%------------------------------------------------------------------------------
% 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_00187_005976__6343700_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1713 ( 453 unt; 427 typ;   0 def)
%            Number of atoms       : 4638 (1069 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives : 15914 ( 417   ~;  67   |; 396   &;12753   @)
%                                         (   0 <=>;2281  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   8 avg)
%            Number of types       :   71 (  70 usr)
%            Number of type conns  : 1983 (1983   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  360 ( 357 usr;  35 con; 0-5 aty)
%            Number of variables   : 4731 ( 609   ^;3915   !; 207   ?;4731   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:11:56.762
%------------------------------------------------------------------------------
% Could-be-implicit typings (70)
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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__Set__Oset_I_Eo_J,type,
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thf(ty_n_tf__a,type,
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% Explicit typings (357)
thf(sy_c_BNF__Cardinal__Arithmetic_OCsum_001t__Epistemic____Logic__Ofm_Itf__a_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Cardinal__Arithmetic_Ocinfinite_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_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__Cardinal__Order__Relation_Ocard__of_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_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_OordIso_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_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__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__Constructions_OordLeq_001t__Epistemic____Logic__Ofm_Itf__a_J_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mtf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OordLeq_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_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__Constructions_OordLeq_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__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_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__Constructions_OordLeq_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
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thf(sy_c_BNF__Wellorder__Constructions_OordLeq_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Set__Oset_It__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_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_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_001tf__a,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_062_Itf__a_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_001tf__a,type,
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thf(sy_c_Epistemic__Logic_OAx4_001tf__a,type,
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thf(sy_c_Epistemic__Logic_OAx5_001tf__a,type,
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thf(sy_c_Epistemic__Logic_OAxB_001tf__a,type,
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thf(sy_c_Epistemic__Logic_OAxT_001tf__a,type,
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thf(sy_c_Epistemic__Logic_Oconsistent_001tf__a,type,
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    member2573411668019888912c_fm_a: produc3834786589927319271c_fm_a > set_Pr4758740512813673671c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__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_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_J,type,
    member2483015056062791440c_fm_a: produc1604098380844112103c_fm_a > set_Pr2738098417088766151c_fm_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__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_J_Mt__Set__Oset_It__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_J_J,type,
    member2407610774516601616c_fm_a: produc6374449310175442151c_fm_a > set_Pr2829732620705830087c_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_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_i,type,
    i: 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_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_1__092_060open_062A_A_092_060turnstile_062_AK_Ai_Ap_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_Aq_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_A_Ip_A_092_060_094bold_062_092_060and_062_Aq_J_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ p ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ q ) @ ( epistemic_K_a @ i @ ( epistemic_Con_a @ p @ q ) ) ) ) ).

% \<open>A \<turnstile> K i p \<^bold>\<longrightarrow> K i q \<^bold>\<longrightarrow> K i (p \<^bold>\<and> q)\<close>
thf(fact_2__092_060open_062A_A_092_060turnstile_062_Ap_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_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ p @ ( epistemic_Imp_a @ q @ ( epistemic_Con_a @ p @ q ) ) ) ).

% \<open>A \<turnstile> p \<^bold>\<longrightarrow> q \<^bold>\<longrightarrow> p \<^bold>\<and> q\<close>
thf(fact_3__092_060open_062A_A_092_060turnstile_062_AK_Ai_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,
    epistemic_AK_a @ a2 @ ( epistemic_K_a @ i @ ( epistemic_Imp_a @ p @ ( epistemic_Imp_a @ q @ ( epistemic_Con_a @ p @ q ) ) ) ) ).

% \<open>A \<turnstile> K i (p \<^bold>\<longrightarrow> q \<^bold>\<longrightarrow> p \<^bold>\<and> q)\<close>
thf(fact_4__092_060open_062A_A_092_060turnstile_062_AK_Ai_Ap_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_A_Iq_A_092_060_094bold_062_092_060longrightarrow_062_Ap_A_092_060_094bold_062_092_060and_062_Aq_J_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ p ) @ ( epistemic_K_a @ i @ ( epistemic_Imp_a @ q @ ( epistemic_Con_a @ p @ q ) ) ) ) ).

% \<open>A \<turnstile> K i p \<^bold>\<longrightarrow> K i (q \<^bold>\<longrightarrow> p \<^bold>\<and> q)\<close>
thf(fact_5_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_6_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_7_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_8_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_9_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_10_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_11_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_12_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_13_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_14_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_15_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_16_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_17_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_18_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_19_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_20_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_21_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_22_Ax,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a] :
      ( ( A @ P )
     => ( epistemic_AK_a @ A @ P ) ) ).

% Ax
thf(fact_23_AK_Osimps,axiom,
    ( epistemic_AK_a
    = ( ^ [A3: epistemic_fm_a > $o,A4: epistemic_fm_a] :
          ( ? [P2: epistemic_fm_a] :
              ( ( A4 = P2 )
              & ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ 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_24_AK_Ocases,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ A2 )
     => ( ~ ! [G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ 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_25_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_26_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_27_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_28_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_29_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_30_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_31_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_32_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_33_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_34_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_35_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_36_duality__taut,axiom,
    ! [I: a,P: epistemic_fm_a,Q: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( 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_37_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_38_fm_Odistinct_I9_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_39_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_40_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_41_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_42_eval_Osimps_I5_J,axiom,
    ! [G4: list_char > $o,H4: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G4 @ H4 @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G4 @ H4 @ P )
       => ( epistemic_eval_a @ G4 @ H4 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_43_mem__Collect__eq,axiom,
    ! [A2: a,P4: a > $o] :
      ( ( member_a @ A2 @ ( collect_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_44_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_45_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_46_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X: a] : ( member_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_47_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_48_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_49_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_50_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_51_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H4: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ Ux @ H4 @ ( epistemic_K_a @ I @ P ) )
      = ( H4 @ ( epistemic_K_a @ I @ P ) ) ) ).

% eval.simps(6)
thf(fact_52_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_53_eval_Osimps_I4_J,axiom,
    ! [G4: list_char > $o,H4: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G4 @ H4 @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G4 @ H4 @ P )
        & ( epistemic_eval_a @ G4 @ H4 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_order__refl,axiom,
    ! [X3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ X3 @ X3 ) ).

% order_refl
thf(fact_71_order__refl,axiom,
    ! [X3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ X3 @ X3 ) ).

% order_refl
thf(fact_72_dual__order_Orefl,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ A2 ) ).

% dual_order.refl
thf(fact_73_dual__order_Orefl,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ A2 ) ).

% dual_order.refl
thf(fact_74_le__funD,axiom,
    ! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o,X3: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ F @ G4 )
     => ( ord_less_eq_o @ ( F @ X3 ) @ ( G4 @ X3 ) ) ) ).

% le_funD
thf(fact_75_le__funE,axiom,
    ! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o,X3: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ F @ G4 )
     => ( ord_less_eq_o @ ( F @ X3 ) @ ( G4 @ X3 ) ) ) ).

% le_funE
thf(fact_76_le__funI,axiom,
    ! [F: epistemic_fm_a > $o,G4: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a] : ( ord_less_eq_o @ ( F @ X2 ) @ ( G4 @ X2 ) )
     => ( ord_le4043730696559282883fm_a_o @ F @ G4 ) ) ).

% le_funI
thf(fact_77_le__fun__def,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [F2: epistemic_fm_a > $o,G: epistemic_fm_a > $o] :
        ! [X: epistemic_fm_a] : ( ord_less_eq_o @ ( F2 @ X ) @ ( G @ X ) ) ) ) ).

% le_fun_def
thf(fact_78_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_79_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_80_verit__comp__simplify1_I2_J,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ A2 ) ).

% verit_comp_simplify1(2)
thf(fact_81_verit__comp__simplify1_I2_J,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ A2 ) ).

% verit_comp_simplify1(2)
thf(fact_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_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_116_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_117_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_118_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_119_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_120_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_121_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_122_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_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_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_131_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_132_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_133_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_134_soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ! [M2: episte6182337868402532512t_unit,W2: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W2 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
           => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_135_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,W2: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member6642669571620171971c_fm_a @ W @ ( episte6390737319716712051t_unit @ M ) )
           => ( episte5333283044364550848c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_136_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,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ P )
       => ( ( P4 @ M )
         => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
           => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_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_146_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_147_fm_Opred__True,axiom,
    ( ( epistemic_pred_fm_a
      @ ^ [Uu2: a] : $true )
    = ( ^ [Uu2: epistemic_fm_a] : $true ) ) ).

% fm.pred_True
thf(fact_148_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_149_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_150_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_151_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_152_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_153_fm_Odistinct_I1_J,axiom,
    ! [X23: list_char] :
      ( epistemic_FF_a
     != ( epistemic_Pro_a @ X23 ) ) ).

% fm.distinct(1)
thf(fact_154_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_155_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_156_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_157_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_158_fm_Opred__inject_I1_J,axiom,
    ! [P4: a > $o] : ( epistemic_pred_fm_a @ P4 @ epistemic_FF_a ) ).

% fm.pred_inject(1)
thf(fact_159_eval_Osimps_I2_J,axiom,
    ! [G4: list_char > $o,Uw: epistemic_fm_a > $o,X3: list_char] :
      ( ( epistemic_eval_a @ G4 @ Uw @ ( epistemic_Pro_a @ X3 ) )
      = ( G4 @ X3 ) ) ).

% eval.simps(2)
thf(fact_160_eval_Osimps_I3_J,axiom,
    ! [G4: list_char > $o,H4: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G4 @ H4 @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G4 @ H4 @ P )
        | ( epistemic_eval_a @ G4 @ H4 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_161_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_162_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_163_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_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_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_183_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_184_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_185_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_186_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_187_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_188_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_189_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_190_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_191_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_192_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_193_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_194_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_195_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_196_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_197_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_198_equalityD1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A = B4 )
     => ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ).

% equalityD1
thf(fact_199_equalityD2,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A = B4 )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ A ) ) ).

% equalityD2
thf(fact_200_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_201_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_202_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_203_subset__refl,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ A ) ).

% subset_refl
thf(fact_204_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_205_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_206_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_207_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_208_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_209_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_210_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_211_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_212_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_213_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_214_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_215_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_216_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_217_symm__trans__Euclid,axiom,
    ! [M: episte1560738328020401952t_unit] :
      ( ( episte5478016696552465318t_unit @ M )
     => ( ( episte8364071018013720454t_unit @ M )
       => ( episte2449151000174023629t_unit @ M ) ) ) ).

% symm_trans_Euclid
thf(fact_218_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_219_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_220_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_221_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_222_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_223_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_224_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_225_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_226_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_227_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_228_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_229_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_230_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_231_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_232_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_233_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_234_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_235_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_236_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_237_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_238_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_239_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_240_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_241_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_242_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_243_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_244_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_245_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_246_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_247_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_248_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_249_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_250_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_251_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_252_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_253_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_254_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_255_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_256_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_257_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_258_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_259_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_260_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_261_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_262_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_263_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_264_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_265_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_266_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_267_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_268_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_269_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_270_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_271_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_272_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_273_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_274_strong__soundness_092_060_094sub_062S_092_060_094sub_0625,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 ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte5478016696552465318t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5
thf(fact_275_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_276_strong__soundness_092_060_094sub_062S_092_060_094sub_0625_H,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_Ax5_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte5478016696552465318t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5'
thf(fact_277_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_278_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_279_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_280_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_281_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_282_prop__restrict,axiom,
    ! [X3: a,Z3: set_a,X6: set_a,P4: a > $o] :
      ( ( member_a @ X3 @ Z3 )
     => ( ( ord_less_eq_set_a @ Z3
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ X6 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_283_prop__restrict,axiom,
    ! [X3: set_Epistemic_fm_a,Z3: set_se5208064806568342746c_fm_a,X6: 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 @ X6 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_284_prop__restrict,axiom,
    ! [X3: epistemic_fm_a,Z3: set_Epistemic_fm_a,X6: 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 @ X6 )
                & ( P4 @ X ) ) ) )
       => ( P4 @ X3 ) ) ) ).

% prop_restrict
thf(fact_285_Collect__restrict,axiom,
    ! [X6: set_a,P4: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ X6 )
            & ( P4 @ X ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_286_Collect__restrict,axiom,
    ! [X6: 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 @ X6 )
            & ( P4 @ X ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_287_Collect__restrict,axiom,
    ! [X6: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ord_le3275665582123262618c_fm_a
      @ ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ X6 )
            & ( P4 @ X ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_288_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_289_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_290_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_291_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_292_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 ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>K
thf(fact_293_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 ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>K
thf(fact_294_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>T
thf(fact_295_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>T
thf(fact_296_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 ) )
     => ! [G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_imply_a @ Ps @ R ) @ ( epistemic_imply_a @ Qs4 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_297_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>4
thf(fact_298_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>4
thf(fact_299_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>5
thf(fact_300_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>5
thf(fact_301_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>B
thf(fact_302_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>B
thf(fact_303_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_304_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_305_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_306_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_307_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_308_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_309_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_310_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_311_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_312_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_313_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_314_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_315_fm_Orel__refl__strong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ra: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ! [Z4: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ X3 ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( episte8246226516352692192c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_316_fm_Orel__refl__strong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ra: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ! [Z4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ X3 ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( episte7774795710028497888c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_317_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_a,Ra: a > a > $o] :
      ( ! [Z4: a] :
          ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ X3 ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( epistemic_rel_fm_a_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_318_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 )
     => ( ! [Z4: set_Epistemic_fm_a,Yb: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte8246226516352692192c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_319_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 )
     => ( ! [Z4: set_Epistemic_fm_a,Yb: epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte6543039790609369600c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_320_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 )
     => ( ! [Z4: epistemic_fm_a,Yb: set_Epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte4430291480098810304c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_321_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 )
     => ( ! [Z4: epistemic_fm_a,Yb: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte7774795710028497888c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_322_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 )
     => ( ! [Z4: set_Epistemic_fm_a,Yb: a] :
            ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte7682788968413056228fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_323_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 )
     => ( ! [Z4: epistemic_fm_a,Yb: a] :
            ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte4428145106359621316fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_324_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 )
     => ( ! [Z4: a,Yb: set_Epistemic_fm_a] :
            ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte6665775379439401564c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_325_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 )
     => ( ! [Z4: a,Yb: epistemic_fm_a] :
            ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( episte8321036160184370300c_fm_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_326_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 )
     => ( ! [Z4: a,Yb: a] :
            ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y ) )
             => ( ( R2 @ Z4 @ Yb )
               => ( Ra @ Z4 @ Yb ) ) ) )
       => ( epistemic_rel_fm_a_a @ Ra @ X3 @ Y ) ) ) ).

% fm.rel_mono_strong
thf(fact_327_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 )
       => ( ! [Z4: set_Epistemic_fm_a,Yb: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte8246226516352692192c_fm_a @ R2 @ X3 @ Y )
            = ( episte8246226516352692192c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_328_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 )
       => ( ! [Z4: set_Epistemic_fm_a,Yb: epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte6543039790609369600c_fm_a @ R2 @ X3 @ Y )
            = ( episte6543039790609369600c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_329_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 )
       => ( ! [Z4: epistemic_fm_a,Yb: set_Epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte4430291480098810304c_fm_a @ R2 @ X3 @ Y )
            = ( episte4430291480098810304c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_330_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 )
       => ( ! [Z4: epistemic_fm_a,Yb: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte7774795710028497888c_fm_a @ R2 @ X3 @ Y )
            = ( episte7774795710028497888c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_331_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 )
       => ( ! [Z4: set_Epistemic_fm_a,Yb: a] :
              ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte7682788968413056228fm_a_a @ R2 @ X3 @ Y )
            = ( episte7682788968413056228fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_332_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 )
       => ( ! [Z4: epistemic_fm_a,Yb: a] :
              ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte4428145106359621316fm_a_a @ R2 @ X3 @ Y )
            = ( episte4428145106359621316fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_333_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 )
       => ( ! [Z4: a,Yb: set_Epistemic_fm_a] :
              ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member536094252920883875c_fm_a @ Yb @ ( episte6227279731293865264c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte6665775379439401564c_fm_a @ R2 @ X3 @ Y )
            = ( episte6665775379439401564c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_334_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 )
       => ( ! [Z4: a,Yb: epistemic_fm_a] :
              ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member6642669571620171971c_fm_a @ Yb @ ( episte9089240958480457552c_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( episte8321036160184370300c_fm_a @ R2 @ X3 @ Y )
            = ( episte8321036160184370300c_fm_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_335_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 )
       => ( ! [Z4: a,Yb: a] :
              ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R2 @ Z4 @ Yb )
                  = ( Ra @ Z4 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_a_a @ R2 @ X3 @ Y )
            = ( epistemic_rel_fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_336_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_337_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_338_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_339_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_340_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_341_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_342_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_343_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_344_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_345_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_346_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_347_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_348_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 )
     => ( ! [Z4: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( P4 @ Z4 )
             => ( Pa @ Z4 ) ) )
       => ( episte1367365995573110961c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_349_fm_Opred__mono__strong,axiom,
    ! [P4: epistemic_fm_a > $o,X3: episte740340785640729014c_fm_a,Pa: epistemic_fm_a > $o] :
      ( ( episte3114992851182798545c_fm_a @ P4 @ X3 )
     => ( ! [Z4: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ X3 ) )
           => ( ( P4 @ Z4 )
             => ( Pa @ Z4 ) ) )
       => ( episte3114992851182798545c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_350_fm_Opred__mono__strong,axiom,
    ! [P4: a > $o,X3: epistemic_fm_a,Pa: a > $o] :
      ( ( epistemic_pred_fm_a @ P4 @ X3 )
     => ( ! [Z4: a] :
            ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( P4 @ Z4 )
             => ( Pa @ Z4 ) ) )
       => ( epistemic_pred_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_351_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 )
     => ( ! [Z4: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z4 @ ( episte6227279731293865264c_fm_a @ Ya ) )
           => ( ( P4 @ Z4 )
              = ( Pa @ Z4 ) ) )
       => ( ( episte1367365995573110961c_fm_a @ P4 @ X3 )
          = ( episte1367365995573110961c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_352_fm_Opred__cong,axiom,
    ! [X3: episte740340785640729014c_fm_a,Ya: episte740340785640729014c_fm_a,P4: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z4: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z4 @ ( episte9089240958480457552c_fm_a @ Ya ) )
           => ( ( P4 @ Z4 )
              = ( Pa @ Z4 ) ) )
       => ( ( episte3114992851182798545c_fm_a @ P4 @ X3 )
          = ( episte3114992851182798545c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_353_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,P4: a > $o,Pa: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z4: a] :
            ( ( member_a @ Z4 @ ( epistemic_set_fm_a @ Ya ) )
           => ( ( P4 @ Z4 )
              = ( Pa @ Z4 ) ) )
       => ( ( epistemic_pred_fm_a @ P4 @ X3 )
          = ( epistemic_pred_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_354_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte6182337868402532512t_unit,W2: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W2 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte6182337868402532512t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: a] :
                ( ( member_a @ X5 @ ( episte6926715892928323059t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte295617885132580260cs_a_a @ M3 @ X5 @ Xa ) )
                 => ( episte295617885132580260cs_a_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_355_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte94448284482925344t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte94448284482925344t_unit,W2: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte94448284482925344t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X5 @ ( episte6390737319716712051t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte5333283044364550848c_fm_a @ M3 @ X5 @ Xa ) )
                 => ( episte5333283044364550848c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_356_soundness__imply,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M3: episte1560738328020401952t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_357_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte6182337868402532512t_unit,W2: a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W2 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M3: episte6182337868402532512t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: a] :
                ( ( member_a @ X5 @ ( episte6926715892928323059t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte295617885132580260cs_a_a @ M3 @ X5 @ Xa ) )
                 => ( episte295617885132580260cs_a_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_358_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte94448284482925344t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte94448284482925344t_unit,W2: epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member6642669571620171971c_fm_a @ W2 @ ( episte6390737319716712051t_unit @ M2 ) )
             => ( episte5333283044364550848c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M3: episte94448284482925344t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X5 @ ( episte6390737319716712051t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte5333283044364550848c_fm_a @ M3 @ X5 @ Xa ) )
                 => ( episte5333283044364550848c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_359_strong__soundness,axiom,
    ! [A: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W2: set_Epistemic_fm_a,P3: epistemic_fm_a] :
          ( ( A @ P3 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W2 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W2 @ P3 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M3: episte1560738328020401952t_unit] :
            ( ( P4 @ M3 )
           => ! [X5: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_360_strong__soundness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a,P4: episte1560738328020401952t_unit > $o] :
      ( ? [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 ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( P4 @ M3 )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K
thf(fact_361_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>S\<^sub>4
thf(fact_362_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>4
thf(fact_363_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>S\<^sub>5'
thf(fact_364_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>5'
thf(fact_365_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_366_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 ) ) ) )
     => ? [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 ) ) ) ) ).

% strong_completeness\<^sub>S\<^sub>5
thf(fact_367_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 ) ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% main\<^sub>S\<^sub>5
thf(fact_368_strong__soundness_092_060_094sub_062T,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 @ epistemic_AxT_a @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte5648423998891577755t_unit @ M3 )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>T
thf(fact_369_strong__soundness_092_060_094sub_062K_092_060_094sub_0624,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 @ epistemic_Ax4_a @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte8364071018013720454t_unit @ M3 )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>4
thf(fact_370_strong__soundness_092_060_094sub_062K_092_060_094sub_062B,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 @ epistemic_AxB_a @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte5478016696552465318t_unit @ M3 )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>B
thf(fact_371_strong__soundness_092_060_094sub_062K_092_060_094sub_0625,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 @ epistemic_Ax5_a @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( episte2449151000174023629t_unit @ M3 )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>5
thf(fact_372_S5__S5_H__assms,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ? [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 ) ) ) )
      = ( ? [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 ) ) ) ) ) ).

% S5_S5'_assms
thf(fact_373_strong__soundness_092_060_094sub_062S_092_060_094sub_0624,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_Ax4_a @ P2 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M3: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M3 )
            & ( episte8364071018013720454t_unit @ M3 ) )
         => ! [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M3 @ X5 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>4
thf(fact_374_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_375_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_376_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_377_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_378_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_379_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_380_imply__conjunct,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_imply_a @ G5 @ P ) @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% imply_conjunct
thf(fact_381_conjunct__imply,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% conjunct_imply
thf(fact_382_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_383_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_384_consistent__def,axiom,
    ( episte2285483198712856226tent_a
    = ( ^ [A3: epistemic_fm_a > $o,S2: set_Epistemic_fm_a] :
          ~ ? [Qs2: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ S2 )
              & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs2 @ epistemic_FF_a ) ) ) ) ) ).

% consistent_def
thf(fact_385_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_386_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_387_consistent__hereditary,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a,S3: set_Epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ S )
     => ( ( ord_le3275665582123262618c_fm_a @ S3 @ S )
       => ( episte2285483198712856226tent_a @ A @ S3 ) ) ) ).

% consistent_hereditary
thf(fact_388_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_389_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_390_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_391_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_392_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_393_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_394_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_395_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_396_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_397_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_398_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_399_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_400_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_401_Shift__def,axiom,
    ( bNF_Gr8437504134799245625c_fm_a
    = ( ^ [Kl: set_li769143395467472256c_fm_a,K: epistemic_fm_a] :
          ( collec5191077796991884427c_fm_a
          @ ^ [Kl2: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ K @ Kl2 ) @ Kl ) ) ) ) ).

% Shift_def
thf(fact_402_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_403_map__ident,axiom,
    ( ( map_Ep7084560364594560580c_fm_a
      @ ^ [X: epistemic_fm_a] : X )
    = ( ^ [Xs2: list_Epistemic_fm_a] : Xs2 ) ) ).

% map_ident
thf(fact_404_list_Omap__ident,axiom,
    ! [T2: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a
        @ ^ [X: epistemic_fm_a] : X
        @ T2 )
      = T2 ) ).

% list.map_ident
thf(fact_405_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_406_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_407_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_408_maximal__extension,axiom,
    ! [A: epistemic_fm_a > $o,V: set_Epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V )
     => ~ ! [W4: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ V @ W4 )
           => ( ( episte2285483198712856226tent_a @ A @ W4 )
             => ~ ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W4 ) ) ) ) ).

% maximal_extension
thf(fact_409_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_410_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_411_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 ) ) )
       => ? [Qs3: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ G5 )
            & ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Qs3 @ P ) ) ) ) ) ).

% strong_completeness
thf(fact_412_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 ) )
             => ! [Z5: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z5 @ ( episte8072386903178013299t_unit @ M4 ) )
                 => ( ( member536094252920883875c_fm_a @ Y4 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) )
                   => ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ X ) )
                     => ( member536094252920883875c_fm_a @ Z5 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ) ).

% Euclidean_def
thf(fact_413_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_414_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_415_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_416_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 ) )
             => ! [Z5: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z5 @ ( episte8072386903178013299t_unit @ M4 ) )
                 => ( ( ( member536094252920883875c_fm_a @ Z5 @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) )
                      & ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Z5 ) ) )
                   => ( member536094252920883875c_fm_a @ X @ ( episte6250069432388174439t_unit @ M4 @ I2 @ Y4 ) ) ) ) ) ) ) ) ).

% transitive_def
thf(fact_417_frame_Oext__inject,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit,W7: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More2: episte1193835314949844379t_unit] :
      ( ( ( episte2888590659910966568t_unit @ W6 @ K2 @ More )
        = ( episte2888590659910966568t_unit @ W7 @ K3 @ More2 ) )
      = ( ( W6 = W7 )
        & ( K2 = K3 )
        & ( More = More2 ) ) ) ).

% frame.ext_inject
thf(fact_418_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_419_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_420_empty__subsetI,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ bot_bo3626323581529592678c_fm_a @ A ) ).

% empty_subsetI
thf(fact_421_empty__def,axiom,
    ( bot_bo1868452413526482246c_fm_a
    = ( collec2519470961442302949c_fm_a
      @ ^ [X: set_Epistemic_fm_a] : $false ) ) ).

% empty_def
thf(fact_422_empty__def,axiom,
    ( bot_bo3626323581529592678c_fm_a
    = ( collec4904205152690461189c_fm_a
      @ ^ [X: epistemic_fm_a] : $false ) ) ).

% empty_def
thf(fact_423_frame_Oselect__convs_I2_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte6250069432388174439t_unit @ ( episte2888590659910966568t_unit @ W6 @ K2 @ More ) )
      = K2 ) ).

% frame.select_convs(2)
thf(fact_424_kripke_Ocases,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K4: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K4 @ ( episte8239586592105053771t_unit @ Pi3 @ product_Unity ) ) ) ).

% kripke.cases
thf(fact_425_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_426_frame_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K4: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More3: episte1193835314949844379t_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K4 @ More3 ) ) ).

% frame.cases_scheme
thf(fact_427_kripke_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W8: set_se5208064806568342746c_fm_a,K4: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o,More3: product_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W8 @ K4 @ ( episte8239586592105053771t_unit @ Pi3 @ More3 ) ) ) ).

% kripke.cases_scheme
thf(fact_428_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_429_kripke_Oselect__convs_I1_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: 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 @ K2 @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = Pi ) ).

% kripke.select_convs(1)
thf(fact_430_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_431_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_432_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_433_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_434_bot_Oextremum,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ bot_bo6433428028861825271fm_a_o @ A2 ) ).

% bot.extremum
thf(fact_435_bot_Oextremum,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ bot_bo3626323581529592678c_fm_a @ A2 ) ).

% bot.extremum
thf(fact_436_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_437_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_438_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_439_frame_Oselect__convs_I1_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte8072386903178013299t_unit @ ( episte2888590659910966568t_unit @ W6 @ K2 @ More ) )
      = W6 ) ).

% frame.select_convs(1)
thf(fact_440_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_441_fm_Osimps_I90_J,axiom,
    ( ( episte9089240958480457552c_fm_a @ episte5073044243917183961c_fm_a )
    = bot_bo3626323581529592678c_fm_a ) ).

% fm.simps(90)
thf(fact_442_fm_Osimps_I90_J,axiom,
    ( ( epistemic_set_fm_a @ epistemic_FF_a )
    = bot_bot_set_a ) ).

% fm.simps(90)
thf(fact_443_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_444_fm_Osimps_I91_J,axiom,
    ! [X23: list_char] :
      ( ( episte9089240958480457552c_fm_a @ ( episte3759128466173231372c_fm_a @ X23 ) )
      = bot_bo3626323581529592678c_fm_a ) ).

% fm.simps(91)
thf(fact_445_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_446_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_447_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_448_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_449_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_450_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_451_frame_Osurjective,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ( R
      = ( episte2888590659910966568t_unit @ ( episte8072386903178013299t_unit @ R ) @ ( episte6250069432388174439t_unit @ R ) @ ( episte3309513806868946049t_unit @ R ) ) ) ).

% frame.surjective
thf(fact_452_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_453_kripke_Oupdate__convs_I2_J,axiom,
    ! [More2: product_unit > product_unit,W6: set_se5208064806568342746c_fm_a,K2: 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 @ K2 @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W6 @ K2 @ ( episte8239586592105053771t_unit @ Pi @ ( More2 @ More ) ) ) ) ).

% kripke.update_convs(2)
thf(fact_454_kripke_Oselect__convs_I2_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: 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 @ K2 @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = More ) ).

% kripke.select_convs(2)
thf(fact_455_frame_Oselect__convs_I3_J,axiom,
    ! [W6: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte3309513806868946049t_unit @ ( episte2888590659910966568t_unit @ W6 @ K2 @ More ) )
      = More ) ).

% frame.select_convs(3)
thf(fact_456_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_457_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,K2: 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 @ K2 @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W6 @ K2 @ ( episte8239586592105053771t_unit @ ( Pi2 @ Pi ) @ More ) ) ) ).

% kripke.update_convs(1)
thf(fact_458_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_459_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_460_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_461_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_462_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_463_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_464_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_465_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_466_Collect__const,axiom,
    ! [P4: $o] :
      ( ( P4
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [S4: set_Epistemic_fm_a] : P4 )
          = top_to5398033090887092778c_fm_a ) )
      & ( ~ P4
       => ( ( collec2519470961442302949c_fm_a
            @ ^ [S4: set_Epistemic_fm_a] : P4 )
          = bot_bo1868452413526482246c_fm_a ) ) ) ).

% Collect_const
thf(fact_467_Collect__const,axiom,
    ! [P4: $o] :
      ( ( P4
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [S4: epistemic_fm_a] : P4 )
          = top_to7796028867103199306c_fm_a ) )
      & ( ~ P4
       => ( ( collec4904205152690461189c_fm_a
            @ ^ [S4: epistemic_fm_a] : P4 )
          = bot_bo3626323581529592678c_fm_a ) ) ) ).

% Collect_const
thf(fact_468_singleton__conv2,axiom,
    ! [A2: a] :
      ( ( collect_a
        @ ( ^ [Y3: a,Z: a] : ( Y3 = Z )
          @ A2 ) )
      = ( insert_a @ A2 @ bot_bot_set_a ) ) ).

% singleton_conv2
thf(fact_469_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_470_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_471_singleton__conv,axiom,
    ! [A2: a] :
      ( ( collect_a
        @ ^ [X: a] : ( X = A2 ) )
      = ( insert_a @ A2 @ bot_bot_set_a ) ) ).

% singleton_conv
thf(fact_472_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_473_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_474_singleton__insert__inj__eq,axiom,
    ! [B: a,A2: a,A: set_a] :
      ( ( ( insert_a @ B @ bot_bot_set_a )
        = ( insert_a @ A2 @ A ) )
      = ( ( A2 = B )
        & ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_475_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_476_singleton__insert__inj__eq_H,axiom,
    ! [A2: a,A: set_a,B: a] :
      ( ( ( insert_a @ A2 @ A )
        = ( insert_a @ B @ bot_bot_set_a ) )
      = ( ( A2 = B )
        & ( ord_less_eq_set_a @ A @ ( insert_a @ B @ bot_bot_set_a ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_477_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_478_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_479_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_480_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_481_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_482_UNIV__def,axiom,
    ( top_to5398033090887092778c_fm_a
    = ( collec2519470961442302949c_fm_a
      @ ^ [X: set_Epistemic_fm_a] : $true ) ) ).

% UNIV_def
thf(fact_483_UNIV__def,axiom,
    ( top_to7796028867103199306c_fm_a
    = ( collec4904205152690461189c_fm_a
      @ ^ [X: epistemic_fm_a] : $true ) ) ).

% UNIV_def
thf(fact_484_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_485_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_486_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_487_insert__Collect,axiom,
    ! [A2: a,P4: a > $o] :
      ( ( insert_a @ A2 @ ( collect_a @ P4 ) )
      = ( collect_a
        @ ^ [U2: a] :
            ( ( U2 != A2 )
           => ( P4 @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_488_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_489_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_490_insert__compr,axiom,
    ( insert_a
    = ( ^ [A4: a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( X = A4 )
              | ( member_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_491_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_492_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_493_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_494_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_495_insert__def,axiom,
    ( insert_a
    = ( ^ [A4: a] :
          ( sup_sup_set_a
          @ ( collect_a
            @ ^ [X: a] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_496_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_497_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_498_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_499_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_500_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_501_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_502_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_503_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_504_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_505_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_506_top__greatest,axiom,
    ! [A2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ A2 @ top_to6710954824118802707fm_a_o ) ).

% top_greatest
thf(fact_507_top__greatest,axiom,
    ! [A2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A2 @ top_to7796028867103199306c_fm_a ) ).

% top_greatest
thf(fact_508_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_509_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_510_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_511_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_512_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_513_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_514_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_515_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_516_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_517_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_518_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_519_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_520_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_521_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_522_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_523_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_524_insert__mono,axiom,
    ! [C2: set_a,D: set_a,A2: a] :
      ( ( ord_less_eq_set_a @ C2 @ D )
     => ( ord_less_eq_set_a @ ( insert_a @ A2 @ C2 ) @ ( insert_a @ A2 @ D ) ) ) ).

% insert_mono
thf(fact_525_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_526_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_527_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_528_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_529_subset__insertI,axiom,
    ! [B4: set_a,A2: a] : ( ord_less_eq_set_a @ B4 @ ( insert_a @ A2 @ B4 ) ) ).

% subset_insertI
thf(fact_530_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_531_subset__insertI2,axiom,
    ! [A: set_a,B4: set_a,B: a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ord_less_eq_set_a @ A @ ( insert_a @ B @ B4 ) ) ) ).

% subset_insertI2
thf(fact_532_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_533_insert__subsetI,axiom,
    ! [X3: a,A: set_a,X6: set_a] :
      ( ( member_a @ X3 @ A )
     => ( ( ord_less_eq_set_a @ X6 @ A )
       => ( ord_less_eq_set_a @ ( insert_a @ X3 @ X6 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_534_insert__subsetI,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,X6: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ( ord_le7112219575281605754c_fm_a @ X6 @ A )
       => ( ord_le7112219575281605754c_fm_a @ ( insert7129737658439086282c_fm_a @ X3 @ X6 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_535_insert__subsetI,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,X6: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X3 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ X6 @ A )
       => ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ X3 @ X6 ) @ A ) ) ) ).

% insert_subsetI
thf(fact_536_subset__UNIV,axiom,
    ! [A: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A @ top_to7796028867103199306c_fm_a ) ).

% subset_UNIV
thf(fact_537_Collect__conv__if2,axiom,
    ! [P4: a > $o,A2: a] :
      ( ( ( P4 @ A2 )
       => ( ( collect_a
            @ ^ [X: a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = ( insert_a @ A2 @ bot_bot_set_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collect_a
            @ ^ [X: a] :
                ( ( A2 = X )
                & ( P4 @ X ) ) )
          = bot_bot_set_a ) ) ) ).

% Collect_conv_if2
thf(fact_538_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_539_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_540_Collect__conv__if,axiom,
    ! [P4: a > $o,A2: a] :
      ( ( ( P4 @ A2 )
       => ( ( collect_a
            @ ^ [X: a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = ( insert_a @ A2 @ bot_bot_set_a ) ) )
      & ( ~ ( P4 @ A2 )
       => ( ( collect_a
            @ ^ [X: a] :
                ( ( X = A2 )
                & ( P4 @ X ) ) )
          = bot_bot_set_a ) ) ) ).

% Collect_conv_if
thf(fact_541_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_542_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_543_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_544_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_545_subset__singletonD,axiom,
    ! [A: set_a,X3: a] :
      ( ( ord_less_eq_set_a @ A @ ( insert_a @ X3 @ bot_bot_set_a ) )
     => ( ( A = bot_bot_set_a )
        | ( A
          = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ).

% subset_singletonD
thf(fact_546_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_547_subset__singleton__iff,axiom,
    ! [X6: set_a,A2: a] :
      ( ( ord_less_eq_set_a @ X6 @ ( insert_a @ A2 @ bot_bot_set_a ) )
      = ( ( X6 = bot_bot_set_a )
        | ( X6
          = ( insert_a @ A2 @ bot_bot_set_a ) ) ) ) ).

% subset_singleton_iff
thf(fact_548_subset__singleton__iff,axiom,
    ! [X6: set_Epistemic_fm_a,A2: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X6 @ ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) )
      = ( ( X6 = bot_bo3626323581529592678c_fm_a )
        | ( X6
          = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% subset_singleton_iff
thf(fact_549_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_550_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_551_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_552_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_553_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_554_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_555_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_556_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_557_frame_Oupdate__convs_I3_J,axiom,
    ! [More2: episte1193835314949844379t_unit > episte1193835314949844379t_unit,W6: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte7964699311158398698c_fm_a @ More2 @ ( episte2888590659910966568t_unit @ W6 @ K2 @ More ) )
      = ( episte2888590659910966568t_unit @ W6 @ K2 @ ( More2 @ More ) ) ) ).

% frame.update_convs(3)
thf(fact_558_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_559_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_560_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_561_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_562_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_563_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_564_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_565_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_566_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_567_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 ) )
     => ~ ! [W4: 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 ) @ W4 ) @ ( 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 ) @ W4 )
             => ( ( finite3304564945125563331c_fm_a @ W4 )
               => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W4 ) ) ) ) ) ) ).

% exists_finite_inconsistent
thf(fact_568_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_569_infinite__UNIV__fm,axiom,
    ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% infinite_UNIV_fm
thf(fact_570_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_571_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_572_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_573_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_574_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_575_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_576_inconsistent__finite,axiom,
    ! [A: epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ S )
     => ? [S5: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ S5 @ S )
          & ( finite3304564945125563331c_fm_a @ S5 )
          & ~ ( episte2285483198712856226tent_a @ A @ S5 ) ) ) ).

% inconsistent_finite
thf(fact_577_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_578_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_579_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_580_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_581_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_582_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_583_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_584_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_585_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_586_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_587_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_588_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_589_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_590_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_591_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_592_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_593_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_594_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_595_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_596_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_597_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_598_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_599_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_600_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_601_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_602_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_603_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_604_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_605_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_606_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_607_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_608_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_609_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_610_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_611_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_612_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_613_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_614_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_615_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_616_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,Z4: set_a] :
              ( ( ord_less_eq_set_a @ Y2 @ X2 )
             => ( ( ord_less_eq_set_a @ Z4 @ X2 )
               => ( ord_less_eq_set_a @ ( F @ Y2 @ Z4 ) @ X2 ) ) )
         => ( ( sup_sup_set_a @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_617_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,Z4: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ Y2 @ X2 )
             => ( ( ord_le4043730696559282883fm_a_o @ Z4 @ X2 )
               => ( ord_le4043730696559282883fm_a_o @ ( F @ Y2 @ Z4 ) @ X2 ) ) )
         => ( ( sup_su6697315146409554831fm_a_o @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_618_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,Z4: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ Y2 @ X2 )
             => ( ( ord_le3275665582123262618c_fm_a @ Z4 @ X2 )
               => ( ord_le3275665582123262618c_fm_a @ ( F @ Y2 @ Z4 ) @ X2 ) ) )
         => ( ( sup_su1367922730591523534c_fm_a @ X3 @ Y )
            = ( F @ X3 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_619_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_620_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_621_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_622_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_623_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_624_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_625_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_626_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_627_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_628_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_629_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_630_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_631_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_632_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_633_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_634_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_635_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_636_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_637_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_638_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_639_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_640_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_641_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_642_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_643_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_644_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_645_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_646_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_647_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_648_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_649_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_650_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_651_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_652_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_653_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_654_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_655_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_656_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_657_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_658_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_659_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_660_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_661_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_662_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_663_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_664_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_665_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_666_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_667_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_668_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_669_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_670_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_671_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_672_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_673_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_674_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_675_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_676_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_677_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_678_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_679_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_680_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_681_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_682_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_683_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_684_infinite__super,axiom,
    ! [S: set_Epistemic_fm_a,T3: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ S @ T3 )
     => ( ~ ( finite3304564945125563331c_fm_a @ S )
       => ~ ( finite3304564945125563331c_fm_a @ T3 ) ) ) ).

% infinite_super
thf(fact_685_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_686_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_687_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_688_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_689_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_690_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_691_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_692_set__rec,axiom,
    ( set_a2
    = ( rec_list_set_a_a @ bot_bot_set_a
      @ ^ [X: a,Uu2: list_a] : ( insert_a @ X ) ) ) ).

% set_rec
thf(fact_693_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_694_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_695_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_696_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_697_mono__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,S6: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ R @ S6 )
     => ( ord_le3275665582123262618c_fm_a @ ( field_Epistemic_fm_a @ R ) @ ( field_Epistemic_fm_a @ S6 ) ) ) ).

% mono_Field
thf(fact_698_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_699_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_700_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_701_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_702_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_703_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_704_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_705_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_706_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_707_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_708_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_709_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_710_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_711_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_712_MCS__Lim__Ord_Oconsistent__hereditary,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a,S3: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( Consistent @ S )
       => ( ( ord_le3275665582123262618c_fm_a @ S3 @ S )
         => ( Consistent @ S3 ) ) ) ) ).

% MCS_Lim_Ord.consistent_hereditary
thf(fact_713_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 )
       => ? [S5: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ S5 @ S )
            & ( finite3304564945125563331c_fm_a @ S5 )
            & ~ ( Consistent @ S5 ) ) ) ) ).

% MCS_Lim_Ord.inconsistent_finite
thf(fact_714_MCS__axioms,axiom,
    ! [A: epistemic_fm_a > $o] : ( maxima1924290459274269190c_fm_a @ ( episte2285483198712856226tent_a @ A ) ) ).

% MCS_axioms
thf(fact_715_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_716_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_717_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_718_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_719_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_720_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_721_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_722_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_723_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_724_MCS_Ointro,axiom,
    ! [Consistent: set_Epistemic_fm_a > $o] :
      ( ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a )
     => ( ! [S7: set_Epistemic_fm_a,S5: set_Epistemic_fm_a] :
            ( ( Consistent @ S7 )
           => ( ( ord_le3275665582123262618c_fm_a @ S5 @ S7 )
             => ( Consistent @ S5 ) ) )
       => ( ! [S7: set_Epistemic_fm_a] :
              ( ~ ( Consistent @ S7 )
             => ? [S8: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S8 @ S7 )
                  & ( finite3304564945125563331c_fm_a @ S8 )
                  & ~ ( Consistent @ S8 ) ) )
         => ( maxima1924290459274269190c_fm_a @ Consistent ) ) ) ) ).

% MCS.intro
thf(fact_725_MCS__def,axiom,
    ( maxima1924290459274269190c_fm_a
    = ( ^ [Consistent2: set_Epistemic_fm_a > $o] :
          ( ~ ( finite3304564945125563331c_fm_a @ top_to7796028867103199306c_fm_a )
          & ! [S2: set_Epistemic_fm_a,S9: set_Epistemic_fm_a] :
              ( ( Consistent2 @ S2 )
             => ( ( ord_le3275665582123262618c_fm_a @ S9 @ S2 )
               => ( Consistent2 @ S9 ) ) )
          & ! [S2: set_Epistemic_fm_a] :
              ( ~ ( Consistent2 @ S2 )
             => ? [S9: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S9 @ S2 )
                  & ( finite3304564945125563331c_fm_a @ S9 )
                  & ~ ( Consistent2 @ S9 ) ) ) ) ) ) ).

% MCS_def
thf(fact_726_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_727_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_728_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_729_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_730_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Product_prod_a_a,X6: set_a,N: a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( finite_finite_a @ X6 )
       => ( ( ord_less_eq_set_a @ X6 @ ( order_underS_a @ R @ N ) )
         => ( ( X6 != bot_bot_set_a )
           => ? [X2: a] :
                ( ( member_a @ X2 @ X6 )
                & ! [Xa2: a] :
                    ( ( member_a @ Xa2 @ X6 )
                   => ( member_a @ Xa2 @ ( order_under_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_731_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,X6: set_se5208064806568342746c_fm_a,N: set_Epistemic_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( finite7364866884270929315c_fm_a @ X6 )
       => ( ( ord_le7112219575281605754c_fm_a @ X6 @ ( order_7871341057202914240c_fm_a @ R @ N ) )
         => ( ( X6 != bot_bo1868452413526482246c_fm_a )
           => ? [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ X6 )
                & ! [Xa2: set_Epistemic_fm_a] :
                    ( ( member536094252920883875c_fm_a @ Xa2 @ X6 )
                   => ( member536094252920883875c_fm_a @ Xa2 @ ( order_4320674923736412895c_fm_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_732_wo__rel_Ofinite__underS__bound,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,X6: set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( bNF_We8255954830765735686c_fm_a @ R )
     => ( ( finite3304564945125563331c_fm_a @ X6 )
       => ( ( ord_le3275665582123262618c_fm_a @ X6 @ ( order_1288088311422721504c_fm_a @ R @ N ) )
         => ( ( X6 != bot_bo3626323581529592678c_fm_a )
           => ? [X2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X2 @ X6 )
                & ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ X6 )
                   => ( member6642669571620171971c_fm_a @ Xa2 @ ( order_1815523470270482687c_fm_a @ R @ X2 ) ) ) ) ) ) ) ) ).

% wo_rel.finite_underS_bound
thf(fact_733_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_734_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_735_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_736_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_737_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_738_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_739_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_740_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_741_wo__rel__r,axiom,
    bNF_We8255954830765735686c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% wo_rel_r
thf(fact_742_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_743_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_744_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_745_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_746_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_747_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_748_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_749_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_750_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_751_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_752_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_753_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_754_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_755_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_756_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_757_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_758_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_759_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_760_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_761_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_762_isLimOrd__r,axiom,
    wellor5744531135217078139c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) ).

% isLimOrd_r
thf(fact_763_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_764_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_765_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_766_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_767_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_768_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_769_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_770_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_771_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_772_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_773_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_774_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_775_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_776_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_777_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_778_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_779_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_780_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_781_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_782_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_783_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_784_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_785_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_786_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_787_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_788_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_789_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_790_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_791_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_792_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_793_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_794_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_795_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_796_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_797_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_798_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_799_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_800_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_801_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_802_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_803_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_804_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_805_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_806_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_807_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_808_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_809_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_810_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_811_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_812_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_813_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_814_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_815_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_816_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_817_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_818_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_819_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_820_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_821_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_822_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_823_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_824_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_825_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_826_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_827_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_828_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_829_wo__rel_Ocases__Total,axiom,
    ! [R: set_Product_prod_a_a,A2: a,B: a,Phi: a > a > $o] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( ord_less_eq_set_a @ ( insert_a @ A2 @ ( insert_a @ B @ bot_bot_set_a ) ) @ ( field_a @ R ) )
       => ( ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A2 @ B ) @ R )
           => ( Phi @ A2 @ B ) )
         => ( ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ B @ A2 ) @ R )
             => ( Phi @ A2 @ B ) )
           => ( Phi @ A2 @ B ) ) ) ) ) ).

% wo_rel.cases_Total
thf(fact_830_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_831_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_832_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_833_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_834_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_835_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_836_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_837_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_838_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_839_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_840_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_841_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_842_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_843_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_844_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_845_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_846_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_847_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_848_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_849_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_850_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_851_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_852_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_853_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_854_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_855_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_856_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_857_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_858_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_859_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_860_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_861_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_862_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_863_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_864_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 )
       => ( ! [S7: set_Epistemic_fm_a,S5: set_Epistemic_fm_a] :
              ( ( Consistent @ S7 )
             => ( ( ord_le3275665582123262618c_fm_a @ S5 @ S7 )
               => ( Consistent @ S5 ) ) )
         => ( ! [S7: set_Epistemic_fm_a] :
                ( ~ ( Consistent @ S7 )
               => ? [S8: set_Epistemic_fm_a] :
                    ( ( ord_le3275665582123262618c_fm_a @ S8 @ S7 )
                    & ( finite3304564945125563331c_fm_a @ S8 )
                    & ~ ( Consistent @ S8 ) ) )
           => ( maxima8116622252184345237c_fm_a @ R @ Consistent ) ) ) ) ) ).

% MCS_Lim_Ord.intro
thf(fact_865_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 )
          & ! [S2: set_Epistemic_fm_a,S9: set_Epistemic_fm_a] :
              ( ( Consistent2 @ S2 )
             => ( ( ord_le3275665582123262618c_fm_a @ S9 @ S2 )
               => ( Consistent2 @ S9 ) ) )
          & ! [S2: set_Epistemic_fm_a] :
              ( ~ ( Consistent2 @ S2 )
             => ? [S9: set_Epistemic_fm_a] :
                  ( ( ord_le3275665582123262618c_fm_a @ S9 @ S2 )
                  & ( finite3304564945125563331c_fm_a @ S9 )
                  & ~ ( Consistent2 @ S9 ) ) ) ) ) ) ).

% MCS_Lim_Ord_def
thf(fact_866_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_867_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_868_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_869_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_870_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_871_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_872_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_873_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_874_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_875_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_876_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_877_the__elem__def,axiom,
    ( the_elem_a
    = ( ^ [X4: set_a] :
          ( the_a
          @ ^ [X: a] :
              ( X4
              = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) ).

% the_elem_def
thf(fact_878_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_879_infinite__Func,axiom,
    ! [A: set_Epistemic_fm_a,B1: a,B23: a,B4: set_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( ord_less_eq_set_a @ ( insert_a @ B1 @ ( insert_a @ B23 @ bot_bot_set_a ) ) @ B4 )
       => ( ( B1 != B23 )
         => ~ ( finite1016825363819911648fm_a_a @ ( bNF_We1622471989791679736fm_a_a @ A @ B4 ) ) ) ) ) ).

% infinite_Func
thf(fact_880_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_881_ordLeq__Func,axiom,
    ! [B1: a,B23: a,B4: set_a,A: set_Epistemic_fm_a] :
      ( ( ord_less_eq_set_a @ ( insert_a @ B1 @ ( insert_a @ B23 @ bot_bot_set_a ) ) @ B4 )
     => ( ( B1 != B23 )
       => ( member2939515678471440220fm_a_a @ ( produc8772851772689315491fm_a_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca4839443212964495725fm_a_a @ ( bNF_We1622471989791679736fm_a_a @ A @ B4 ) ) ) @ bNF_We7379407385213540796fm_a_a ) ) ) ).

% ordLeq_Func
thf(fact_882_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_883_sup__Inf1__distrib,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( sup_su1367922730591523534c_fm_a @ X3 @ ( lattic7927669795667837335c_fm_a @ A ) )
          = ( lattic7927669795667837335c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [Uu2: set_Epistemic_fm_a] :
                ? [A4: set_Epistemic_fm_a] :
                  ( ( Uu2
                    = ( sup_su1367922730591523534c_fm_a @ X3 @ A4 ) )
                  & ( member536094252920883875c_fm_a @ A4 @ A ) ) ) ) ) ) ) ).

% sup_Inf1_distrib
thf(fact_884_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_885_sup__Inf2__distrib,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ( finite7364866884270929315c_fm_a @ B4 )
         => ( ( B4 != bot_bo1868452413526482246c_fm_a )
           => ( ( sup_su1367922730591523534c_fm_a @ ( lattic7927669795667837335c_fm_a @ A ) @ ( lattic7927669795667837335c_fm_a @ B4 ) )
              = ( lattic7927669795667837335c_fm_a
                @ ( collec2519470961442302949c_fm_a
                  @ ^ [Uu2: set_Epistemic_fm_a] :
                    ? [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
                      ( ( Uu2
                        = ( sup_su1367922730591523534c_fm_a @ A4 @ B2 ) )
                      & ( member536094252920883875c_fm_a @ A4 @ A )
                      & ( member536094252920883875c_fm_a @ B2 @ B4 ) ) ) ) ) ) ) ) ) ).

% sup_Inf2_distrib
thf(fact_886_sup__Inf2__distrib,axiom,
    ! [A: set_set_a,B4: set_set_a] :
      ( ( finite_finite_set_a @ A )
     => ( ( A != bot_bot_set_set_a )
       => ( ( finite_finite_set_a @ B4 )
         => ( ( B4 != bot_bot_set_set_a )
           => ( ( sup_sup_set_a @ ( lattic8209813465164889211_set_a @ A ) @ ( lattic8209813465164889211_set_a @ B4 ) )
              = ( lattic8209813465164889211_set_a
                @ ( collect_set_a
                  @ ^ [Uu2: set_a] :
                    ? [A4: set_a,B2: set_a] :
                      ( ( Uu2
                        = ( sup_sup_set_a @ A4 @ B2 ) )
                      & ( member_set_a @ A4 @ A )
                      & ( member_set_a @ B2 @ B4 ) ) ) ) ) ) ) ) ) ).

% sup_Inf2_distrib
thf(fact_887_finite__Collect__bounded__ex,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
              ? [Y4: set_Epistemic_fm_a] :
                ( ( P4 @ Y4 )
                & ( Q4 @ X @ Y4 ) ) ) )
        = ( ! [Y4: set_Epistemic_fm_a] :
              ( ( P4 @ Y4 )
             => ( finite7364866884270929315c_fm_a
                @ ( collec2519470961442302949c_fm_a
                  @ ^ [X: set_Epistemic_fm_a] : ( Q4 @ X @ Y4 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_888_finite__Collect__bounded__ex,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
              ? [Y4: set_Epistemic_fm_a] :
                ( ( P4 @ Y4 )
                & ( Q4 @ X @ Y4 ) ) ) )
        = ( ! [Y4: set_Epistemic_fm_a] :
              ( ( P4 @ Y4 )
             => ( finite3304564945125563331c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [X: epistemic_fm_a] : ( Q4 @ X @ Y4 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_889_finite__Collect__bounded__ex,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
              ? [Y4: epistemic_fm_a] :
                ( ( P4 @ Y4 )
                & ( Q4 @ X @ Y4 ) ) ) )
        = ( ! [Y4: epistemic_fm_a] :
              ( ( P4 @ Y4 )
             => ( finite7364866884270929315c_fm_a
                @ ( collec2519470961442302949c_fm_a
                  @ ^ [X: set_Epistemic_fm_a] : ( Q4 @ X @ Y4 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_890_finite__Collect__bounded__ex,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
              ? [Y4: epistemic_fm_a] :
                ( ( P4 @ Y4 )
                & ( Q4 @ X @ Y4 ) ) ) )
        = ( ! [Y4: epistemic_fm_a] :
              ( ( P4 @ Y4 )
             => ( finite3304564945125563331c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [X: epistemic_fm_a] : ( Q4 @ X @ Y4 ) ) ) ) ) ) ) ).

% finite_Collect_bounded_ex
thf(fact_891_finite__image__set2,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) )
       => ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [Uu2: set_Epistemic_fm_a] :
              ? [X: set_Epistemic_fm_a,Y4: set_Epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_892_finite__image__set2,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) )
       => ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [Uu2: epistemic_fm_a] :
              ? [X: set_Epistemic_fm_a,Y4: set_Epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_893_finite__image__set2,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) )
       => ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [Uu2: set_Epistemic_fm_a] :
              ? [X: set_Epistemic_fm_a,Y4: epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_894_finite__image__set2,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) )
       => ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [Uu2: epistemic_fm_a] :
              ? [X: set_Epistemic_fm_a,Y4: epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_895_finite__image__set2,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o,F: epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) )
       => ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [Uu2: set_Epistemic_fm_a] :
              ? [X: epistemic_fm_a,Y4: set_Epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_896_finite__image__set2,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o,F: epistemic_fm_a > set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ Q4 ) )
       => ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [Uu2: epistemic_fm_a] :
              ? [X: epistemic_fm_a,Y4: set_Epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_897_finite__image__set2,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) )
       => ( finite7364866884270929315c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [Uu2: set_Epistemic_fm_a] :
              ? [X: epistemic_fm_a,Y4: epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_898_finite__image__set2,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ Q4 ) )
       => ( finite3304564945125563331c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [Uu2: epistemic_fm_a] :
              ? [X: epistemic_fm_a,Y4: epistemic_fm_a] :
                ( ( Uu2
                  = ( F @ X @ Y4 ) )
                & ( P4 @ X )
                & ( Q4 @ Y4 ) ) ) ) ) ) ).

% finite_image_set2
thf(fact_899_finite__image__set,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [Uu2: set_Epistemic_fm_a] :
            ? [X: set_Epistemic_fm_a] :
              ( ( Uu2
                = ( F @ X ) )
              & ( P4 @ X ) ) ) ) ) ).

% finite_image_set
thf(fact_900_finite__image__set,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) )
     => ( finite3304564945125563331c_fm_a
        @ ( collec4904205152690461189c_fm_a
          @ ^ [Uu2: epistemic_fm_a] :
            ? [X: set_Epistemic_fm_a] :
              ( ( Uu2
                = ( F @ X ) )
              & ( P4 @ X ) ) ) ) ) ).

% finite_image_set
thf(fact_901_finite__image__set,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [Uu2: set_Epistemic_fm_a] :
            ? [X: epistemic_fm_a] :
              ( ( Uu2
                = ( F @ X ) )
              & ( P4 @ X ) ) ) ) ) ).

% finite_image_set
thf(fact_902_finite__image__set,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) )
     => ( finite3304564945125563331c_fm_a
        @ ( collec4904205152690461189c_fm_a
          @ ^ [Uu2: epistemic_fm_a] :
            ? [X: epistemic_fm_a] :
              ( ( Uu2
                = ( F @ X ) )
              & ( P4 @ X ) ) ) ) ) ).

% finite_image_set
thf(fact_903_Collect__insert,axiom,
    ! [R2: a > a,J1: a,J2: set_a] :
      ( ( collect_a
        @ ^ [Uu2: a] :
          ? [J3: a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member_a @ J3 @ ( insert_a @ J1 @ J2 ) ) ) )
      = ( insert_a @ ( R2 @ J1 )
        @ ( collect_a
          @ ^ [Uu2: a] :
            ? [J3: a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_904_Collect__insert,axiom,
    ! [R2: set_Epistemic_fm_a > a,J1: set_Epistemic_fm_a,J2: set_se5208064806568342746c_fm_a] :
      ( ( collect_a
        @ ^ [Uu2: a] :
          ? [J3: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member536094252920883875c_fm_a @ J3 @ ( insert7129737658439086282c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert_a @ ( R2 @ J1 )
        @ ( collect_a
          @ ^ [Uu2: a] :
            ? [J3: set_Epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member536094252920883875c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_905_Collect__insert,axiom,
    ! [R2: epistemic_fm_a > a,J1: epistemic_fm_a,J2: set_Epistemic_fm_a] :
      ( ( collect_a
        @ ^ [Uu2: a] :
          ? [J3: epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member6642669571620171971c_fm_a @ J3 @ ( insert7817948963269374698c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert_a @ ( R2 @ J1 )
        @ ( collect_a
          @ ^ [Uu2: a] :
            ? [J3: epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member6642669571620171971c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_906_Collect__insert,axiom,
    ! [R2: a > set_Epistemic_fm_a,J1: a,J2: set_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [J3: a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member_a @ J3 @ ( insert_a @ J1 @ J2 ) ) ) )
      = ( insert7129737658439086282c_fm_a @ ( R2 @ J1 )
        @ ( collec2519470961442302949c_fm_a
          @ ^ [Uu2: set_Epistemic_fm_a] :
            ? [J3: a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_907_Collect__insert,axiom,
    ! [R2: set_Epistemic_fm_a > set_Epistemic_fm_a,J1: set_Epistemic_fm_a,J2: set_se5208064806568342746c_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [J3: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member536094252920883875c_fm_a @ J3 @ ( insert7129737658439086282c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert7129737658439086282c_fm_a @ ( R2 @ J1 )
        @ ( collec2519470961442302949c_fm_a
          @ ^ [Uu2: set_Epistemic_fm_a] :
            ? [J3: set_Epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member536094252920883875c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_908_Collect__insert,axiom,
    ! [R2: epistemic_fm_a > set_Epistemic_fm_a,J1: epistemic_fm_a,J2: set_Epistemic_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [J3: epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member6642669571620171971c_fm_a @ J3 @ ( insert7817948963269374698c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert7129737658439086282c_fm_a @ ( R2 @ J1 )
        @ ( collec2519470961442302949c_fm_a
          @ ^ [Uu2: set_Epistemic_fm_a] :
            ? [J3: epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member6642669571620171971c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_909_Collect__insert,axiom,
    ! [R2: a > epistemic_fm_a,J1: a,J2: set_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [J3: a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member_a @ J3 @ ( insert_a @ J1 @ J2 ) ) ) )
      = ( insert7817948963269374698c_fm_a @ ( R2 @ J1 )
        @ ( collec4904205152690461189c_fm_a
          @ ^ [Uu2: epistemic_fm_a] :
            ? [J3: a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_910_Collect__insert,axiom,
    ! [R2: set_Epistemic_fm_a > epistemic_fm_a,J1: set_Epistemic_fm_a,J2: set_se5208064806568342746c_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [J3: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member536094252920883875c_fm_a @ J3 @ ( insert7129737658439086282c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert7817948963269374698c_fm_a @ ( R2 @ J1 )
        @ ( collec4904205152690461189c_fm_a
          @ ^ [Uu2: epistemic_fm_a] :
            ? [J3: set_Epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member536094252920883875c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_911_Collect__insert,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a,J1: epistemic_fm_a,J2: set_Epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [J3: epistemic_fm_a] :
            ( ( Uu2
              = ( R2 @ J3 ) )
            & ( member6642669571620171971c_fm_a @ J3 @ ( insert7817948963269374698c_fm_a @ J1 @ J2 ) ) ) )
      = ( insert7817948963269374698c_fm_a @ ( R2 @ J1 )
        @ ( collec4904205152690461189c_fm_a
          @ ^ [Uu2: epistemic_fm_a] :
            ? [J3: epistemic_fm_a] :
              ( ( Uu2
                = ( R2 @ J3 ) )
              & ( member6642669571620171971c_fm_a @ J3 @ J2 ) ) ) ) ) ).

% Collect_insert
thf(fact_912_card__of__inj__rel,axiom,
    ! [R2: set_Pr4537461906582779015c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Y7: set_Epistemic_fm_a] :
          ( ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ X2 @ Y2 ) @ R2 )
         => ( ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ X2 @ Y7 ) @ R2 )
           => ( Y2 = Y7 ) ) )
     => ( member2407610774516601616c_fm_a
        @ ( produc5569453956477096791c_fm_a
          @ ( bNF_Ca2234214912197128534c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [Y4: set_Epistemic_fm_a] :
                ? [X: set_Epistemic_fm_a] : ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ X @ Y4 ) @ R2 ) ) )
          @ ( bNF_Ca2234214912197128534c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [X: set_Epistemic_fm_a] :
                ? [Y4: set_Epistemic_fm_a] : ( member6846535391323571920c_fm_a @ ( produc7744651086898197655c_fm_a @ X @ Y4 ) @ R2 ) ) ) )
        @ bNF_We1521092302956861159c_fm_a ) ) ).

% card_of_inj_rel
thf(fact_913_card__of__inj__rel,axiom,
    ! [R2: set_Pr8704351555129029223c_fm_a] :
      ( ! [X2: epistemic_fm_a,Y2: set_Epistemic_fm_a,Y7: set_Epistemic_fm_a] :
          ( ( member4818202340005250224c_fm_a @ ( produc4556709532593425015c_fm_a @ X2 @ Y2 ) @ R2 )
         => ( ( member4818202340005250224c_fm_a @ ( produc4556709532593425015c_fm_a @ X2 @ Y7 ) @ R2 )
           => ( Y2 = Y7 ) ) )
     => ( member2483015056062791440c_fm_a
        @ ( produc9004553225164312407c_fm_a
          @ ( bNF_Ca2234214912197128534c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [Y4: set_Epistemic_fm_a] :
                ? [X: epistemic_fm_a] : ( member4818202340005250224c_fm_a @ ( produc4556709532593425015c_fm_a @ X @ Y4 ) @ R2 ) ) )
          @ ( bNF_Ca1305897159876240246c_fm_a
            @ ( collec4904205152690461189c_fm_a
              @ ^ [X: epistemic_fm_a] :
                ? [Y4: set_Epistemic_fm_a] : ( member4818202340005250224c_fm_a @ ( produc4556709532593425015c_fm_a @ X @ Y4 ) @ R2 ) ) ) )
        @ bNF_We3240852806290328839c_fm_a ) ) ).

% card_of_inj_rel
thf(fact_914_card__of__inj__rel,axiom,
    ! [R2: set_Pr8826056995237917351c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a,Y2: epistemic_fm_a,Y7: epistemic_fm_a] :
          ( ( member1928953963652080880c_fm_a @ ( produc6669457843103984311c_fm_a @ X2 @ Y2 ) @ R2 )
         => ( ( member1928953963652080880c_fm_a @ ( produc6669457843103984311c_fm_a @ X2 @ Y7 ) @ R2 )
           => ( Y2 = Y7 ) ) )
     => ( member2298073897539299088c_fm_a
        @ ( produc8794081022805088087c_fm_a
          @ ( bNF_Ca1305897159876240246c_fm_a
            @ ( collec4904205152690461189c_fm_a
              @ ^ [Y4: epistemic_fm_a] :
                ? [X: set_Epistemic_fm_a] : ( member1928953963652080880c_fm_a @ ( produc6669457843103984311c_fm_a @ X @ Y4 ) @ R2 ) ) )
          @ ( bNF_Ca2234214912197128534c_fm_a
            @ ( collec2519470961442302949c_fm_a
              @ ^ [X: set_Epistemic_fm_a] :
                ? [Y4: epistemic_fm_a] : ( member1928953963652080880c_fm_a @ ( produc6669457843103984311c_fm_a @ X @ Y4 ) @ R2 ) ) ) )
        @ bNF_We1128104495779769543c_fm_a ) ) ).

% card_of_inj_rel
thf(fact_915_card__of__inj__rel,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a] :
      ( ! [X2: epistemic_fm_a,Y2: epistemic_fm_a,Y7: epistemic_fm_a] :
          ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y2 ) @ R2 )
         => ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y7 ) @ R2 )
           => ( Y2 = Y7 ) ) )
     => ( member1688387778307953424c_fm_a
        @ ( produc7431400533060703063c_fm_a
          @ ( bNF_Ca1305897159876240246c_fm_a
            @ ( collec4904205152690461189c_fm_a
              @ ^ [Y4: epistemic_fm_a] :
                ? [X: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R2 ) ) )
          @ ( bNF_Ca1305897159876240246c_fm_a
            @ ( collec4904205152690461189c_fm_a
              @ ^ [X: epistemic_fm_a] :
                ? [Y4: epistemic_fm_a] : ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) @ R2 ) ) ) )
        @ bNF_We8976657667165594343c_fm_a ) ) ).

% card_of_inj_rel
thf(fact_916_card__of__mono1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a ) ) ).

% card_of_mono1
thf(fact_917_card__of__Func__mono,axiom,
    ! [A1: set_Epistemic_fm_a,A23: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A1 @ A23 )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( member5994151988976616464c_fm_a @ ( produc4714088577910911575c_fm_a @ ( bNF_Ca7196388322009124745c_fm_a @ ( bNF_We4818972062080617492c_fm_a @ A1 @ B4 ) ) @ ( bNF_Ca7196388322009124745c_fm_a @ ( bNF_We4818972062080617492c_fm_a @ A23 @ B4 ) ) ) @ bNF_We8812984459868641459c_fm_a ) ) ) ).

% card_of_Func_mono
thf(fact_918_range__constant,axiom,
    ! [X3: a] :
      ( ( image_7228943142519265129fm_a_a
        @ ^ [Uu2: epistemic_fm_a] : X3
        @ top_to7796028867103199306c_fm_a )
      = ( insert_a @ X3 @ bot_bot_set_a ) ) ).

% range_constant
thf(fact_919_range__constant,axiom,
    ! [X3: epistemic_fm_a] :
      ( ( image_4449434806354059013c_fm_a
        @ ^ [Uu2: epistemic_fm_a] : X3
        @ top_to7796028867103199306c_fm_a )
      = ( insert7817948963269374698c_fm_a @ X3 @ bot_bo3626323581529592678c_fm_a ) ) ).

% range_constant
thf(fact_920_image__Collect__subsetI,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > a,B4: set_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_less_eq_set_a @ ( image_4497856574827002249fm_a_a @ F @ ( collec2519470961442302949c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_921_image__Collect__subsetI,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_922_image__Collect__subsetI,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > a,B4: set_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_less_eq_set_a @ ( image_7228943142519265129fm_a_a @ F @ ( collec4904205152690461189c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_923_image__Collect__subsetI,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_924_image__Collect__subsetI,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_925_image__Collect__subsetI,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( P4 @ X2 )
         => ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P4 ) ) @ B4 ) ) ).

% image_Collect_subsetI
thf(fact_926_setcompr__eq__image,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [X: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( P4 @ X ) ) )
      = ( image_8582343580727714565c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_927_setcompr__eq__image,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( P4 @ X ) ) )
      = ( image_1263732536703906021c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_928_setcompr__eq__image,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [X: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( P4 @ X ) ) )
      = ( image_3376480847214465317c_fm_a @ F @ ( collec2519470961442302949c_fm_a @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_929_setcompr__eq__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( P4 @ X ) ) )
      = ( image_4449434806354059013c_fm_a @ F @ ( collec4904205152690461189c_fm_a @ P4 ) ) ) ).

% setcompr_eq_image
thf(fact_930_Setcompr__eq__image,axiom,
    ! [F: a > set_Epistemic_fm_a,A: set_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [X: a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member_a @ X @ A ) ) )
      = ( image_3480842985853347585c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_931_Setcompr__eq__image,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [X: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member536094252920883875c_fm_a @ X @ A ) ) )
      = ( image_8582343580727714565c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_932_Setcompr__eq__image,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [Uu2: set_Epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member6642669571620171971c_fm_a @ X @ A ) ) )
      = ( image_1263732536703906021c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_933_Setcompr__eq__image,axiom,
    ! [F: a > epistemic_fm_a,A: set_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [X: a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member_a @ X @ A ) ) )
      = ( image_1898462159489238305c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_934_Setcompr__eq__image,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [X: set_Epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member536094252920883875c_fm_a @ X @ A ) ) )
      = ( image_3376480847214465317c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_935_Setcompr__eq__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [Uu2: epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( ( Uu2
              = ( F @ X ) )
            & ( member6642669571620171971c_fm_a @ X @ A ) ) )
      = ( image_4449434806354059013c_fm_a @ F @ A ) ) ).

% Setcompr_eq_image
thf(fact_936_all__subset__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( ! [B3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ B3 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
           => ( P4 @ B3 ) ) )
      = ( ! [B3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ B3 @ A )
           => ( P4 @ ( image_4449434806354059013c_fm_a @ F @ B3 ) ) ) ) ) ).

% all_subset_image
thf(fact_937_image__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ ( image_4449434806354059013c_fm_a @ F @ B4 ) ) ) ).

% image_mono
thf(fact_938_image__subsetI,axiom,
    ! [A: set_a,F: a > a,B4: set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_939_image__subsetI,axiom,
    ! [A: set_a,F: a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_940_image__subsetI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > a,B4: set_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_less_eq_set_a @ ( image_4497856574827002249fm_a_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_941_image__subsetI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_942_image__subsetI,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > a,B4: set_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ( member_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_less_eq_set_a @ ( image_7228943142519265129fm_a_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_943_image__subsetI,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ( member536094252920883875c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le7112219575281605754c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_944_image__subsetI,axiom,
    ! [A: set_a,F: a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( image_1898462159489238305c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_945_image__subsetI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( member6642669571620171971c_fm_a @ ( F @ X2 ) @ B4 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ A ) @ B4 ) ) ).

% image_subsetI
thf(fact_946_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_947_subset__imageE,axiom,
    ! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
     => ~ ! [C3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ C3 @ A )
           => ( B4
             != ( image_4449434806354059013c_fm_a @ F @ C3 ) ) ) ) ).

% subset_imageE
thf(fact_948_subset__image__iff,axiom,
    ! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
      = ( ? [AA: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ AA @ A )
            & ( B4
              = ( image_4449434806354059013c_fm_a @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_949_rangeE,axiom,
    ! [B: a,F: epistemic_fm_a > a] :
      ( ( member_a @ B @ ( image_7228943142519265129fm_a_a @ F @ top_to7796028867103199306c_fm_a ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_950_rangeE,axiom,
    ! [B: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( image_1263732536703906021c_fm_a @ F @ top_to7796028867103199306c_fm_a ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_951_rangeE,axiom,
    ! [B: epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( image_4449434806354059013c_fm_a @ F @ top_to7796028867103199306c_fm_a ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( B
           != ( F @ X2 ) ) ) ).

% rangeE
thf(fact_952_imageE,axiom,
    ! [B: a,F: a > a,A: set_a] :
      ( ( member_a @ B @ ( image_a_a @ F @ A ) )
     => ~ ! [X2: a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_953_imageE,axiom,
    ! [B: a,F: set_Epistemic_fm_a > a,A: set_se5208064806568342746c_fm_a] :
      ( ( member_a @ B @ ( image_4497856574827002249fm_a_a @ F @ A ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_954_imageE,axiom,
    ! [B: a,F: epistemic_fm_a > a,A: set_Epistemic_fm_a] :
      ( ( member_a @ B @ ( image_7228943142519265129fm_a_a @ F @ A ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_955_imageE,axiom,
    ! [B: set_Epistemic_fm_a,F: a > set_Epistemic_fm_a,A: set_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( image_3480842985853347585c_fm_a @ F @ A ) )
     => ~ ! [X2: a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_956_imageE,axiom,
    ! [B: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( image_8582343580727714565c_fm_a @ F @ A ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_957_imageE,axiom,
    ! [B: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( image_1263732536703906021c_fm_a @ F @ A ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member6642669571620171971c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_958_imageE,axiom,
    ! [B: epistemic_fm_a,F: a > epistemic_fm_a,A: set_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( image_1898462159489238305c_fm_a @ F @ A ) )
     => ~ ! [X2: a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_959_imageE,axiom,
    ! [B: epistemic_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( image_3376480847214465317c_fm_a @ F @ A ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( B
              = ( F @ X2 ) )
           => ~ ( member536094252920883875c_fm_a @ X2 @ A ) ) ) ).

% imageE
thf(fact_960_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_961_Compr__image__eq,axiom,
    ! [F: a > a,A: set_a,P4: a > $o] :
      ( ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ ( image_a_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_a_a @ F
        @ ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_962_Compr__image__eq,axiom,
    ! [F: set_Epistemic_fm_a > a,A: set_se5208064806568342746c_fm_a,P4: a > $o] :
      ( ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ ( image_4497856574827002249fm_a_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_4497856574827002249fm_a_a @ F
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_963_Compr__image__eq,axiom,
    ! [F: epistemic_fm_a > a,A: set_Epistemic_fm_a,P4: a > $o] :
      ( ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ ( image_7228943142519265129fm_a_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_7228943142519265129fm_a_a @ F
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_964_Compr__image__eq,axiom,
    ! [F: a > set_Epistemic_fm_a,A: set_a,P4: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( image_3480842985853347585c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_3480842985853347585c_fm_a @ F
        @ ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_965_Compr__image__eq,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( image_8582343580727714565c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_8582343580727714565c_fm_a @ F
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_966_Compr__image__eq,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( image_1263732536703906021c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_1263732536703906021c_fm_a @ F
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_967_Compr__image__eq,axiom,
    ! [F: a > epistemic_fm_a,A: set_a,P4: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( image_1898462159489238305c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_1898462159489238305c_fm_a @ F
        @ ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_968_Compr__image__eq,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,A: set_se5208064806568342746c_fm_a,P4: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( image_3376480847214465317c_fm_a @ F @ A ) )
            & ( P4 @ X ) ) )
      = ( image_3376480847214465317c_fm_a @ F
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ A )
              & ( P4 @ ( F @ X ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_969_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_970_pigeonhole__infinite,axiom,
    ! [A: set_a,F: a > epistemic_fm_a] :
      ( ~ ( finite_finite_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ ( image_1898462159489238305c_fm_a @ F @ A ) )
       => ? [X2: a] :
            ( ( member_a @ X2 @ A )
            & ~ ( finite_finite_a
                @ ( collect_a
                  @ ^ [A4: a] :
                      ( ( member_a @ A4 @ A )
                      & ( ( F @ A4 )
                        = ( F @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite
thf(fact_971_pigeonhole__infinite,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ~ ( finite7364866884270929315c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ A ) )
       => ? [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
            & ~ ( finite7364866884270929315c_fm_a
                @ ( collec2519470961442302949c_fm_a
                  @ ^ [A4: set_Epistemic_fm_a] :
                      ( ( member536094252920883875c_fm_a @ A4 @ A )
                      & ( ( F @ A4 )
                        = ( F @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite
thf(fact_972_pigeonhole__infinite,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) )
       => ? [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
            & ~ ( finite3304564945125563331c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [A4: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ A4 @ A )
                      & ( ( F @ A4 )
                        = ( F @ X2 ) ) ) ) ) ) ) ) ).

% pigeonhole_infinite
thf(fact_973_range__subsetD,axiom,
    ! [F: epistemic_fm_a > a,B4: set_a,I: epistemic_fm_a] :
      ( ( ord_less_eq_set_a @ ( image_7228943142519265129fm_a_a @ F @ top_to7796028867103199306c_fm_a ) @ B4 )
     => ( member_a @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_974_range__subsetD,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,B4: set_se5208064806568342746c_fm_a,I: epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ top_to7796028867103199306c_fm_a ) @ B4 )
     => ( member536094252920883875c_fm_a @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_975_range__subsetD,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,B4: set_Epistemic_fm_a,I: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ top_to7796028867103199306c_fm_a ) @ B4 )
     => ( member6642669571620171971c_fm_a @ ( F @ I ) @ B4 ) ) ).

% range_subsetD
thf(fact_976_all__finite__subset__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( ! [B3: set_Epistemic_fm_a] :
            ( ( ( finite3304564945125563331c_fm_a @ B3 )
              & ( ord_le3275665582123262618c_fm_a @ B3 @ ( image_4449434806354059013c_fm_a @ F @ A ) ) )
           => ( P4 @ B3 ) ) )
      = ( ! [B3: set_Epistemic_fm_a] :
            ( ( ( finite3304564945125563331c_fm_a @ B3 )
              & ( ord_le3275665582123262618c_fm_a @ B3 @ A ) )
           => ( P4 @ ( image_4449434806354059013c_fm_a @ F @ B3 ) ) ) ) ) ).

% all_finite_subset_image
thf(fact_977_ex__finite__subset__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( ? [B3: set_Epistemic_fm_a] :
            ( ( finite3304564945125563331c_fm_a @ B3 )
            & ( ord_le3275665582123262618c_fm_a @ B3 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
            & ( P4 @ B3 ) ) )
      = ( ? [B3: set_Epistemic_fm_a] :
            ( ( finite3304564945125563331c_fm_a @ B3 )
            & ( ord_le3275665582123262618c_fm_a @ B3 @ A )
            & ( P4 @ ( image_4449434806354059013c_fm_a @ F @ B3 ) ) ) ) ) ).

% ex_finite_subset_image
thf(fact_978_finite__subset__image,axiom,
    ! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ B4 )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
       => ? [C3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ C3 @ A )
            & ( finite3304564945125563331c_fm_a @ C3 )
            & ( B4
              = ( image_4449434806354059013c_fm_a @ F @ C3 ) ) ) ) ) ).

% finite_subset_image
thf(fact_979_finite__surj,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
       => ( finite3304564945125563331c_fm_a @ B4 ) ) ) ).

% finite_surj
thf(fact_980_finite__range__imageI,axiom,
    ! [G4: epistemic_fm_a > epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ ( image_4449434806354059013c_fm_a @ G4 @ top_to7796028867103199306c_fm_a ) )
     => ( finite3304564945125563331c_fm_a
        @ ( image_4449434806354059013c_fm_a
          @ ^ [X: epistemic_fm_a] : ( F @ ( G4 @ X ) )
          @ top_to7796028867103199306c_fm_a ) ) ) ).

% finite_range_imageI
thf(fact_981_full__SetCompr__eq,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [U2: set_Epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( U2
            = ( F @ X ) ) )
      = ( image_1263732536703906021c_fm_a @ F @ top_to7796028867103199306c_fm_a ) ) ).

% full_SetCompr_eq
thf(fact_982_full__SetCompr__eq,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [U2: epistemic_fm_a] :
          ? [X: epistemic_fm_a] :
            ( U2
            = ( F @ X ) ) )
      = ( image_4449434806354059013c_fm_a @ F @ top_to7796028867103199306c_fm_a ) ) ).

% full_SetCompr_eq
thf(fact_983_image__constant,axiom,
    ! [X3: a,A: set_a,C: a] :
      ( ( member_a @ X3 @ A )
     => ( ( image_a_a
          @ ^ [X: a] : C
          @ A )
        = ( insert_a @ C @ bot_bot_set_a ) ) ) ).

% image_constant
thf(fact_984_image__constant,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,C: a] :
      ( ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ( image_4497856574827002249fm_a_a
          @ ^ [X: set_Epistemic_fm_a] : C
          @ A )
        = ( insert_a @ C @ bot_bot_set_a ) ) ) ).

% image_constant
thf(fact_985_image__constant,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,C: a] :
      ( ( member6642669571620171971c_fm_a @ X3 @ A )
     => ( ( image_7228943142519265129fm_a_a
          @ ^ [X: epistemic_fm_a] : C
          @ A )
        = ( insert_a @ C @ bot_bot_set_a ) ) ) ).

% image_constant
thf(fact_986_image__constant,axiom,
    ! [X3: a,A: set_a,C: epistemic_fm_a] :
      ( ( member_a @ X3 @ A )
     => ( ( image_1898462159489238305c_fm_a
          @ ^ [X: a] : C
          @ A )
        = ( insert7817948963269374698c_fm_a @ C @ bot_bo3626323581529592678c_fm_a ) ) ) ).

% image_constant
thf(fact_987_image__constant,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,C: epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ( image_3376480847214465317c_fm_a
          @ ^ [X: set_Epistemic_fm_a] : C
          @ A )
        = ( insert7817948963269374698c_fm_a @ C @ bot_bo3626323581529592678c_fm_a ) ) ) ).

% image_constant
thf(fact_988_image__constant,axiom,
    ! [X3: epistemic_fm_a,A: set_Epistemic_fm_a,C: epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X3 @ A )
     => ( ( image_4449434806354059013c_fm_a
          @ ^ [X: epistemic_fm_a] : C
          @ A )
        = ( insert7817948963269374698c_fm_a @ C @ bot_bo3626323581529592678c_fm_a ) ) ) ).

% image_constant
thf(fact_989_image__constant__conv,axiom,
    ! [A: set_Epistemic_fm_a,C: a] :
      ( ( ( A = bot_bo3626323581529592678c_fm_a )
       => ( ( image_7228943142519265129fm_a_a
            @ ^ [X: epistemic_fm_a] : C
            @ A )
          = bot_bot_set_a ) )
      & ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( image_7228943142519265129fm_a_a
            @ ^ [X: epistemic_fm_a] : C
            @ A )
          = ( insert_a @ C @ bot_bot_set_a ) ) ) ) ).

% image_constant_conv
thf(fact_990_image__constant__conv,axiom,
    ! [A: set_Epistemic_fm_a,C: epistemic_fm_a] :
      ( ( ( A = bot_bo3626323581529592678c_fm_a )
       => ( ( image_4449434806354059013c_fm_a
            @ ^ [X: epistemic_fm_a] : C
            @ A )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( image_4449434806354059013c_fm_a
            @ ^ [X: epistemic_fm_a] : C
            @ A )
          = ( insert7817948963269374698c_fm_a @ C @ bot_bo3626323581529592678c_fm_a ) ) ) ) ).

% image_constant_conv
thf(fact_991_surj__imp__ordLeq,axiom,
    ! [B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( image_4449434806354059013c_fm_a @ F @ A ) )
     => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a ) ) ).

% surj_imp_ordLeq
thf(fact_992_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_993_extendL__def,axiom,
    ! [Rec: epistemic_fm_a > set_Epistemic_fm_a,N: epistemic_fm_a] :
      ( ( maxima7895811076573853563c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ Rec @ N )
      = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ Rec @ ( order_1288088311422721504c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ N ) ) ) ) ).

% extendL_def
thf(fact_994_card__of__Func__UNIV,axiom,
    ! [B4: set_Epistemic_fm_a] :
      ( member5994151988976616464c_fm_a
      @ ( produc4714088577910911575c_fm_a @ ( bNF_Ca7196388322009124745c_fm_a @ ( bNF_We4818972062080617492c_fm_a @ top_to7796028867103199306c_fm_a @ B4 ) )
        @ ( bNF_Ca7196388322009124745c_fm_a
          @ ( collec8583107250894946746c_fm_a
            @ ^ [F2: epistemic_fm_a > epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F2 @ top_to7796028867103199306c_fm_a ) @ B4 ) ) ) )
      @ bNF_We8075338327528360864c_fm_a ) ).

% card_of_Func_UNIV
thf(fact_995_finite__UN__I,axiom,
    ! [A: set_a,B4: a > set_Epistemic_fm_a] :
      ( ( finite_finite_a @ A )
     => ( ! [A6: a] :
            ( ( member_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite3304564945125563331c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) ) ) ) ).

% finite_UN_I
thf(fact_996_finite__UN__I,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ! [A6: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite3304564945125563331c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ) ).

% finite_UN_I
thf(fact_997_finite__UN__I,axiom,
    ! [A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ! [A6: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite3304564945125563331c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ) ).

% finite_UN_I
thf(fact_998_internalize__card__of__ordLeq2,axiom,
    ! [A: set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) ) @ bNF_We8976657667165594343c_fm_a )
      = ( ? [B3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ B3 @ C2 )
            & ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ B3 ) ) @ bNF_We2357358836176181844c_fm_a )
            & ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B3 ) @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) ) @ bNF_We8976657667165594343c_fm_a ) ) ) ) ).

% internalize_card_of_ordLeq2
thf(fact_999_card__of__UNION__ordLeq__infinite,axiom,
    ! [B4: set_Epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ B4 )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ I4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a )
       => ( ! [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ I4 )
             => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( A @ X2 ) ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a ) )
         => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a ) ) ) ) ).

% card_of_UNION_ordLeq_infinite
thf(fact_1000_wo__rel_Oofilter__under__Union,axiom,
    ! [R: set_Product_prod_a_a,A: set_a] :
      ( ( bNF_We1162827675446709994_rel_a @ R )
     => ( ( order_ofilter_a @ R @ A )
       => ( A
          = ( comple2307003609928055243_set_a
            @ ( collect_set_a
              @ ^ [Uu2: set_a] :
                ? [A4: a] :
                  ( ( Uu2
                    = ( order_under_a @ R @ A4 ) )
                  & ( member_a @ A4 @ A ) ) ) ) ) ) ) ).

% wo_rel.ofilter_under_Union
thf(fact_1001_wo__rel_Oofilter__under__Union,axiom,
    ! [R: set_Pr4537461906582779015c_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( bNF_We8880040591803976934c_fm_a @ R )
     => ( ( order_7372089894593676944c_fm_a @ R @ A )
       => ( A
          = ( comple7261557488043011271c_fm_a
            @ ( collec4484617205158951365c_fm_a
              @ ^ [Uu2: set_se5208064806568342746c_fm_a] :
                ? [A4: set_Epistemic_fm_a] :
                  ( ( Uu2
                    = ( order_4320674923736412895c_fm_a @ R @ A4 ) )
                  & ( member536094252920883875c_fm_a @ A4 @ A ) ) ) ) ) ) ) ).

% wo_rel.ofilter_under_Union
thf(fact_1002_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_1003_internalize__card__of__ordLeq,axiom,
    ! [A: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ R ) @ bNF_We8976657667165594343c_fm_a )
      = ( ? [B3: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ B3 @ ( field_Epistemic_fm_a @ R ) )
            & ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ B3 ) ) @ bNF_We2357358836176181844c_fm_a )
            & ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B3 ) @ R ) @ bNF_We8976657667165594343c_fm_a ) ) ) ) ).

% internalize_card_of_ordLeq
thf(fact_1004_MCS__Lim__Ord_OExtend__def,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,Consistent: set_Epistemic_fm_a > $o,S: set_Epistemic_fm_a] :
      ( ( maxima8116622252184345237c_fm_a @ R @ Consistent )
     => ( ( maxima2580775624958445067c_fm_a @ R @ Consistent @ S )
        = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ ( maxima1168816336865142315c_fm_a @ R @ Consistent @ S ) @ ( field_Epistemic_fm_a @ R ) ) ) ) ) ).

% MCS_Lim_Ord.Extend_def
thf(fact_1005_UN__insert,axiom,
    ! [B4: epistemic_fm_a > set_Epistemic_fm_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ ( insert7817948963269374698c_fm_a @ A2 @ A ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ).

% UN_insert
thf(fact_1006_UN__insert,axiom,
    ! [B4: a > set_Epistemic_fm_a,A2: a,A: set_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ ( insert_a @ A2 @ A ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) ) ) ).

% UN_insert
thf(fact_1007_UN__insert,axiom,
    ! [B4: epistemic_fm_a > set_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ ( insert7817948963269374698c_fm_a @ A2 @ A ) ) )
      = ( sup_sup_set_a @ ( B4 @ A2 ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ A ) ) ) ) ).

% UN_insert
thf(fact_1008_UN__insert,axiom,
    ! [B4: a > set_a,A2: a,A: set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_a_set_a @ B4 @ ( insert_a @ A2 @ A ) ) )
      = ( sup_sup_set_a @ ( B4 @ A2 ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B4 @ A ) ) ) ) ).

% UN_insert
thf(fact_1009_UN__simps_I3_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_a,B4: epistemic_fm_a > set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ A @ ( B4 @ X ) )
              @ C2 ) )
          = bot_bot_set_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ A @ ( B4 @ X ) )
              @ C2 ) )
          = ( sup_sup_set_a @ A @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) ) ) ) ) ).

% UN_simps(3)
thf(fact_1010_UN__simps_I3_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ A @ ( B4 @ X ) )
              @ C2 ) )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ A @ ( B4 @ X ) )
              @ C2 ) )
          = ( sup_su1367922730591523534c_fm_a @ A @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) ) ) ) ) ).

% UN_simps(3)
thf(fact_1011_UN__simps_I2_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: epistemic_fm_a > set_a,B4: set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ ( A @ X ) @ B4 )
              @ C2 ) )
          = bot_bot_set_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ ( A @ X ) @ B4 )
              @ C2 ) )
          = ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ C2 ) ) @ B4 ) ) ) ) ).

% UN_simps(2)
thf(fact_1012_UN__simps_I2_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ ( A @ X ) @ B4 )
              @ C2 ) )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ ( A @ X ) @ B4 )
              @ C2 ) )
          = ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ C2 ) ) @ B4 ) ) ) ) ).

% UN_simps(2)
thf(fact_1013_UN__I,axiom,
    ! [A2: a,A: set_a,B: a,B4: a > set_a] :
      ( ( member_a @ A2 @ A )
     => ( ( member_a @ B @ ( B4 @ A2 ) )
       => ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1014_UN__I,axiom,
    ! [A2: a,A: set_a,B: set_Epistemic_fm_a,B4: a > set_se5208064806568342746c_fm_a] :
      ( ( member_a @ A2 @ A )
     => ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_4864492491237557473c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1015_UN__I,axiom,
    ! [A2: a,A: set_a,B: epistemic_fm_a,B4: a > set_Epistemic_fm_a] :
      ( ( member_a @ A2 @ A )
     => ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1016_UN__I,axiom,
    ! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: a,B4: set_Epistemic_fm_a > set_a] :
      ( ( member536094252920883875c_fm_a @ A2 @ A )
     => ( ( member_a @ B @ ( B4 @ A2 ) )
       => ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1017_UN__I,axiom,
    ! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ A2 @ A )
     => ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_3447524139502481637c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1018_UN__I,axiom,
    ! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B: epistemic_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ A2 @ A )
     => ( ( member6642669571620171971c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1019_UN__I,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: a,B4: epistemic_fm_a > set_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ A )
     => ( ( member_a @ B @ ( B4 @ A2 ) )
       => ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1020_UN__I,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: set_Epistemic_fm_a,B4: epistemic_fm_a > set_se5208064806568342746c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ A )
     => ( ( member536094252920883875c_fm_a @ B @ ( B4 @ A2 ) )
       => ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_2544827684617158341c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_I
thf(fact_1021_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_1022_UN__constant,axiom,
    ! [A: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ( A = bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [Y4: epistemic_fm_a] : C
              @ A ) )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [Y4: epistemic_fm_a] : C
              @ A ) )
          = C ) ) ) ).

% UN_constant
thf(fact_1023_UN__Un,axiom,
    ! [M: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ B4 ) ) ) ) ).

% UN_Un
thf(fact_1024_UN__Un,axiom,
    ! [M: epistemic_fm_a > set_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) )
      = ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ A ) ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ B4 ) ) ) ) ).

% UN_Un
thf(fact_1025_UN__Un,axiom,
    ! [M: a > set_Epistemic_fm_a,A: set_a,B4: set_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ ( sup_sup_set_a @ A @ B4 ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ B4 ) ) ) ) ).

% UN_Un
thf(fact_1026_UN__Un,axiom,
    ! [M: a > set_a,A: set_a,B4: set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ ( sup_sup_set_a @ A @ B4 ) ) )
      = ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ A ) ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ B4 ) ) ) ) ).

% UN_Un
thf(fact_1027_UN__simps_I1_J,axiom,
    ! [C2: set_Epistemic_fm_a,A2: a,B4: epistemic_fm_a > set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( insert_a @ A2 @ ( B4 @ X ) )
              @ C2 ) )
          = bot_bot_set_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( insert_a @ A2 @ ( B4 @ X ) )
              @ C2 ) )
          = ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) ) ) ) ) ).

% UN_simps(1)
thf(fact_1028_UN__simps_I1_J,axiom,
    ! [C2: set_Epistemic_fm_a,A2: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
              @ C2 ) )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
              @ C2 ) )
          = ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) ) ) ) ) ).

% UN_simps(1)
thf(fact_1029_UN__singleton,axiom,
    ! [A: set_a] :
      ( ( comple2307003609928055243_set_a
        @ ( image_a_set_a
          @ ^ [X: a] : ( insert_a @ X @ bot_bot_set_a )
          @ A ) )
      = A ) ).

% UN_singleton
thf(fact_1030_UN__singleton,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a
        @ ( image_1263732536703906021c_fm_a
          @ ^ [X: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ X @ bot_bo3626323581529592678c_fm_a )
          @ A ) )
      = A ) ).

% UN_singleton
thf(fact_1031_Sup__upper2,axiom,
    ! [U3: epistemic_fm_a > $o,A: set_Epistemic_fm_a_o,V4: epistemic_fm_a > $o] :
      ( ( member4486839677911940090fm_a_o @ U3 @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ V4 @ U3 )
       => ( ord_le4043730696559282883fm_a_o @ V4 @ ( comple310706794042174646fm_a_o @ A ) ) ) ) ).

% Sup_upper2
thf(fact_1032_Sup__upper2,axiom,
    ! [U3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,V4: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ U3 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ V4 @ U3 )
       => ( ord_le3275665582123262618c_fm_a @ V4 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ) ).

% Sup_upper2
thf(fact_1033_Sup__le__iff,axiom,
    ! [A: set_Epistemic_fm_a_o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ B )
      = ( ! [X: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X @ A )
           => ( ord_le4043730696559282883fm_a_o @ X @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1034_Sup__le__iff,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ B )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ A )
           => ( ord_le3275665582123262618c_fm_a @ X @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1035_Sup__upper,axiom,
    ! [X3: epistemic_fm_a > $o,A: set_Epistemic_fm_a_o] :
      ( ( member4486839677911940090fm_a_o @ X3 @ A )
     => ( ord_le4043730696559282883fm_a_o @ X3 @ ( comple310706794042174646fm_a_o @ A ) ) ) ).

% Sup_upper
thf(fact_1036_Sup__upper,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X3 @ A )
     => ( ord_le3275665582123262618c_fm_a @ X3 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ).

% Sup_upper
thf(fact_1037_Sup__least,axiom,
    ! [A: set_Epistemic_fm_a_o,Z2: epistemic_fm_a > $o] :
      ( ! [X2: epistemic_fm_a > $o] :
          ( ( member4486839677911940090fm_a_o @ X2 @ A )
         => ( ord_le4043730696559282883fm_a_o @ X2 @ Z2 ) )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ Z2 ) ) ).

% Sup_least
thf(fact_1038_Sup__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,Z2: set_Epistemic_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( ord_le3275665582123262618c_fm_a @ X2 @ Z2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ Z2 ) ) ).

% Sup_least
thf(fact_1039_Sup__mono,axiom,
    ! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
      ( ! [A6: epistemic_fm_a > $o] :
          ( ( member4486839677911940090fm_a_o @ A6 @ A )
         => ? [X5: epistemic_fm_a > $o] :
              ( ( member4486839677911940090fm_a_o @ X5 @ B4 )
              & ( ord_le4043730696559282883fm_a_o @ A6 @ X5 ) ) )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ ( comple310706794042174646fm_a_o @ B4 ) ) ) ).

% Sup_mono
thf(fact_1040_Sup__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [A6: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ A6 @ A )
         => ? [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ A6 @ X5 ) ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).

% Sup_mono
thf(fact_1041_Sup__eqI,axiom,
    ! [A: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ! [Y2: epistemic_fm_a > $o] :
          ( ( member4486839677911940090fm_a_o @ Y2 @ A )
         => ( ord_le4043730696559282883fm_a_o @ Y2 @ X3 ) )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ! [Z6: epistemic_fm_a > $o] :
                ( ( member4486839677911940090fm_a_o @ Z6 @ A )
               => ( ord_le4043730696559282883fm_a_o @ Z6 @ Y2 ) )
           => ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
       => ( ( comple310706794042174646fm_a_o @ A )
          = X3 ) ) ) ).

% Sup_eqI
thf(fact_1042_Sup__eqI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ! [Y2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ Y2 @ A )
         => ( ord_le3275665582123262618c_fm_a @ Y2 @ X3 ) )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ! [Z6: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ Z6 @ A )
               => ( ord_le3275665582123262618c_fm_a @ Z6 @ Y2 ) )
           => ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
       => ( ( comple7868773486375872231c_fm_a @ A )
          = X3 ) ) ) ).

% Sup_eqI
thf(fact_1043_Union__subsetI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ? [Y5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ X2 @ Y5 ) ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).

% Union_subsetI
thf(fact_1044_Union__upper,axiom,
    ! [B4: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ B4 @ A )
     => ( ord_le3275665582123262618c_fm_a @ B4 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ).

% Union_upper
thf(fact_1045_Union__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,C2: set_Epistemic_fm_a] :
      ( ! [X7: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X7 @ A )
         => ( ord_le3275665582123262618c_fm_a @ X7 @ C2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ C2 ) ) ).

% Union_least
thf(fact_1046_Union__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).

% Union_mono
thf(fact_1047_SUP__UNIV__bool__expand,axiom,
    ! [A: $o > set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_2964458278485386983c_fm_a @ A @ top_top_set_o ) )
      = ( sup_su1367922730591523534c_fm_a @ ( A @ $true ) @ ( A @ $false ) ) ) ).

% SUP_UNIV_bool_expand
thf(fact_1048_SUP__UNIV__bool__expand,axiom,
    ! [A: $o > set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_o_set_a @ A @ top_top_set_o ) )
      = ( sup_sup_set_a @ ( A @ $true ) @ ( A @ $false ) ) ) ).

% SUP_UNIV_bool_expand
thf(fact_1049_UN__bool__eq,axiom,
    ! [A: $o > set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_2964458278485386983c_fm_a @ A @ top_top_set_o ) )
      = ( sup_su1367922730591523534c_fm_a @ ( A @ $true ) @ ( A @ $false ) ) ) ).

% UN_bool_eq
thf(fact_1050_UN__bool__eq,axiom,
    ! [A: $o > set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_o_set_a @ A @ top_top_set_o ) )
      = ( sup_sup_set_a @ ( A @ $true ) @ ( A @ $false ) ) ) ).

% UN_bool_eq
thf(fact_1051_Un__eq__UN,axiom,
    ( sup_su1367922730591523534c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( comple7868773486375872231c_fm_a
          @ ( image_2964458278485386983c_fm_a
            @ ^ [B2: $o] : ( if_set2375185401397246656c_fm_a @ B2 @ A3 @ B3 )
            @ top_top_set_o ) ) ) ) ).

% Un_eq_UN
thf(fact_1052_Un__eq__UN,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( comple2307003609928055243_set_a
          @ ( image_o_set_a
            @ ^ [B2: $o] : ( if_set_a @ B2 @ A3 @ B3 )
            @ top_top_set_o ) ) ) ) ).

% Un_eq_UN
thf(fact_1053_UN__E,axiom,
    ! [B: a,B4: a > set_a,A: set_a] :
      ( ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B4 @ A ) ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ~ ( member_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1054_UN__E,axiom,
    ! [B: a,B4: set_Epistemic_fm_a > set_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ B4 @ A ) ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ~ ( member_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1055_UN__E,axiom,
    ! [B: a,B4: epistemic_fm_a > set_a,A: set_Epistemic_fm_a] :
      ( ( member_a @ B @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ A ) ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ~ ( member_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1056_UN__E,axiom,
    ! [B: set_Epistemic_fm_a,B4: a > set_se5208064806568342746c_fm_a,A: set_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_4864492491237557473c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1057_UN__E,axiom,
    ! [B: set_Epistemic_fm_a,B4: set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_3447524139502481637c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1058_UN__E,axiom,
    ! [B: set_Epistemic_fm_a,B4: epistemic_fm_a > set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ B @ ( comple7261557488043011271c_fm_a @ ( image_2544827684617158341c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ~ ( member536094252920883875c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1059_UN__E,axiom,
    ! [B: epistemic_fm_a,B4: a > set_Epistemic_fm_a,A: set_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1060_UN__E,axiom,
    ! [B: epistemic_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a] :
      ( ( member6642669571620171971c_fm_a @ B @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) )
     => ~ ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ~ ( member6642669571620171971c_fm_a @ B @ ( B4 @ X2 ) ) ) ) ).

% UN_E
thf(fact_1061_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_1062_SUP__eq,axiom,
    ! [A: set_a,B4: set_a,F: a > set_Epistemic_fm_a,G4: a > set_Epistemic_fm_a] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: a] :
              ( ( member_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: a] :
            ( ( member_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1063_SUP__eq,axiom,
    ! [A: set_a,B4: set_a,F: a > epistemic_fm_a > $o,G4: a > epistemic_fm_a > $o] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: a] :
              ( ( member_a @ X5 @ B4 )
              & ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: a] :
            ( ( member_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le4043730696559282883fm_a_o @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) )
          = ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1064_SUP__eq,axiom,
    ! [A: set_a,B4: set_Epistemic_fm_a,F: a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1065_SUP__eq,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: a > set_Epistemic_fm_a] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ? [X5: a] :
              ( ( member_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: a] :
            ( ( member_a @ J4 @ B4 )
           => ? [X5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1066_SUP__eq,axiom,
    ! [A: set_a,B4: set_Epistemic_fm_a,F: a > epistemic_fm_a > $o,G4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X5 @ B4 )
              & ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le4043730696559282883fm_a_o @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) )
          = ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1067_SUP__eq,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: a > epistemic_fm_a > $o] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ? [X5: a] :
              ( ( member_a @ X5 @ B4 )
              & ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: a] :
            ( ( member_a @ J4 @ B4 )
           => ? [X5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X5 @ A )
                & ( ord_le4043730696559282883fm_a_o @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
          = ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1068_SUP__eq,axiom,
    ! [A: set_a,B4: set_se5208064806568342746c_fm_a,F: a > set_Epistemic_fm_a,G4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1069_SUP__eq,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,G4: a > set_Epistemic_fm_a] :
      ( ! [I3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ I3 @ A )
         => ? [X5: a] :
              ( ( member_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: a] :
            ( ( member_a @ J4 @ B4 )
           => ? [X5: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1070_SUP__eq,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ? [X5: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X5 @ B4 )
              & ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ J4 @ B4 )
           => ? [X5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X5 @ A )
                & ( ord_le3275665582123262618c_fm_a @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
          = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1071_SUP__eq,axiom,
    ! [A: set_a,B4: set_se5208064806568342746c_fm_a,F: a > epistemic_fm_a > $o,G4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ? [X5: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X5 @ B4 )
              & ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ ( G4 @ X5 ) ) ) )
     => ( ! [J4: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ J4 @ B4 )
           => ? [X5: a] :
                ( ( member_a @ X5 @ A )
                & ( ord_le4043730696559282883fm_a_o @ ( G4 @ J4 ) @ ( F @ X5 ) ) ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) )
          = ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_eq
thf(fact_1072_less__eq__Sup,axiom,
    ! [A: set_Epistemic_fm_a_o,U3: epistemic_fm_a > $o] :
      ( ! [V5: epistemic_fm_a > $o] :
          ( ( member4486839677911940090fm_a_o @ V5 @ A )
         => ( ord_le4043730696559282883fm_a_o @ U3 @ V5 ) )
     => ( ( A != bot_bo4908879468608929837fm_a_o )
       => ( ord_le4043730696559282883fm_a_o @ U3 @ ( comple310706794042174646fm_a_o @ A ) ) ) ) ).

% less_eq_Sup
thf(fact_1073_less__eq__Sup,axiom,
    ! [A: set_se5208064806568342746c_fm_a,U3: set_Epistemic_fm_a] :
      ( ! [V5: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ V5 @ A )
         => ( ord_le3275665582123262618c_fm_a @ U3 @ V5 ) )
     => ( ( A != bot_bo1868452413526482246c_fm_a )
       => ( ord_le3275665582123262618c_fm_a @ U3 @ ( comple7868773486375872231c_fm_a @ A ) ) ) ) ).

% less_eq_Sup
thf(fact_1074_Sup__subset__mono,axiom,
    ! [A: set_Epistemic_fm_a_o,B4: set_Epistemic_fm_a_o] :
      ( ( ord_le4525777775358908921fm_a_o @ A @ B4 )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ A ) @ ( comple310706794042174646fm_a_o @ B4 ) ) ) ).

% Sup_subset_mono
thf(fact_1075_Sup__subset__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ A ) @ ( comple7868773486375872231c_fm_a @ B4 ) ) ) ).

% Sup_subset_mono
thf(fact_1076_SUP__eqI,axiom,
    ! [A: set_a,F: a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ! [I5: a] :
                ( ( member_a @ I5 @ A )
               => ( ord_le4043730696559282883fm_a_o @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1077_SUP__eqI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ! [I3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ! [I5: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ I5 @ A )
               => ( ord_le4043730696559282883fm_a_o @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1078_SUP__eqI,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: epistemic_fm_a > $o] :
            ( ! [I5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ I5 @ A )
               => ( ord_le4043730696559282883fm_a_o @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 ) )
       => ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1079_SUP__eqI,axiom,
    ! [A: set_a,F: a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ! [I5: a] :
                ( ( member_a @ I5 @ A )
               => ( ord_le3275665582123262618c_fm_a @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1080_SUP__eqI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ! [I3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ! [I5: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ I5 @ A )
               => ( ord_le3275665582123262618c_fm_a @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1081_SUP__eqI,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ X3 ) )
     => ( ! [Y2: set_Epistemic_fm_a] :
            ( ! [I5: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ I5 @ A )
               => ( ord_le3275665582123262618c_fm_a @ ( F @ I5 ) @ Y2 ) )
           => ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 ) )
       => ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) )
          = X3 ) ) ) ).

% SUP_eqI
thf(fact_1082_SUP__least,axiom,
    ! [A: set_a,F: a > epistemic_fm_a > $o,U3: epistemic_fm_a > $o] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ U3 ) )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1083_SUP__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,U3: epistemic_fm_a > $o] :
      ( ! [I3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ U3 ) )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1084_SUP__least,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,U3: epistemic_fm_a > $o] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ( ord_le4043730696559282883fm_a_o @ ( F @ I3 ) @ U3 ) )
     => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1085_SUP__least,axiom,
    ! [A: set_a,F: a > set_Epistemic_fm_a,U3: set_Epistemic_fm_a] :
      ( ! [I3: a] :
          ( ( member_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ U3 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1086_SUP__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,U3: set_Epistemic_fm_a] :
      ( ! [I3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ U3 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1087_SUP__least,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,U3: set_Epistemic_fm_a] :
      ( ! [I3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ I3 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( F @ I3 ) @ U3 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ U3 ) ) ).

% SUP_least
thf(fact_1088_SUP__upper,axiom,
    ! [I: a,A: set_a,F: a > epistemic_fm_a > $o] :
      ( ( member_a @ I @ A )
     => ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1089_SUP__upper,axiom,
    ! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ I @ A )
     => ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1090_SUP__upper,axiom,
    ! [I: epistemic_fm_a,A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ I @ A )
     => ( ord_le4043730696559282883fm_a_o @ ( F @ I ) @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1091_SUP__upper,axiom,
    ! [I: a,A: set_a,F: a > set_Epistemic_fm_a] :
      ( ( member_a @ I @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1092_SUP__upper,axiom,
    ! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ I @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1093_SUP__upper,axiom,
    ! [I: epistemic_fm_a,A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ I @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( F @ I ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) ) ) ).

% SUP_upper
thf(fact_1094_SUP__upper2,axiom,
    ! [I: a,A: set_a,U3: epistemic_fm_a > $o,F: a > epistemic_fm_a > $o] :
      ( ( member_a @ I @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ U3 @ ( F @ I ) )
       => ( ord_le4043730696559282883fm_a_o @ U3 @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1095_SUP__upper2,axiom,
    ! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,U3: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ I @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ U3 @ ( F @ I ) )
       => ( ord_le4043730696559282883fm_a_o @ U3 @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1096_SUP__upper2,axiom,
    ! [I: epistemic_fm_a,A: set_Epistemic_fm_a,U3: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ I @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ U3 @ ( F @ I ) )
       => ( ord_le4043730696559282883fm_a_o @ U3 @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1097_SUP__upper2,axiom,
    ! [I: a,A: set_a,U3: set_Epistemic_fm_a,F: a > set_Epistemic_fm_a] :
      ( ( member_a @ I @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ U3 @ ( F @ I ) )
       => ( ord_le3275665582123262618c_fm_a @ U3 @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1098_SUP__upper2,axiom,
    ! [I: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,U3: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ I @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ U3 @ ( F @ I ) )
       => ( ord_le3275665582123262618c_fm_a @ U3 @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1099_SUP__upper2,axiom,
    ! [I: epistemic_fm_a,A: set_Epistemic_fm_a,U3: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ I @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ U3 @ ( F @ I ) )
       => ( ord_le3275665582123262618c_fm_a @ U3 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) ) ) ) ).

% SUP_upper2
thf(fact_1100_SUP__absorb,axiom,
    ! [K5: a,I4: set_a,A: a > set_Epistemic_fm_a] :
      ( ( member_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1101_SUP__absorb,axiom,
    ! [K5: set_Epistemic_fm_a,I4: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1102_SUP__absorb,axiom,
    ! [K5: epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1103_SUP__absorb,axiom,
    ! [K5: a,I4: set_a,A: a > set_a] :
      ( ( member_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_a_set_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1104_SUP__absorb,axiom,
    ! [K5: set_Epistemic_fm_a,I4: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a > set_a] :
      ( ( member536094252920883875c_fm_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1105_SUP__absorb,axiom,
    ! [K5: epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_a] :
      ( ( member6642669571620171971c_fm_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1106_UN__empty,axiom,
    ! [B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ bot_bo3626323581529592678c_fm_a ) )
      = bot_bo3626323581529592678c_fm_a ) ).

% UN_empty
thf(fact_1107_UN__mono,axiom,
    ! [A: set_a,B4: set_a,F: a > set_Epistemic_fm_a,G4: a > set_Epistemic_fm_a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% UN_mono
thf(fact_1108_UN__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,G4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% UN_mono
thf(fact_1109_UN__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% UN_mono
thf(fact_1110_UN__least,axiom,
    ! [A: set_a,B4: a > set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ C2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) @ C2 ) ) ).

% UN_least
thf(fact_1111_UN__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ C2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) @ C2 ) ) ).

% UN_least
thf(fact_1112_UN__least,axiom,
    ! [A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ C2 ) )
     => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) @ C2 ) ) ).

% UN_least
thf(fact_1113_UN__upper,axiom,
    ! [A2: a,A: set_a,B4: a > set_Epistemic_fm_a] :
      ( ( member_a @ A2 @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) ) ) ).

% UN_upper
thf(fact_1114_UN__upper,axiom,
    ! [A2: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ A2 @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ).

% UN_upper
thf(fact_1115_UN__upper,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ A )
     => ( ord_le3275665582123262618c_fm_a @ ( B4 @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ).

% UN_upper
thf(fact_1116_UN__insert__distrib,axiom,
    ! [U3: a,A: set_a,A2: epistemic_fm_a,B4: a > set_Epistemic_fm_a] :
      ( ( member_a @ U3 @ A )
     => ( ( comple7868773486375872231c_fm_a
          @ ( image_3480842985853347585c_fm_a
            @ ^ [X: a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1117_UN__insert__distrib,axiom,
    ! [U3: a,A: set_a,A2: a,B4: a > set_a] :
      ( ( member_a @ U3 @ A )
     => ( ( comple2307003609928055243_set_a
          @ ( image_a_set_a
            @ ^ [X: a] : ( insert_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1118_UN__insert__distrib,axiom,
    ! [U3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,A2: epistemic_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ U3 @ A )
     => ( ( comple7868773486375872231c_fm_a
          @ ( image_8582343580727714565c_fm_a
            @ ^ [X: set_Epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1119_UN__insert__distrib,axiom,
    ! [U3: set_Epistemic_fm_a,A: set_se5208064806568342746c_fm_a,A2: a,B4: set_Epistemic_fm_a > set_a] :
      ( ( member536094252920883875c_fm_a @ U3 @ A )
     => ( ( comple2307003609928055243_set_a
          @ ( image_7006806330250622697_set_a
            @ ^ [X: set_Epistemic_fm_a] : ( insert_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1120_UN__insert__distrib,axiom,
    ! [U3: epistemic_fm_a,A: set_Epistemic_fm_a,A2: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ U3 @ A )
     => ( ( comple7868773486375872231c_fm_a
          @ ( image_1263732536703906021c_fm_a
            @ ^ [X: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1121_UN__insert__distrib,axiom,
    ! [U3: epistemic_fm_a,A: set_Epistemic_fm_a,A2: a,B4: epistemic_fm_a > set_a] :
      ( ( member6642669571620171971c_fm_a @ U3 @ A )
     => ( ( comple2307003609928055243_set_a
          @ ( image_7937322393147004105_set_a
            @ ^ [X: epistemic_fm_a] : ( insert_a @ A2 @ ( B4 @ X ) )
            @ A ) )
        = ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ A ) ) ) ) ) ).

% UN_insert_distrib
thf(fact_1122_UN__absorb,axiom,
    ! [K5: a,I4: set_a,A: a > set_Epistemic_fm_a] :
      ( ( member_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1123_UN__absorb,axiom,
    ! [K5: set_Epistemic_fm_a,I4: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1124_UN__absorb,axiom,
    ! [K5: epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ K5 @ I4 )
     => ( ( sup_su1367922730591523534c_fm_a @ ( A @ K5 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) )
        = ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1125_UN__absorb,axiom,
    ! [K5: a,I4: set_a,A: a > set_a] :
      ( ( member_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_a_set_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1126_UN__absorb,axiom,
    ! [K5: set_Epistemic_fm_a,I4: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a > set_a] :
      ( ( member536094252920883875c_fm_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_7006806330250622697_set_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1127_UN__absorb,axiom,
    ! [K5: epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_a] :
      ( ( member6642669571620171971c_fm_a @ K5 @ I4 )
     => ( ( sup_sup_set_a @ ( A @ K5 ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ I4 ) ) )
        = ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ I4 ) ) ) ) ).

% UN_absorb
thf(fact_1128_SUP__eq__iff,axiom,
    ! [I4: set_a,C: epistemic_fm_a > $o,F: a > epistemic_fm_a > $o] :
      ( ( I4 != bot_bot_set_a )
     => ( ! [I3: a] :
            ( ( member_a @ I3 @ I4 )
           => ( ord_le4043730696559282883fm_a_o @ C @ ( F @ I3 ) ) )
       => ( ( ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ I4 ) )
            = C )
          = ( ! [X: a] :
                ( ( member_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1129_SUP__eq__iff,axiom,
    ! [I4: set_se5208064806568342746c_fm_a,C: epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( I4 != bot_bo1868452413526482246c_fm_a )
     => ( ! [I3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ I3 @ I4 )
           => ( ord_le4043730696559282883fm_a_o @ C @ ( F @ I3 ) ) )
       => ( ( ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ I4 ) )
            = C )
          = ( ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1130_SUP__eq__iff,axiom,
    ! [I4: set_Epistemic_fm_a,C: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( I4 != bot_bo3626323581529592678c_fm_a )
     => ( ! [I3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ I3 @ I4 )
           => ( ord_le4043730696559282883fm_a_o @ C @ ( F @ I3 ) ) )
       => ( ( ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ I4 ) )
            = C )
          = ( ! [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1131_SUP__eq__iff,axiom,
    ! [I4: set_a,C: set_Epistemic_fm_a,F: a > set_Epistemic_fm_a] :
      ( ( I4 != bot_bot_set_a )
     => ( ! [I3: a] :
            ( ( member_a @ I3 @ I4 )
           => ( ord_le3275665582123262618c_fm_a @ C @ ( F @ I3 ) ) )
       => ( ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ I4 ) )
            = C )
          = ( ! [X: a] :
                ( ( member_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1132_SUP__eq__iff,axiom,
    ! [I4: set_se5208064806568342746c_fm_a,C: set_Epistemic_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( I4 != bot_bo1868452413526482246c_fm_a )
     => ( ! [I3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ I3 @ I4 )
           => ( ord_le3275665582123262618c_fm_a @ C @ ( F @ I3 ) ) )
       => ( ( ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ I4 ) )
            = C )
          = ( ! [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1133_SUP__eq__iff,axiom,
    ! [I4: set_Epistemic_fm_a,C: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( I4 != bot_bo3626323581529592678c_fm_a )
     => ( ! [I3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ I3 @ I4 )
           => ( ord_le3275665582123262618c_fm_a @ C @ ( F @ I3 ) ) )
       => ( ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ I4 ) )
            = C )
          = ( ! [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ I4 )
               => ( ( F @ X )
                  = C ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1134_SUP__subset__mono,axiom,
    ! [A: set_a,B4: set_a,F: a > epistemic_fm_a > $o,G4: a > epistemic_fm_a > $o] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1135_SUP__subset__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,G4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1136_SUP__subset__mono,axiom,
    ! [A: set_a,B4: set_a,F: a > set_Epistemic_fm_a,G4: a > set_Epistemic_fm_a] :
      ( ( ord_less_eq_set_a @ A @ B4 )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1137_SUP__subset__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,G4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ B4 )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1138_SUP__subset__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,G4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1139_SUP__subset__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,G4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ ( G4 @ X2 ) ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ G4 @ B4 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1140_SUP__empty,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ bot_bo3626323581529592678c_fm_a ) )
      = bot_bo3626323581529592678c_fm_a ) ).

% SUP_empty
thf(fact_1141_SUP__constant,axiom,
    ! [A: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ( A = bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [Y4: epistemic_fm_a] : C
              @ A ) )
          = bot_bo3626323581529592678c_fm_a ) )
      & ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [Y4: epistemic_fm_a] : C
              @ A ) )
          = C ) ) ) ).

% SUP_constant
thf(fact_1142_SUP__insert,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ ( insert7817948963269374698c_fm_a @ A2 @ A ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( F @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) ) ) ).

% SUP_insert
thf(fact_1143_SUP__insert,axiom,
    ! [F: a > set_Epistemic_fm_a,A2: a,A: set_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ ( insert_a @ A2 @ A ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( F @ A2 ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) ) ) ).

% SUP_insert
thf(fact_1144_SUP__insert,axiom,
    ! [F: epistemic_fm_a > set_a,A2: epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ F @ ( insert7817948963269374698c_fm_a @ A2 @ A ) ) )
      = ( sup_sup_set_a @ ( F @ A2 ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ F @ A ) ) ) ) ).

% SUP_insert
thf(fact_1145_SUP__insert,axiom,
    ! [F: a > set_a,A2: a,A: set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_a_set_a @ F @ ( insert_a @ A2 @ A ) ) )
      = ( sup_sup_set_a @ ( F @ A2 ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ F @ A ) ) ) ) ).

% SUP_insert
thf(fact_1146_SUP__union,axiom,
    ! [M: epistemic_fm_a > set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ M @ B4 ) ) ) ) ).

% SUP_union
thf(fact_1147_SUP__union,axiom,
    ! [M: epistemic_fm_a > set_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ ( sup_su1367922730591523534c_fm_a @ A @ B4 ) ) )
      = ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ A ) ) @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ M @ B4 ) ) ) ) ).

% SUP_union
thf(fact_1148_SUP__union,axiom,
    ! [M: a > set_Epistemic_fm_a,A: set_a,B4: set_a] :
      ( ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ ( sup_sup_set_a @ A @ B4 ) ) )
      = ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ A ) ) @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ M @ B4 ) ) ) ) ).

% SUP_union
thf(fact_1149_SUP__union,axiom,
    ! [M: a > set_a,A: set_a,B4: set_a] :
      ( ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ ( sup_sup_set_a @ A @ B4 ) ) )
      = ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ A ) ) @ ( comple2307003609928055243_set_a @ ( image_a_set_a @ M @ B4 ) ) ) ) ).

% SUP_union
thf(fact_1150_Collect__ex__eq,axiom,
    ! [P4: set_Epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
          ? [X4: epistemic_fm_a] : ( P4 @ X @ X4 ) )
      = ( comple7261557488043011271c_fm_a
        @ ( image_2544827684617158341c_fm_a
          @ ^ [Y4: epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ^ [X: set_Epistemic_fm_a] : ( P4 @ X @ Y4 ) )
          @ top_to7796028867103199306c_fm_a ) ) ) ).

% Collect_ex_eq
thf(fact_1151_Collect__ex__eq,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
          ? [X4: epistemic_fm_a] : ( P4 @ X @ X4 ) )
      = ( comple7868773486375872231c_fm_a
        @ ( image_1263732536703906021c_fm_a
          @ ^ [Y4: epistemic_fm_a] :
              ( collec4904205152690461189c_fm_a
              @ ^ [X: epistemic_fm_a] : ( P4 @ X @ Y4 ) )
          @ top_to7796028867103199306c_fm_a ) ) ) ).

% Collect_ex_eq
thf(fact_1152_UN__extend__simps_I1_J,axiom,
    ! [C2: set_Epistemic_fm_a,A2: a,B4: epistemic_fm_a > set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) )
          = ( insert_a @ A2 @ bot_bot_set_a ) ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( insert_a @ A2 @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) )
          = ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( insert_a @ A2 @ ( B4 @ X ) )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(1)
thf(fact_1153_UN__extend__simps_I1_J,axiom,
    ! [C2: set_Epistemic_fm_a,A2: epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) )
          = ( insert7817948963269374698c_fm_a @ A2 @ bot_bo3626323581529592678c_fm_a ) ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( insert7817948963269374698c_fm_a @ A2 @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) )
          = ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ A2 @ ( B4 @ X ) )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(1)
thf(fact_1154_UN__extend__simps_I3_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( sup_su1367922730591523534c_fm_a @ A @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) )
          = A ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( sup_su1367922730591523534c_fm_a @ A @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ B4 @ C2 ) ) )
          = ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ A @ ( B4 @ X ) )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(3)
thf(fact_1155_UN__extend__simps_I3_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_a,B4: epistemic_fm_a > set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( sup_sup_set_a @ A @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) )
          = A ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( sup_sup_set_a @ A @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ B4 @ C2 ) ) )
          = ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ A @ ( B4 @ X ) )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(3)
thf(fact_1156_UN__extend__simps_I2_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ C2 ) ) @ B4 )
          = B4 ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( sup_su1367922730591523534c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ C2 ) ) @ B4 )
          = ( comple7868773486375872231c_fm_a
            @ ( image_1263732536703906021c_fm_a
              @ ^ [X: epistemic_fm_a] : ( sup_su1367922730591523534c_fm_a @ ( A @ X ) @ B4 )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(2)
thf(fact_1157_UN__extend__simps_I2_J,axiom,
    ! [C2: set_Epistemic_fm_a,A: epistemic_fm_a > set_a,B4: set_a] :
      ( ( ( C2 = bot_bo3626323581529592678c_fm_a )
       => ( ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ C2 ) ) @ B4 )
          = B4 ) )
      & ( ( C2 != bot_bo3626323581529592678c_fm_a )
       => ( ( sup_sup_set_a @ ( comple2307003609928055243_set_a @ ( image_7937322393147004105_set_a @ A @ C2 ) ) @ B4 )
          = ( comple2307003609928055243_set_a
            @ ( image_7937322393147004105_set_a
              @ ^ [X: epistemic_fm_a] : ( sup_sup_set_a @ ( A @ X ) @ B4 )
              @ C2 ) ) ) ) ) ).

% UN_extend_simps(2)
thf(fact_1158_finite__subset__Union,axiom,
    ! [A: set_Epistemic_fm_a,B8: set_se5208064806568342746c_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ ( comple7868773486375872231c_fm_a @ B8 ) )
       => ~ ! [F5: set_se5208064806568342746c_fm_a] :
              ( ( finite7364866884270929315c_fm_a @ F5 )
             => ( ( ord_le7112219575281605754c_fm_a @ F5 @ B8 )
               => ~ ( ord_le3275665582123262618c_fm_a @ A @ ( comple7868773486375872231c_fm_a @ F5 ) ) ) ) ) ) ).

% finite_subset_Union
thf(fact_1159_Sup__set__def,axiom,
    ( comple2307003609928055243_set_a
    = ( ^ [A3: set_set_a] :
          ( collect_a
          @ ^ [X: a] : ( complete_Sup_Sup_o @ ( image_set_a_o @ ( member_a @ X ) @ A3 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1160_Sup__set__def,axiom,
    ( comple7261557488043011271c_fm_a
    = ( ^ [A3: set_se8609989359752948410c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] : ( complete_Sup_Sup_o @ ( image_5152694684804562371fm_a_o @ ( member536094252920883875c_fm_a @ X ) @ A3 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1161_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_1162_SUP__Sup__eq,axiom,
    ! [S: set_set_a] :
      ( ( complete_Sup_Sup_a_o
        @ ( image_set_a_a_o
          @ ^ [I2: set_a,X: a] : ( member_a @ X @ I2 )
          @ S ) )
      = ( ^ [X: a] : ( member_a @ X @ ( comple2307003609928055243_set_a @ S ) ) ) ) ).

% SUP_Sup_eq
thf(fact_1163_SUP__Sup__eq,axiom,
    ! [S: set_se8609989359752948410c_fm_a] :
      ( ( comple5897411722154495702fm_a_o
        @ ( image_1826592184436450840fm_a_o
          @ ^ [I2: set_se5208064806568342746c_fm_a,X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ I2 )
          @ S ) )
      = ( ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ ( comple7261557488043011271c_fm_a @ S ) ) ) ) ).

% SUP_Sup_eq
thf(fact_1164_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_1165_cSup__eq__maximum,axiom,
    ! [Z2: epistemic_fm_a > $o,X6: set_Epistemic_fm_a_o] :
      ( ( member4486839677911940090fm_a_o @ Z2 @ X6 )
     => ( ! [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ X6 )
           => ( ord_le4043730696559282883fm_a_o @ X2 @ Z2 ) )
       => ( ( comple310706794042174646fm_a_o @ X6 )
          = Z2 ) ) ) ).

% cSup_eq_maximum
thf(fact_1166_cSup__eq__maximum,axiom,
    ! [Z2: set_Epistemic_fm_a,X6: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Z2 @ X6 )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ X6 )
           => ( ord_le3275665582123262618c_fm_a @ X2 @ Z2 ) )
       => ( ( comple7868773486375872231c_fm_a @ X6 )
          = Z2 ) ) ) ).

% cSup_eq_maximum
thf(fact_1167_cSup__least,axiom,
    ! [X6: set_Epistemic_fm_a_o,Z2: epistemic_fm_a > $o] :
      ( ( X6 != bot_bo4908879468608929837fm_a_o )
     => ( ! [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ X6 )
           => ( ord_le4043730696559282883fm_a_o @ X2 @ Z2 ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ X6 ) @ Z2 ) ) ) ).

% cSup_least
thf(fact_1168_cSup__least,axiom,
    ! [X6: set_se5208064806568342746c_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( X6 != bot_bo1868452413526482246c_fm_a )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ X6 )
           => ( ord_le3275665582123262618c_fm_a @ X2 @ Z2 ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ X6 ) @ Z2 ) ) ) ).

% cSup_least
thf(fact_1169_cSup__eq__non__empty,axiom,
    ! [X6: set_Epistemic_fm_a_o,A2: epistemic_fm_a > $o] :
      ( ( X6 != bot_bo4908879468608929837fm_a_o )
     => ( ! [X2: epistemic_fm_a > $o] :
            ( ( member4486839677911940090fm_a_o @ X2 @ X6 )
           => ( ord_le4043730696559282883fm_a_o @ X2 @ A2 ) )
       => ( ! [Y2: epistemic_fm_a > $o] :
              ( ! [X5: epistemic_fm_a > $o] :
                  ( ( member4486839677911940090fm_a_o @ X5 @ X6 )
                 => ( ord_le4043730696559282883fm_a_o @ X5 @ Y2 ) )
             => ( ord_le4043730696559282883fm_a_o @ A2 @ Y2 ) )
         => ( ( comple310706794042174646fm_a_o @ X6 )
            = A2 ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1170_cSup__eq__non__empty,axiom,
    ! [X6: set_se5208064806568342746c_fm_a,A2: set_Epistemic_fm_a] :
      ( ( X6 != bot_bo1868452413526482246c_fm_a )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ X6 )
           => ( ord_le3275665582123262618c_fm_a @ X2 @ A2 ) )
       => ( ! [Y2: set_Epistemic_fm_a] :
              ( ! [X5: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ X5 @ X6 )
                 => ( ord_le3275665582123262618c_fm_a @ X5 @ Y2 ) )
             => ( ord_le3275665582123262618c_fm_a @ A2 @ Y2 ) )
         => ( ( comple7868773486375872231c_fm_a @ X6 )
            = A2 ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1171_le__cSup__finite,axiom,
    ! [X6: set_Epistemic_fm_a_o,X3: epistemic_fm_a > $o] :
      ( ( finite5407549452671652090fm_a_o @ X6 )
     => ( ( member4486839677911940090fm_a_o @ X3 @ X6 )
       => ( ord_le4043730696559282883fm_a_o @ X3 @ ( comple310706794042174646fm_a_o @ X6 ) ) ) ) ).

% le_cSup_finite
thf(fact_1172_le__cSup__finite,axiom,
    ! [X6: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ X6 )
     => ( ( member536094252920883875c_fm_a @ X3 @ X6 )
       => ( ord_le3275665582123262618c_fm_a @ X3 @ ( comple7868773486375872231c_fm_a @ X6 ) ) ) ) ).

% le_cSup_finite
thf(fact_1173_cSUP__least,axiom,
    ! [A: set_a,F: a > epistemic_fm_a > $o,M: epistemic_fm_a > $o] :
      ( ( A != bot_bot_set_a )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ M ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_3809950421912819996fm_a_o @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1174_cSUP__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a > $o,M: epistemic_fm_a > $o] :
      ( ( A != bot_bo1868452413526482246c_fm_a )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ M ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_6902499629341727256fm_a_o @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1175_cSUP__least,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a > $o,M: epistemic_fm_a > $o] :
      ( ( A != bot_bo3626323581529592678c_fm_a )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le4043730696559282883fm_a_o @ ( F @ X2 ) @ M ) )
       => ( ord_le4043730696559282883fm_a_o @ ( comple310706794042174646fm_a_o @ ( image_2381060403230254136fm_a_o @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1176_cSUP__least,axiom,
    ! [A: set_a,F: a > set_Epistemic_fm_a,M: set_Epistemic_fm_a] :
      ( ( A != bot_bot_set_a )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ M ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1177_cSUP__least,axiom,
    ! [A: set_se5208064806568342746c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a,M: set_Epistemic_fm_a] :
      ( ( A != bot_bo1868452413526482246c_fm_a )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ M ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1178_cSUP__least,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > set_Epistemic_fm_a,M: set_Epistemic_fm_a] :
      ( ( A != bot_bo3626323581529592678c_fm_a )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( F @ X2 ) @ M ) )
       => ( ord_le3275665582123262618c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ F @ A ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1179_card__of__UNION__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
     => ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ I4 ) @ R ) @ bNF_We8976657667165594343c_fm_a )
         => ( ! [X2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X2 @ I4 )
               => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( A @ X2 ) ) @ R ) @ bNF_We8976657667165594343c_fm_a ) )
           => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) ) @ R ) @ bNF_We8976657667165594343c_fm_a ) ) ) ) ) ).

% card_of_UNION_ordLeq_infinite_Field
thf(fact_1180_cardSuc__UNION,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,As: set_Epistemic_fm_a > set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
       => ( ( bNF_Ca702919080654562212c_fm_a @ ( bNF_Ca7212779861630621316c_fm_a @ R ) @ As )
         => ( ( ord_le3275665582123262618c_fm_a @ B4 @ ( comple7868773486375872231c_fm_a @ ( image_8582343580727714565c_fm_a @ As @ ( field_3462791820427926727c_fm_a @ ( bNF_Ca7212779861630621316c_fm_a @ R ) ) ) ) )
           => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ R ) @ bNF_We8976657667165594343c_fm_a )
             => ? [X2: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ X2 @ ( field_3462791820427926727c_fm_a @ ( bNF_Ca7212779861630621316c_fm_a @ R ) ) )
                  & ( ord_le3275665582123262618c_fm_a @ B4 @ ( As @ X2 ) ) ) ) ) ) ) ) ).

% cardSuc_UNION
thf(fact_1181_Card__order__omax2,axiom,
    ! [I4: set_a,A: a > set_Epistemic_fm_a] :
      ( ( finite_finite_a @ I4 )
     => ( ( I4 != bot_bot_set_a )
       => ( bNF_Ca1219376963944715160c_fm_a
          @ ( field_Epistemic_fm_a
            @ ( wellor3187545346614422966c_fm_a
              @ ( collec3225794002482277362c_fm_a
                @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                  ? [I2: a] :
                    ( ( Uu2
                      = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                    & ( member_a @ I2 @ I4 ) ) ) ) )
          @ ( wellor3187545346614422966c_fm_a
            @ ( collec3225794002482277362c_fm_a
              @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                ? [I2: a] :
                  ( ( Uu2
                    = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                  & ( member_a @ I2 @ I4 ) ) ) ) ) ) ) ).

% Card_order_omax2
thf(fact_1182_Card__order__omax2,axiom,
    ! [I4: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ I4 )
     => ( ( I4 != bot_bo1868452413526482246c_fm_a )
       => ( bNF_Ca1219376963944715160c_fm_a
          @ ( field_Epistemic_fm_a
            @ ( wellor3187545346614422966c_fm_a
              @ ( collec3225794002482277362c_fm_a
                @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                  ? [I2: set_Epistemic_fm_a] :
                    ( ( Uu2
                      = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                    & ( member536094252920883875c_fm_a @ I2 @ I4 ) ) ) ) )
          @ ( wellor3187545346614422966c_fm_a
            @ ( collec3225794002482277362c_fm_a
              @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                ? [I2: set_Epistemic_fm_a] :
                  ( ( Uu2
                    = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                  & ( member536094252920883875c_fm_a @ I2 @ I4 ) ) ) ) ) ) ) ).

% Card_order_omax2
thf(fact_1183_Card__order__omax2,axiom,
    ! [I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ I4 )
     => ( ( I4 != bot_bo3626323581529592678c_fm_a )
       => ( bNF_Ca1219376963944715160c_fm_a
          @ ( field_Epistemic_fm_a
            @ ( wellor3187545346614422966c_fm_a
              @ ( collec3225794002482277362c_fm_a
                @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                  ? [I2: epistemic_fm_a] :
                    ( ( Uu2
                      = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                    & ( member6642669571620171971c_fm_a @ I2 @ I4 ) ) ) ) )
          @ ( wellor3187545346614422966c_fm_a
            @ ( collec3225794002482277362c_fm_a
              @ ^ [Uu2: set_Pr8948481099588399239c_fm_a] :
                ? [I2: epistemic_fm_a] :
                  ( ( Uu2
                    = ( bNF_Ca1305897159876240246c_fm_a @ ( A @ I2 ) ) )
                  & ( member6642669571620171971c_fm_a @ I2 @ I4 ) ) ) ) ) ) ) ).

% Card_order_omax2
thf(fact_1184_set__list__bind,axiom,
    ! [Xs: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( bind_E8451893407412458119c_fm_a @ Xs @ F ) )
      = ( comple7868773486375872231c_fm_a
        @ ( image_1263732536703906021c_fm_a
          @ ^ [X: epistemic_fm_a] : ( set_Epistemic_fm_a2 @ ( F @ X ) )
          @ ( set_Epistemic_fm_a2 @ Xs ) ) ) ) ).

% set_list_bind
thf(fact_1185_image__fold__insert,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( image_7228943142519265129fm_a_a @ F @ A )
        = ( finite698359878623453964_set_a
          @ ^ [K: epistemic_fm_a] : ( insert_a @ ( F @ K ) )
          @ bot_bot_set_a
          @ A ) ) ) ).

% image_fold_insert
thf(fact_1186_image__fold__insert,axiom,
    ! [A: set_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( image_4449434806354059013c_fm_a @ F @ A )
        = ( finite4625312738069190824c_fm_a
          @ ^ [K: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ ( F @ K ) )
          @ bot_bo3626323581529592678c_fm_a
          @ A ) ) ) ).

% image_fold_insert
thf(fact_1187_Cinfinite__limit__finite,axiom,
    ! [X6: set_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ X6 )
     => ( ( ord_le3275665582123262618c_fm_a @ X6 @ ( field_Epistemic_fm_a @ R ) )
       => ( ( ( bNF_Ca4995477200058113210c_fm_a @ R )
            & ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R ) )
         => ? [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ ( field_Epistemic_fm_a @ R ) )
              & ! [Xa2: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Xa2 @ X6 )
                 => ( ( Xa2 != X2 )
                    & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ Xa2 @ X2 ) @ R ) ) ) ) ) ) ) ).

% Cinfinite_limit_finite
thf(fact_1188_Set__filter__fold,axiom,
    ! [A: set_a,P4: a > $o] :
      ( ( finite_finite_a @ A )
     => ( ( filter_a @ P4 @ A )
        = ( finite_fold_a_set_a
          @ ^ [X: a,A9: set_a] : ( if_set_a @ ( P4 @ X ) @ ( insert_a @ X @ A9 ) @ A9 )
          @ bot_bot_set_a
          @ A ) ) ) ).

% Set_filter_fold
thf(fact_1189_Set__filter__fold,axiom,
    ! [A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( filter6053540574317342667c_fm_a @ P4 @ A )
        = ( finite4625312738069190824c_fm_a
          @ ^ [X: epistemic_fm_a,A9: set_Epistemic_fm_a] : ( if_set2375185401397246656c_fm_a @ ( P4 @ X ) @ ( insert7817948963269374698c_fm_a @ X @ A9 ) @ A9 )
          @ bot_bo3626323581529592678c_fm_a
          @ A ) ) ) ).

% Set_filter_fold
thf(fact_1190_Id__on__fold,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( id_on_Epistemic_fm_a @ A )
        = ( finite1238595690337548085c_fm_a
          @ ^ [X: epistemic_fm_a] : ( insert4108635152042037623c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ X ) )
          @ bot_bo7958537672377389811c_fm_a
          @ A ) ) ) ).

% Id_on_fold
thf(fact_1191_Set_Ofilter__def,axiom,
    ( filter_a
    = ( ^ [P6: a > $o,A3: set_a] :
          ( collect_a
          @ ^ [A4: a] :
              ( ( member_a @ A4 @ A3 )
              & ( P6 @ A4 ) ) ) ) ) ).

% Set.filter_def
thf(fact_1192_Set_Ofilter__def,axiom,
    ( filter7881760030630619563c_fm_a
    = ( ^ [P6: set_Epistemic_fm_a > $o,A3: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [A4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ A4 @ A3 )
              & ( P6 @ A4 ) ) ) ) ) ).

% Set.filter_def
thf(fact_1193_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_1194_Id__on__set,axiom,
    ! [Xs: list_Epistemic_fm_a] :
      ( ( id_on_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ Xs ) )
      = ( set_Pr6083076219314900284c_fm_a
        @ ( map_Ep3772490588942954449c_fm_a
          @ ^ [X: epistemic_fm_a] : ( produc8582950737844404375c_fm_a @ X @ X )
          @ Xs ) ) ) ).

% Id_on_set
thf(fact_1195_comp__fun__commute__filter__fold,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( finite5697817978436579121c_fm_a
      @ ^ [X: epistemic_fm_a,A9: set_Epistemic_fm_a] : ( if_set2375185401397246656c_fm_a @ ( P4 @ X ) @ ( insert7817948963269374698c_fm_a @ X @ A9 ) @ A9 ) ) ).

% comp_fun_commute_filter_fold
thf(fact_1196_comp__fun__commute__filter__fold,axiom,
    ! [P4: a > $o] :
      ( finite3518785373051244337_set_a
      @ ^ [X: a,A9: set_a] : ( if_set_a @ ( P4 @ X ) @ ( insert_a @ X @ A9 ) @ A9 ) ) ).

% comp_fun_commute_filter_fold
thf(fact_1197_card__of__Times__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ R ) @ bNF_We8976657667165594343c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ R ) @ bNF_We8976657667165594343c_fm_a )
         => ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
           => ( member409366557251323088c_fm_a
              @ ( produc5656221390238592791c_fm_a
                @ ( bNF_Ca6881012448374897667c_fm_a
                  @ ( produc1842838987370488648c_fm_a @ A
                    @ ^ [Uu2: epistemic_fm_a] : B4 ) )
                @ R )
              @ bNF_We3091034443223189274c_fm_a ) ) ) ) ) ).

% card_of_Times_ordLeq_infinite_Field
thf(fact_1198_card__of__Sigma__ordLeq__infinite__Field,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
     => ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ I4 ) @ R ) @ bNF_We8976657667165594343c_fm_a )
         => ( ! [X2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X2 @ I4 )
               => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( A @ X2 ) ) @ R ) @ bNF_We8976657667165594343c_fm_a ) )
           => ( member409366557251323088c_fm_a @ ( produc5656221390238592791c_fm_a @ ( bNF_Ca6881012448374897667c_fm_a @ ( produc1842838987370488648c_fm_a @ I4 @ A ) ) @ R ) @ bNF_We3091034443223189274c_fm_a ) ) ) ) ) ).

% card_of_Sigma_ordLeq_infinite_Field
thf(fact_1199_finite__SigmaI,axiom,
    ! [A: set_a,B4: a > set_Epistemic_fm_a] :
      ( ( finite_finite_a @ A )
     => ( ! [A6: a] :
            ( ( member_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite1292243718865155564c_fm_a @ ( produc5208094418251083748c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI
thf(fact_1200_finite__SigmaI,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a @ A )
     => ( ! [A6: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite67421731821866992c_fm_a @ ( produc8471739406029261160c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI
thf(fact_1201_finite__SigmaI,axiom,
    ! [A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ! [A6: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite8252611493601906128c_fm_a @ ( produc1842838987370488648c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI
thf(fact_1202_Times__empty,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : B4 )
        = bot_bo7958537672377389811c_fm_a )
      = ( ( A = bot_bo3626323581529592678c_fm_a )
        | ( B4 = bot_bo3626323581529592678c_fm_a ) ) ) ).

% Times_empty
thf(fact_1203_UNIV__Times__UNIV,axiom,
    ( ( produc1842838987370488648c_fm_a @ top_to7796028867103199306c_fm_a
      @ ^ [Uu2: epistemic_fm_a] : top_to7796028867103199306c_fm_a )
    = top_to4207332589035249111c_fm_a ) ).

% UNIV_Times_UNIV
thf(fact_1204_insert__Times__insert,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( produc1842838987370488648c_fm_a @ ( insert7817948963269374698c_fm_a @ A2 @ A )
        @ ^ [Uu2: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ B @ B4 ) )
      = ( insert4108635152042037623c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B )
        @ ( sup_su6976870698533002843c_fm_a
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ B @ B4 ) )
          @ ( produc1842838987370488648c_fm_a @ ( insert7817948963269374698c_fm_a @ A2 @ A )
            @ ^ [Uu2: epistemic_fm_a] : B4 ) ) ) ) ).

% insert_Times_insert
thf(fact_1205_insert__Times__insert,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,B: a,B4: set_a] :
      ( ( produc1315203364426334764fm_a_a @ ( insert7817948963269374698c_fm_a @ A2 @ A )
        @ ^ [Uu2: epistemic_fm_a] : ( insert_a @ B @ B4 ) )
      = ( insert1410039673467329627fm_a_a @ ( produc5862136535777583099fm_a_a @ A2 @ B )
        @ ( sup_su4084311784973742783fm_a_a
          @ ( produc1315203364426334764fm_a_a @ A
            @ ^ [Uu2: epistemic_fm_a] : ( insert_a @ B @ B4 ) )
          @ ( produc1315203364426334764fm_a_a @ ( insert7817948963269374698c_fm_a @ A2 @ A )
            @ ^ [Uu2: epistemic_fm_a] : B4 ) ) ) ) ).

% insert_Times_insert
thf(fact_1206_insert__Times__insert,axiom,
    ! [A2: a,A: set_a,B: epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( produc5208094418251083748c_fm_a @ ( insert_a @ A2 @ A )
        @ ^ [Uu2: a] : ( insert7817948963269374698c_fm_a @ B @ B4 ) )
      = ( insert1445131663523073555c_fm_a @ ( produc531655552747556275c_fm_a @ A2 @ B )
        @ ( sup_su913185004018452599c_fm_a
          @ ( produc5208094418251083748c_fm_a @ A
            @ ^ [Uu2: a] : ( insert7817948963269374698c_fm_a @ B @ B4 ) )
          @ ( produc5208094418251083748c_fm_a @ ( insert_a @ A2 @ A )
            @ ^ [Uu2: a] : B4 ) ) ) ) ).

% insert_Times_insert
thf(fact_1207_insert__Times__insert,axiom,
    ! [A2: a,A: set_a,B: a,B4: set_a] :
      ( ( product_Sigma_a_a @ ( insert_a @ A2 @ A )
        @ ^ [Uu2: a] : ( insert_a @ B @ B4 ) )
      = ( insert4534936382041156343od_a_a @ ( product_Pair_a_a @ A2 @ B )
        @ ( sup_su3048258781599657691od_a_a
          @ ( product_Sigma_a_a @ A
            @ ^ [Uu2: a] : ( insert_a @ B @ B4 ) )
          @ ( product_Sigma_a_a @ ( insert_a @ A2 @ A )
            @ ^ [Uu2: a] : B4 ) ) ) ) ).

% insert_Times_insert
thf(fact_1208_card__of__Times2,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A != bot_bo3626323581529592678c_fm_a )
     => ( member4645468574724510032c_fm_a
        @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 )
          @ ( bNF_Ca6881012448374897667c_fm_a
            @ ( produc1842838987370488648c_fm_a @ A
              @ ^ [Uu2: epistemic_fm_a] : B4 ) ) )
        @ bNF_We6875281775109948148c_fm_a ) ) ).

% card_of_Times2
thf(fact_1209_card__of__Times1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( A != bot_bo3626323581529592678c_fm_a )
     => ( member4645468574724510032c_fm_a
        @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 )
          @ ( bNF_Ca6881012448374897667c_fm_a
            @ ( produc1842838987370488648c_fm_a @ B4
              @ ^ [Uu2: epistemic_fm_a] : A ) ) )
        @ bNF_We6875281775109948148c_fm_a ) ) ).

% card_of_Times1
thf(fact_1210_card__of__Times__same__infinite,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( member409366557251323088c_fm_a
        @ ( produc5656221390238592791c_fm_a
          @ ( bNF_Ca6881012448374897667c_fm_a
            @ ( produc1842838987370488648c_fm_a @ A
              @ ^ [Uu2: epistemic_fm_a] : A ) )
          @ ( bNF_Ca1305897159876240246c_fm_a @ A ) )
        @ bNF_We6280552541581264903c_fm_a ) ) ).

% card_of_Times_same_infinite
thf(fact_1211_times__eq__iff,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : B4 )
        = ( produc1842838987370488648c_fm_a @ C2
          @ ^ [Uu2: epistemic_fm_a] : D ) )
      = ( ( ( A = C2 )
          & ( B4 = D ) )
        | ( ( ( A = bot_bo3626323581529592678c_fm_a )
            | ( B4 = bot_bo3626323581529592678c_fm_a ) )
          & ( ( C2 = bot_bo3626323581529592678c_fm_a )
            | ( D = bot_bo3626323581529592678c_fm_a ) ) ) ) ) ).

% times_eq_iff
thf(fact_1212_infinite__cartesian__product,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ~ ( finite3304564945125563331c_fm_a @ B4 )
       => ~ ( finite8252611493601906128c_fm_a
            @ ( produc1842838987370488648c_fm_a @ A
              @ ^ [Uu2: epistemic_fm_a] : B4 ) ) ) ) ).

% infinite_cartesian_product
thf(fact_1213_finite__cartesian__product,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( finite8252611493601906128c_fm_a
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : B4 ) ) ) ) ).

% finite_cartesian_product
thf(fact_1214_card__of__Times3,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( member4645468574724510032c_fm_a
      @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
        @ ( bNF_Ca6881012448374897667c_fm_a
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : A ) ) )
      @ bNF_We6875281775109948148c_fm_a ) ).

% card_of_Times3
thf(fact_1215_Sigma__mono,axiom,
    ! [A: set_a,C2: set_a,B4: a > set_Epistemic_fm_a,D: a > set_Epistemic_fm_a] :
      ( ( ord_less_eq_set_a @ A @ C2 )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ ( D @ X2 ) ) )
       => ( ord_le8572035018066832451c_fm_a @ ( produc5208094418251083748c_fm_a @ A @ B4 ) @ ( produc5208094418251083748c_fm_a @ C2 @ D ) ) ) ) ).

% Sigma_mono
thf(fact_1216_Sigma__mono,axiom,
    ! [A: set_se5208064806568342746c_fm_a,C2: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a,D: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A @ C2 )
     => ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ ( D @ X2 ) ) )
       => ( ord_le8983658301677062727c_fm_a @ ( produc8471739406029261160c_fm_a @ A @ B4 ) @ ( produc8471739406029261160c_fm_a @ C2 @ D ) ) ) ) ).

% Sigma_mono
thf(fact_1217_Sigma__mono,axiom,
    ! [A: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a,D: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ C2 )
     => ( ! [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A )
           => ( ord_le3275665582123262618c_fm_a @ ( B4 @ X2 ) @ ( D @ X2 ) ) )
       => ( ord_le8222437384497874983c_fm_a @ ( produc1842838987370488648c_fm_a @ A @ B4 ) @ ( produc1842838987370488648c_fm_a @ C2 @ D ) ) ) ) ).

% Sigma_mono
thf(fact_1218_finite__cartesian__product__iff,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( finite8252611493601906128c_fm_a
        @ ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : B4 ) )
      = ( ( A = bot_bo3626323581529592678c_fm_a )
        | ( B4 = bot_bo3626323581529592678c_fm_a )
        | ( ( finite3304564945125563331c_fm_a @ A )
          & ( finite3304564945125563331c_fm_a @ B4 ) ) ) ) ).

% finite_cartesian_product_iff
thf(fact_1219_finite__cartesian__productD2,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( finite8252611493601906128c_fm_a
        @ ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : B4 ) )
     => ( ( A != bot_bo3626323581529592678c_fm_a )
       => ( finite3304564945125563331c_fm_a @ B4 ) ) ) ).

% finite_cartesian_productD2
thf(fact_1220_finite__cartesian__productD1,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( finite8252611493601906128c_fm_a
        @ ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : B4 ) )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( finite3304564945125563331c_fm_a @ A ) ) ) ).

% finite_cartesian_productD1
thf(fact_1221_finite__SigmaI2,axiom,
    ! [A: set_a,B4: a > set_Epistemic_fm_a] :
      ( ( finite_finite_a
        @ ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A )
              & ( ( B4 @ X )
               != bot_bo3626323581529592678c_fm_a ) ) ) )
     => ( ! [A6: a] :
            ( ( member_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite1292243718865155564c_fm_a @ ( produc5208094418251083748c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI2
thf(fact_1222_finite__SigmaI2,axiom,
    ! [A: set_se5208064806568342746c_fm_a,B4: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite7364866884270929315c_fm_a
        @ ( collec2519470961442302949c_fm_a
          @ ^ [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ A )
              & ( ( B4 @ X )
               != bot_bo3626323581529592678c_fm_a ) ) ) )
     => ( ! [A6: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite67421731821866992c_fm_a @ ( produc8471739406029261160c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI2
thf(fact_1223_finite__SigmaI2,axiom,
    ! [A: set_Epistemic_fm_a,B4: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a
        @ ( collec4904205152690461189c_fm_a
          @ ^ [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ A )
              & ( ( B4 @ X )
               != bot_bo3626323581529592678c_fm_a ) ) ) )
     => ( ! [A6: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ A6 @ A )
           => ( finite3304564945125563331c_fm_a @ ( B4 @ A6 ) ) )
       => ( finite8252611493601906128c_fm_a @ ( produc1842838987370488648c_fm_a @ A @ B4 ) ) ) ) ).

% finite_SigmaI2
thf(fact_1224_Times__subset__cancel2,axiom,
    ! [X3: a,C2: set_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( member_a @ X3 @ C2 )
     => ( ( ord_le2519789762167346827fm_a_a
          @ ( produc1315203364426334764fm_a_a @ A
            @ ^ [Uu2: epistemic_fm_a] : C2 )
          @ ( produc1315203364426334764fm_a_a @ B4
            @ ^ [Uu2: epistemic_fm_a] : C2 ) )
        = ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1225_Times__subset__cancel2,axiom,
    ! [X3: set_Epistemic_fm_a,C2: set_se5208064806568342746c_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ X3 @ C2 )
     => ( ( ord_le8861952861568174599c_fm_a
          @ ( produc6358991095518701864c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : C2 )
          @ ( produc6358991095518701864c_fm_a @ B4
            @ ^ [Uu2: epistemic_fm_a] : C2 ) )
        = ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1226_Times__subset__cancel2,axiom,
    ! [X3: epistemic_fm_a,C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X3 @ C2 )
     => ( ( ord_le8222437384497874983c_fm_a
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : C2 )
          @ ( produc1842838987370488648c_fm_a @ B4
            @ ^ [Uu2: epistemic_fm_a] : C2 ) )
        = ( ord_le3275665582123262618c_fm_a @ A @ B4 ) ) ) ).

% Times_subset_cancel2
thf(fact_1227_card__of__Times__singl2,axiom,
    ! [A: set_Epistemic_fm_a,B: a] :
      ( member5314060011585795664c_fm_a
      @ ( produc5391312561857647255c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
        @ ( bNF_Ca4086118263059731103c_fm_a
          @ ( produc5208094418251083748c_fm_a @ ( insert_a @ B @ bot_bot_set_a )
            @ ^ [Uu2: a] : A ) ) )
      @ bNF_We1465234745361447805c_fm_a ) ).

% card_of_Times_singl2
thf(fact_1228_card__of__Times__singl2,axiom,
    ! [A: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( member4645468574724510032c_fm_a
      @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
        @ ( bNF_Ca6881012448374897667c_fm_a
          @ ( produc1842838987370488648c_fm_a @ ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a )
            @ ^ [Uu2: epistemic_fm_a] : A ) ) )
      @ bNF_We841427836613247969c_fm_a ) ).

% card_of_Times_singl2
thf(fact_1229_card__of__Times__singl1,axiom,
    ! [A: set_Epistemic_fm_a,B: a] :
      ( member5060544704923670608fm_a_a
      @ ( produc5849999179561628823fm_a_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
        @ ( bNF_Ca4051026273003987175fm_a_a
          @ ( produc1315203364426334764fm_a_a @ A
            @ ^ [Uu2: epistemic_fm_a] : ( insert_a @ B @ bot_bot_set_a ) ) ) )
      @ bNF_We1430142755305703877fm_a_a ) ).

% card_of_Times_singl1
thf(fact_1230_card__of__Times__singl1,axiom,
    ! [A: set_Epistemic_fm_a,B: epistemic_fm_a] :
      ( member4645468574724510032c_fm_a
      @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
        @ ( bNF_Ca6881012448374897667c_fm_a
          @ ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : ( insert7817948963269374698c_fm_a @ B @ bot_bo3626323581529592678c_fm_a ) ) ) )
      @ bNF_We841427836613247969c_fm_a ) ).

% card_of_Times_singl1
thf(fact_1231_Card__order__Times__same__infinite,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
       => ( member409366557251323088c_fm_a
          @ ( produc5656221390238592791c_fm_a
            @ ( bNF_Ca6881012448374897667c_fm_a
              @ ( produc1842838987370488648c_fm_a @ ( field_Epistemic_fm_a @ R )
                @ ^ [Uu2: epistemic_fm_a] : ( field_Epistemic_fm_a @ R ) ) )
            @ R )
          @ bNF_We3091034443223189274c_fm_a ) ) ) ).

% Card_order_Times_same_infinite
thf(fact_1232_Card__order__Times3,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] :
      ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
     => ( member4645468574724510032c_fm_a
        @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( field_Epistemic_fm_a @ R ) )
          @ ( bNF_Ca6881012448374897667c_fm_a
            @ ( produc1842838987370488648c_fm_a @ ( field_Epistemic_fm_a @ R )
              @ ^ [Uu2: epistemic_fm_a] : ( field_Epistemic_fm_a @ R ) ) ) )
        @ bNF_We6875281775109948148c_fm_a ) ) ).

% Card_order_Times3
thf(fact_1233_card__of__Times__mono,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) @ ( bNF_Ca1305897159876240246c_fm_a @ D ) ) @ bNF_We8976657667165594343c_fm_a )
       => ( member2573411668019888912c_fm_a
          @ ( produc8718295563965258583c_fm_a
            @ ( bNF_Ca6881012448374897667c_fm_a
              @ ( produc1842838987370488648c_fm_a @ A
                @ ^ [Uu2: epistemic_fm_a] : C2 ) )
            @ ( bNF_Ca6881012448374897667c_fm_a
              @ ( produc1842838987370488648c_fm_a @ B4
                @ ^ [Uu2: epistemic_fm_a] : D ) ) )
          @ bNF_We720002453486882215c_fm_a ) ) ) ).

% card_of_Times_mono
thf(fact_1234_times__subset__iff,axiom,
    ! [A: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a
        @ ( produc1842838987370488648c_fm_a @ A
          @ ^ [Uu2: epistemic_fm_a] : C2 )
        @ ( produc1842838987370488648c_fm_a @ B4
          @ ^ [Uu2: epistemic_fm_a] : D ) )
      = ( ( A = bot_bo3626323581529592678c_fm_a )
        | ( C2 = bot_bo3626323581529592678c_fm_a )
        | ( ( ord_le3275665582123262618c_fm_a @ A @ B4 )
          & ( ord_le3275665582123262618c_fm_a @ C2 @ D ) ) ) ) ).

% times_subset_iff
thf(fact_1235_card__of__Times__cong,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a,C2: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We2357358836176181844c_fm_a )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) @ ( bNF_Ca1305897159876240246c_fm_a @ D ) ) @ bNF_We2357358836176181844c_fm_a )
       => ( member2573411668019888912c_fm_a
          @ ( produc8718295563965258583c_fm_a
            @ ( bNF_Ca6881012448374897667c_fm_a
              @ ( produc1842838987370488648c_fm_a @ A
                @ ^ [Uu2: epistemic_fm_a] : C2 ) )
            @ ( bNF_Ca6881012448374897667c_fm_a
              @ ( produc1842838987370488648c_fm_a @ B4
                @ ^ [Uu2: epistemic_fm_a] : D ) ) )
          @ bNF_We3666070555351734292c_fm_a ) ) ) ).

% card_of_Times_cong
thf(fact_1236_comp__fun__commute__Pow__fold,axiom,
    ( finite2334730654167944465c_fm_a
    @ ^ [X: epistemic_fm_a,A3: set_se5208064806568342746c_fm_a] : ( sup_su4305657963326700718c_fm_a @ A3 @ ( image_8582343580727714565c_fm_a @ ( insert7817948963269374698c_fm_a @ X ) @ A3 ) ) ) ).

% comp_fun_commute_Pow_fold
thf(fact_1237_comp__fun__commute__Pow__fold,axiom,
    ( finite312795530508511377_set_a
    @ ^ [X: a,A3: set_set_a] : ( sup_sup_set_set_a @ A3 @ ( image_set_a_set_a @ ( insert_a @ X ) @ A3 ) ) ) ).

% comp_fun_commute_Pow_fold
thf(fact_1238_card__of__Times__ordLeq__infinite,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ C2 )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A ) @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) ) @ bNF_We8976657667165594343c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( member409366557251323088c_fm_a
            @ ( produc5656221390238592791c_fm_a
              @ ( bNF_Ca6881012448374897667c_fm_a
                @ ( produc1842838987370488648c_fm_a @ A
                  @ ^ [Uu2: epistemic_fm_a] : B4 ) )
              @ ( bNF_Ca1305897159876240246c_fm_a @ C2 ) )
            @ bNF_We3091034443223189274c_fm_a ) ) ) ) ).

% card_of_Times_ordLeq_infinite
thf(fact_1239_card__of__Sigma__ordLeq__infinite,axiom,
    ! [B4: set_Epistemic_fm_a,I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ B4 )
     => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ I4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a )
       => ( ! [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ I4 )
             => ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( A @ X2 ) ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We8976657667165594343c_fm_a ) )
         => ( member409366557251323088c_fm_a @ ( produc5656221390238592791c_fm_a @ ( bNF_Ca6881012448374897667c_fm_a @ ( produc1842838987370488648c_fm_a @ I4 @ A ) ) @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) ) @ bNF_We3091034443223189274c_fm_a ) ) ) ) ).

% card_of_Sigma_ordLeq_infinite
thf(fact_1240_card__of__Times__infinite,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( ( member409366557251323088c_fm_a
              @ ( produc5656221390238592791c_fm_a
                @ ( bNF_Ca6881012448374897667c_fm_a
                  @ ( produc1842838987370488648c_fm_a @ A
                    @ ^ [Uu2: epistemic_fm_a] : B4 ) )
                @ ( bNF_Ca1305897159876240246c_fm_a @ A ) )
              @ bNF_We6280552541581264903c_fm_a )
            & ( member409366557251323088c_fm_a
              @ ( produc5656221390238592791c_fm_a
                @ ( bNF_Ca6881012448374897667c_fm_a
                  @ ( produc1842838987370488648c_fm_a @ B4
                    @ ^ [Uu2: epistemic_fm_a] : A ) )
                @ ( bNF_Ca1305897159876240246c_fm_a @ A ) )
              @ bNF_We6280552541581264903c_fm_a ) ) ) ) ) ).

% card_of_Times_infinite
thf(fact_1241_card__of__Times__infinite__simps_I1_J,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( member409366557251323088c_fm_a
            @ ( produc5656221390238592791c_fm_a
              @ ( bNF_Ca6881012448374897667c_fm_a
                @ ( produc1842838987370488648c_fm_a @ A
                  @ ^ [Uu2: epistemic_fm_a] : B4 ) )
              @ ( bNF_Ca1305897159876240246c_fm_a @ A ) )
            @ bNF_We6280552541581264903c_fm_a ) ) ) ) ).

% card_of_Times_infinite_simps(1)
thf(fact_1242_card__of__Times__infinite__simps_I3_J,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( member409366557251323088c_fm_a
            @ ( produc5656221390238592791c_fm_a
              @ ( bNF_Ca6881012448374897667c_fm_a
                @ ( produc1842838987370488648c_fm_a @ B4
                  @ ^ [Uu2: epistemic_fm_a] : A ) )
              @ ( bNF_Ca1305897159876240246c_fm_a @ A ) )
            @ bNF_We6280552541581264903c_fm_a ) ) ) ) ).

% card_of_Times_infinite_simps(3)
thf(fact_1243_card__of__Times__infinite__simps_I2_J,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( member4645468574724510032c_fm_a
            @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
              @ ( bNF_Ca6881012448374897667c_fm_a
                @ ( produc1842838987370488648c_fm_a @ A
                  @ ^ [Uu2: epistemic_fm_a] : B4 ) ) )
            @ bNF_We841427836613247969c_fm_a ) ) ) ) ).

% card_of_Times_infinite_simps(2)
thf(fact_1244_card__of__Times__infinite__simps_I4_J,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ A )
     => ( ( B4 != bot_bo3626323581529592678c_fm_a )
       => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ B4 ) @ ( bNF_Ca1305897159876240246c_fm_a @ A ) ) @ bNF_We8976657667165594343c_fm_a )
         => ( member4645468574724510032c_fm_a
            @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ A )
              @ ( bNF_Ca6881012448374897667c_fm_a
                @ ( produc1842838987370488648c_fm_a @ B4
                  @ ^ [Uu2: epistemic_fm_a] : A ) ) )
            @ bNF_We841427836613247969c_fm_a ) ) ) ) ).

% card_of_Times_infinite_simps(4)
thf(fact_1245_product__fold,axiom,
    ! [A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( finite3304564945125563331c_fm_a @ A )
     => ( ( finite3304564945125563331c_fm_a @ B4 )
       => ( ( produc1842838987370488648c_fm_a @ A
            @ ^ [Uu2: epistemic_fm_a] : B4 )
          = ( finite1238595690337548085c_fm_a
            @ ^ [X: epistemic_fm_a,Z5: set_Pr8948481099588399239c_fm_a] :
                ( finite1238595690337548085c_fm_a
                @ ^ [Y4: epistemic_fm_a] : ( insert4108635152042037623c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y4 ) )
                @ Z5
                @ B4 )
            @ bot_bo7958537672377389811c_fm_a
            @ A ) ) ) ) ).

% product_fold
thf(fact_1246_Card__order__Times__infinite,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a,P: set_Pr8948481099588399239c_fm_a] :
      ( ~ ( finite3304564945125563331c_fm_a @ ( field_Epistemic_fm_a @ R ) )
     => ( ( bNF_Ca1219376963944715160c_fm_a @ ( field_Epistemic_fm_a @ R ) @ R )
       => ( ( ( field_Epistemic_fm_a @ P )
           != bot_bo3626323581529592678c_fm_a )
         => ( ( member1688387778307953424c_fm_a @ ( produc7431400533060703063c_fm_a @ P @ R ) @ bNF_We8976657667165594343c_fm_a )
           => ( ( member409366557251323088c_fm_a
                @ ( produc5656221390238592791c_fm_a
                  @ ( bNF_Ca6881012448374897667c_fm_a
                    @ ( produc1842838987370488648c_fm_a @ ( field_Epistemic_fm_a @ R )
                      @ ^ [Uu2: epistemic_fm_a] : ( field_Epistemic_fm_a @ P ) ) )
                  @ R )
                @ bNF_We6280552541581264903c_fm_a )
              & ( member409366557251323088c_fm_a
                @ ( produc5656221390238592791c_fm_a
                  @ ( bNF_Ca6881012448374897667c_fm_a
                    @ ( produc1842838987370488648c_fm_a @ ( field_Epistemic_fm_a @ P )
                      @ ^ [Uu2: epistemic_fm_a] : ( field_Epistemic_fm_a @ R ) ) )
                  @ R )
                @ bNF_We6280552541581264903c_fm_a ) ) ) ) ) ) ).

% Card_order_Times_infinite
thf(fact_1247_set__product,axiom,
    ! [Xs: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( set_Pr6083076219314900284c_fm_a @ ( produc2272133018058081349c_fm_a @ Xs @ Ys ) )
      = ( produc1842838987370488648c_fm_a @ ( set_Epistemic_fm_a2 @ Xs )
        @ ^ [Uu2: epistemic_fm_a] : ( set_Epistemic_fm_a2 @ Ys ) ) ) ).

% set_product
thf(fact_1248_SIGMA__CSUM,axiom,
    ! [I4: set_Epistemic_fm_a,As: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( bNF_Ca6881012448374897667c_fm_a @ ( produc1842838987370488648c_fm_a @ I4 @ As ) )
      = ( bNF_Ca4314308936289822400c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ I4 )
        @ ^ [I2: epistemic_fm_a] : ( bNF_Ca1305897159876240246c_fm_a @ ( As @ I2 ) ) ) ) ).

% SIGMA_CSUM
thf(fact_1249_card__of__UNION__Sigma2,axiom,
    ! [I4: set_a,A: a > set_Epistemic_fm_a] :
      ( ! [I3: a,J4: a] :
          ( ( ord_less_eq_set_a @ ( insert_a @ I3 @ ( insert_a @ J4 @ bot_bot_set_a ) ) @ I4 )
         => ( ( I3 != J4 )
           => ( ( inf_in2882328776738922472c_fm_a @ ( A @ I3 ) @ ( A @ J4 ) )
              = bot_bo3626323581529592678c_fm_a ) ) )
     => ( member5314060011585795664c_fm_a @ ( produc5391312561857647255c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_3480842985853347585c_fm_a @ A @ I4 ) ) ) @ ( bNF_Ca4086118263059731103c_fm_a @ ( produc5208094418251083748c_fm_a @ I4 @ A ) ) ) @ bNF_We1465234745361447805c_fm_a ) ) ).

% card_of_UNION_Sigma2
thf(fact_1250_card__of__UNION__Sigma2,axiom,
    ! [I4: set_Epistemic_fm_a,A: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [I3: epistemic_fm_a,J4: epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ ( insert7817948963269374698c_fm_a @ I3 @ ( insert7817948963269374698c_fm_a @ J4 @ bot_bo3626323581529592678c_fm_a ) ) @ I4 )
         => ( ( I3 != J4 )
           => ( ( inf_in2882328776738922472c_fm_a @ ( A @ I3 ) @ ( A @ J4 ) )
              = bot_bo3626323581529592678c_fm_a ) ) )
     => ( member4645468574724510032c_fm_a @ ( produc8691474596463329175c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ ( comple7868773486375872231c_fm_a @ ( image_1263732536703906021c_fm_a @ A @ I4 ) ) ) @ ( bNF_Ca6881012448374897667c_fm_a @ ( produc1842838987370488648c_fm_a @ I4 @ A ) ) ) @ bNF_We841427836613247969c_fm_a ) ) ).

% card_of_UNION_Sigma2
thf(fact_1251_inf_Obounded__iff,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ ( inf_in3606484609122063093fm_a_o @ B @ C ) )
      = ( ( ord_le4043730696559282883fm_a_o @ A2 @ B )
        & ( ord_le4043730696559282883fm_a_o @ A2 @ C ) ) ) ).

% inf.bounded_iff
thf(fact_1252_inf_Obounded__iff,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ ( inf_in2882328776738922472c_fm_a @ B @ C ) )
      = ( ( ord_le3275665582123262618c_fm_a @ A2 @ B )
        & ( ord_le3275665582123262618c_fm_a @ A2 @ C ) ) ) ).

% inf.bounded_iff
thf(fact_1253_le__inf__iff,axiom,
    ! [X3: epistemic_fm_a > $o,Y: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ Y @ Z2 ) )
      = ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y )
        & ( ord_le4043730696559282883fm_a_o @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_1254_le__inf__iff,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ Y @ Z2 ) )
      = ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y )
        & ( ord_le3275665582123262618c_fm_a @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_1255_Int__subset__iff,axiom,
    ! [C2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C2 @ ( inf_in2882328776738922472c_fm_a @ A @ B4 ) )
      = ( ( ord_le3275665582123262618c_fm_a @ C2 @ A )
        & ( ord_le3275665582123262618c_fm_a @ C2 @ B4 ) ) ) ).

% Int_subset_iff
thf(fact_1256_if__image__distrib,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > epistemic_fm_a,G4: set_Epistemic_fm_a > epistemic_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( image_3376480847214465317c_fm_a
        @ ^ [X: set_Epistemic_fm_a] : ( if_Epistemic_fm_a @ ( P4 @ X ) @ ( F @ X ) @ ( G4 @ X ) )
        @ S )
      = ( sup_su1367922730591523534c_fm_a @ ( image_3376480847214465317c_fm_a @ F @ ( inf_in1884693029477671368c_fm_a @ S @ ( collec2519470961442302949c_fm_a @ P4 ) ) )
        @ ( image_3376480847214465317c_fm_a @ G4
          @ ( inf_in1884693029477671368c_fm_a @ S
            @ ( collec2519470961442302949c_fm_a
              @ ^ [X: set_Epistemic_fm_a] :
                  ~ ( P4 @ X ) ) ) ) ) ) ).

% if_image_distrib
thf(fact_1257_if__image__distrib,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,G4: epistemic_fm_a > epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( image_4449434806354059013c_fm_a
        @ ^ [X: epistemic_fm_a] : ( if_Epistemic_fm_a @ ( P4 @ X ) @ ( F @ X ) @ ( G4 @ X ) )
        @ S )
      = ( sup_su1367922730591523534c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ ( inf_in2882328776738922472c_fm_a @ S @ ( collec4904205152690461189c_fm_a @ P4 ) ) )
        @ ( image_4449434806354059013c_fm_a @ G4
          @ ( inf_in2882328776738922472c_fm_a @ S
            @ ( collec4904205152690461189c_fm_a
              @ ^ [X: epistemic_fm_a] :
                  ~ ( P4 @ X ) ) ) ) ) ) ).

% if_image_distrib
thf(fact_1258_if__image__distrib,axiom,
    ! [P4: set_Epistemic_fm_a > $o,F: set_Epistemic_fm_a > a,G4: set_Epistemic_fm_a > a,S: set_se5208064806568342746c_fm_a] :
      ( ( image_4497856574827002249fm_a_a
        @ ^ [X: set_Epistemic_fm_a] : ( if_a @ ( P4 @ X ) @ ( F @ X ) @ ( G4 @ X ) )
        @ S )
      = ( sup_sup_set_a @ ( image_4497856574827002249fm_a_a @ F @ ( inf_in1884693029477671368c_fm_a @ S @ ( collec2519470961442302949c_fm_a @ P4 ) ) )
        @ ( image_4497856574827002249fm_a_a @ G4
          @ ( inf_in1884693029477671368c_fm_a @ S
            @ ( collec2519470961442302949c_fm_a
              @ ^ [X: set_Epistemic_fm_a] :
                  ~ ( P4 @ X ) ) ) ) ) ) ).

% if_image_distrib
thf(fact_1259_if__image__distrib,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > a,G4: epistemic_fm_a > a,S: set_Epistemic_fm_a] :
      ( ( image_7228943142519265129fm_a_a
        @ ^ [X: epistemic_fm_a] : ( if_a @ ( P4 @ X ) @ ( F @ X ) @ ( G4 @ X ) )
        @ S )
      = ( sup_sup_set_a @ ( image_7228943142519265129fm_a_a @ F @ ( inf_in2882328776738922472c_fm_a @ S @ ( collec4904205152690461189c_fm_a @ P4 ) ) )
        @ ( image_7228943142519265129fm_a_a @ G4
          @ ( inf_in2882328776738922472c_fm_a @ S
            @ ( collec4904205152690461189c_fm_a
              @ ^ [X: epistemic_fm_a] :
                  ~ ( P4 @ X ) ) ) ) ) ) ).

% if_image_distrib
thf(fact_1260_inf_OcoboundedI2,axiom,
    ! [B: epistemic_fm_a > $o,C: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B @ C )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A2 @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_1261_inf_OcoboundedI2,axiom,
    ! [B: set_Epistemic_fm_a,C: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B @ C )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A2 @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_1262_inf_OcoboundedI1,axiom,
    ! [A2: epistemic_fm_a > $o,C: epistemic_fm_a > $o,B: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A2 @ C )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A2 @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_1263_inf_OcoboundedI1,axiom,
    ! [A2: set_Epistemic_fm_a,C: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A2 @ C )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A2 @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_1264_inf_Oabsorb__iff2,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [B2: epistemic_fm_a > $o,A4: epistemic_fm_a > $o] :
          ( ( inf_in3606484609122063093fm_a_o @ A4 @ B2 )
          = B2 ) ) ) ).

% inf.absorb_iff2
thf(fact_1265_inf_Oabsorb__iff2,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [B2: set_Epistemic_fm_a,A4: set_Epistemic_fm_a] :
          ( ( inf_in2882328776738922472c_fm_a @ A4 @ B2 )
          = B2 ) ) ) ).

% inf.absorb_iff2
thf(fact_1266_inf_Oabsorb__iff1,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
          ( ( inf_in3606484609122063093fm_a_o @ A4 @ B2 )
          = A4 ) ) ) ).

% inf.absorb_iff1
thf(fact_1267_inf_Oabsorb__iff1,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
          ( ( inf_in2882328776738922472c_fm_a @ A4 @ B2 )
          = A4 ) ) ) ).

% inf.absorb_iff1
thf(fact_1268_inf_Ocobounded2,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A2 @ B ) @ B ) ).

% inf.cobounded2
thf(fact_1269_inf_Ocobounded2,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A2 @ B ) @ B ) ).

% inf.cobounded2
thf(fact_1270_inf_Ocobounded1,axiom,
    ! [A2: epistemic_fm_a > $o,B: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A2 @ B ) @ A2 ) ).

% inf.cobounded1
thf(fact_1271_inf_Ocobounded1,axiom,
    ! [A2: set_Epistemic_fm_a,B: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A2 @ B ) @ A2 ) ).

% inf.cobounded1
thf(fact_1272_inf_Oorder__iff,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [A4: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
          ( A4
          = ( inf_in3606484609122063093fm_a_o @ A4 @ B2 ) ) ) ) ).

% inf.order_iff
thf(fact_1273_inf_Oorder__iff,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
          ( A4
          = ( inf_in2882328776738922472c_fm_a @ A4 @ B2 ) ) ) ) ).

% inf.order_iff
thf(fact_1274_inf__greatest,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 @ X3 @ Z2 )
       => ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ Y @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_1275_inf__greatest,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 @ X3 @ Z2 )
       => ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ Y @ Z2 ) ) ) ) ).

% inf_greatest

% Helper facts (9)
thf(help_If_2_1_If_001tf__a_T,axiom,
    ! [X3: a,Y: a] :
      ( ( if_a @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__a_T,axiom,
    ! [X3: a,Y: a] :
      ( ( if_a @ $true @ X3 @ Y )
      = X3 ) ).

thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( if_set_a @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( if_set_a @ $true @ X3 @ Y )
      = X3 ) ).

thf(help_If_2_1_If_001t__Epistemic____Logic__Ofm_Itf__a_J_T,axiom,
    ! [X3: epistemic_fm_a,Y: epistemic_fm_a] :
      ( ( if_Epistemic_fm_a @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Epistemic____Logic__Ofm_Itf__a_J_T,axiom,
    ! [X3: epistemic_fm_a,Y: epistemic_fm_a] :
      ( ( if_Epistemic_fm_a @ $true @ X3 @ Y )
      = X3 ) ).

thf(help_If_3_1_If_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
    ! [P4: $o] :
      ( ( P4 = $true )
      | ( P4 = $false ) ) ).

thf(help_If_2_1_If_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( if_set2375185401397246656c_fm_a @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
    ! [X3: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( if_set2375185401397246656c_fm_a @ $true @ X3 @ Y )
      = X3 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    epistemic_AK_a @ a2 @ ( 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 ) ) ) ).

%------------------------------------------------------------------------------