         => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) @ A2 ) @ R ) ) ) ) ).

% wo_rel.supr_least_Above
thf(fact_1220_wo__rel_Oequals__supr__Above,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ A2 @ ( order_606786824185998874c_fm_a @ R @ B4 ) )
         => ( ! [A8: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ A8 @ ( order_606786824185998874c_fm_a @ R @ B4 ) )
               => ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_supr_Above
thf(fact_1221_wo__rel_Oequals__supr__Above,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a,A2: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( member_a @ A2 @ ( order_Above_a @ R @ B4 ) )
         => ( ! [A8: a] :
                ( ( member_a @ A8 @ ( order_Above_a @ R @ B4 ) )
               => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We1039243157376381174supr_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_supr_Above
thf(fact_1222_wo__rel_Oequals__supr__Above,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a,A2: produc2203834439629243303c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ A2 @ ( order_2949878883090327239c_fm_a @ R @ B4 ) )
         => ( ! [A8: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ A8 @ ( order_2949878883090327239c_fm_a @ R @ B4 ) )
               => ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_supr_Above
thf(fact_1223_wo__rel_Oequals__supr__Above,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ A2 @ ( order_2640561719628066874c_fm_a @ R @ B4 ) )
         => ( ! [A8: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ A8 @ ( order_2640561719628066874c_fm_a @ R @ B4 ) )
               => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ A8 ) @ R ) )
           => ( A2
              = ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) ) ) ) ) ) ).

% wo_rel.equals_supr_Above
thf(fact_1224_wo__rel_Osupr__Above,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( ord_le7112219575281605754c_fm_a @ B4 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( ( order_606786824185998874c_fm_a @ R @ B4 )
           != bot_bo1868452413526482246c_fm_a )
         => ( member536094252920883875c_fm_a @ ( bNF_We2920625255559816434c_fm_a @ R @ B4 ) @ ( order_606786824185998874c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.supr_Above
thf(fact_1225_wo__rel_Osupr__Above,axiom,
    ! [R: set_Product_prod_a_a,B4: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ B4 @ ( field_a @ R ) )
       => ( ( ( order_Above_a @ R @ B4 )
           != bot_bot_set_a )
         => ( member_a @ ( bNF_We1039243157376381174supr_a @ R @ B4 ) @ ( order_Above_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.supr_Above
thf(fact_1226_wo__rel_Osupr__Above,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,B4: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_We1383345719562751891c_fm_a @ R )
     => ( ( ord_le8222437384497874983c_fm_a @ B4 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( ( order_2949878883090327239c_fm_a @ R @ B4 )
           != bot_bo7958537672377389811c_fm_a )
         => ( member5029746173879296720c_fm_a @ ( bNF_We8469788483847803295c_fm_a @ R @ B4 ) @ ( order_2949878883090327239c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.supr_Above
thf(fact_1227_wo__rel_Osupr__Above,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( order_2640561719628066874c_fm_a @ R @ B4 )
           != bot_bo3626323581529592678c_fm_a )
         => ( member6642669571620171971c_fm_a @ ( bNF_We3666122547472320274c_fm_a @ R @ B4 ) @ ( order_2640561719628066874c_fm_a @ R @ B4 ) ) ) ) ) ).

% wo_rel.supr_Above
thf(fact_1228_underS__incl__iff,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( order_5511511401533808303c_fm_a @ ( field_3462791820427926727c_fm_a @ R ) @ R )
     => ( ( member536094252920883875c_fm_a @ A2 @ ( field_3462791820427926727c_fm_a @ R ) )
       => ( ( member536094252920883875c_fm_a @ B @ ( field_3462791820427926727c_fm_a @ R ) )
         => ( ( ord_le7112219575281605754c_fm_a @ ( order_7871341057202914240c_fm_a @ R @ A2 ) @ ( order_7871341057202914240c_fm_a @ R @ B ) )
            = ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ A2 @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_1229_underS__incl__iff,axiom,
    ! [R: set_Product_prod_a_a,A2: a,B: a] :
      ( ( order_8768733634509060147r_on_a @ ( field_a @ R ) @ R )
     => ( ( member_a @ A2 @ ( field_a @ R ) )
       => ( ( member_a @ B @ ( field_a @ R ) )
         => ( ( ord_less_eq_set_a @ ( order_underS_a @ R @ A2 ) @ ( order_underS_a @ R @ B ) )
            = ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_1230_underS__incl__iff,axiom,
    ! [R: set_Pr6593897923388255431c_fm_a,A2: produc2203834439629243303c_fm_a,B: produc2203834439629243303c_fm_a] :
      ( ( order_4016684746863976668c_fm_a @ ( field_4566226324314649332c_fm_a @ R ) @ R )
     => ( ( member5029746173879296720c_fm_a @ A2 @ ( field_4566226324314649332c_fm_a @ R ) )
       => ( ( member5029746173879296720c_fm_a @ B @ ( field_4566226324314649332c_fm_a @ R ) )
         => ( ( ord_le8222437384497874983c_fm_a @ ( order_7711974919420625261c_fm_a @ R @ A2 ) @ ( order_7711974919420625261c_fm_a @ R @ B ) )
            = ( member7118756715807017744c_fm_a @ ( produc6913131759110486871c_fm_a @ A2 @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_1231_underS__incl__iff,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A2: epistemic_fm_a,B: epistemic_fm_a] :
      ( ( order_5410817246541083855c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ( member6642669571620171971c_fm_a @ A2 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( member6642669571620171971c_fm_a @ B @ ( field_Epistemic_fm_a @ R ) )
         => ( ( ord_le3275665582123262618c_fm_a @ ( order_1288088311422721504c_fm_a @ R @ A2 ) @ ( order_1288088311422721504c_fm_a @ R @ B ) )
            = ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_1232_wo__rel_Ominim__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( bNF_We6247850539267499238c_fm_a @ R @ A )
        = ( the_Epistemic_fm_a @ ( bNF_We541765430379730896c_fm_a @ R @ A ) ) ) ) ).

% wo_rel.minim_def
thf(fact_1233_the1__equality_H,axiom,
    ! [P4: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( uniq_Epistemic_fm_a @ P4 )
     => ( ( P4 @ A2 )
       => ( ( the_Epistemic_fm_a @ P4 )
          = A2 ) ) ) ).

% the1_equality'
thf(fact_1234_the__elem__def,axiom,
    ( the_el2173195877760541071c_fm_a
    = ( ^ [X4: set_Epistemic_fm_a] :
          ( the_Epistemic_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( X4
              = ( insert7817948963269374698c_fm_a @ X @ bot_bo3626323581529592678c_fm_a ) ) ) ) ) ).

% the_elem_def
thf(fact_1235_Linear__order__Well__order__iff,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] :
      ( ( order_5410817246541083855c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
        = ( ! [A3: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ A3 @ ( field_Epistemic_fm_a @ R ) )
             => ( ( A3 != bot_bo3626323581529592678c_fm_a )
               => ? [X: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ X @ A3 )
                    & ! [Y4: epistemic_fm_a] :
                        ( ( member6642669571620171971c_fm_a @ Y4 @ A3 )
                       => ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R ) ) ) ) ) ) ) ) ).

% Linear_order_Well_order_iff
thf(fact_1236_MCS__Lim__Ord_OWELL,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R ) ) ).

% MCS_Lim_Ord.WELL
thf(fact_1237_WELL,axiom,
    order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% WELL
thf(fact_1238_under__mono,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,I: epistemic_fm_a,J: epistemic_fm_a] :
      ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ I @ J ) @ R )
       => ( ord_le3275665582123262618c_fm_a @ ( order_1815523470270482687c_fm_a @ R @ I ) @ ( order_1815523470270482687c_fm_a @ R @ J ) ) ) ) ).

% under_mono
thf(fact_1239_MCS__Lim__Ord_Ointro,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o] :
      ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ( wellor5744531135217078139c_fm_a @ R )
       => ( ! [S6: set_Epistemic_fm_a,S3: set_Epistemic_fm_a] :
              ( ( Consistent @ S6 )
             => ( ( ord_le3275665582123262618c_fm_a @ S3 @ S6 )
               => ( Consistent @ S3 ) ) )
         => ( ! [S6: set_Epistemic_fm_a] :
                ( ~ ( Consistent @ S6 )
               => ? [S7: set_Epistemic_fm_a] :
                    ( ( ord_le3275665582123262618c_fm_a @ S7 @ S6 )
                    & ( finite3304564945125563331c_fm_a @ S7 )
                    & ~ ( Consistent @ S7 ) ) )
           => ( maxima8116622252184345237c_fm_a @ R @ Consistent ) ) ) ) ) ).

% MCS_Lim_Ord.intro
thf(fact_1240_MCS__Lim__Ord__def,axiom,
    ( maxima8116622252184345237c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,Consistent2: set_Epistemic_fm_a > $o] :
          ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R4 ) @ R4 )
          & ( wellor5744531135217078139c_fm_a @ R4 )
          & ! [S4: set_Epistemic_fm_a,S8: set_Epistemic_fm_a] :
              ( ( Consistent2 @ S4 )
             => ( ( ord_le3275665582123262618c_fm_a @ S8 @ S4 )
               => ( Consistent2 @ S8 ) ) )
          & ! [S4: set_Epistemic_fm_a] :
              ( ~ ( Consistent2 @ S4 )
             => ? [S8: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S8 @ S4 )
                  & ( finite3304564945125563331c_fm_a @ S8 )
                  & ~ ( Consistent2 @ S8 ) ) ) ) ) ) ).

% MCS_Lim_Ord_def
thf(fact_1241_MCS__Lim__Ord_OisLimOrd__r,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( wellor5744531135217078139c_fm_a @ R ) ) ).

% MCS_Lim_Ord.isLimOrd_r
thf(fact_1242_isLimOrd__r,axiom,
    wellor5744531135217078139c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% isLimOrd_r
thf(fact_1243_relChain__under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] :
      ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( bNF_Ca794817592588119428c_fm_a @ R @ ( order_1815523470270482687c_fm_a @ R ) ) ) ).

% relChain_under
thf(fact_1244_infinite__Func,axiom,
    ! [A: set_Epistemic_fm_a,B1: epistemic_fm_a,B23: epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ B1 @ ( insert7817948963269374698c_fm_a @ B23 @ bot_bo3626323581529592678c_fm_a ) ) @ B4 )
       => ( ( B1 != B23 )
         => ~ ( finite8130236415186311548c_fm_a @ ( bNF_We4818972062080617492c_fm_a @ A @ B4 ) ) ) ) ) ).

% infinite_Func
thf(fact_1245_wo__rel_Oofilter__UnderS,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
       => ( order_7157697347518734512c_fm_a @ R @ ( order_2700047599516024256c_fm_a @ R @ A ) ) ) ) ).

% wo_rel.ofilter_UnderS
thf(fact_1246_wo__rel_Oofilter__linord,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( order_7157697347518734512c_fm_a @ R @ A )
       => ( ( order_7157697347518734512c_fm_a @ R @ B4 )
         => ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
            | ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ) ) ) ).

% wo_rel.ofilter_linord
thf(fact_1247_ofilter__def,axiom,
    ( order_7157697347518734512c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,A3: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ A3 @ ( field_Epistemic_fm_a @ R4 ) )
          & ! [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A3 )
             => ( ord_le3275665582123262618c_fm_a @ ( order_1815523470270482687c_fm_a @ R4 @ X ) @ A3 ) ) ) ) ) ).

% ofilter_def
thf(fact_1248_wo__rel_Oofilter__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( order_7157697347518734512c_fm_a @ R @ A )
        = ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
          & ! [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A )
             => ( ord_le3275665582123262618c_fm_a @ ( order_1815523470270482687c_fm_a @ R @ X ) @ A ) ) ) ) ) ).

% wo_rel.ofilter_def
thf(fact_1249_wo__rel_Oofilter__Under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ ( field_Epistemic_fm_a @ R ) )
       => ( order_7157697347518734512c_fm_a @ R @ ( order_2859517270982914335c_fm_a @ R @ A ) ) ) ) ).

% wo_rel.ofilter_Under
thf(fact_1250_relChain__def,axiom,
    ( bNF_Ca2465453702661558361fm_a_o
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,As: epistemic_fm_a > epistemic_fm_a > $o] :
        ! [I2: epistemic_fm_a,J2: epistemic_fm_a] :
          ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ I2 @ J2 ) @ R4 )
         => ( ord_le4043730696559282883fm_a_o @ ( As @ I2 ) @ ( As @ J2 ) ) ) ) ) ).

% relChain_def
thf(fact_1251_relChain__def,axiom,
    ( bNF_Ca794817592588119428c_fm_a
    = ( ^ [R4: set_Pr8948481099588399239c_fm_a,As: epistemic_fm_a > set_Epistemic_fm_a] :
        ! [I2: epistemic_fm_a,J2: epistemic_fm_a] :
          ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ I2 @ J2 ) @ R4 )
         => ( ord_le3275665582123262618c_fm_a @ ( As @ I2 ) @ ( As @ J2 ) ) ) ) ) ).

% relChain_def
thf(fact_1252_ordLeq__Func,axiom,
    ! [B1: epistemic_fm_a,B23: epistemic_fm_a,B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ B1 @ ( insert7817948963269374698c_fm_a @ B23 @ bot_bo3626323581529592678c_fm_a ) ) @ B4 )
     => ( ( B1 != B23 )
       => ( member5250668776978656404c_fm_a @ ( produc707058088808417755c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca7196388322009124745c_fm_a @ ( bNF_We4818972062080617492c_fm_a @ A @ B4 ) ) ) @ bNF_We5212170316383168344c_fm_a ) ) ) ).

% ordLeq_Func
thf(fact_1253_sup__Inf1__distrib,axiom,
    ! [A: set_set_a,X3: set_a] :
      ( ( finite_finite_set_a @ A )
     => ( ( A != bot_bot_set_set_a )
       => ( ( sup_sup_set_a @ X3 @ ( lattic8209813465164889211_set_a @ A ) )
          = ( lattic8209813465164889211_set_a
            @ ( collect_set_a
              @ ^ [Uu2: set_a] :
                ? [A4: set_a] :
                  ( ( Uu2
                    = ( sup_sup_set_a @ X3 @ A4 ) )
                  & ( member_set_a @ A4 @ A ) ) ) ) ) ) ) ).

% sup_Inf1_distrib
thf(fact_1254_sup__Inf1__distrib,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ A )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ( sup_su6697315146409554831fm_a_o @ X3 @ ( lattic8370817070757793286fm_a_o @ A ) )
          = ( lattic8370817070757793286fm_a_o
            @ ( collec3226785624747288888fm_a_o
              @ ^ [Uu2: epistemic_fm_a > $o] :
                ? [A4: epistemic_fm_a > $o] :
                  ( ( Uu2
                    = ( sup_su6697315146409554831fm_a_o @ X3 @ A4 ) )
                  & ( member4486839677911940090fm_a_o @ A4 @ A ) ) ) ) ) ) ) ).

% sup_Inf1_distrib
thf(fact_1255_image__subsetI,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_1256_imageE,axiom,
    ! [B: epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( image_4449434806354059013c_fm_a @ F @ A ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_1257_Compr__image__eq,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( image_4449434806354059013c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_4449434806354059013c_fm_a @ F
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1258_Extend__def,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S )
      = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ ( maxima1168816336865142315c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A ) @ S ) @ ( field_Epistemic_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ) ) ) ) ).

% Extend_def
thf(fact_1259_wo__rel_Oofilter__under__Union,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( order_7157697347518734512c_fm_a @ R @ A )
       => ( A
          = ( comple7868773486375872231c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [Uu2: set_Epistemic_fm_a] :
                ? [A4: epistemic_fm_a] :
                  ( ( Uu2
                    = ( order_1815523470270482687c_fm_a @ R @ A4 ) )
                  & ( member6642669571620171971c_fm_a @ A4 @ A ) ) ) ) ) ) ) ).

% wo_rel.ofilter_under_Union
thf(fact_1260_UN__I,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ A )
     => ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1261_UN__E,axiom,
    ! [B: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1262_SUP__Sup__eq,axiom,
    ! [S: set_se5208064806568342746c_fm_a] :
      ( ( comple310706794042174646fm_a_o
        @ ( image_6902499629341727256fm_a_o
          @ ^ [I2: set_Epistemic_fm_a,X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ I2 )
          @ S ) )
      = ( ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ ( comple7868773486375872231c_fm_a @ S ) ) ) ) ).

% SUP_Sup_eq
thf(fact_1263_Sup__set__def,axiom,
    ( comple7868773486375872231c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] : ( complete_Sup_Sup_o @ ( image_3094577733827872675fm_a_o @ ( member6642669571620171971c_fm_a @ X ) @ A3 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1264_Set_Ofilter__def,axiom,
    ( filter6053540574317342667c_fm_a
    = ( ^ [P6: epistemic_fm_a > $o,A3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [A4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ A4 @ A3 )
              & ( P6 @ A4 ) ) ) ) ) ).

% Set.filter_def
thf(fact_1265_Int__def,axiom,
    ( inf_in2882328776738922472c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A3 )
              & ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ) ).

% Int_def
thf(fact_1266_Int__Collect,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ P4 ) ) )
      = ( ( member6642669571620171971c_fm_a @ X3 @ A )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_1267_Int__Collect__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ( P4 @ X2 )
             => ( Q4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ P4 ) ) @ ( inf_in2882328776738922472c_fm_a @ B4 @ ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1268_Restr__iff,axiom,
    ! [A2: epistemic_fm_a,B: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a] :
      ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B )
        @ ( inf_in4981605569433919093c_fm_a @ R
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : A ) ) )
      = ( ( member6642669571620171971c_fm_a @ A2 @ A )
        & ( member6642669571620171971c_fm_a @ B @ A )
        & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B ) @ R ) ) ) ).

% Restr_iff
thf(fact_1269_inter__Set__filter,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ B4 )
     => ( ( inf_in2882328776738922472c_fm_a @ A @ B4 )
        = ( filter6053540574317342667c_fm_a
          @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A )
          @ B4 ) ) ) ).

% inter_Set_filter
thf(fact_1270_ofilter__Restr__under,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( order_6624744507358568120c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ( order_7157697347518734512c_fm_a @ R @ A )
       => ( ( member6642669571620171971c_fm_a @ A2 @ A )
         => ( ( order_1815523470270482687c_fm_a
              @ ( inf_in4981605569433919093c_fm_a @ R
                @ ( produc1842838987370488648c_fm_a @ A
                  @ ^ [Uu2: epistemic_fm_a] : A ) )
              @ A2 )
            = ( order_1815523470270482687c_fm_a @ R @ A2 ) ) ) ) ) ).

% ofilter_Restr_under
thf(fact_1271_inf__set__def,axiom,
    ( inf_in2882328776738922472c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ( inf_in3606484609122063093fm_a_o
            @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A3 )
            @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ) ).

% inf_set_def
thf(fact_1272_inf__Int__eq,axiom,
    ! [R2: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( inf_in3606484609122063093fm_a_o
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ R2 )
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ S ) )
      = ( ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ ( inf_in2882328776738922472c_fm_a @ R2 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_1273_finite__inverse__image__gen,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( inj_on1950397435265702513c_fm_a @ F @ D )
       => ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [J2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ J2 @ D )
                & ( member6642669571620171971c_fm_a @ ( F @ J2 ) @ A ) ) ) ) ) ) ).

% finite_inverse_image_gen
thf(fact_1274_inj__on__image__mem__iff,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( inj_on1950397435265702513c_fm_a @ F @ B4 )
     => ( ( member6642669571620171971c_fm_a @ A2 @ B4 )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
         => ( ( member6642669571620171971c_fm_a @ ( F @ A2 ) @ ( image_4449434806354059013c_fm_a @ F @ A ) )
            = ( member6642669571620171971c_fm_a @ A2 @ A ) ) ) ) ) ).

% inj_on_image_mem_iff
thf(fact_1275_the__inv__into__into,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,X3: epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( inj_on1950397435265702513c_fm_a @ F @ A )
     => ( ( member6642669571620171971c_fm_a @ X3 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
       => ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
         => ( member6642669571620171971c_fm_a @ ( the_in5018756904006898867c_fm_a @ A @ F @ X3 ) @ B4 ) ) ) ) ).

% the_inv_into_into

% Conjectures (1)
thf(conj_0,conjecture,
    member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ p @ ( epistemic_Imp_a @ q @ ( epistemic_Con_a @ p @ q ) ) ) @ v ).

%------------------------------------------------------------------------------