%------------------------------------------------------------------------------
% 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_00291_009569__6578178_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1642 ( 657 unt; 359 typ;   0 def)
%            Number of atoms       : 4271 (1367 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives : 14189 ( 437   ~;  68   |; 275   &;11524   @)
%                                         (   0 <=>;1885  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Number of types       :   40 (  39 usr)
%            Number of type conns  : 1666 (1666   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  323 ( 320 usr;  19 con; 0-5 aty)
%            Number of variables   : 4530 ( 415   ^;3995   !; 120   ?;4530   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:12:16.600
%------------------------------------------------------------------------------
% Could-be-implicit typings (39)
thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_Mt__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Product____Type__Ounit_J_J,type,
    episte1560738328020401952t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_Mt__Set__Oset_Itf__b_J_Mt__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_Itf__b_J_Mt__Product____Type__Ounit_J_J,type,
    episte8559422309061589728t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_Mt__Set__Oset_I_Eo_J_Mt__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_I_Eo_J_Mt__Product____Type__Ounit_J_J,type,
    episte4442589092411611552t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_I_Eo_Mt__Set__Oset_I_Eo_J_Mt__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_I_Eo_J_Mt__Product____Type__Ounit_J_J,type,
    episte399968703042273926t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__b_Mtf__b_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__b_Mt__Product____Type__Ounit_J_J,type,
    episte4519467831615171103t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__b_Mtf__a_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__a_Mt__Product____Type__Ounit_J_J,type,
    episte7477074710132283359t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_Mtf__b_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__b_Mt__Product____Type__Ounit_J_J,type,
    episte3224730989885420256t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_Mtf__a_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__a_Mt__Product____Type__Ounit_J_J,type,
    episte6182337868402532512t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_I_Eo_Mtf__b_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__b_Mt__Product____Type__Ounit_J_J,type,
    episte2543566300658443718t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_I_Eo_Mtf__a_Mt__Epistemic____Logic__Okripke__Okripke____ext_Itf__a_Mt__Product____Type__Ounit_J_J,type,
    episte5501173179175555974t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__b_M_Eo_Mt__Epistemic____Logic__Okripke__Okripke____ext_I_Eo_Mt__Product____Type__Ounit_J_J,type,
    episte6655095512717024223t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_Itf__a_M_Eo_Mt__Epistemic____Logic__Okripke__Okripke____ext_I_Eo_Mt__Product____Type__Ounit_J_J,type,
    episte3259645218793129376t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Oframe__Oframe____ext_I_Eo_M_Eo_Mt__Epistemic____Logic__Okripke__Okripke____ext_I_Eo_Mt__Product____Type__Ounit_J_J,type,
    episte8859593475650739846t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Product____Type__Ounit_J,type,
    episte1193835314949844379t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    set_Pr8948481099588399239c_fm_a: $tType ).

thf(ty_n_t__Epistemic____Logic__Okripke__Okripke____ext_Itf__b_Mt__Product____Type__Ounit_J,type,
    episte2291185870209430742t_unit: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    episte5999154429349999510c_fm_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    set_se5208064806568342746c_fm_a: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte740340785640729014c_fm_a: $tType ).

thf(ty_n_t__List__Olist_It__Epistemic____Logic__Ofm_Itf__b_J_J,type,
    list_Epistemic_fm_b: $tType ).

thf(ty_n_t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    list_Epistemic_fm_a: $tType ).

thf(ty_n_t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__b_J_J,type,
    set_Epistemic_fm_b: $tType ).

thf(ty_n_t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    set_Epistemic_fm_a: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_It__Set__Oset_Itf__b_J_J,type,
    epistemic_fm_set_b: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_It__Set__Oset_I_Eo_J_J,type,
    epistemic_fm_set_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
    set_set_b: $tType ).

thf(ty_n_t__List__Olist_It__Set__Oset_I_Eo_J_J,type,
    list_set_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    set_set_o: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_Itf__b_J,type,
    epistemic_fm_b: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_Itf__a_J,type,
    epistemic_fm_a: $tType ).

thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
    list_char: $tType ).

thf(ty_n_t__Epistemic____Logic__Ofm_I_Eo_J,type,
    epistemic_fm_o: $tType ).

thf(ty_n_t__Product____Type__Ounit,type,
    product_unit: $tType ).

thf(ty_n_t__Set__Oset_Itf__b_J,type,
    set_b: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

thf(ty_n_t__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (320)
thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    bNF_Ca1305897159876240246c_fm_a: set_Epistemic_fm_a > set_Pr8948481099588399239c_fm_a ).

thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_I_Eo_J,type,
    boolea379910186789422830_set_o: ( set_o > set_o > set_o ) > ( set_o > set_o > set_o ) > ( set_o > set_o ) > set_o > set_o > $o ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001_Eo,type,
    complete_Inf_Inf_o: set_o > $o ).

thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_Eo_J,type,
    comple3063163877087187839_set_o: set_set_o > set_o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_Eo_J,type,
    comple90263536869209701_set_o: set_set_o > set_o ).

thf(sy_c_Epistemic__Logic_OAK_001_Eo,type,
    epistemic_AK_o: ( epistemic_fm_o > $o ) > epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_OAK_001tf__a,type,
    epistemic_AK_a: ( epistemic_fm_a > $o ) > epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_OAK_001tf__b,type,
    epistemic_AK_b: ( epistemic_fm_b > $o ) > epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_OAx4_001_Eo,type,
    epistemic_Ax4_o: epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_OAx4_001tf__a,type,
    epistemic_Ax4_a: epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_OAx4_001tf__b,type,
    epistemic_Ax4_b: epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_OAx5_001_Eo,type,
    epistemic_Ax5_o: epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_OAx5_001tf__a,type,
    epistemic_Ax5_a: epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_OAx5_001tf__b,type,
    epistemic_Ax5_b: epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_OAxB_001_Eo,type,
    epistemic_AxB_o: epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_OAxB_001tf__a,type,
    epistemic_AxB_a: epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_OAxB_001tf__b,type,
    epistemic_AxB_b: epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_OAxT_001_Eo,type,
    epistemic_AxT_o: epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_OAxT_001tf__a,type,
    epistemic_AxT_a: epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_OAxT_001tf__b,type,
    epistemic_AxT_b: epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001_Eo_001t__Epistemic____Logic__Okripke__Okripke____ext_I_Eo_Mt__Product____Type__Ounit_J,type,
    episte2052337558702062413t_unit: episte3259645218793129376t_unit > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001t__Set__Oset_I_Eo_J_001t__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_I_Eo_J_Mt__Product____Type__Ounit_J,type,
    episte905247779971886925t_unit: episte4442589092411611552t_unit > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_001t__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Product____Type__Ounit_J,type,
    episte2449151000174023629t_unit: episte1560738328020401952t_unit > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001t__Set__Oset_Itf__b_J_001t__Epistemic____Logic__Okripke__Okripke____ext_It__Set__Oset_Itf__b_J_Mt__Product____Type__Ounit_J,type,
    episte3789892348602042125t_unit: episte8559422309061589728t_unit > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001tf__a_001t__Epistemic____Logic__Okripke__Okripke____ext_Itf__a_Mt__Product____Type__Ounit_J,type,
    episte2339904321507024205t_unit: episte6182337868402532512t_unit > $o ).

thf(sy_c_Epistemic__Logic_OEuclidean_001tf__a_001tf__b_001t__Epistemic____Logic__Okripke__Okripke____ext_Itf__b_Mt__Product____Type__Ounit_J,type,
    episte6418945320598494989t_unit: episte3224730989885420256t_unit > $o ).

thf(sy_c_Epistemic__Logic_Oconsistent_001tf__a,type,
    episte2285483198712856226tent_a: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Oeval_001_Eo,type,
    epistemic_eval_o: ( list_char > $o ) > ( epistemic_fm_o > $o ) > epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_Oeval_001tf__a,type,
    epistemic_eval_a: ( list_char > $o ) > ( epistemic_fm_a > $o ) > epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Oeval_001tf__b,type,
    epistemic_eval_b: ( list_char > $o ) > ( epistemic_fm_b > $o ) > epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001_Eo,type,
    epistemic_Con_o: epistemic_fm_o > epistemic_fm_o > epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001t__Set__Oset_I_Eo_J,type,
    epistemic_Con_set_o: epistemic_fm_set_o > epistemic_fm_set_o > epistemic_fm_set_o ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte8719284489194433015c_fm_a: episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001t__Set__Oset_Itf__b_J,type,
    epistemic_Con_set_b: epistemic_fm_set_b > epistemic_fm_set_b > epistemic_fm_set_b ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001tf__a,type,
    epistemic_Con_a: epistemic_fm_a > epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OCon_001tf__b,type,
    epistemic_Con_b: epistemic_fm_b > epistemic_fm_b > epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001_Eo,type,
    epistemic_Dis_o: epistemic_fm_o > epistemic_fm_o > epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001t__Set__Oset_I_Eo_J,type,
    epistemic_Dis_set_o: epistemic_fm_set_o > epistemic_fm_set_o > epistemic_fm_set_o ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte9190102072588321003c_fm_a: episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001t__Set__Oset_Itf__b_J,type,
    epistemic_Dis_set_b: epistemic_fm_set_b > epistemic_fm_set_b > epistemic_fm_set_b ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001tf__a,type,
    epistemic_Dis_a: epistemic_fm_a > epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_ODis_001tf__b,type,
    epistemic_Dis_b: epistemic_fm_b > epistemic_fm_b > epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_OFF_001_Eo,type,
    epistemic_FF_o: epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_OFF_001tf__a,type,
    epistemic_FF_a: epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OFF_001tf__b,type,
    epistemic_FF_b: epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001_Eo,type,
    epistemic_Imp_o: epistemic_fm_o > epistemic_fm_o > epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001t__Set__Oset_I_Eo_J,type,
    epistemic_Imp_set_o: epistemic_fm_set_o > epistemic_fm_set_o > epistemic_fm_set_o ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte5200161025749276397c_fm_a: episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001t__Set__Oset_Itf__b_J,type,
    epistemic_Imp_set_b: epistemic_fm_set_b > epistemic_fm_set_b > epistemic_fm_set_b ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001tf__a,type,
    epistemic_Imp_a: epistemic_fm_a > epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OImp_001tf__b,type,
    epistemic_Imp_b: epistemic_fm_b > epistemic_fm_b > epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001_Eo,type,
    epistemic_K_o: $o > epistemic_fm_o > epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001t__Set__Oset_I_Eo_J,type,
    epistemic_K_set_o: set_o > epistemic_fm_set_o > epistemic_fm_set_o ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte3013695276341575662c_fm_a: set_Epistemic_fm_a > episte5999154429349999510c_fm_a > episte5999154429349999510c_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001t__Set__Oset_Itf__b_J,type,
    epistemic_K_set_b: set_b > epistemic_fm_set_b > epistemic_fm_set_b ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001tf__a,type,
    epistemic_K_a: a > epistemic_fm_a > epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OK_001tf__b,type,
    epistemic_K_b: b > epistemic_fm_b > epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_OPro_001_Eo,type,
    epistemic_Pro_o: list_char > epistemic_fm_o ).

thf(sy_c_Epistemic__Logic_Ofm_OPro_001tf__a,type,
    epistemic_Pro_a: list_char > epistemic_fm_a ).

thf(sy_c_Epistemic__Logic_Ofm_OPro_001tf__b,type,
    epistemic_Pro_b: list_char > epistemic_fm_b ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001_Eo,type,
    epistemic_pred_fm_o: ( $o > $o ) > epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    episte3114992851182798545c_fm_a: ( epistemic_fm_a > $o ) > episte740340785640729014c_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001t__Set__Oset_I_Eo_J,type,
    episte2463951554458028079_set_o: ( set_o > $o ) > epistemic_fm_set_o > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    episte1367365995573110961c_fm_a: ( set_Epistemic_fm_a > $o ) > episte5999154429349999510c_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001t__Set__Oset_Itf__b_J,type,
    episte1592375260622591510_set_b: ( set_b > $o ) > epistemic_fm_set_b > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001tf__a,type,
    epistemic_pred_fm_a: ( a > $o ) > epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Opred__fm_001tf__b,type,
    epistemic_pred_fm_b: ( b > $o ) > epistemic_fm_b > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Orel__fm_001_Eo_001_Eo,type,
    epistemic_rel_fm_o_o: ( $o > $o > $o ) > epistemic_fm_o > epistemic_fm_o > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Orel__fm_001_Eo_001tf__a,type,
    epistemic_rel_fm_o_a: ( $o > a > $o ) > epistemic_fm_o > epistemic_fm_a > $o ).

thf(sy_c_Epistemic__Logic_Ofm_Orel__fm_001_Eo_001tf__b,type,
    epistemic_rel_fm_o_b: ( $o > b > $o ) > epistemic_fm_o > epistemic_fm_b > $o ).

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thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__b_M_Eo_J,type,
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thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
    bot_bot_set_b: set_b ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__b_M_Eo_J,type,
    ord_less_b_o: ( b > $o ) > ( b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
    ord_less_set_o: set_o > set_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__b_J,type,
    ord_less_set_b: set_b > set_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_I_Eo_J_M_Eo_J,type,
    ord_le1608183570384977833fm_o_o: ( epistemic_fm_o > $o ) > ( epistemic_fm_o > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_It__Epistemic____Logic__Ofm_Itf__a_J_J_M_Eo_J,type,
    ord_le7240545311762076327fm_a_o: ( episte740340785640729014c_fm_a > $o ) > ( episte740340785640729014c_fm_a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J_J,type,
    ord_le3934200179093585166fm_a_o: ( epistemic_fm_a > epistemic_fm_a > $o ) > ( epistemic_fm_a > epistemic_fm_a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J,type,
    ord_le4043730696559282883fm_a_o: ( epistemic_fm_a > $o ) > ( epistemic_fm_a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_Itf__b_J_M_062_It__Epistemic____Logic__Ofm_Itf__b_J_M_Eo_J_J,type,
    ord_le7238499765113434702fm_b_o: ( epistemic_fm_b > epistemic_fm_b > $o ) > ( epistemic_fm_b > epistemic_fm_b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Epistemic____Logic__Ofm_Itf__b_J_M_Eo_J,type,
    ord_le1256275114586606850fm_b_o: ( epistemic_fm_b > $o ) > ( epistemic_fm_b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
    ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
    ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J,type,
    ord_less_eq_b_b_o: ( b > b > $o ) > ( b > b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__b_M_Eo_J,type,
    ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
    ord_less_eq_o: $o > $o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    ord_le3275665582123262618c_fm_a: set_Epistemic_fm_a > set_Epistemic_fm_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__b_J_J,type,
    ord_le3346699622169608603c_fm_b: set_Epistemic_fm_b > set_Epistemic_fm_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    ord_le4374716579403074808_set_o: set_set_o > set_set_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    ord_le7112219575281605754c_fm_a: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__b_J_J,type,
    ord_le3795704787696855135_set_b: set_set_b > set_set_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
    ord_less_eq_set_b: set_b > set_b > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_M_Eo_J,type,
    top_top_o_o: $o > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
    top_top_set_o: set_o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    top_to7796028867103199306c_fm_a: set_Epistemic_fm_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    top_top_set_set_o: set_set_o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
    top_top_set_b: set_b ).

thf(sy_c_Product__Type_OUnity,type,
    product_Unity: product_unit ).

thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(sy_c_Set_OCollect_001_Eo,type,
    collect_o: ( $o > $o ) > set_o ).

thf(sy_c_Set_OCollect_001t__Epistemic____Logic__Ofm_Itf__a_J,type,
    collec4904205152690461189c_fm_a: ( epistemic_fm_a > $o ) > set_Epistemic_fm_a ).

thf(sy_c_Set_OCollect_001t__Set__Oset_I_Eo_J,type,
    collect_set_o: ( set_o > $o ) > set_set_o ).

thf(sy_c_Set_OCollect_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    collec2519470961442302949c_fm_a: ( set_Epistemic_fm_a > $o ) > set_se5208064806568342746c_fm_a ).

thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__b_J,type,
    collect_set_b: ( set_b > $o ) > set_set_b ).

thf(sy_c_Set_OCollect_001tf__a,type,
    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_OCollect_001tf__b,type,
    collect_b: ( b > $o ) > set_b ).

thf(sy_c_Set_OPow_001_Eo,type,
    pow_o: set_o > set_set_o ).

thf(sy_c_Set_Obind_001_Eo_001_Eo,type,
    bind_o_o: set_o > ( $o > set_o ) > set_o ).

thf(sy_c_Set_Ofilter_001tf__b,type,
    filter_b: ( b > $o ) > set_b > set_b ).

thf(sy_c_Set_Oimage_001_Eo_001_Eo,type,
    image_o_o: ( $o > $o ) > set_o > set_o ).

thf(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_I_Eo_J,type,
    image_o_set_o: ( $o > set_o ) > set_o > set_set_o ).

thf(sy_c_Set_Oimage_001_Eo_001tf__b,type,
    image_o_b: ( $o > b ) > set_o > set_b ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_Itf__b_J_001t__Set__Oset_Itf__b_J,type,
    image_set_b_set_b: ( set_b > set_b ) > set_set_b > set_set_b ).

thf(sy_c_Set_Oimage_001tf__b_001_Eo,type,
    image_b_o: ( b > $o ) > set_b > set_o ).

thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
    image_b_b: ( b > b ) > set_b > set_b ).

thf(sy_c_Set_Oinsert_001_Eo,type,
    insert_o: $o > set_o > set_o ).

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

thf(sy_c_Set_Oinsert_001t__Set__Oset_I_Eo_J,type,
    insert_set_o: set_o > set_set_o > set_set_o ).

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

thf(sy_c_Set_Oinsert_001tf__b,type,
    insert_b: b > set_b > set_b ).

thf(sy_c_Set_Ois__empty_001_Eo,type,
    is_empty_o: set_o > $o ).

thf(sy_c_Set_Ois__singleton_001_Eo,type,
    is_singleton_o: set_o > $o ).

thf(sy_c_Set_Ois__singleton_001tf__b,type,
    is_singleton_b: set_b > $o ).

thf(sy_c_Set_Opairwise_001_Eo,type,
    pairwise_o: ( $o > $o > $o ) > set_o > $o ).

thf(sy_c_Set_Opairwise_001tf__b,type,
    pairwise_b: ( b > b > $o ) > set_b > $o ).

thf(sy_c_Set_Oremove_001_Eo,type,
    remove_o: $o > set_o > set_o ).

thf(sy_c_Set_Oremove_001tf__b,type,
    remove_b: b > set_b > set_b ).

thf(sy_c_Set_Othe__elem_001_Eo,type,
    the_elem_o: set_o > $o ).

thf(sy_c_Set_Ovimage_001_Eo_001_Eo,type,
    vimage_o_o: ( $o > $o ) > set_o > set_o ).

thf(sy_c_Set_Ovimage_001_Eo_001tf__b,type,
    vimage_o_b: ( $o > b ) > set_b > set_o ).

thf(sy_c_Set_Ovimage_001tf__b_001_Eo,type,
    vimage_b_o: ( b > $o ) > set_o > set_b ).

thf(sy_c_Set_Ovimage_001tf__b_001tf__b,type,
    vimage_b_b: ( b > b ) > set_b > set_b ).

thf(sy_c_Stalnaker__Logic_OAx__2_001_Eo,type,
    stalnaker_Ax_2_o: epistemic_fm_o > $o ).

thf(sy_c_Stalnaker__Logic_OAx__2_001tf__a,type,
    stalnaker_Ax_2_a: epistemic_fm_a > $o ).

thf(sy_c_Stalnaker__Logic_OAx__2_001tf__b,type,
    stalnaker_Ax_2_b: epistemic_fm_b > $o ).

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

thf(sy_c_Stalnaker__Logic_Oweakly__directed_001tf__a_001t__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J,type,
    stalna9100096441501500634c_fm_a: episte1560738328020401952t_unit > $o ).

thf(sy_c_Stalnaker__Logic_Oweakly__directed_001tf__a_001tf__b,type,
    stalna7560619637984394463ed_a_b: episte3224730989885420256t_unit > $o ).

thf(sy_c_member_001_Eo,type,
    member_o: $o > set_o > $o ).

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

thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
    member_set_o: set_o > set_set_o > $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__b_J,type,
    member_set_b: set_b > set_set_b > $o ).

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

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_v_M,type,
    m: episte3224730989885420256t_unit ).

thf(sy_v_i,type,
    i: a ).

thf(sy_v_p,type,
    p: epistemic_fm_a ).

thf(sy_v_w,type,
    w: b ).

% Relevant facts (1279)
thf(fact_0_assms_I1_J,axiom,
    stalna7560619637984394463ed_a_b @ m ).

% assms(1)
thf(fact_1_assms_I2_J,axiom,
    member_b @ w @ ( episte1782384855165018035t_unit @ m ) ).

% assms(2)
thf(fact_2_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_3_Imp__intro,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( ( episte295617885132580261cs_a_b @ M @ W @ P )
       => ( episte295617885132580261cs_a_b @ M @ W @ Q ) )
     => ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ P @ Q ) ) ) ).

% Imp_intro
thf(fact_4_fm_Oinject_I5_J,axiom,
    ! [X61: b,X62: epistemic_fm_b,Y61: b,Y62: epistemic_fm_b] :
      ( ( ( epistemic_K_b @ X61 @ X62 )
        = ( epistemic_K_b @ Y61 @ Y62 ) )
      = ( ( X61 = Y61 )
        & ( X62 = Y62 ) ) ) ).

% fm.inject(5)
thf(fact_5_fm_Oinject_I5_J,axiom,
    ! [X61: $o,X62: epistemic_fm_o,Y61: $o,Y62: epistemic_fm_o] :
      ( ( ( epistemic_K_o @ X61 @ X62 )
        = ( epistemic_K_o @ Y61 @ Y62 ) )
      = ( ( X61 = Y61 )
        & ( X62 = Y62 ) ) ) ).

% fm.inject(5)
thf(fact_6_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_7_fm_Oinject_I4_J,axiom,
    ! [X51: epistemic_fm_b,X52: epistemic_fm_b,Y51: epistemic_fm_b,Y52: epistemic_fm_b] :
      ( ( ( epistemic_Imp_b @ X51 @ X52 )
        = ( epistemic_Imp_b @ Y51 @ Y52 ) )
      = ( ( X51 = Y51 )
        & ( X52 = Y52 ) ) ) ).

% fm.inject(4)
thf(fact_8_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_9_Ax__2_Ocases,axiom,
    ! [A: epistemic_fm_o] :
      ( ( stalnaker_Ax_2_o @ A )
     => ~ ! [I: $o,P2: epistemic_fm_o] :
            ( A
           != ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ P2 ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ P2 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ).

% Ax_2.cases
thf(fact_10_Ax__2_Ocases,axiom,
    ! [A: epistemic_fm_b] :
      ( ( stalnaker_Ax_2_b @ A )
     => ~ ! [I: b,P2: epistemic_fm_b] :
            ( A
           != ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ P2 ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ P2 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ).

% Ax_2.cases
thf(fact_11_Ax__2_Ocases,axiom,
    ! [A: epistemic_fm_a] :
      ( ( stalnaker_Ax_2_a @ A )
     => ~ ! [I: a,P2: epistemic_fm_a] :
            ( A
           != ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P2 ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% Ax_2.cases
thf(fact_12_Ax__2_Osimps,axiom,
    ( stalnaker_Ax_2_o
    = ( ^ [A2: epistemic_fm_o] :
        ? [I2: $o,P3: epistemic_fm_o] :
          ( A2
          = ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ P3 ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ P3 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ) ).

% Ax_2.simps
thf(fact_13_Ax__2_Osimps,axiom,
    ( stalnaker_Ax_2_b
    = ( ^ [A2: epistemic_fm_b] :
        ? [I2: b,P3: epistemic_fm_b] :
          ( A2
          = ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ P3 ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ P3 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ) ).

% Ax_2.simps
thf(fact_14_Ax__2_Osimps,axiom,
    ( stalnaker_Ax_2_a
    = ( ^ [A2: epistemic_fm_a] :
        ? [I2: a,P3: epistemic_fm_a] :
          ( A2
          = ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P3 ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% Ax_2.simps
thf(fact_15_Ax__2_Ointros,axiom,
    ! [I3: $o,P: epistemic_fm_o] : ( stalnaker_Ax_2_o @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ).

% Ax_2.intros
thf(fact_16_Ax__2_Ointros,axiom,
    ! [I3: b,P: epistemic_fm_b] : ( stalnaker_Ax_2_b @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ).

% Ax_2.intros
thf(fact_17_Ax__2_Ointros,axiom,
    ! [I3: a,P: epistemic_fm_a] : ( stalnaker_Ax_2_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% Ax_2.intros
thf(fact_18_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_19_semantics_Osimps_I1_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b] :
      ~ ( episte295617885132580261cs_a_b @ M @ W @ epistemic_FF_a ) ).

% semantics.simps(1)
thf(fact_20_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_21_semantics_Osimps_I5_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( episte295617885132580261cs_a_b @ M @ W @ P )
       => ( episte295617885132580261cs_a_b @ M @ W @ Q ) ) ) ).

% semantics.simps(5)
thf(fact_22_fm_Odistinct_I9_J,axiom,
    ! [X61: b,X62: epistemic_fm_b] :
      ( epistemic_FF_b
     != ( epistemic_K_b @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_23_fm_Odistinct_I9_J,axiom,
    ! [X61: $o,X62: epistemic_fm_o] :
      ( epistemic_FF_o
     != ( epistemic_K_o @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_24_fm_Odistinct_I9_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_25_fm_Odistinct_I7_J,axiom,
    ! [X51: epistemic_fm_o,X52: epistemic_fm_o] :
      ( epistemic_FF_o
     != ( epistemic_Imp_o @ X51 @ X52 ) ) ).

% fm.distinct(7)
thf(fact_26_fm_Odistinct_I7_J,axiom,
    ! [X51: epistemic_fm_b,X52: epistemic_fm_b] :
      ( epistemic_FF_b
     != ( epistemic_Imp_b @ X51 @ X52 ) ) ).

% fm.distinct(7)
thf(fact_27_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_28_fm_Odistinct_I29_J,axiom,
    ! [X51: epistemic_fm_o,X52: epistemic_fm_o,X61: $o,X62: epistemic_fm_o] :
      ( ( epistemic_Imp_o @ X51 @ X52 )
     != ( epistemic_K_o @ X61 @ X62 ) ) ).

% fm.distinct(29)
thf(fact_29_fm_Odistinct_I29_J,axiom,
    ! [X51: epistemic_fm_b,X52: epistemic_fm_b,X61: b,X62: epistemic_fm_b] :
      ( ( epistemic_Imp_b @ X51 @ X52 )
     != ( epistemic_K_b @ X61 @ X62 ) ) ).

% fm.distinct(29)
thf(fact_30_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_31_generalization,axiom,
    ! [P: epistemic_fm_a,W: b,M: episte3224730989885420256t_unit,I3: a] :
      ( ! [M2: episte3224730989885420256t_unit,X: b] :
          ( ( member_b @ X @ ( episte1782384855165018035t_unit @ M2 ) )
         => ( episte295617885132580261cs_a_b @ M2 @ X @ P ) )
     => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
       => ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_32_generalization,axiom,
    ! [P: epistemic_fm_a,W: $o,M: episte3259645218793129376t_unit,I3: a] :
      ( ! [M2: episte3259645218793129376t_unit,X: $o] :
          ( ( member_o @ X @ ( episte876160520765907443t_unit @ M2 ) )
         => ( episte1100597067981672766cs_a_o @ M2 @ X @ P ) )
     => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
       => ( episte1100597067981672766cs_a_o @ M @ W @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_33_generalization,axiom,
    ! [P: epistemic_fm_a,W: a,M: episte6182337868402532512t_unit,I3: a] :
      ( ! [M2: episte6182337868402532512t_unit,X: a] :
          ( ( member_a @ X @ ( episte6926715892928323059t_unit @ M2 ) )
         => ( episte295617885132580260cs_a_a @ M2 @ X @ P ) )
     => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
       => ( episte295617885132580260cs_a_a @ M @ W @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_34_generalization,axiom,
    ! [P: epistemic_fm_b,W: b,M: episte4519467831615171103t_unit,I3: b] :
      ( ! [M2: episte4519467831615171103t_unit,X: b] :
          ( ( member_b @ X @ ( episte7096680817873233778t_unit @ M2 ) )
         => ( episte6731534340014680036cs_b_b @ M2 @ X @ P ) )
     => ( ( member_b @ W @ ( episte7096680817873233778t_unit @ M ) )
       => ( episte6731534340014680036cs_b_b @ M @ W @ ( epistemic_K_b @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_35_generalization,axiom,
    ! [P: epistemic_fm_b,W: $o,M: episte6655095512717024223t_unit,I3: b] :
      ( ! [M2: episte6655095512717024223t_unit,X: $o] :
          ( ( member_o @ X @ ( episte8156305138475616434t_unit @ M2 ) )
         => ( episte7424746705372054269cs_b_o @ M2 @ X @ P ) )
     => ( ( member_o @ W @ ( episte8156305138475616434t_unit @ M ) )
       => ( episte7424746705372054269cs_b_o @ M @ W @ ( epistemic_K_b @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_36_generalization,axiom,
    ! [P: epistemic_fm_b,W: a,M: episte7477074710132283359t_unit,I3: b] :
      ( ! [M2: episte7477074710132283359t_unit,X: a] :
          ( ( member_a @ X @ ( episte3017639818781762994t_unit @ M2 ) )
         => ( episte6731534340014680035cs_b_a @ M2 @ X @ P ) )
     => ( ( member_a @ W @ ( episte3017639818781762994t_unit @ M ) )
       => ( episte6731534340014680035cs_b_a @ M @ W @ ( epistemic_K_b @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_37_generalization,axiom,
    ! [P: epistemic_fm_o,W: b,M: episte2543566300658443718t_unit,I3: $o] :
      ( ! [M2: episte2543566300658443718t_unit,X: b] :
          ( ( member_b @ X @ ( episte9142089827432095385t_unit @ M2 ) )
         => ( episte1021116911515925003cs_o_b @ M2 @ X @ P ) )
     => ( ( member_b @ W @ ( episte9142089827432095385t_unit @ M ) )
       => ( episte1021116911515925003cs_o_b @ M @ W @ ( epistemic_K_o @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_38_generalization,axiom,
    ! [P: epistemic_fm_o,W: $o,M: episte8859593475650739846t_unit,I3: $o] :
      ( ! [M2: episte8859593475650739846t_unit,X: $o] :
          ( ( member_o @ X @ ( episte1038022579713443545t_unit @ M2 ) )
         => ( episte4695001281782364324cs_o_o @ M2 @ X @ P ) )
     => ( ( member_o @ W @ ( episte1038022579713443545t_unit @ M ) )
       => ( episte4695001281782364324cs_o_o @ M @ W @ ( epistemic_K_o @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_39_generalization,axiom,
    ! [P: epistemic_fm_o,W: a,M: episte5501173179175555974t_unit,I3: $o] :
      ( ! [M2: episte5501173179175555974t_unit,X: a] :
          ( ( member_a @ X @ ( episte5063048828340624601t_unit @ M2 ) )
         => ( episte1021116911515925002cs_o_a @ M2 @ X @ P ) )
     => ( ( member_a @ W @ ( episte5063048828340624601t_unit @ M ) )
       => ( episte1021116911515925002cs_o_a @ M @ W @ ( epistemic_K_o @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_40_generalization,axiom,
    ! [P: epistemic_fm_a,W: set_o,M: episte4442589092411611552t_unit,I3: a] :
      ( ! [M2: episte4442589092411611552t_unit,X: set_o] :
          ( ( member_set_o @ X @ ( episte7994720633578350067t_unit @ M2 ) )
         => ( episte5787648899026124830_set_o @ M2 @ X @ P ) )
     => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
       => ( episte5787648899026124830_set_o @ M @ W @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% generalization
thf(fact_41_truth,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,I3: a,P: epistemic_fm_a] :
      ( ( episte3426825378771607259t_unit @ M )
     => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
       => ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_42_truth,axiom,
    ! [M: episte2543566300658443718t_unit,W: b,I3: $o,P: epistemic_fm_o] :
      ( ( episte4955991936609055169t_unit @ M )
     => ( ( member_b @ W @ ( episte9142089827432095385t_unit @ M ) )
       => ( episte1021116911515925003cs_o_b @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_43_truth,axiom,
    ! [M: episte8859593475650739846t_unit,W: $o,I3: $o,P: epistemic_fm_o] :
      ( ( episte6484863922062934529t_unit @ M )
     => ( ( member_o @ W @ ( episte1038022579713443545t_unit @ M ) )
       => ( episte4695001281782364324cs_o_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_44_truth,axiom,
    ! [M: episte5501173179175555974t_unit,W: a,I3: $o,P: epistemic_fm_o] :
      ( ( episte876950937517584385t_unit @ M )
     => ( ( member_a @ W @ ( episte5063048828340624601t_unit @ M ) )
       => ( episte1021116911515925002cs_o_a @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_45_truth,axiom,
    ! [M: episte3259645218793129376t_unit,W: $o,I3: a,P: epistemic_fm_a] :
      ( ( episte2671743178186770715t_unit @ M )
     => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
       => ( episte1100597067981672766cs_a_o @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_46_truth,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I3: 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 @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_47_truth,axiom,
    ! [M: episte4519467831615171103t_unit,W: b,I3: b,P: epistemic_fm_b] :
      ( ( episte8741121341479823002t_unit @ M )
     => ( ( member_b @ W @ ( episte7096680817873233778t_unit @ M ) )
       => ( episte6731534340014680036cs_b_b @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_48_truth,axiom,
    ! [M: episte6655095512717024223t_unit,W: $o,I3: b,P: epistemic_fm_b] :
      ( ( episte728515759041703898t_unit @ M )
     => ( ( member_o @ W @ ( episte8156305138475616434t_unit @ M ) )
       => ( episte7424746705372054269cs_b_o @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_49_truth,axiom,
    ! [M: episte7477074710132283359t_unit,W: a,I3: b,P: epistemic_fm_b] :
      ( ( episte4662080342388352218t_unit @ M )
     => ( ( member_a @ W @ ( episte3017639818781762994t_unit @ M ) )
       => ( episte6731534340014680035cs_b_a @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_50_truth,axiom,
    ! [M: episte399968703042273926t_unit,W: set_o,I3: $o,P: epistemic_fm_o] :
      ( ( episte603136233781302785t_unit @ M )
     => ( ( member_set_o @ W @ ( episte7065225365757467353t_unit @ M ) )
       => ( episte1745421503759077252_set_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ P ) ) ) ) ).

% truth
thf(fact_51_pos__introspection,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,I3: a,P: epistemic_fm_a] :
      ( ( episte9018110198556821958t_unit @ M )
     => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
       => ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_52_pos__introspection,axiom,
    ! [M: episte2543566300658443718t_unit,W: b,I3: $o,P: epistemic_fm_o] :
      ( ( episte7950819053531357740t_unit @ M )
     => ( ( member_b @ W @ ( episte9142089827432095385t_unit @ M ) )
       => ( episte1021116911515925003cs_o_b @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_53_pos__introspection,axiom,
    ! [M: episte8859593475650739846t_unit,W: $o,I3: $o,P: epistemic_fm_o] :
      ( ( episte4142360316505390444t_unit @ M )
     => ( ( member_o @ W @ ( episte1038022579713443545t_unit @ M ) )
       => ( episte4695001281782364324cs_o_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_54_pos__introspection,axiom,
    ! [M: episte5501173179175555974t_unit,W: a,I3: $o,P: epistemic_fm_o] :
      ( ( episte3871778054439886956t_unit @ M )
     => ( ( member_a @ W @ ( episte5063048828340624601t_unit @ M ) )
       => ( episte1021116911515925002cs_o_a @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_55_pos__introspection,axiom,
    ! [M: episte3259645218793129376t_unit,W: $o,I3: a,P: epistemic_fm_a] :
      ( ( episte1265558571371986694t_unit @ M )
     => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
       => ( episte1100597067981672766cs_a_o @ M @ W @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_56_pos__introspection,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I3: 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 @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_57_pos__introspection,axiom,
    ! [M: episte4519467831615171103t_unit,W: b,I3: b,P: epistemic_fm_b] :
      ( ( episte5109034124410261893t_unit @ M )
     => ( ( member_b @ W @ ( episte7096680817873233778t_unit @ M ) )
       => ( episte6731534340014680036cs_b_b @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_K_b @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_58_pos__introspection,axiom,
    ! [M: episte6655095512717024223t_unit,W: $o,I3: b,P: epistemic_fm_b] :
      ( ( episte8545703189081695685t_unit @ M )
     => ( ( member_o @ W @ ( episte8156305138475616434t_unit @ M ) )
       => ( episte7424746705372054269cs_b_o @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_K_b @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_59_pos__introspection,axiom,
    ! [M: episte7477074710132283359t_unit,W: a,I3: b,P: epistemic_fm_b] :
      ( ( episte1029993125318791109t_unit @ M )
     => ( ( member_a @ W @ ( episte3017639818781762994t_unit @ M ) )
       => ( episte6731534340014680035cs_b_a @ M @ W @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_K_b @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_60_pos__introspection,axiom,
    ! [M: episte399968703042273926t_unit,W: set_o,I3: $o,P: epistemic_fm_o] :
      ( ( episte6499144448312146284t_unit @ M )
     => ( ( member_set_o @ W @ ( episte7065225365757467353t_unit @ M ) )
       => ( episte1745421503759077252_set_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ) ) ).

% pos_introspection
thf(fact_61_AxB_Ointros,axiom,
    ! [P: epistemic_fm_o,I3: $o] : ( epistemic_AxB_o @ ( epistemic_Imp_o @ P @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ).

% AxB.intros
thf(fact_62_AxB_Ointros,axiom,
    ! [P: epistemic_fm_b,I3: b] : ( epistemic_AxB_b @ ( epistemic_Imp_b @ P @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ).

% AxB.intros
thf(fact_63_AxB_Ointros,axiom,
    ! [P: epistemic_fm_a,I3: a] : ( epistemic_AxB_a @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% AxB.intros
thf(fact_64_AxB_Osimps,axiom,
    ( epistemic_AxB_o
    = ( ^ [A2: epistemic_fm_o] :
        ? [P3: epistemic_fm_o,I2: $o] :
          ( A2
          = ( epistemic_Imp_o @ P3 @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ P3 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ) ).

% AxB.simps
thf(fact_65_AxB_Osimps,axiom,
    ( epistemic_AxB_b
    = ( ^ [A2: epistemic_fm_b] :
        ? [P3: epistemic_fm_b,I2: b] :
          ( A2
          = ( epistemic_Imp_b @ P3 @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ P3 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ) ).

% AxB.simps
thf(fact_66_AxB_Osimps,axiom,
    ( epistemic_AxB_a
    = ( ^ [A2: epistemic_fm_a] :
        ? [P3: epistemic_fm_a,I2: a] :
          ( A2
          = ( epistemic_Imp_a @ P3 @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% AxB.simps
thf(fact_67_AxB_Ocases,axiom,
    ! [A: epistemic_fm_o] :
      ( ( epistemic_AxB_o @ A )
     => ~ ! [P2: epistemic_fm_o,I: $o] :
            ( A
           != ( epistemic_Imp_o @ P2 @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ P2 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ).

% AxB.cases
thf(fact_68_AxB_Ocases,axiom,
    ! [A: epistemic_fm_b] :
      ( ( epistemic_AxB_b @ A )
     => ~ ! [P2: epistemic_fm_b,I: b] :
            ( A
           != ( epistemic_Imp_b @ P2 @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ P2 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ).

% AxB.cases
thf(fact_69_AxB_Ocases,axiom,
    ! [A: epistemic_fm_a] :
      ( ( epistemic_AxB_a @ A )
     => ~ ! [P2: epistemic_fm_a,I: a] :
            ( A
           != ( epistemic_Imp_a @ P2 @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% AxB.cases
thf(fact_70_Ax5_Ointros,axiom,
    ! [I3: $o,P: epistemic_fm_o] : ( epistemic_Ax5_o @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ).

% Ax5.intros
thf(fact_71_Ax5_Ointros,axiom,
    ! [I3: b,P: epistemic_fm_b] : ( epistemic_Ax5_b @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ).

% Ax5.intros
thf(fact_72_Ax5_Ointros,axiom,
    ! [I3: a,P: epistemic_fm_a] : ( epistemic_Ax5_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% Ax5.intros
thf(fact_73_Ax5_Osimps,axiom,
    ( epistemic_Ax5_o
    = ( ^ [A2: epistemic_fm_o] :
        ? [I2: $o,P3: epistemic_fm_o] :
          ( A2
          = ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ P3 @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ P3 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_74_Ax5_Osimps,axiom,
    ( epistemic_Ax5_b
    = ( ^ [A2: epistemic_fm_b] :
        ? [I2: b,P3: epistemic_fm_b] :
          ( A2
          = ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ P3 @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ P3 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_75_Ax5_Osimps,axiom,
    ( epistemic_Ax5_a
    = ( ^ [A2: epistemic_fm_a] :
        ? [I2: a,P3: epistemic_fm_a] :
          ( A2
          = ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_76_Ax5_Ocases,axiom,
    ! [A: epistemic_fm_o] :
      ( ( epistemic_Ax5_o @ A )
     => ~ ! [I: $o,P2: epistemic_fm_o] :
            ( A
           != ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ P2 @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ P2 @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ).

% Ax5.cases
thf(fact_77_Ax5_Ocases,axiom,
    ! [A: epistemic_fm_b] :
      ( ( epistemic_Ax5_b @ A )
     => ~ ! [I: b,P2: epistemic_fm_b] :
            ( A
           != ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ P2 @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ P2 @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ).

% Ax5.cases
thf(fact_78_Ax5_Ocases,axiom,
    ! [A: epistemic_fm_a] :
      ( ( epistemic_Ax5_a @ A )
     => ~ ! [I: a,P2: epistemic_fm_a] :
            ( A
           != ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% Ax5.cases
thf(fact_79_weakly__directed__def,axiom,
    ( stalna9100096441501500634c_fm_a
    = ( ^ [M3: episte1560738328020401952t_unit] :
        ! [I2: a,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
         => ! [Y: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y @ ( episte8072386903178013299t_unit @ M3 ) )
             => ! [Z: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z @ ( episte8072386903178013299t_unit @ M3 ) )
                 => ( ( ( member536094252920883875c_fm_a @ Z @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) )
                      & ( member536094252920883875c_fm_a @ Y @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) ) )
                   => ? [Aa: set_Epistemic_fm_a] :
                        ( ( member536094252920883875c_fm_a @ Aa @ ( episte8072386903178013299t_unit @ M3 ) )
                        & ( member536094252920883875c_fm_a @ Aa @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Z ) )
                        & ( member536094252920883875c_fm_a @ Aa @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ) ).

% weakly_directed_def
thf(fact_80_weakly__directed__def,axiom,
    ( stalna7560619637984394463ed_a_b
    = ( ^ [M3: episte3224730989885420256t_unit] :
        ! [I2: a,X2: b] :
          ( ( member_b @ X2 @ ( episte1782384855165018035t_unit @ M3 ) )
         => ! [Y: b] :
              ( ( member_b @ Y @ ( episte1782384855165018035t_unit @ M3 ) )
             => ! [Z: b] :
                  ( ( member_b @ Z @ ( episte1782384855165018035t_unit @ M3 ) )
                 => ( ( ( member_b @ Z @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) )
                      & ( member_b @ Y @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) ) )
                   => ? [Aa: b] :
                        ( ( member_b @ Aa @ ( episte1782384855165018035t_unit @ M3 ) )
                        & ( member_b @ Aa @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Z ) )
                        & ( member_b @ Aa @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ) ).

% weakly_directed_def
thf(fact_81_neg__introspection,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,I3: a,P: epistemic_fm_a] :
      ( ( episte4899516349225340390t_unit @ M )
     => ( ( episte9018110198556821958t_unit @ M )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_82_neg__introspection,axiom,
    ! [M: episte2543566300658443718t_unit,W: b,I3: $o,P: epistemic_fm_o] :
      ( ( episte242693516716275276t_unit @ M )
     => ( ( episte7950819053531357740t_unit @ M )
       => ( ( member_b @ W @ ( episte9142089827432095385t_unit @ M ) )
         => ( episte1021116911515925003cs_o_b @ M @ W @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_83_neg__introspection,axiom,
    ! [M: episte8859593475650739846t_unit,W: $o,I3: $o,P: epistemic_fm_o] :
      ( ( episte2818820560449417612t_unit @ M )
     => ( ( episte4142360316505390444t_unit @ M )
       => ( ( member_o @ W @ ( episte1038022579713443545t_unit @ M ) )
         => ( episte4695001281782364324cs_o_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_84_neg__introspection,axiom,
    ! [M: episte5501173179175555974t_unit,W: a,I3: $o,P: epistemic_fm_o] :
      ( ( episte5387024554479580300t_unit @ M )
     => ( ( episte3871778054439886956t_unit @ M )
       => ( ( member_a @ W @ ( episte5063048828340624601t_unit @ M ) )
         => ( episte1021116911515925002cs_o_a @ M @ W @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_85_neg__introspection,axiom,
    ! [M: episte3259645218793129376t_unit,W: $o,I3: a,P: epistemic_fm_a] :
      ( ( episte2022334575264998182t_unit @ M )
     => ( ( episte1265558571371986694t_unit @ M )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_86_neg__introspection,axiom,
    ! [M: episte6182337868402532512t_unit,W: a,I3: 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 @ I3 @ P ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_87_neg__introspection,axiom,
    ! [M: episte4519467831615171103t_unit,W: b,I3: b,P: epistemic_fm_b] :
      ( ( episte990440275078780325t_unit @ M )
     => ( ( episte5109034124410261893t_unit @ M )
       => ( ( member_b @ W @ ( episte7096680817873233778t_unit @ M ) )
         => ( episte6731534340014680036cs_b_b @ M @ W @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_88_neg__introspection,axiom,
    ! [M: episte6655095512717024223t_unit,W: $o,I3: b,P: epistemic_fm_b] :
      ( ( episte79107156119931365t_unit @ M )
     => ( ( episte8545703189081695685t_unit @ M )
       => ( ( member_o @ W @ ( episte8156305138475616434t_unit @ M ) )
         => ( episte7424746705372054269cs_b_o @ M @ W @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_89_neg__introspection,axiom,
    ! [M: episte7477074710132283359t_unit,W: a,I3: b,P: epistemic_fm_b] :
      ( ( episte6134771312842085349t_unit @ M )
     => ( ( episte1029993125318791109t_unit @ M )
       => ( ( member_a @ W @ ( episte3017639818781762994t_unit @ M ) )
         => ( episte6731534340014680035cs_b_a @ M @ W @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_90_neg__introspection,axiom,
    ! [M: episte399968703042273926t_unit,W: set_o,I3: $o,P: epistemic_fm_o] :
      ( ( episte6049797970692746636t_unit @ M )
     => ( ( episte6499144448312146284t_unit @ M )
       => ( ( member_set_o @ W @ ( episte7065225365757467353t_unit @ M ) )
         => ( episte1745421503759077252_set_o @ M @ W @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ) ) ) ) ).

% neg_introspection
thf(fact_91_transitive__def,axiom,
    ( episte8364071018013720454t_unit
    = ( ^ [M3: episte1560738328020401952t_unit] :
        ! [I2: a,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
         => ! [Y: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y @ ( episte8072386903178013299t_unit @ M3 ) )
             => ! [Z: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z @ ( episte8072386903178013299t_unit @ M3 ) )
                 => ( ( ( member536094252920883875c_fm_a @ Z @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Y ) )
                      & ( member536094252920883875c_fm_a @ X2 @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Z ) ) )
                   => ( member536094252920883875c_fm_a @ X2 @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ).

% transitive_def
thf(fact_92_transitive__def,axiom,
    ( episte9018110198556821958t_unit
    = ( ^ [M3: episte3224730989885420256t_unit] :
        ! [I2: a,X2: b] :
          ( ( member_b @ X2 @ ( episte1782384855165018035t_unit @ M3 ) )
         => ! [Y: b] :
              ( ( member_b @ Y @ ( episte1782384855165018035t_unit @ M3 ) )
             => ! [Z: b] :
                  ( ( member_b @ Z @ ( episte1782384855165018035t_unit @ M3 ) )
                 => ( ( ( member_b @ Z @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Y ) )
                      & ( member_b @ X2 @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Z ) ) )
                   => ( member_b @ X2 @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ).

% transitive_def
thf(fact_93_symmetric__def,axiom,
    ( episte5478016696552465318t_unit
    = ( ^ [M3: episte1560738328020401952t_unit] :
        ! [I2: a,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
         => ! [Y: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y @ ( episte8072386903178013299t_unit @ M3 ) )
             => ( ( member536094252920883875c_fm_a @ X2 @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Y ) )
                = ( member536094252920883875c_fm_a @ Y @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) ) ) ) ) ) ) ).

% symmetric_def
thf(fact_94_symmetric__def,axiom,
    ( episte4899516349225340390t_unit
    = ( ^ [M3: episte3224730989885420256t_unit] :
        ! [I2: a,X2: b] :
          ( ( member_b @ X2 @ ( episte1782384855165018035t_unit @ M3 ) )
         => ! [Y: b] :
              ( ( member_b @ Y @ ( episte1782384855165018035t_unit @ M3 ) )
             => ( ( member_b @ X2 @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Y ) )
                = ( member_b @ Y @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) ) ) ) ) ) ) ).

% symmetric_def
thf(fact_95_reflexive__def,axiom,
    ( episte5648423998891577755t_unit
    = ( ^ [M3: episte1560738328020401952t_unit] :
        ! [I2: a,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
         => ( member536094252920883875c_fm_a @ X2 @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) ) ) ) ) ).

% reflexive_def
thf(fact_96_reflexive__def,axiom,
    ( episte3426825378771607259t_unit
    = ( ^ [M3: episte3224730989885420256t_unit] :
        ! [I2: a,X2: b] :
          ( ( member_b @ X2 @ ( episte1782384855165018035t_unit @ M3 ) )
         => ( member_b @ X2 @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) ) ) ) ) ).

% reflexive_def
thf(fact_97_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte2022334575264998182t_unit @ M )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_98_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte1938654652935425830t_unit @ M )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_99_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte3701050113606757862t_unit @ M )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_100_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_101_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_102_soundness__AxB,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( epistemic_AxB_a @ P )
     => ( ( episte4899516349225340390t_unit @ M )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_AxB
thf(fact_103_refl__Euclid__equiv,axiom,
    ! [M: episte3224730989885420256t_unit] :
      ( ( episte3426825378771607259t_unit @ M )
     => ( ( episte6418945320598494989t_unit @ M )
       => ( ( episte3426825378771607259t_unit @ M )
          & ( episte4899516349225340390t_unit @ M )
          & ( episte9018110198556821958t_unit @ M ) ) ) ) ).

% refl_Euclid_equiv
thf(fact_104_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_105_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte2671743178186770715t_unit @ M )
          & ( episte2022334575264998182t_unit @ M )
          & ( episte1265558571371986694t_unit @ M ) )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_106_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte1753692356642032923t_unit @ M )
          & ( episte1938654652935425830t_unit @ M )
          & ( episte3979770203462150918t_unit @ M ) )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_107_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte4299101107980113627t_unit @ M )
          & ( episte3701050113606757862t_unit @ M )
          & ( episte1388884068568345030t_unit @ M ) )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_108_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_109_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_110_soundness__AxT5,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax5_a @ P ) )
     => ( ( ( episte3426825378771607259t_unit @ M )
          & ( episte4899516349225340390t_unit @ M )
          & ( episte9018110198556821958t_unit @ M ) )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT5
thf(fact_111_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte2052337558702062413t_unit @ M )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_112_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte905247779971886925t_unit @ M )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_113_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte3789892348602042125t_unit @ M )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_114_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_115_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_116_soundness__Ax5,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( epistemic_Ax5_a @ P )
     => ( ( episte6418945320598494989t_unit @ M )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_Ax5
thf(fact_117_symm__trans__Euclid,axiom,
    ! [M: episte3224730989885420256t_unit] :
      ( ( episte4899516349225340390t_unit @ M )
     => ( ( episte9018110198556821958t_unit @ M )
       => ( episte6418945320598494989t_unit @ M ) ) ) ).

% symm_trans_Euclid
thf(fact_118_symm__trans__Euclid,axiom,
    ! [M: episte1560738328020401952t_unit] :
      ( ( episte5478016696552465318t_unit @ M )
     => ( ( episte8364071018013720454t_unit @ M )
       => ( episte2449151000174023629t_unit @ M ) ) ) ).

% symm_trans_Euclid
thf(fact_119_Euclidean__def,axiom,
    ( episte2449151000174023629t_unit
    = ( ^ [M3: episte1560738328020401952t_unit] :
        ! [I2: a,X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
         => ! [Y: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ Y @ ( episte8072386903178013299t_unit @ M3 ) )
             => ! [Z: set_Epistemic_fm_a] :
                  ( ( member536094252920883875c_fm_a @ Z @ ( episte8072386903178013299t_unit @ M3 ) )
                 => ( ( member536094252920883875c_fm_a @ Y @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) )
                   => ( ( member536094252920883875c_fm_a @ Z @ ( episte6250069432388174439t_unit @ M3 @ I2 @ X2 ) )
                     => ( member536094252920883875c_fm_a @ Z @ ( episte6250069432388174439t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ) ).

% Euclidean_def
thf(fact_120_Euclidean__def,axiom,
    ( episte6418945320598494989t_unit
    = ( ^ [M3: episte3224730989885420256t_unit] :
        ! [I2: a,X2: b] :
          ( ( member_b @ X2 @ ( episte1782384855165018035t_unit @ M3 ) )
         => ! [Y: b] :
              ( ( member_b @ Y @ ( episte1782384855165018035t_unit @ M3 ) )
             => ! [Z: b] :
                  ( ( member_b @ Z @ ( episte1782384855165018035t_unit @ M3 ) )
                 => ( ( member_b @ Y @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) )
                   => ( ( member_b @ Z @ ( episte1071096959727133607t_unit @ M3 @ I2 @ X2 ) )
                     => ( member_b @ Z @ ( episte1071096959727133607t_unit @ M3 @ I2 @ Y ) ) ) ) ) ) ) ) ) ).

% Euclidean_def
thf(fact_121_frame_Oequality,axiom,
    ! [R: episte1560738328020401952t_unit,R2: episte1560738328020401952t_unit] :
      ( ( ( episte8072386903178013299t_unit @ R )
        = ( episte8072386903178013299t_unit @ R2 ) )
     => ( ( ( episte6250069432388174439t_unit @ R )
          = ( episte6250069432388174439t_unit @ R2 ) )
       => ( ( ( episte3309513806868946049t_unit @ R )
            = ( episte3309513806868946049t_unit @ R2 ) )
         => ( R = R2 ) ) ) ) ).

% frame.equality
thf(fact_122_frame_Oequality,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit] :
      ( ( ( episte1782384855165018035t_unit @ R )
        = ( episte1782384855165018035t_unit @ R2 ) )
     => ( ( ( episte1071096959727133607t_unit @ R )
          = ( episte1071096959727133607t_unit @ R2 ) )
       => ( ( ( episte6669210725420356545t_unit @ R )
            = ( episte6669210725420356545t_unit @ R2 ) )
         => ( R = R2 ) ) ) ) ).

% frame.equality
thf(fact_123_semantics_Osimps_I6_J,axiom,
    ! [M: episte4519467831615171103t_unit,W: b,I3: b,P: epistemic_fm_b] :
      ( ( episte6731534340014680036cs_b_b @ M @ W @ ( epistemic_K_b @ I3 @ P ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ ( inf_inf_set_b @ ( episte7096680817873233778t_unit @ M ) @ ( episte6385392922435349350t_unit @ M @ I3 @ W ) ) )
           => ( episte6731534340014680036cs_b_b @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_124_semantics_Osimps_I6_J,axiom,
    ! [M: episte2543566300658443718t_unit,W: b,I3: $o,P: epistemic_fm_o] :
      ( ( episte1021116911515925003cs_o_b @ M @ W @ ( epistemic_K_o @ I3 @ P ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ ( inf_inf_set_b @ ( episte9142089827432095385t_unit @ M ) @ ( episte3109837587766369421t_unit @ M @ I3 @ W ) ) )
           => ( episte1021116911515925003cs_o_b @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_125_semantics_Osimps_I6_J,axiom,
    ! [M: episte3259645218793129376t_unit,W: $o,I3: a,P: epistemic_fm_a] :
      ( ( episte1100597067981672766cs_a_o @ M @ W @ ( epistemic_K_a @ I3 @ P ) )
      = ( ! [X2: $o] :
            ( ( member_o @ X2 @ ( inf_inf_set_o @ ( episte876160520765907443t_unit @ M ) @ ( episte6681579530201160167t_unit @ M @ I3 @ W ) ) )
           => ( episte1100597067981672766cs_a_o @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_126_semantics_Osimps_I6_J,axiom,
    ! [M: episte6655095512717024223t_unit,W: $o,I3: b,P: epistemic_fm_b] :
      ( ( episte7424746705372054269cs_b_o @ M @ W @ ( epistemic_K_b @ I3 @ P ) )
      = ( ! [X2: $o] :
            ( ( member_o @ X2 @ ( inf_inf_set_o @ ( episte8156305138475616434t_unit @ M ) @ ( episte4738352111056093350t_unit @ M @ I3 @ W ) ) )
           => ( episte7424746705372054269cs_b_o @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_127_semantics_Osimps_I6_J,axiom,
    ! [M: episte8859593475650739846t_unit,W: $o,I3: $o,P: epistemic_fm_o] :
      ( ( episte4695001281782364324cs_o_o @ M @ W @ ( epistemic_K_o @ I3 @ P ) )
      = ( ! [X2: $o] :
            ( ( member_o @ X2 @ ( inf_inf_set_o @ ( episte1038022579713443545t_unit @ M ) @ ( episte5693609662886803661t_unit @ M @ I3 @ W ) ) )
           => ( episte4695001281782364324cs_o_o @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_128_semantics_Osimps_I6_J,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I3: a,P: epistemic_fm_a] :
      ( ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_K_a @ I3 @ P ) )
      = ( ! [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ ( inf_in1884693029477671368c_fm_a @ ( episte8072386903178013299t_unit @ M ) @ ( episte6250069432388174439t_unit @ M @ I3 @ W ) ) )
           => ( episte7081087998767065248c_fm_a @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_129_semantics_Osimps_I6_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,I3: a,P: epistemic_fm_a] :
      ( ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_K_a @ I3 @ P ) )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ ( inf_inf_set_b @ ( episte1782384855165018035t_unit @ M ) @ ( episte1071096959727133607t_unit @ M @ I3 @ W ) ) )
           => ( episte295617885132580261cs_a_b @ M @ X2 @ P ) ) ) ) ).

% semantics.simps(6)
thf(fact_130_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte1265558571371986694t_unit @ M )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_131_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte3979770203462150918t_unit @ M )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_132_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte1388884068568345030t_unit @ M )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_133_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_134_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_135_soundness__Ax4,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( epistemic_Ax4_a @ P )
     => ( ( episte9018110198556821958t_unit @ M )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_Ax4
thf(fact_136_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte2671743178186770715t_unit @ M )
          & ( episte2022334575264998182t_unit @ M )
          & ( episte1265558571371986694t_unit @ M ) )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_137_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte1753692356642032923t_unit @ M )
          & ( episte1938654652935425830t_unit @ M )
          & ( episte3979770203462150918t_unit @ M ) )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_138_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte4299101107980113627t_unit @ M )
          & ( episte3701050113606757862t_unit @ M )
          & ( episte1388884068568345030t_unit @ M ) )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_139_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_140_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_141_soundness__AxTB4,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_AxB_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte3426825378771607259t_unit @ M )
          & ( episte4899516349225340390t_unit @ M )
          & ( episte9018110198556821958t_unit @ M ) )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_AxTB4
thf(fact_142_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte2671743178186770715t_unit @ M )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_143_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte1753692356642032923t_unit @ M )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_144_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte4299101107980113627t_unit @ M )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_145_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_146_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_147_soundness__AxT,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( epistemic_AxT_a @ P )
     => ( ( episte3426825378771607259t_unit @ M )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT
thf(fact_148_duality__taut,axiom,
    ! [I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o,G: list_char > $o,H: epistemic_fm_o > $o] : ( epistemic_eval_o @ G @ H @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ Q @ epistemic_FF_o ) ) ) @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ Q @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ) ).

% duality_taut
thf(fact_149_duality__taut,axiom,
    ! [I3: b,P: epistemic_fm_b,Q: epistemic_fm_b,G: list_char > $o,H: epistemic_fm_b > $o] : ( epistemic_eval_b @ G @ H @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ Q @ epistemic_FF_b ) ) ) @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ Q @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) ) ) ).

% duality_taut
thf(fact_150_duality__taut,axiom,
    ! [I3: a,P: epistemic_fm_a,Q: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) ) ) ).

% duality_taut
thf(fact_151_eval_Osimps_I5_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b] :
      ( ( epistemic_eval_b @ G2 @ H2 @ ( epistemic_Imp_b @ P @ Q ) )
      = ( ( epistemic_eval_b @ G2 @ H2 @ P )
       => ( epistemic_eval_b @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_152_eval_Osimps_I5_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
       => ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_153_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H2: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] :
      ( ( epistemic_eval_b @ Ux @ H2 @ ( epistemic_K_b @ I3 @ P ) )
      = ( H2 @ ( epistemic_K_b @ I3 @ P ) ) ) ).

% eval.simps(6)
thf(fact_154_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H2: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] :
      ( ( epistemic_eval_o @ Ux @ H2 @ ( epistemic_K_o @ I3 @ P ) )
      = ( H2 @ ( epistemic_K_o @ I3 @ P ) ) ) ).

% eval.simps(6)
thf(fact_155_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H2: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ Ux @ H2 @ ( epistemic_K_a @ I3 @ P ) )
      = ( H2 @ ( epistemic_K_a @ I3 @ P ) ) ) ).

% eval.simps(6)
thf(fact_156_eval_Osimps_I1_J,axiom,
    ! [Uu: list_char > $o,Uv: epistemic_fm_o > $o] :
      ~ ( epistemic_eval_o @ Uu @ Uv @ epistemic_FF_o ) ).

% eval.simps(1)
thf(fact_157_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_158_mem__Collect__eq,axiom,
    ! [A: set_o,P4: set_o > $o] :
      ( ( member_set_o @ A @ ( collect_set_o @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_159_mem__Collect__eq,axiom,
    ! [A: set_b,P4: set_b > $o] :
      ( ( member_set_b @ A @ ( collect_set_b @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_160_mem__Collect__eq,axiom,
    ! [A: a,P4: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_161_mem__Collect__eq,axiom,
    ! [A: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ A @ ( collec2519470961442302949c_fm_a @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_162_mem__Collect__eq,axiom,
    ! [A: epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ A @ ( collec4904205152690461189c_fm_a @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_163_mem__Collect__eq,axiom,
    ! [A: $o,P4: $o > $o] :
      ( ( member_o @ A @ ( collect_o @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_164_mem__Collect__eq,axiom,
    ! [A: b,P4: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P4 ) )
      = ( P4 @ A ) ) ).

% mem_Collect_eq
thf(fact_165_Collect__mem__eq,axiom,
    ! [A3: set_set_o] :
      ( ( collect_set_o
        @ ^ [X2: set_o] : ( member_set_o @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_166_Collect__mem__eq,axiom,
    ! [A3: set_set_b] :
      ( ( collect_set_b
        @ ^ [X2: set_b] : ( member_set_b @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_167_Collect__mem__eq,axiom,
    ! [A3: set_a] :
      ( ( collect_a
        @ ^ [X2: a] : ( member_a @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_168_Collect__mem__eq,axiom,
    ! [A3: set_se5208064806568342746c_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_169_Collect__mem__eq,axiom,
    ! [A3: set_Epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_170_Collect__mem__eq,axiom,
    ! [A3: set_o] :
      ( ( collect_o
        @ ^ [X2: $o] : ( member_o @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_171_Collect__mem__eq,axiom,
    ! [A3: set_b] :
      ( ( collect_b
        @ ^ [X2: b] : ( member_b @ X2 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_172_Collect__cong,axiom,
    ! [P4: b > $o,Q2: b > $o] :
      ( ! [X: b] :
          ( ( P4 @ X )
          = ( Q2 @ X ) )
     => ( ( collect_b @ P4 )
        = ( collect_b @ Q2 ) ) ) ).

% Collect_cong
thf(fact_173_Collect__cong,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q2: set_Epistemic_fm_a > $o] :
      ( ! [X: set_Epistemic_fm_a] :
          ( ( P4 @ X )
          = ( Q2 @ X ) )
     => ( ( collec2519470961442302949c_fm_a @ P4 )
        = ( collec2519470961442302949c_fm_a @ Q2 ) ) ) ).

% Collect_cong
thf(fact_174_Collect__cong,axiom,
    ! [P4: epistemic_fm_a > $o,Q2: epistemic_fm_a > $o] :
      ( ! [X: epistemic_fm_a] :
          ( ( P4 @ X )
          = ( Q2 @ X ) )
     => ( ( collec4904205152690461189c_fm_a @ P4 )
        = ( collec4904205152690461189c_fm_a @ Q2 ) ) ) ).

% Collect_cong
thf(fact_175_Collect__cong,axiom,
    ! [P4: $o > $o,Q2: $o > $o] :
      ( ! [X: $o] :
          ( ( P4 @ X )
          = ( Q2 @ X ) )
     => ( ( collect_o @ P4 )
        = ( collect_o @ Q2 ) ) ) ).

% Collect_cong
thf(fact_176_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_177_tautology,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ P )
     => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ).

% tautology
thf(fact_178_AxT_Ointros,axiom,
    ! [I3: $o,P: epistemic_fm_o] : ( epistemic_AxT_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ P ) ) ).

% AxT.intros
thf(fact_179_AxT_Ointros,axiom,
    ! [I3: b,P: epistemic_fm_b] : ( epistemic_AxT_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ P ) ) ).

% AxT.intros
thf(fact_180_AxT_Ointros,axiom,
    ! [I3: a,P: epistemic_fm_a] : ( epistemic_AxT_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ P ) ) ).

% AxT.intros
thf(fact_181_AxT_Osimps,axiom,
    ( epistemic_AxT_o
    = ( ^ [A2: epistemic_fm_o] :
        ? [I2: $o,P3: epistemic_fm_o] :
          ( A2
          = ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ P3 ) @ P3 ) ) ) ) ).

% AxT.simps
thf(fact_182_AxT_Osimps,axiom,
    ( epistemic_AxT_b
    = ( ^ [A2: epistemic_fm_b] :
        ? [I2: b,P3: epistemic_fm_b] :
          ( A2
          = ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ P3 ) @ P3 ) ) ) ) ).

% AxT.simps
thf(fact_183_AxT_Osimps,axiom,
    ( epistemic_AxT_a
    = ( ^ [A2: epistemic_fm_a] :
        ? [I2: a,P3: epistemic_fm_a] :
          ( A2
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P3 ) @ P3 ) ) ) ) ).

% AxT.simps
thf(fact_184_AxT_Ocases,axiom,
    ! [A: epistemic_fm_o] :
      ( ( epistemic_AxT_o @ A )
     => ~ ! [I: $o,P2: epistemic_fm_o] :
            ( A
           != ( epistemic_Imp_o @ ( epistemic_K_o @ I @ P2 ) @ P2 ) ) ) ).

% AxT.cases
thf(fact_185_AxT_Ocases,axiom,
    ! [A: epistemic_fm_b] :
      ( ( epistemic_AxT_b @ A )
     => ~ ! [I: b,P2: epistemic_fm_b] :
            ( A
           != ( epistemic_Imp_b @ ( epistemic_K_b @ I @ P2 ) @ P2 ) ) ) ).

% AxT.cases
thf(fact_186_AxT_Ocases,axiom,
    ! [A: epistemic_fm_a] :
      ( ( epistemic_AxT_a @ A )
     => ~ ! [I: a,P2: epistemic_fm_a] :
            ( A
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P2 ) @ P2 ) ) ) ).

% AxT.cases
thf(fact_187_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte2671743178186770715t_unit @ M )
          & ( episte1265558571371986694t_unit @ M ) )
       => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
         => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_188_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte1753692356642032923t_unit @ M )
          & ( episte3979770203462150918t_unit @ M ) )
       => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
         => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_189_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte4299101107980113627t_unit @ M )
          & ( episte1388884068568345030t_unit @ M ) )
       => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
         => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_190_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_191_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_192_soundness__AxT4,axiom,
    ! [P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ( ( epistemic_AxT_a @ P )
        | ( epistemic_Ax4_a @ P ) )
     => ( ( ( episte3426825378771607259t_unit @ M )
          & ( episte9018110198556821958t_unit @ M ) )
       => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
         => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ).

% soundness_AxT4
thf(fact_193_Ax4_Ointros,axiom,
    ! [I3: $o,P: epistemic_fm_o] : ( epistemic_Ax4_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ).

% Ax4.intros
thf(fact_194_Ax4_Ointros,axiom,
    ! [I3: b,P: epistemic_fm_b] : ( epistemic_Ax4_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_K_b @ I3 @ P ) ) ) ) ).

% Ax4.intros
thf(fact_195_Ax4_Ointros,axiom,
    ! [I3: a,P: epistemic_fm_a] : ( epistemic_Ax4_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% Ax4.intros
thf(fact_196_Ax4_Osimps,axiom,
    ( epistemic_Ax4_o
    = ( ^ [A2: epistemic_fm_o] :
        ? [I2: $o,P3: epistemic_fm_o] :
          ( A2
          = ( epistemic_Imp_o @ ( epistemic_K_o @ I2 @ P3 ) @ ( epistemic_K_o @ I2 @ ( epistemic_K_o @ I2 @ P3 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_197_Ax4_Osimps,axiom,
    ( epistemic_Ax4_b
    = ( ^ [A2: epistemic_fm_b] :
        ? [I2: b,P3: epistemic_fm_b] :
          ( A2
          = ( epistemic_Imp_b @ ( epistemic_K_b @ I2 @ P3 ) @ ( epistemic_K_b @ I2 @ ( epistemic_K_b @ I2 @ P3 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_198_Ax4_Osimps,axiom,
    ( epistemic_Ax4_a
    = ( ^ [A2: epistemic_fm_a] :
        ? [I2: a,P3: epistemic_fm_a] :
          ( A2
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P3 ) @ ( epistemic_K_a @ I2 @ ( epistemic_K_a @ I2 @ P3 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_199_Ax4_Ocases,axiom,
    ! [A: epistemic_fm_o] :
      ( ( epistemic_Ax4_o @ A )
     => ~ ! [I: $o,P2: epistemic_fm_o] :
            ( A
           != ( epistemic_Imp_o @ ( epistemic_K_o @ I @ P2 ) @ ( epistemic_K_o @ I @ ( epistemic_K_o @ I @ P2 ) ) ) ) ) ).

% Ax4.cases
thf(fact_200_Ax4_Ocases,axiom,
    ! [A: epistemic_fm_b] :
      ( ( epistemic_Ax4_b @ A )
     => ~ ! [I: b,P2: epistemic_fm_b] :
            ( A
           != ( epistemic_Imp_b @ ( epistemic_K_b @ I @ P2 ) @ ( epistemic_K_b @ I @ ( epistemic_K_b @ I @ P2 ) ) ) ) ) ).

% Ax4.cases
thf(fact_201_Ax4_Ocases,axiom,
    ! [A: epistemic_fm_a] :
      ( ( epistemic_Ax4_a @ A )
     => ~ ! [I: a,P2: epistemic_fm_a] :
            ( A
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P2 ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P2 ) ) ) ) ) ).

% Ax4.cases
thf(fact_202_IntI,axiom,
    ! [C: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ C @ A3 )
     => ( ( member536094252920883875c_fm_a @ C @ B )
       => ( member536094252920883875c_fm_a @ C @ ( inf_in1884693029477671368c_fm_a @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_203_IntI,axiom,
    ! [C: set_o,A3: set_set_o,B: set_set_o] :
      ( ( member_set_o @ C @ A3 )
     => ( ( member_set_o @ C @ B )
       => ( member_set_o @ C @ ( inf_inf_set_set_o @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_204_IntI,axiom,
    ! [C: set_b,A3: set_set_b,B: set_set_b] :
      ( ( member_set_b @ C @ A3 )
     => ( ( member_set_b @ C @ B )
       => ( member_set_b @ C @ ( inf_inf_set_set_b @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_205_IntI,axiom,
    ! [C: a,A3: set_a,B: set_a] :
      ( ( member_a @ C @ A3 )
     => ( ( member_a @ C @ B )
       => ( member_a @ C @ ( inf_inf_set_a @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_206_IntI,axiom,
    ! [C: $o,A3: set_o,B: set_o] :
      ( ( member_o @ C @ A3 )
     => ( ( member_o @ C @ B )
       => ( member_o @ C @ ( inf_inf_set_o @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_207_IntI,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ A3 )
     => ( ( member_b @ C @ B )
       => ( member_b @ C @ ( inf_inf_set_b @ A3 @ B ) ) ) ) ).

% IntI
thf(fact_208_Int__iff,axiom,
    ! [C: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ C @ ( inf_in1884693029477671368c_fm_a @ A3 @ B ) )
      = ( ( member536094252920883875c_fm_a @ C @ A3 )
        & ( member536094252920883875c_fm_a @ C @ B ) ) ) ).

% Int_iff
thf(fact_209_Int__iff,axiom,
    ! [C: set_o,A3: set_set_o,B: set_set_o] :
      ( ( member_set_o @ C @ ( inf_inf_set_set_o @ A3 @ B ) )
      = ( ( member_set_o @ C @ A3 )
        & ( member_set_o @ C @ B ) ) ) ).

% Int_iff
thf(fact_210_Int__iff,axiom,
    ! [C: set_b,A3: set_set_b,B: set_set_b] :
      ( ( member_set_b @ C @ ( inf_inf_set_set_b @ A3 @ B ) )
      = ( ( member_set_b @ C @ A3 )
        & ( member_set_b @ C @ B ) ) ) ).

% Int_iff
thf(fact_211_Int__iff,axiom,
    ! [C: a,A3: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B ) )
      = ( ( member_a @ C @ A3 )
        & ( member_a @ C @ B ) ) ) ).

% Int_iff
thf(fact_212_Int__iff,axiom,
    ! [C: $o,A3: set_o,B: set_o] :
      ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B ) )
      = ( ( member_o @ C @ A3 )
        & ( member_o @ C @ B ) ) ) ).

% Int_iff
thf(fact_213_Int__iff,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A3 @ B ) )
      = ( ( member_b @ C @ A3 )
        & ( member_b @ C @ B ) ) ) ).

% Int_iff
thf(fact_214_inf_Oidem,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ) ).

% inf.idem
thf(fact_215_inf_Oidem,axiom,
    ! [A: b > $o] :
      ( ( inf_inf_b_o @ A @ A )
      = A ) ).

% inf.idem
thf(fact_216_inf_Oidem,axiom,
    ! [A: set_o] :
      ( ( inf_inf_set_o @ A @ A )
      = A ) ).

% inf.idem
thf(fact_217_inf_Oidem,axiom,
    ! [A: $o] :
      ( ( inf_inf_o @ A @ A )
      = A ) ).

% inf.idem
thf(fact_218_inf__idem,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_219_inf__idem,axiom,
    ! [X3: b > $o] :
      ( ( inf_inf_b_o @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_220_inf__idem,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_221_inf__idem,axiom,
    ! [X3: $o] :
      ( ( inf_inf_o @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_222_inf_Oleft__idem,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B2 ) )
      = ( inf_inf_set_b @ A @ B2 ) ) ).

% inf.left_idem
thf(fact_223_inf_Oleft__idem,axiom,
    ! [A: b > $o,B2: b > $o] :
      ( ( inf_inf_b_o @ A @ ( inf_inf_b_o @ A @ B2 ) )
      = ( inf_inf_b_o @ A @ B2 ) ) ).

% inf.left_idem
thf(fact_224_inf_Oleft__idem,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( inf_inf_set_o @ A @ ( inf_inf_set_o @ A @ B2 ) )
      = ( inf_inf_set_o @ A @ B2 ) ) ).

% inf.left_idem
thf(fact_225_inf_Oleft__idem,axiom,
    ! [A: $o,B2: $o] :
      ( ( inf_inf_o @ A @ ( inf_inf_o @ A @ B2 ) )
      = ( inf_inf_o @ A @ B2 ) ) ).

% inf.left_idem
thf(fact_226_inf__left__idem,axiom,
    ! [X3: set_b,Y2: set_b] :
      ( ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ X3 @ Y2 ) )
      = ( inf_inf_set_b @ X3 @ Y2 ) ) ).

% inf_left_idem
thf(fact_227_inf__left__idem,axiom,
    ! [X3: b > $o,Y2: b > $o] :
      ( ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ X3 @ Y2 ) )
      = ( inf_inf_b_o @ X3 @ Y2 ) ) ).

% inf_left_idem
thf(fact_228_inf__left__idem,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ X3 @ Y2 ) )
      = ( inf_inf_set_o @ X3 @ Y2 ) ) ).

% inf_left_idem
thf(fact_229_inf__left__idem,axiom,
    ! [X3: $o,Y2: $o] :
      ( ( inf_inf_o @ X3 @ ( inf_inf_o @ X3 @ Y2 ) )
      = ( inf_inf_o @ X3 @ Y2 ) ) ).

% inf_left_idem
thf(fact_230_inf_Oright__idem,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B2 ) @ B2 )
      = ( inf_inf_set_b @ A @ B2 ) ) ).

% inf.right_idem
thf(fact_231_inf_Oright__idem,axiom,
    ! [A: b > $o,B2: b > $o] :
      ( ( inf_inf_b_o @ ( inf_inf_b_o @ A @ B2 ) @ B2 )
      = ( inf_inf_b_o @ A @ B2 ) ) ).

% inf.right_idem
thf(fact_232_inf_Oright__idem,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ A @ B2 ) @ B2 )
      = ( inf_inf_set_o @ A @ B2 ) ) ).

% inf.right_idem
thf(fact_233_inf_Oright__idem,axiom,
    ! [A: $o,B2: $o] :
      ( ( inf_inf_o @ ( inf_inf_o @ A @ B2 ) @ B2 )
      = ( inf_inf_o @ A @ B2 ) ) ).

% inf.right_idem
thf(fact_234_inf__right__idem,axiom,
    ! [X3: set_b,Y2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ Y2 )
      = ( inf_inf_set_b @ X3 @ Y2 ) ) ).

% inf_right_idem
thf(fact_235_inf__right__idem,axiom,
    ! [X3: b > $o,Y2: b > $o] :
      ( ( inf_inf_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ Y2 )
      = ( inf_inf_b_o @ X3 @ Y2 ) ) ).

% inf_right_idem
thf(fact_236_inf__right__idem,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ Y2 )
      = ( inf_inf_set_o @ X3 @ Y2 ) ) ).

% inf_right_idem
thf(fact_237_inf__right__idem,axiom,
    ! [X3: $o,Y2: $o] :
      ( ( inf_inf_o @ ( inf_inf_o @ X3 @ Y2 ) @ Y2 )
      = ( inf_inf_o @ X3 @ Y2 ) ) ).

% inf_right_idem
thf(fact_238_inf__apply,axiom,
    ( inf_inf_b_o
    = ( ^ [F: b > $o,G4: b > $o,X2: b] : ( inf_inf_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) ) ) ).

% inf_apply
thf(fact_239_frame_Osurjective,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ( R
      = ( episte2888590659910966568t_unit @ ( episte8072386903178013299t_unit @ R ) @ ( episte6250069432388174439t_unit @ R ) @ ( episte3309513806868946049t_unit @ R ) ) ) ).

% frame.surjective
thf(fact_240_frame_Osurjective,axiom,
    ! [R: episte3224730989885420256t_unit] :
      ( R
      = ( episte4938218340073005086t_unit @ ( episte1782384855165018035t_unit @ R ) @ ( episte1071096959727133607t_unit @ R ) @ ( episte6669210725420356545t_unit @ R ) ) ) ).

% frame.surjective
thf(fact_241_frame_Ounfold__congs_I3_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: episte2291185870209430742t_unit,F2: episte2291185870209430742t_unit > episte2291185870209430742t_unit,F3: episte2291185870209430742t_unit > episte2291185870209430742t_unit] :
      ( ( R = R2 )
     => ( ( ( episte6669210725420356545t_unit @ R2 )
          = V )
       => ( ! [V2: episte2291185870209430742t_unit] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte2553589567909738282it_a_b @ F2 @ R )
            = ( episte2553589567909738282it_a_b @ F3 @ R2 ) ) ) ) ) ).

% frame.unfold_congs(3)
thf(fact_242_frame_Oext__inject,axiom,
    ! [W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit,W3: set_b,K2: a > b > set_b,More2: episte2291185870209430742t_unit] :
      ( ( ( episte4938218340073005086t_unit @ W2 @ K @ More )
        = ( episte4938218340073005086t_unit @ W3 @ K2 @ More2 ) )
      = ( ( W2 = W3 )
        & ( K = K2 )
        & ( More = More2 ) ) ) ).

% frame.ext_inject
thf(fact_243_frame_Oext__inject,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit,W3: set_se5208064806568342746c_fm_a,K2: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More2: episte1193835314949844379t_unit] :
      ( ( ( episte2888590659910966568t_unit @ W2 @ K @ More )
        = ( episte2888590659910966568t_unit @ W3 @ K2 @ More2 ) )
      = ( ( W2 = W3 )
        & ( K = K2 )
        & ( More = More2 ) ) ) ).

% frame.ext_inject
thf(fact_244_frame_Oupdate__convs_I3_J,axiom,
    ! [More2: episte2291185870209430742t_unit > episte2291185870209430742t_unit,W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte2553589567909738282it_a_b @ More2 @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = ( episte4938218340073005086t_unit @ W2 @ K @ ( More2 @ More ) ) ) ).

% frame.update_convs(3)
thf(fact_245_frame_Oupdate__convs_I3_J,axiom,
    ! [More2: episte1193835314949844379t_unit > episte1193835314949844379t_unit,W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte7964699311158398698c_fm_a @ More2 @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = ( episte2888590659910966568t_unit @ W2 @ K @ ( More2 @ More ) ) ) ).

% frame.update_convs(3)
thf(fact_246_frame_Ocases__scheme,axiom,
    ! [R: episte3224730989885420256t_unit] :
      ~ ! [W4: set_b,K3: a > b > set_b,More3: episte2291185870209430742t_unit] :
          ( R
         != ( episte4938218340073005086t_unit @ W4 @ K3 @ More3 ) ) ).

% frame.cases_scheme
thf(fact_247_frame_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W4: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More3: episte1193835314949844379t_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W4 @ K3 @ More3 ) ) ).

% frame.cases_scheme
thf(fact_248_frame_Oselect__convs_I1_J,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte8072386903178013299t_unit @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = W2 ) ).

% frame.select_convs(1)
thf(fact_249_frame_Oselect__convs_I1_J,axiom,
    ! [W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte1782384855165018035t_unit @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = W2 ) ).

% frame.select_convs(1)
thf(fact_250_frame_Oselect__convs_I2_J,axiom,
    ! [W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte1071096959727133607t_unit @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = K ) ).

% frame.select_convs(2)
thf(fact_251_frame_Oselect__convs_I2_J,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte6250069432388174439t_unit @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = K ) ).

% frame.select_convs(2)
thf(fact_252_frame_Oselect__convs_I3_J,axiom,
    ! [W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte6669210725420356545t_unit @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = More ) ).

% frame.select_convs(3)
thf(fact_253_frame_Oselect__convs_I3_J,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte3309513806868946049t_unit @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = More ) ).

% frame.select_convs(3)
thf(fact_254_inf__fun__def,axiom,
    ( inf_inf_b_o
    = ( ^ [F: b > $o,G4: b > $o,X2: b] : ( inf_inf_o @ ( F @ X2 ) @ ( G4 @ X2 ) ) ) ) ).

% inf_fun_def
thf(fact_255_inf__left__commute,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) )
      = ( inf_inf_set_b @ Y2 @ ( inf_inf_set_b @ X3 @ Z2 ) ) ) ).

% inf_left_commute
thf(fact_256_inf__left__commute,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) )
      = ( inf_inf_b_o @ Y2 @ ( inf_inf_b_o @ X3 @ Z2 ) ) ) ).

% inf_left_commute
thf(fact_257_inf__left__commute,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) )
      = ( inf_inf_set_o @ Y2 @ ( inf_inf_set_o @ X3 @ Z2 ) ) ) ).

% inf_left_commute
thf(fact_258_inf__left__commute,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( inf_inf_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) )
      = ( inf_inf_o @ Y2 @ ( inf_inf_o @ X3 @ Z2 ) ) ) ).

% inf_left_commute
thf(fact_259_inf_Oleft__commute,axiom,
    ! [B2: set_b,A: set_b,C: set_b] :
      ( ( inf_inf_set_b @ B2 @ ( inf_inf_set_b @ A @ C ) )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B2 @ C ) ) ) ).

% inf.left_commute
thf(fact_260_inf_Oleft__commute,axiom,
    ! [B2: b > $o,A: b > $o,C: b > $o] :
      ( ( inf_inf_b_o @ B2 @ ( inf_inf_b_o @ A @ C ) )
      = ( inf_inf_b_o @ A @ ( inf_inf_b_o @ B2 @ C ) ) ) ).

% inf.left_commute
thf(fact_261_inf_Oleft__commute,axiom,
    ! [B2: set_o,A: set_o,C: set_o] :
      ( ( inf_inf_set_o @ B2 @ ( inf_inf_set_o @ A @ C ) )
      = ( inf_inf_set_o @ A @ ( inf_inf_set_o @ B2 @ C ) ) ) ).

% inf.left_commute
thf(fact_262_inf_Oleft__commute,axiom,
    ! [B2: $o,A: $o,C: $o] :
      ( ( inf_inf_o @ B2 @ ( inf_inf_o @ A @ C ) )
      = ( inf_inf_o @ A @ ( inf_inf_o @ B2 @ C ) ) ) ).

% inf.left_commute
thf(fact_263_inf__commute,axiom,
    ( inf_inf_set_b
    = ( ^ [X2: set_b,Y: set_b] : ( inf_inf_set_b @ Y @ X2 ) ) ) ).

% inf_commute
thf(fact_264_inf__commute,axiom,
    ( inf_inf_b_o
    = ( ^ [X2: b > $o,Y: b > $o] : ( inf_inf_b_o @ Y @ X2 ) ) ) ).

% inf_commute
thf(fact_265_inf__commute,axiom,
    ( inf_inf_set_o
    = ( ^ [X2: set_o,Y: set_o] : ( inf_inf_set_o @ Y @ X2 ) ) ) ).

% inf_commute
thf(fact_266_inf__commute,axiom,
    ( inf_inf_o
    = ( ^ [X2: $o,Y: $o] : ( inf_inf_o @ Y @ X2 ) ) ) ).

% inf_commute
thf(fact_267_inf_Ocommute,axiom,
    ( inf_inf_set_b
    = ( ^ [A2: set_b,B3: set_b] : ( inf_inf_set_b @ B3 @ A2 ) ) ) ).

% inf.commute
thf(fact_268_inf_Ocommute,axiom,
    ( inf_inf_b_o
    = ( ^ [A2: b > $o,B3: b > $o] : ( inf_inf_b_o @ B3 @ A2 ) ) ) ).

% inf.commute
thf(fact_269_inf_Ocommute,axiom,
    ( inf_inf_set_o
    = ( ^ [A2: set_o,B3: set_o] : ( inf_inf_set_o @ B3 @ A2 ) ) ) ).

% inf.commute
thf(fact_270_inf_Ocommute,axiom,
    ( inf_inf_o
    = ( ^ [A2: $o,B3: $o] : ( inf_inf_o @ B3 @ A2 ) ) ) ).

% inf.commute
thf(fact_271_inf__assoc,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) ) ) ).

% inf_assoc
thf(fact_272_inf__assoc,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( inf_inf_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) ) ) ).

% inf_assoc
thf(fact_273_inf__assoc,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) ) ) ).

% inf_assoc
thf(fact_274_inf__assoc,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( inf_inf_o @ ( inf_inf_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) ) ) ).

% inf_assoc
thf(fact_275_inf_Oassoc,axiom,
    ! [A: set_b,B2: set_b,C: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B2 ) @ C )
      = ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B2 @ C ) ) ) ).

% inf.assoc
thf(fact_276_inf_Oassoc,axiom,
    ! [A: b > $o,B2: b > $o,C: b > $o] :
      ( ( inf_inf_b_o @ ( inf_inf_b_o @ A @ B2 ) @ C )
      = ( inf_inf_b_o @ A @ ( inf_inf_b_o @ B2 @ C ) ) ) ).

% inf.assoc
thf(fact_277_inf_Oassoc,axiom,
    ! [A: set_o,B2: set_o,C: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ A @ B2 ) @ C )
      = ( inf_inf_set_o @ A @ ( inf_inf_set_o @ B2 @ C ) ) ) ).

% inf.assoc
thf(fact_278_inf_Oassoc,axiom,
    ! [A: $o,B2: $o,C: $o] :
      ( ( inf_inf_o @ ( inf_inf_o @ A @ B2 ) @ C )
      = ( inf_inf_o @ A @ ( inf_inf_o @ B2 @ C ) ) ) ).

% inf.assoc
thf(fact_279_inf__sup__aci_I1_J,axiom,
    ( inf_inf_set_b
    = ( ^ [X2: set_b,Y: set_b] : ( inf_inf_set_b @ Y @ X2 ) ) ) ).

% inf_sup_aci(1)
thf(fact_280_inf__sup__aci_I1_J,axiom,
    ( inf_inf_b_o
    = ( ^ [X2: b > $o,Y: b > $o] : ( inf_inf_b_o @ Y @ X2 ) ) ) ).

% inf_sup_aci(1)
thf(fact_281_inf__sup__aci_I1_J,axiom,
    ( inf_inf_set_o
    = ( ^ [X2: set_o,Y: set_o] : ( inf_inf_set_o @ Y @ X2 ) ) ) ).

% inf_sup_aci(1)
thf(fact_282_inf__sup__aci_I1_J,axiom,
    ( inf_inf_o
    = ( ^ [X2: $o,Y: $o] : ( inf_inf_o @ Y @ X2 ) ) ) ).

% inf_sup_aci(1)
thf(fact_283_inf__sup__aci_I2_J,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) ) ) ).

% inf_sup_aci(2)
thf(fact_284_inf__sup__aci_I2_J,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( inf_inf_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) ) ) ).

% inf_sup_aci(2)
thf(fact_285_inf__sup__aci_I2_J,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) ) ) ).

% inf_sup_aci(2)
thf(fact_286_inf__sup__aci_I2_J,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( inf_inf_o @ ( inf_inf_o @ X3 @ Y2 ) @ Z2 )
      = ( inf_inf_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) ) ) ).

% inf_sup_aci(2)
thf(fact_287_inf__sup__aci_I3_J,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) )
      = ( inf_inf_set_b @ Y2 @ ( inf_inf_set_b @ X3 @ Z2 ) ) ) ).

% inf_sup_aci(3)
thf(fact_288_inf__sup__aci_I3_J,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) )
      = ( inf_inf_b_o @ Y2 @ ( inf_inf_b_o @ X3 @ Z2 ) ) ) ).

% inf_sup_aci(3)
thf(fact_289_inf__sup__aci_I3_J,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) )
      = ( inf_inf_set_o @ Y2 @ ( inf_inf_set_o @ X3 @ Z2 ) ) ) ).

% inf_sup_aci(3)
thf(fact_290_inf__sup__aci_I3_J,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( inf_inf_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) )
      = ( inf_inf_o @ Y2 @ ( inf_inf_o @ X3 @ Z2 ) ) ) ).

% inf_sup_aci(3)
thf(fact_291_inf__sup__aci_I4_J,axiom,
    ! [X3: set_b,Y2: set_b] :
      ( ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ X3 @ Y2 ) )
      = ( inf_inf_set_b @ X3 @ Y2 ) ) ).

% inf_sup_aci(4)
thf(fact_292_inf__sup__aci_I4_J,axiom,
    ! [X3: b > $o,Y2: b > $o] :
      ( ( inf_inf_b_o @ X3 @ ( inf_inf_b_o @ X3 @ Y2 ) )
      = ( inf_inf_b_o @ X3 @ Y2 ) ) ).

% inf_sup_aci(4)
thf(fact_293_inf__sup__aci_I4_J,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ X3 @ Y2 ) )
      = ( inf_inf_set_o @ X3 @ Y2 ) ) ).

% inf_sup_aci(4)
thf(fact_294_inf__sup__aci_I4_J,axiom,
    ! [X3: $o,Y2: $o] :
      ( ( inf_inf_o @ X3 @ ( inf_inf_o @ X3 @ Y2 ) )
      = ( inf_inf_o @ X3 @ Y2 ) ) ).

% inf_sup_aci(4)
thf(fact_295_Int__left__commute,axiom,
    ! [A3: set_b,B: set_b,C2: set_b] :
      ( ( inf_inf_set_b @ A3 @ ( inf_inf_set_b @ B @ C2 ) )
      = ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A3 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_296_Int__left__commute,axiom,
    ! [A3: set_o,B: set_o,C2: set_o] :
      ( ( inf_inf_set_o @ A3 @ ( inf_inf_set_o @ B @ C2 ) )
      = ( inf_inf_set_o @ B @ ( inf_inf_set_o @ A3 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_297_Int__left__absorb,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A3 @ ( inf_inf_set_b @ A3 @ B ) )
      = ( inf_inf_set_b @ A3 @ B ) ) ).

% Int_left_absorb
thf(fact_298_Int__left__absorb,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( inf_inf_set_o @ A3 @ ( inf_inf_set_o @ A3 @ B ) )
      = ( inf_inf_set_o @ A3 @ B ) ) ).

% Int_left_absorb
thf(fact_299_Int__commute,axiom,
    ( inf_inf_set_b
    = ( ^ [A4: set_b,B4: set_b] : ( inf_inf_set_b @ B4 @ A4 ) ) ) ).

% Int_commute
thf(fact_300_Int__commute,axiom,
    ( inf_inf_set_o
    = ( ^ [A4: set_o,B4: set_o] : ( inf_inf_set_o @ B4 @ A4 ) ) ) ).

% Int_commute
thf(fact_301_Int__absorb,axiom,
    ! [A3: set_b] :
      ( ( inf_inf_set_b @ A3 @ A3 )
      = A3 ) ).

% Int_absorb
thf(fact_302_Int__absorb,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ A3 @ A3 )
      = A3 ) ).

% Int_absorb
thf(fact_303_Int__assoc,axiom,
    ! [A3: set_b,B: set_b,C2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A3 @ B ) @ C2 )
      = ( inf_inf_set_b @ A3 @ ( inf_inf_set_b @ B @ C2 ) ) ) ).

% Int_assoc
thf(fact_304_Int__assoc,axiom,
    ! [A3: set_o,B: set_o,C2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ A3 @ B ) @ C2 )
      = ( inf_inf_set_o @ A3 @ ( inf_inf_set_o @ B @ C2 ) ) ) ).

% Int_assoc
thf(fact_305_IntD2,axiom,
    ! [C: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ C @ ( inf_in1884693029477671368c_fm_a @ A3 @ B ) )
     => ( member536094252920883875c_fm_a @ C @ B ) ) ).

% IntD2
thf(fact_306_IntD2,axiom,
    ! [C: set_o,A3: set_set_o,B: set_set_o] :
      ( ( member_set_o @ C @ ( inf_inf_set_set_o @ A3 @ B ) )
     => ( member_set_o @ C @ B ) ) ).

% IntD2
thf(fact_307_IntD2,axiom,
    ! [C: set_b,A3: set_set_b,B: set_set_b] :
      ( ( member_set_b @ C @ ( inf_inf_set_set_b @ A3 @ B ) )
     => ( member_set_b @ C @ B ) ) ).

% IntD2
thf(fact_308_IntD2,axiom,
    ! [C: a,A3: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B ) )
     => ( member_a @ C @ B ) ) ).

% IntD2
thf(fact_309_IntD2,axiom,
    ! [C: $o,A3: set_o,B: set_o] :
      ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B ) )
     => ( member_o @ C @ B ) ) ).

% IntD2
thf(fact_310_IntD2,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A3 @ B ) )
     => ( member_b @ C @ B ) ) ).

% IntD2
thf(fact_311_IntD1,axiom,
    ! [C: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ C @ ( inf_in1884693029477671368c_fm_a @ A3 @ B ) )
     => ( member536094252920883875c_fm_a @ C @ A3 ) ) ).

% IntD1
thf(fact_312_IntD1,axiom,
    ! [C: set_o,A3: set_set_o,B: set_set_o] :
      ( ( member_set_o @ C @ ( inf_inf_set_set_o @ A3 @ B ) )
     => ( member_set_o @ C @ A3 ) ) ).

% IntD1
thf(fact_313_IntD1,axiom,
    ! [C: set_b,A3: set_set_b,B: set_set_b] :
      ( ( member_set_b @ C @ ( inf_inf_set_set_b @ A3 @ B ) )
     => ( member_set_b @ C @ A3 ) ) ).

% IntD1
thf(fact_314_IntD1,axiom,
    ! [C: a,A3: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B ) )
     => ( member_a @ C @ A3 ) ) ).

% IntD1
thf(fact_315_IntD1,axiom,
    ! [C: $o,A3: set_o,B: set_o] :
      ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B ) )
     => ( member_o @ C @ A3 ) ) ).

% IntD1
thf(fact_316_IntD1,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A3 @ B ) )
     => ( member_b @ C @ A3 ) ) ).

% IntD1
thf(fact_317_IntE,axiom,
    ! [C: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ( member536094252920883875c_fm_a @ C @ ( inf_in1884693029477671368c_fm_a @ A3 @ B ) )
     => ~ ( ( member536094252920883875c_fm_a @ C @ A3 )
         => ~ ( member536094252920883875c_fm_a @ C @ B ) ) ) ).

% IntE
thf(fact_318_IntE,axiom,
    ! [C: set_o,A3: set_set_o,B: set_set_o] :
      ( ( member_set_o @ C @ ( inf_inf_set_set_o @ A3 @ B ) )
     => ~ ( ( member_set_o @ C @ A3 )
         => ~ ( member_set_o @ C @ B ) ) ) ).

% IntE
thf(fact_319_IntE,axiom,
    ! [C: set_b,A3: set_set_b,B: set_set_b] :
      ( ( member_set_b @ C @ ( inf_inf_set_set_b @ A3 @ B ) )
     => ~ ( ( member_set_b @ C @ A3 )
         => ~ ( member_set_b @ C @ B ) ) ) ).

% IntE
thf(fact_320_IntE,axiom,
    ! [C: a,A3: set_a,B: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A3 @ B ) )
     => ~ ( ( member_a @ C @ A3 )
         => ~ ( member_a @ C @ B ) ) ) ).

% IntE
thf(fact_321_IntE,axiom,
    ! [C: $o,A3: set_o,B: set_o] :
      ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B ) )
     => ~ ( ( member_o @ C @ A3 )
         => ~ ( member_o @ C @ B ) ) ) ).

% IntE
thf(fact_322_IntE,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A3 @ B ) )
     => ~ ( ( member_b @ C @ A3 )
         => ~ ( member_b @ C @ B ) ) ) ).

% IntE
thf(fact_323_frame_Ofold__congs_I3_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: episte2291185870209430742t_unit,F2: episte2291185870209430742t_unit > episte2291185870209430742t_unit,F3: episte2291185870209430742t_unit > episte2291185870209430742t_unit] :
      ( ( R = R2 )
     => ( ( ( episte6669210725420356545t_unit @ R2 )
          = V )
       => ( ! [V2: episte2291185870209430742t_unit] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte2553589567909738282it_a_b @ F2 @ R )
            = ( episte2553589567909738282it_a_b @ F3 @ R2 ) ) ) ) ) ).

% frame.fold_congs(3)
thf(fact_324_distribution,axiom,
    ! [M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( episte7081087998767065248c_fm_a @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ).

% distribution
thf(fact_325_distribution,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ).

% distribution
thf(fact_326_boolean__algebra__cancel_Oinf2,axiom,
    ! [B: set_b,K4: set_b,B2: set_b,A: set_b] :
      ( ( B
        = ( inf_inf_set_b @ K4 @ B2 ) )
     => ( ( inf_inf_set_b @ A @ B )
        = ( inf_inf_set_b @ K4 @ ( inf_inf_set_b @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_327_boolean__algebra__cancel_Oinf2,axiom,
    ! [B: b > $o,K4: b > $o,B2: b > $o,A: b > $o] :
      ( ( B
        = ( inf_inf_b_o @ K4 @ B2 ) )
     => ( ( inf_inf_b_o @ A @ B )
        = ( inf_inf_b_o @ K4 @ ( inf_inf_b_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_328_boolean__algebra__cancel_Oinf2,axiom,
    ! [B: set_o,K4: set_o,B2: set_o,A: set_o] :
      ( ( B
        = ( inf_inf_set_o @ K4 @ B2 ) )
     => ( ( inf_inf_set_o @ A @ B )
        = ( inf_inf_set_o @ K4 @ ( inf_inf_set_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_329_boolean__algebra__cancel_Oinf2,axiom,
    ! [B: $o,K4: $o,B2: $o,A: $o] :
      ( ( B
        = ( inf_inf_o @ K4 @ B2 ) )
     => ( ( inf_inf_o @ A @ B )
        = ( inf_inf_o @ K4 @ ( inf_inf_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_330_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: set_b,K4: set_b,A: set_b,B2: set_b] :
      ( ( A3
        = ( inf_inf_set_b @ K4 @ A ) )
     => ( ( inf_inf_set_b @ A3 @ B2 )
        = ( inf_inf_set_b @ K4 @ ( inf_inf_set_b @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_331_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: b > $o,K4: b > $o,A: b > $o,B2: b > $o] :
      ( ( A3
        = ( inf_inf_b_o @ K4 @ A ) )
     => ( ( inf_inf_b_o @ A3 @ B2 )
        = ( inf_inf_b_o @ K4 @ ( inf_inf_b_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_332_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: set_o,K4: set_o,A: set_o,B2: set_o] :
      ( ( A3
        = ( inf_inf_set_o @ K4 @ A ) )
     => ( ( inf_inf_set_o @ A3 @ B2 )
        = ( inf_inf_set_o @ K4 @ ( inf_inf_set_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_333_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: $o,K4: $o,A: $o,B2: $o] :
      ( ( A3
        = ( inf_inf_o @ K4 @ A ) )
     => ( ( inf_inf_o @ A3 @ B2 )
        = ( inf_inf_o @ K4 @ ( inf_inf_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_334_frame_Oupdate__convs_I1_J,axiom,
    ! [W3: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a,W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte8842944213534508900t_unit @ W3 @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = ( episte2888590659910966568t_unit @ ( W3 @ W2 ) @ K @ More ) ) ).

% frame.update_convs(1)
thf(fact_335_frame_Oupdate__convs_I1_J,axiom,
    ! [W3: set_b > set_b,W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte3904078566835727962t_unit @ W3 @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = ( episte4938218340073005086t_unit @ ( W3 @ W2 ) @ K @ More ) ) ).

% frame.update_convs(1)
thf(fact_336_frame_Ofold__congs_I2_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: a > b > set_b,F2: ( a > b > set_b ) > a > b > set_b,F3: ( a > b > set_b ) > a > b > set_b] :
      ( ( R = R2 )
     => ( ( ( episte1071096959727133607t_unit @ R2 )
          = V )
       => ( ! [V2: a > b > set_b] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte5760896158387330320t_unit @ F2 @ R )
            = ( episte5760896158387330320t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.fold_congs(2)
thf(fact_337_frame_Ounfold__congs_I2_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: a > b > set_b,F2: ( a > b > set_b ) > a > b > set_b,F3: ( a > b > set_b ) > a > b > set_b] :
      ( ( R = R2 )
     => ( ( ( episte1071096959727133607t_unit @ R2 )
          = V )
       => ( ! [V2: a > b > set_b] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte5760896158387330320t_unit @ F2 @ R )
            = ( episte5760896158387330320t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.unfold_congs(2)
thf(fact_338_frame_Ounfold__congs_I1_J,axiom,
    ! [R: episte1560738328020401952t_unit,R2: episte1560738328020401952t_unit,V: set_se5208064806568342746c_fm_a,F2: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a,F3: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a] :
      ( ( R = R2 )
     => ( ( ( episte8072386903178013299t_unit @ R2 )
          = V )
       => ( ! [V2: set_se5208064806568342746c_fm_a] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte8842944213534508900t_unit @ F2 @ R )
            = ( episte8842944213534508900t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.unfold_congs(1)
thf(fact_339_frame_Ounfold__congs_I1_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: set_b,F2: set_b > set_b,F3: set_b > set_b] :
      ( ( R = R2 )
     => ( ( ( episte1782384855165018035t_unit @ R2 )
          = V )
       => ( ! [V2: set_b] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte3904078566835727962t_unit @ F2 @ R )
            = ( episte3904078566835727962t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.unfold_congs(1)
thf(fact_340_frame_Ofold__congs_I1_J,axiom,
    ! [R: episte1560738328020401952t_unit,R2: episte1560738328020401952t_unit,V: set_se5208064806568342746c_fm_a,F2: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a,F3: set_se5208064806568342746c_fm_a > set_se5208064806568342746c_fm_a] :
      ( ( R = R2 )
     => ( ( ( episte8072386903178013299t_unit @ R2 )
          = V )
       => ( ! [V2: set_se5208064806568342746c_fm_a] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte8842944213534508900t_unit @ F2 @ R )
            = ( episte8842944213534508900t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.fold_congs(1)
thf(fact_341_frame_Ofold__congs_I1_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: set_b,F2: set_b > set_b,F3: set_b > set_b] :
      ( ( R = R2 )
     => ( ( ( episte1782384855165018035t_unit @ R2 )
          = V )
       => ( ! [V2: set_b] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte3904078566835727962t_unit @ F2 @ R )
            = ( episte3904078566835727962t_unit @ F3 @ R2 ) ) ) ) ) ).

% frame.fold_congs(1)
thf(fact_342_frame_Oupdate__convs_I2_J,axiom,
    ! [K2: ( a > b > set_b ) > a > b > set_b,W2: set_b,K: a > b > set_b,More: episte2291185870209430742t_unit] :
      ( ( episte5760896158387330320t_unit @ K2 @ ( episte4938218340073005086t_unit @ W2 @ K @ More ) )
      = ( episte4938218340073005086t_unit @ W2 @ ( K2 @ K ) @ More ) ) ).

% frame.update_convs(2)
thf(fact_343_frame_Oupdate__convs_I2_J,axiom,
    ! [K2: ( a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a ) > a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,More: episte1193835314949844379t_unit] :
      ( ( episte7087520964475219152t_unit @ K2 @ ( episte2888590659910966568t_unit @ W2 @ K @ More ) )
      = ( episte2888590659910966568t_unit @ W2 @ ( K2 @ K ) @ More ) ) ).

% frame.update_convs(2)
thf(fact_344_kripke_Oequality,axiom,
    ! [R: episte1560738328020401952t_unit,R2: episte1560738328020401952t_unit] :
      ( ( ( episte8072386903178013299t_unit @ R )
        = ( episte8072386903178013299t_unit @ R2 ) )
     => ( ( ( episte6250069432388174439t_unit @ R )
          = ( episte6250069432388174439t_unit @ R2 ) )
       => ( ( ( episte2398645135750866164t_unit @ R )
            = ( episte2398645135750866164t_unit @ R2 ) )
         => ( ( ( episte5479201149095757850t_unit @ R )
              = ( episte5479201149095757850t_unit @ R2 ) )
           => ( R = R2 ) ) ) ) ) ).

% kripke.equality
thf(fact_345_kripke_Oequality,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit] :
      ( ( ( episte1782384855165018035t_unit @ R )
        = ( episte1782384855165018035t_unit @ R2 ) )
     => ( ( ( episte1071096959727133607t_unit @ R )
          = ( episte1071096959727133607t_unit @ R2 ) )
       => ( ( ( episte5693316124195166255t_unit @ R )
            = ( episte5693316124195166255t_unit @ R2 ) )
         => ( ( ( episte7270682542085591125t_unit @ R )
              = ( episte7270682542085591125t_unit @ R2 ) )
           => ( R = R2 ) ) ) ) ) ).

% kripke.equality
thf(fact_346_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_347_fm_Oinject_I3_J,axiom,
    ! [X41: epistemic_fm_b,X42: epistemic_fm_b,Y41: epistemic_fm_b,Y42: epistemic_fm_b] :
      ( ( ( epistemic_Con_b @ X41 @ X42 )
        = ( epistemic_Con_b @ Y41 @ Y42 ) )
      = ( ( X41 = Y41 )
        & ( X42 = Y42 ) ) ) ).

% fm.inject(3)
thf(fact_348_fm_Odistinct_I25_J,axiom,
    ! [X41: epistemic_fm_b,X42: epistemic_fm_b,X51: epistemic_fm_b,X52: epistemic_fm_b] :
      ( ( epistemic_Con_b @ X41 @ X42 )
     != ( epistemic_Imp_b @ X51 @ X52 ) ) ).

% fm.distinct(25)
thf(fact_349_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_350_fm_Odistinct_I27_J,axiom,
    ! [X41: epistemic_fm_o,X42: epistemic_fm_o,X61: $o,X62: epistemic_fm_o] :
      ( ( epistemic_Con_o @ X41 @ X42 )
     != ( epistemic_K_o @ X61 @ X62 ) ) ).

% fm.distinct(27)
thf(fact_351_fm_Odistinct_I27_J,axiom,
    ! [X41: epistemic_fm_b,X42: epistemic_fm_b,X61: b,X62: epistemic_fm_b] :
      ( ( epistemic_Con_b @ X41 @ X42 )
     != ( epistemic_K_b @ X61 @ X62 ) ) ).

% fm.distinct(27)
thf(fact_352_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_353_fm_Odistinct_I5_J,axiom,
    ! [X41: epistemic_fm_o,X42: epistemic_fm_o] :
      ( epistemic_FF_o
     != ( epistemic_Con_o @ X41 @ X42 ) ) ).

% fm.distinct(5)
thf(fact_354_fm_Odistinct_I5_J,axiom,
    ! [X41: epistemic_fm_b,X42: epistemic_fm_b] :
      ( epistemic_FF_b
     != ( epistemic_Con_b @ X41 @ X42 ) ) ).

% fm.distinct(5)
thf(fact_355_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_356_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_357_semantics_Osimps_I4_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( episte295617885132580261cs_a_b @ M @ W @ P )
        & ( episte295617885132580261cs_a_b @ M @ W @ Q ) ) ) ).

% semantics.simps(4)
thf(fact_358_eval_Osimps_I4_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
        & ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_359_eval_Osimps_I4_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b] :
      ( ( epistemic_eval_b @ G2 @ H2 @ ( epistemic_Con_b @ P @ Q ) )
      = ( ( epistemic_eval_b @ G2 @ H2 @ P )
        & ( epistemic_eval_b @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_360_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_361_kripke_Osurjective,axiom,
    ! [R: episte3224730989885420256t_unit] :
      ( R
      = ( episte4938218340073005086t_unit @ ( episte1782384855165018035t_unit @ R ) @ ( episte1071096959727133607t_unit @ R ) @ ( episte6143282164508887558t_unit @ ( episte5693316124195166255t_unit @ R ) @ ( episte7270682542085591125t_unit @ R ) ) ) ) ).

% kripke.surjective
thf(fact_362_kripke_Ounfold__congs_I4_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: product_unit,F2: product_unit > product_unit,F3: product_unit > product_unit] :
      ( ( R = R2 )
     => ( ( ( episte7270682542085591125t_unit @ R2 )
          = V )
       => ( ! [V2: product_unit] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte5119575119384494574it_a_b @ F2 @ R )
            = ( episte5119575119384494574it_a_b @ F3 @ R2 ) ) ) ) ) ).

% kripke.unfold_congs(4)
thf(fact_363_kripke_Ofold__congs_I4_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: product_unit,F2: product_unit > product_unit,F3: product_unit > product_unit] :
      ( ( R = R2 )
     => ( ( ( episte7270682542085591125t_unit @ R2 )
          = V )
       => ( ! [V2: product_unit] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte5119575119384494574it_a_b @ F2 @ R )
            = ( episte5119575119384494574it_a_b @ F3 @ R2 ) ) ) ) ) ).

% kripke.fold_congs(4)
thf(fact_364_AK_Osimps,axiom,
    ( epistemic_AK_o
    = ( ^ [A4: epistemic_fm_o > $o,A2: epistemic_fm_o] :
          ( ? [P3: epistemic_fm_o] :
              ( ( A2 = P3 )
              & ! [G4: list_char > $o,H4: epistemic_fm_o > $o] : ( epistemic_eval_o @ G4 @ H4 @ P3 ) )
          | ? [I2: $o,P3: epistemic_fm_o,Q3: epistemic_fm_o] :
              ( A2
              = ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I2 @ P3 ) @ ( epistemic_K_o @ I2 @ ( epistemic_Imp_o @ P3 @ Q3 ) ) ) @ ( epistemic_K_o @ I2 @ Q3 ) ) )
          | ? [P3: epistemic_fm_o] :
              ( ( A2 = P3 )
              & ( A4 @ P3 ) )
          | ? [P3: epistemic_fm_o,Q3: epistemic_fm_o] :
              ( ( A2 = Q3 )
              & ( epistemic_AK_o @ A4 @ P3 )
              & ( epistemic_AK_o @ A4 @ ( epistemic_Imp_o @ P3 @ Q3 ) ) )
          | ? [P3: epistemic_fm_o,I2: $o] :
              ( ( A2
                = ( epistemic_K_o @ I2 @ P3 ) )
              & ( epistemic_AK_o @ A4 @ P3 ) ) ) ) ) ).

% AK.simps
thf(fact_365_AK_Osimps,axiom,
    ( epistemic_AK_b
    = ( ^ [A4: epistemic_fm_b > $o,A2: epistemic_fm_b] :
          ( ? [P3: epistemic_fm_b] :
              ( ( A2 = P3 )
              & ! [G4: list_char > $o,H4: epistemic_fm_b > $o] : ( epistemic_eval_b @ G4 @ H4 @ P3 ) )
          | ? [I2: b,P3: epistemic_fm_b,Q3: epistemic_fm_b] :
              ( A2
              = ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I2 @ P3 ) @ ( epistemic_K_b @ I2 @ ( epistemic_Imp_b @ P3 @ Q3 ) ) ) @ ( epistemic_K_b @ I2 @ Q3 ) ) )
          | ? [P3: epistemic_fm_b] :
              ( ( A2 = P3 )
              & ( A4 @ P3 ) )
          | ? [P3: epistemic_fm_b,Q3: epistemic_fm_b] :
              ( ( A2 = Q3 )
              & ( epistemic_AK_b @ A4 @ P3 )
              & ( epistemic_AK_b @ A4 @ ( epistemic_Imp_b @ P3 @ Q3 ) ) )
          | ? [P3: epistemic_fm_b,I2: b] :
              ( ( A2
                = ( epistemic_K_b @ I2 @ P3 ) )
              & ( epistemic_AK_b @ A4 @ P3 ) ) ) ) ) ).

% AK.simps
thf(fact_366_AK_Osimps,axiom,
    ( epistemic_AK_a
    = ( ^ [A4: epistemic_fm_a > $o,A2: epistemic_fm_a] :
          ( ? [P3: epistemic_fm_a] :
              ( ( A2 = P3 )
              & ! [G4: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G4 @ H4 @ P3 ) )
          | ? [I2: a,P3: epistemic_fm_a,Q3: epistemic_fm_a] :
              ( A2
              = ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I2 @ P3 ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P3 @ Q3 ) ) ) @ ( epistemic_K_a @ I2 @ Q3 ) ) )
          | ? [P3: epistemic_fm_a] :
              ( ( A2 = P3 )
              & ( A4 @ P3 ) )
          | ? [P3: epistemic_fm_a,Q3: epistemic_fm_a] :
              ( ( A2 = Q3 )
              & ( epistemic_AK_a @ A4 @ P3 )
              & ( epistemic_AK_a @ A4 @ ( epistemic_Imp_a @ P3 @ Q3 ) ) )
          | ? [P3: epistemic_fm_a,I2: a] :
              ( ( A2
                = ( epistemic_K_a @ I2 @ P3 ) )
              & ( epistemic_AK_a @ A4 @ P3 ) ) ) ) ) ).

% AK.simps
thf(fact_367_AK_Ocases,axiom,
    ! [A3: epistemic_fm_o > $o,A: epistemic_fm_o] :
      ( ( epistemic_AK_o @ A3 @ A )
     => ( ~ ! [G: list_char > $o,H: epistemic_fm_o > $o] : ( epistemic_eval_o @ G @ H @ A )
       => ( ! [I: $o,P2: epistemic_fm_o,Q4: epistemic_fm_o] :
              ( A
             != ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I @ P2 ) @ ( epistemic_K_o @ I @ ( epistemic_Imp_o @ P2 @ Q4 ) ) ) @ ( epistemic_K_o @ I @ Q4 ) ) )
         => ( ~ ( A3 @ A )
           => ( ! [P2: epistemic_fm_o] :
                  ( ( epistemic_AK_o @ A3 @ P2 )
                 => ~ ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ P2 @ A ) ) )
             => ~ ! [P2: epistemic_fm_o] :
                    ( ? [I: $o] :
                        ( A
                        = ( epistemic_K_o @ I @ P2 ) )
                   => ~ ( epistemic_AK_o @ A3 @ P2 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_368_AK_Ocases,axiom,
    ! [A3: epistemic_fm_b > $o,A: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ A )
     => ( ~ ! [G: list_char > $o,H: epistemic_fm_b > $o] : ( epistemic_eval_b @ G @ H @ A )
       => ( ! [I: b,P2: epistemic_fm_b,Q4: epistemic_fm_b] :
              ( A
             != ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I @ P2 ) @ ( epistemic_K_b @ I @ ( epistemic_Imp_b @ P2 @ Q4 ) ) ) @ ( epistemic_K_b @ I @ Q4 ) ) )
         => ( ~ ( A3 @ A )
           => ( ! [P2: epistemic_fm_b] :
                  ( ( epistemic_AK_b @ A3 @ P2 )
                 => ~ ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P2 @ A ) ) )
             => ~ ! [P2: epistemic_fm_b] :
                    ( ? [I: b] :
                        ( A
                        = ( epistemic_K_b @ I @ P2 ) )
                   => ~ ( epistemic_AK_b @ A3 @ P2 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_369_AK_Ocases,axiom,
    ! [A3: epistemic_fm_a > $o,A: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ A )
     => ( ~ ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ A )
       => ( ! [I: a,P2: epistemic_fm_a,Q4: epistemic_fm_a] :
              ( A
             != ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P2 ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P2 @ Q4 ) ) ) @ ( epistemic_K_a @ I @ Q4 ) ) )
         => ( ~ ( A3 @ A )
           => ( ! [P2: epistemic_fm_a] :
                  ( ( epistemic_AK_a @ A3 @ P2 )
                 => ~ ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P2 @ A ) ) )
             => ~ ! [P2: epistemic_fm_a] :
                    ( ? [I: a] :
                        ( A
                        = ( epistemic_K_a @ I @ P2 ) )
                   => ~ ( epistemic_AK_a @ A3 @ P2 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_370_K__thm,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ Q @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_Con_o @ P @ Q ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ).

% K_thm
thf(fact_371_K__thm,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ Q @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_Con_b @ P @ Q ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ).

% K_thm
thf(fact_372_K__thm,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ P @ Q ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ).

% K_thm
thf(fact_373_kripke_Ounfold__congs_I3_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: b > list_char > $o,F2: ( b > list_char > $o ) > b > list_char > $o,F3: ( b > list_char > $o ) > b > list_char > $o] :
      ( ( R = R2 )
     => ( ( ( episte5693316124195166255t_unit @ R2 )
          = V )
       => ( ! [V2: b > list_char > $o] :
              ( ( V2 = V )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte7164994875842154440t_unit @ F2 @ R )
            = ( episte7164994875842154440t_unit @ F3 @ R2 ) ) ) ) ) ).

% kripke.unfold_congs(3)
thf(fact_374_kripke_Ofold__congs_I3_J,axiom,
    ! [R: episte3224730989885420256t_unit,R2: episte3224730989885420256t_unit,V: b > list_char > $o,F2: ( b > list_char > $o ) > b > list_char > $o,F3: ( b > list_char > $o ) > b > list_char > $o] :
      ( ( R = R2 )
     => ( ( ( episte5693316124195166255t_unit @ R2 )
          = V )
       => ( ! [V2: b > list_char > $o] :
              ( ( V = V2 )
             => ( ( F2 @ V2 )
                = ( F3 @ V2 ) ) )
         => ( ( episte7164994875842154440t_unit @ F2 @ R )
            = ( episte7164994875842154440t_unit @ F3 @ R2 ) ) ) ) ) ).

% kripke.fold_congs(3)
thf(fact_375_A2,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ Q ) ) ) @ ( epistemic_K_o @ I3 @ Q ) ) ) ).

% A2
thf(fact_376_A2,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ Q ) ) ) @ ( epistemic_K_b @ I3 @ Q ) ) ) ).

% A2
thf(fact_377_A2,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ).

% A2
thf(fact_378_kripke_Oext__inject,axiom,
    ! [Pi: b > list_char > $o,More: product_unit,Pi2: b > list_char > $o,More2: product_unit] :
      ( ( ( episte6143282164508887558t_unit @ Pi @ More )
        = ( episte6143282164508887558t_unit @ Pi2 @ More2 ) )
      = ( ( Pi = Pi2 )
        & ( More = More2 ) ) ) ).

% kripke.ext_inject
thf(fact_379_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_380_Ax,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a] :
      ( ( A3 @ P )
     => ( epistemic_AK_a @ A3 @ P ) ) ).

% Ax
thf(fact_381_kripke_Oext__induct,axiom,
    ! [P4: episte2291185870209430742t_unit > $o,R: episte2291185870209430742t_unit] :
      ( ! [Pi3: b > list_char > $o,More3: product_unit] : ( P4 @ ( episte6143282164508887558t_unit @ Pi3 @ More3 ) )
     => ( P4 @ R ) ) ).

% kripke.ext_induct
thf(fact_382_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_383_kripke_Ocases__scheme,axiom,
    ! [R: episte3224730989885420256t_unit] :
      ~ ! [W4: set_b,K3: a > b > set_b,Pi3: b > list_char > $o,More3: product_unit] :
          ( R
         != ( episte4938218340073005086t_unit @ W4 @ K3 @ ( episte6143282164508887558t_unit @ Pi3 @ More3 ) ) ) ).

% kripke.cases_scheme
thf(fact_384_kripke_Ocases__scheme,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W4: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o,More3: product_unit] :
          ( R
         != ( episte2888590659910966568t_unit @ W4 @ K3 @ ( episte8239586592105053771t_unit @ Pi3 @ More3 ) ) ) ).

% kripke.cases_scheme
thf(fact_385_kripke_Oupdate__convs_I1_J,axiom,
    ! [Pi2: ( b > list_char > $o ) > b > list_char > $o,W2: set_b,K: a > b > set_b,Pi: b > list_char > $o,More: product_unit] :
      ( ( episte7164994875842154440t_unit @ Pi2 @ ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ Pi @ More ) ) )
      = ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ ( Pi2 @ Pi ) @ More ) ) ) ).

% kripke.update_convs(1)
thf(fact_386_kripke_Oupdate__convs_I1_J,axiom,
    ! [Pi2: ( set_Epistemic_fm_a > list_char > $o ) > set_Epistemic_fm_a > list_char > $o,W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte1857908288096881731t_unit @ Pi2 @ ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ ( Pi2 @ Pi ) @ More ) ) ) ).

% kripke.update_convs(1)
thf(fact_387_kripke_Oupdate__convs_I2_J,axiom,
    ! [More2: product_unit > product_unit,W2: set_b,K: a > b > set_b,Pi: b > list_char > $o,More: product_unit] :
      ( ( episte5119575119384494574it_a_b @ More2 @ ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ Pi @ More ) ) )
      = ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ Pi @ ( More2 @ More ) ) ) ) ).

% kripke.update_convs(2)
thf(fact_388_kripke_Oupdate__convs_I2_J,axiom,
    ! [More2: product_unit > product_unit,W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte9120385895580347753c_fm_a @ More2 @ ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ Pi @ ( More2 @ More ) ) ) ) ).

% kripke.update_convs(2)
thf(fact_389_K__imp__trans,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b,R: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ Q ) )
     => ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ Q @ R ) )
       => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ R ) ) ) ) ).

% K_imp_trans
thf(fact_390_K__imp__trans,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ Q ) )
     => ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ Q @ R ) )
       => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans
thf(fact_391_K__imp__trans_H,axiom,
    ! [A3: epistemic_fm_b > $o,Q: epistemic_fm_b,R: epistemic_fm_b,P: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ Q @ R ) )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ P @ Q ) @ ( epistemic_Imp_b @ P @ R ) ) ) ) ).

% K_imp_trans'
thf(fact_392_K__imp__trans_H,axiom,
    ! [A3: epistemic_fm_a > $o,Q: epistemic_fm_a,R: epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ Q @ R ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans'
thf(fact_393_R1,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ P )
     => ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ Q ) )
       => ( epistemic_AK_b @ A3 @ Q ) ) ) ).

% R1
thf(fact_394_R1,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ P )
     => ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ Q ) )
       => ( epistemic_AK_a @ A3 @ Q ) ) ) ).

% R1
thf(fact_395_K__trans,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b,R: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ P @ Q ) @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ Q @ R ) @ ( epistemic_Imp_b @ P @ R ) ) ) ) ).

% K_trans
thf(fact_396_K__trans,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( 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_397_R2,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,I3: b] :
      ( ( epistemic_AK_b @ A3 @ P )
     => ( epistemic_AK_b @ A3 @ ( epistemic_K_b @ I3 @ P ) ) ) ).

% R2
thf(fact_398_R2,axiom,
    ! [A3: epistemic_fm_o > $o,P: epistemic_fm_o,I3: $o] :
      ( ( epistemic_AK_o @ A3 @ P )
     => ( epistemic_AK_o @ A3 @ ( epistemic_K_o @ I3 @ P ) ) ) ).

% R2
thf(fact_399_R2,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,I3: a] :
      ( ( epistemic_AK_a @ A3 @ P )
     => ( epistemic_AK_a @ A3 @ ( epistemic_K_a @ I3 @ P ) ) ) ).

% R2
thf(fact_400_A1,axiom,
    ! [P: epistemic_fm_a,A3: epistemic_fm_a > $o] :
      ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ P )
     => ( epistemic_AK_a @ A3 @ P ) ) ).

% A1
thf(fact_401_K__A2_H,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ Q ) ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ Q ) ) ) ) ).

% K_A2'
thf(fact_402_K__A2_H,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ Q ) ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ Q ) ) ) ) ).

% K_A2'
thf(fact_403_K__A2_H,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ Q ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ) ).

% K_A2'
thf(fact_404_K__map,axiom,
    ! [A3: epistemic_fm_o > $o,P: epistemic_fm_o,Q: epistemic_fm_o,I3: $o] :
      ( ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ P @ Q ) )
     => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ Q ) ) ) ) ).

% K_map
thf(fact_405_K__map,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b,I3: b] :
      ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ Q ) )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ Q ) ) ) ) ).

% K_map
thf(fact_406_K__map,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,I3: a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ Q ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ) ).

% K_map
thf(fact_407_K__multi__imply,axiom,
    ! [A3: epistemic_fm_b > $o,A: epistemic_fm_b,B2: epistemic_fm_b,C: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ A @ ( epistemic_Imp_b @ B2 @ C ) ) )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Con_b @ A @ B2 ) @ C ) ) ) ).

% K_multi_imply
thf(fact_408_K__multi__imply,axiom,
    ! [A3: epistemic_fm_a > $o,A: epistemic_fm_a,B2: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ A @ ( epistemic_Imp_a @ B2 @ C ) ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ A @ B2 ) @ C ) ) ) ).

% K_multi_imply
thf(fact_409_K__imply__multi,axiom,
    ! [A3: epistemic_fm_b > $o,A: epistemic_fm_b,B2: epistemic_fm_b,C: epistemic_fm_b] :
      ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ A @ B2 ) )
     => ( ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ A @ C ) )
       => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ A @ ( epistemic_Con_b @ B2 @ C ) ) ) ) ) ).

% K_imply_multi
thf(fact_410_K__imply__multi,axiom,
    ! [A3: epistemic_fm_a > $o,A: epistemic_fm_a,B2: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ A @ B2 ) )
     => ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ A @ C ) )
       => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ A @ ( epistemic_Con_a @ B2 @ C ) ) ) ) ) ).

% K_imply_multi
thf(fact_411_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte3259645218793129376t_unit > $o,P: epistemic_fm_a,M: episte3259645218793129376t_unit,W: $o] :
      ( ! [M2: episte3259645218793129376t_unit,W5: $o,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_o @ W5 @ ( episte876160520765907443t_unit @ M2 ) )
             => ( episte1100597067981672766cs_a_o @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member_o @ W @ ( episte876160520765907443t_unit @ M ) )
           => ( episte1100597067981672766cs_a_o @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_412_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte4442589092411611552t_unit > $o,P: epistemic_fm_a,M: episte4442589092411611552t_unit,W: set_o] :
      ( ! [M2: episte4442589092411611552t_unit,W5: set_o,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_set_o @ W5 @ ( episte7994720633578350067t_unit @ M2 ) )
             => ( episte5787648899026124830_set_o @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member_set_o @ W @ ( episte7994720633578350067t_unit @ M ) )
           => ( episte5787648899026124830_set_o @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_413_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte8559422309061589728t_unit > $o,P: epistemic_fm_a,M: episte8559422309061589728t_unit,W: set_b] :
      ( ! [M2: episte8559422309061589728t_unit,W5: set_b,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_set_b @ W5 @ ( episte2726209618768418739t_unit @ M2 ) )
             => ( episte586216548244424325_set_b @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member_set_b @ W @ ( episte2726209618768418739t_unit @ M ) )
           => ( episte586216548244424325_set_b @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_414_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,P: epistemic_fm_a,M: episte6182337868402532512t_unit,W: a] :
      ( ! [M2: episte6182337868402532512t_unit,W5: a,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W5 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member_a @ W @ ( episte6926715892928323059t_unit @ M ) )
           => ( episte295617885132580260cs_a_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_415_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,P: epistemic_fm_a,M: episte1560738328020401952t_unit,W: set_Epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W5: set_Epistemic_fm_a,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W5 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member536094252920883875c_fm_a @ W @ ( episte8072386903178013299t_unit @ M ) )
           => ( episte7081087998767065248c_fm_a @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_416_soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte3224730989885420256t_unit > $o,P: epistemic_fm_a,M: episte3224730989885420256t_unit,W: b] :
      ( ! [M2: episte3224730989885420256t_unit,W5: b,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_b @ W5 @ ( episte1782384855165018035t_unit @ M2 ) )
             => ( episte295617885132580261cs_a_b @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ P )
       => ( ( P4 @ M )
         => ( ( member_b @ W @ ( episte1782384855165018035t_unit @ M ) )
           => ( episte295617885132580261cs_a_b @ M @ W @ P ) ) ) ) ) ).

% soundness
thf(fact_417_kripke_Oselect__convs_I1_J,axiom,
    ! [W2: set_b,K: a > b > set_b,Pi: b > list_char > $o,More: product_unit] :
      ( ( episte5693316124195166255t_unit @ ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ Pi @ More ) ) )
      = Pi ) ).

% kripke.select_convs(1)
thf(fact_418_kripke_Oselect__convs_I1_J,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte2398645135750866164t_unit @ ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = Pi ) ).

% kripke.select_convs(1)
thf(fact_419_kripke_Oselect__convs_I2_J,axiom,
    ! [W2: set_b,K: a > b > set_b,Pi: b > list_char > $o,More: product_unit] :
      ( ( episte7270682542085591125t_unit @ ( episte4938218340073005086t_unit @ W2 @ K @ ( episte6143282164508887558t_unit @ Pi @ More ) ) )
      = More ) ).

% kripke.select_convs(2)
thf(fact_420_kripke_Oselect__convs_I2_J,axiom,
    ! [W2: set_se5208064806568342746c_fm_a,K: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi: set_Epistemic_fm_a > list_char > $o,More: product_unit] :
      ( ( episte5479201149095757850t_unit @ ( episte2888590659910966568t_unit @ W2 @ K @ ( episte8239586592105053771t_unit @ Pi @ More ) ) )
      = More ) ).

% kripke.select_convs(2)
thf(fact_421_K__LK,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) ) ).

% K_LK
thf(fact_422_K__LK,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) ) ).

% K_LK
thf(fact_423_K__LK,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) ) ).

% K_LK
thf(fact_424_K__L__dual,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ P ) ) ) ).

% K_L_dual
thf(fact_425_K__L__dual,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ P ) ) ) ).

% K_L_dual
thf(fact_426_K__L__dual,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ P ) ) ) ).

% K_L_dual
thf(fact_427_K__conjunction__in,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Con_o @ P @ Q ) ) @ ( epistemic_Con_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_428_K__conjunction__in,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Con_b @ P @ Q ) ) @ ( epistemic_Con_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_429_K__conjunction__in,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Con_a @ P @ Q ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_430_K__conjunction__out,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ Q ) ) @ ( epistemic_K_o @ I3 @ ( epistemic_Con_o @ P @ Q ) ) ) ) ).

% K_conjunction_out
thf(fact_431_K__conjunction__out,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ Q ) ) @ ( epistemic_K_b @ I3 @ ( epistemic_Con_b @ P @ Q ) ) ) ) ).

% K_conjunction_out
thf(fact_432_K__conjunction__out,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ Q ) ) @ ( epistemic_K_a @ I3 @ ( epistemic_Con_a @ P @ Q ) ) ) ) ).

% K_conjunction_out
thf(fact_433_K__conj__imply__factor,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o,Q: epistemic_fm_o,R: epistemic_fm_o] : ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_Con_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ Q ) ) @ R ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Con_o @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_434_K__conj__imply__factor,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b,Q: epistemic_fm_b,R: epistemic_fm_b] : ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_Con_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ Q ) ) @ R ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Con_b @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_435_K__conj__imply__factor,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ Q ) ) @ R ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Con_a @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_436_KB4__5,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_AxB_o @ A3 )
     => ( ( ord_le1608183570384977833fm_o_o @ epistemic_Ax4_o @ A3 )
       => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ) ).

% KB4_5
thf(fact_437_KB4__5,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_AxB_b @ A3 )
     => ( ( ord_le1256275114586606850fm_b_o @ epistemic_Ax4_b @ A3 )
       => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ) ).

% KB4_5
thf(fact_438_KB4__5,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A3 )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A3 )
       => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% KB4_5
thf(fact_439_S5_H__B,axiom,
    ! [A3: epistemic_fm_o > $o,P: epistemic_fm_o,I3: $o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_AxT_o @ A3 )
     => ( ( ord_le1608183570384977833fm_o_o @ epistemic_Ax5_o @ A3 )
       => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ P @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ) ) ).

% S5'_B
thf(fact_440_S5_H__B,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,I3: b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_AxT_b @ A3 )
     => ( ( ord_le1256275114586606850fm_b_o @ epistemic_Ax5_b @ A3 )
       => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ) ) ).

% S5'_B
thf(fact_441_S5_H__B,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,I3: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A3 )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A3 )
       => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% S5'_B
thf(fact_442_S5_H__4,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_AxT_o @ A3 )
     => ( ( ord_le1608183570384977833fm_o_o @ epistemic_Ax5_o @ A3 )
       => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ ( epistemic_K_o @ I3 @ ( epistemic_K_o @ I3 @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_443_S5_H__4,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_AxT_b @ A3 )
     => ( ( ord_le1256275114586606850fm_b_o @ epistemic_Ax5_b @ A3 )
       => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ ( epistemic_K_b @ I3 @ ( epistemic_K_b @ I3 @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_444_S5_H__4,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A3 )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A3 )
       => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_445_K5__L,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_Ax5_o @ A3 )
     => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ P ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_K_o @ I3 @ P ) ) ) ) ).

% K5_L
thf(fact_446_K5__L,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_Ax5_b @ A3 )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ P ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_K_b @ I3 @ P ) ) ) ) ).

% K5_L
thf(fact_447_K5__L,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A3 )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ P ) ) ) ) ).

% K5_L
thf(fact_448_K4__L,axiom,
    ! [A3: epistemic_fm_o > $o,I3: $o,P: epistemic_fm_o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_Ax4_o @ A3 )
     => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ epistemic_FF_o ) ) @ epistemic_FF_o ) @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ).

% K4_L
thf(fact_449_K4__L,axiom,
    ! [A3: epistemic_fm_b > $o,I3: b,P: epistemic_fm_b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_Ax4_b @ A3 )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ epistemic_FF_b ) ) @ epistemic_FF_b ) @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ).

% K4_L
thf(fact_450_K4__L,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A3 )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% K4_L
thf(fact_451_T__L,axiom,
    ! [A3: epistemic_fm_o > $o,P: epistemic_fm_o,I3: $o] :
      ( ( ord_le1608183570384977833fm_o_o @ epistemic_AxT_o @ A3 )
     => ( epistemic_AK_o @ A3 @ ( epistemic_Imp_o @ P @ ( epistemic_Imp_o @ ( epistemic_K_o @ I3 @ ( epistemic_Imp_o @ P @ epistemic_FF_o ) ) @ epistemic_FF_o ) ) ) ) ).

% T_L
thf(fact_452_T__L,axiom,
    ! [A3: epistemic_fm_b > $o,P: epistemic_fm_b,I3: b] :
      ( ( ord_le1256275114586606850fm_b_o @ epistemic_AxT_b @ A3 )
     => ( epistemic_AK_b @ A3 @ ( epistemic_Imp_b @ P @ ( epistemic_Imp_b @ ( epistemic_K_b @ I3 @ ( epistemic_Imp_b @ P @ epistemic_FF_b ) ) @ epistemic_FF_b ) ) ) ) ).

% T_L
thf(fact_453_T__L,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,I3: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A3 )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% T_L
thf(fact_454_S5__S5_H,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P3: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P3 )
            | ( epistemic_AxB_a @ P3 )
            | ( epistemic_Ax4_a @ P3 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P3: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P3 )
            | ( epistemic_Ax5_a @ P3 ) )
        @ P ) ) ).

% S5_S5'
thf(fact_455_S5_H__S5,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P3: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P3 )
            | ( epistemic_Ax5_a @ P3 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P3: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P3 )
            | ( epistemic_AxB_a @ P3 )
            | ( epistemic_Ax4_a @ P3 ) )
        @ P ) ) ).

% S5'_S5
thf(fact_456_fm_Oinject_I1_J,axiom,
    ! [X22: list_char,Y22: list_char] :
      ( ( ( epistemic_Pro_a @ X22 )
        = ( epistemic_Pro_a @ Y22 ) )
      = ( X22 = Y22 ) ) ).

% fm.inject(1)
thf(fact_457_fm_Oinject_I1_J,axiom,
    ! [X22: list_char,Y22: list_char] :
      ( ( ( epistemic_Pro_o @ X22 )
        = ( epistemic_Pro_o @ Y22 ) )
      = ( X22 = Y22 ) ) ).

% fm.inject(1)
thf(fact_458_fm_Oinject_I2_J,axiom,
    ! [X31: epistemic_fm_a,X32: epistemic_fm_a,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( ( epistemic_Dis_a @ X31 @ X32 )
        = ( epistemic_Dis_a @ Y31 @ Y32 ) )
      = ( ( X31 = Y31 )
        & ( X32 = Y32 ) ) ) ).

% fm.inject(2)
thf(fact_459_fm_Oinject_I2_J,axiom,
    ! [X31: epistemic_fm_b,X32: epistemic_fm_b,Y31: epistemic_fm_b,Y32: epistemic_fm_b] :
      ( ( ( epistemic_Dis_b @ X31 @ X32 )
        = ( epistemic_Dis_b @ Y31 @ Y32 ) )
      = ( ( X31 = Y31 )
        & ( X32 = Y32 ) ) ) ).

% fm.inject(2)
thf(fact_460_le__inf__iff,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( ord_less_eq_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) )
      = ( ( ord_less_eq_o @ X3 @ Y2 )
        & ( ord_less_eq_o @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_461_le__inf__iff,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ Y2 @ Z2 ) )
      = ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 )
        & ( ord_le4043730696559282883fm_a_o @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_462_le__inf__iff,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ Y2 @ Z2 ) )
      = ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 )
        & ( ord_le3275665582123262618c_fm_a @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_463_le__inf__iff,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( ord_less_eq_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) )
      = ( ( ord_less_eq_set_b @ X3 @ Y2 )
        & ( ord_less_eq_set_b @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_464_le__inf__iff,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( ord_less_eq_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) )
      = ( ( ord_less_eq_b_o @ X3 @ Y2 )
        & ( ord_less_eq_b_o @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_465_le__inf__iff,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( ord_less_eq_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) )
      = ( ( ord_less_eq_set_o @ X3 @ Y2 )
        & ( ord_less_eq_set_o @ X3 @ Z2 ) ) ) ).

% le_inf_iff
thf(fact_466_inf_Obounded__iff,axiom,
    ! [A: $o,B2: $o,C: $o] :
      ( ( ord_less_eq_o @ A @ ( inf_inf_o @ B2 @ C ) )
      = ( ( ord_less_eq_o @ A @ B2 )
        & ( ord_less_eq_o @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_467_inf_Obounded__iff,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ ( inf_in3606484609122063093fm_a_o @ B2 @ C ) )
      = ( ( ord_le4043730696559282883fm_a_o @ A @ B2 )
        & ( ord_le4043730696559282883fm_a_o @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_468_inf_Obounded__iff,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ ( inf_in2882328776738922472c_fm_a @ B2 @ C ) )
      = ( ( ord_le3275665582123262618c_fm_a @ A @ B2 )
        & ( ord_le3275665582123262618c_fm_a @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_469_inf_Obounded__iff,axiom,
    ! [A: set_b,B2: set_b,C: set_b] :
      ( ( ord_less_eq_set_b @ A @ ( inf_inf_set_b @ B2 @ C ) )
      = ( ( ord_less_eq_set_b @ A @ B2 )
        & ( ord_less_eq_set_b @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_470_inf_Obounded__iff,axiom,
    ! [A: b > $o,B2: b > $o,C: b > $o] :
      ( ( ord_less_eq_b_o @ A @ ( inf_inf_b_o @ B2 @ C ) )
      = ( ( ord_less_eq_b_o @ A @ B2 )
        & ( ord_less_eq_b_o @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_471_inf_Obounded__iff,axiom,
    ! [A: set_o,B2: set_o,C: set_o] :
      ( ( ord_less_eq_set_o @ A @ ( inf_inf_set_o @ B2 @ C ) )
      = ( ( ord_less_eq_set_o @ A @ B2 )
        & ( ord_less_eq_set_o @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_472_Int__def,axiom,
    ( inf_inf_set_set_o
    = ( ^ [A4: set_set_o,B4: set_set_o] :
          ( collect_set_o
          @ ^ [X2: set_o] :
              ( ( member_set_o @ X2 @ A4 )
              & ( member_set_o @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_473_Int__def,axiom,
    ( inf_inf_set_set_b
    = ( ^ [A4: set_set_b,B4: set_set_b] :
          ( collect_set_b
          @ ^ [X2: set_b] :
              ( ( member_set_b @ X2 @ A4 )
              & ( member_set_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_474_Int__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A4: set_a,B4: set_a] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ A4 )
              & ( member_a @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_475_Int__def,axiom,
    ( inf_in1884693029477671368c_fm_a
    = ( ^ [A4: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [X2: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X2 @ A4 )
              & ( member536094252920883875c_fm_a @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_476_Int__def,axiom,
    ( inf_in2882328776738922472c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [X2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X2 @ A4 )
              & ( member6642669571620171971c_fm_a @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_477_Int__def,axiom,
    ( inf_inf_set_o
    = ( ^ [A4: set_o,B4: set_o] :
          ( collect_o
          @ ^ [X2: $o] :
              ( ( member_o @ X2 @ A4 )
              & ( member_o @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_478_Int__def,axiom,
    ( inf_inf_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ A4 )
              & ( member_b @ X2 @ B4 ) ) ) ) ) ).

% Int_def
thf(fact_479_Int__Collect,axiom,
    ! [X3: set_o,A3: set_set_o,P4: set_o > $o] :
      ( ( member_set_o @ X3 @ ( inf_inf_set_set_o @ A3 @ ( collect_set_o @ P4 ) ) )
      = ( ( member_set_o @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_480_Int__Collect,axiom,
    ! [X3: set_b,A3: set_set_b,P4: set_b > $o] :
      ( ( member_set_b @ X3 @ ( inf_inf_set_set_b @ A3 @ ( collect_set_b @ P4 ) ) )
      = ( ( member_set_b @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_481_Int__Collect,axiom,
    ! [X3: a,A3: set_a,P4: a > $o] :
      ( ( member_a @ X3 @ ( inf_inf_set_a @ A3 @ ( collect_a @ P4 ) ) )
      = ( ( member_a @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_482_Int__Collect,axiom,
    ! [X3: set_Epistemic_fm_a,A3: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ X3 @ ( inf_in1884693029477671368c_fm_a @ A3 @ ( collec2519470961442302949c_fm_a @ P4 ) ) )
      = ( ( member536094252920883875c_fm_a @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_483_Int__Collect,axiom,
    ! [X3: epistemic_fm_a,A3: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ A3 @ ( collec4904205152690461189c_fm_a @ P4 ) ) )
      = ( ( member6642669571620171971c_fm_a @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_484_Int__Collect,axiom,
    ! [X3: $o,A3: set_o,P4: $o > $o] :
      ( ( member_o @ X3 @ ( inf_inf_set_o @ A3 @ ( collect_o @ P4 ) ) )
      = ( ( member_o @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_485_Int__Collect,axiom,
    ! [X3: b,A3: set_b,P4: b > $o] :
      ( ( member_b @ X3 @ ( inf_inf_set_b @ A3 @ ( collect_b @ P4 ) ) )
      = ( ( member_b @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% Int_Collect
thf(fact_486_inf__set__def,axiom,
    ( inf_inf_set_set_o
    = ( ^ [A4: set_set_o,B4: set_set_o] :
          ( collect_set_o
          @ ( inf_inf_set_o_o
            @ ^ [X2: set_o] : ( member_set_o @ X2 @ A4 )
            @ ^ [X2: set_o] : ( member_set_o @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_487_inf__set__def,axiom,
    ( inf_inf_set_set_b
    = ( ^ [A4: set_set_b,B4: set_set_b] :
          ( collect_set_b
          @ ( inf_inf_set_b_o
            @ ^ [X2: set_b] : ( member_set_b @ X2 @ A4 )
            @ ^ [X2: set_b] : ( member_set_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_488_inf__set__def,axiom,
    ( inf_inf_set_a
    = ( ^ [A4: set_a,B4: set_a] :
          ( collect_a
          @ ( inf_inf_a_o
            @ ^ [X2: a] : ( member_a @ X2 @ A4 )
            @ ^ [X2: a] : ( member_a @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_489_inf__set__def,axiom,
    ( inf_in1884693029477671368c_fm_a
    = ( ^ [A4: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ( inf_in5938521974262266133fm_a_o
            @ ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ A4 )
            @ ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_490_inf__set__def,axiom,
    ( inf_in2882328776738922472c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ( inf_in3606484609122063093fm_a_o
            @ ^ [X2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X2 @ A4 )
            @ ^ [X2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_491_inf__set__def,axiom,
    ( inf_inf_set_o
    = ( ^ [A4: set_o,B4: set_o] :
          ( collect_o
          @ ( inf_inf_o_o
            @ ^ [X2: $o] : ( member_o @ X2 @ A4 )
            @ ^ [X2: $o] : ( member_o @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_492_inf__set__def,axiom,
    ( inf_inf_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ( inf_inf_b_o
            @ ^ [X2: b] : ( member_b @ X2 @ A4 )
            @ ^ [X2: b] : ( member_b @ X2 @ B4 ) ) ) ) ) ).

% inf_set_def
thf(fact_493_Collect__conj__eq,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q2: set_Epistemic_fm_a > $o] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X2: set_Epistemic_fm_a] :
            ( ( P4 @ X2 )
            & ( Q2 @ X2 ) ) )
      = ( inf_in1884693029477671368c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q2 ) ) ) ).

% Collect_conj_eq
thf(fact_494_Collect__conj__eq,axiom,
    ! [P4: epistemic_fm_a > $o,Q2: epistemic_fm_a > $o] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X2: epistemic_fm_a] :
            ( ( P4 @ X2 )
            & ( Q2 @ X2 ) ) )
      = ( inf_in2882328776738922472c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q2 ) ) ) ).

% Collect_conj_eq
thf(fact_495_Collect__conj__eq,axiom,
    ! [P4: b > $o,Q2: b > $o] :
      ( ( collect_b
        @ ^ [X2: b] :
            ( ( P4 @ X2 )
            & ( Q2 @ X2 ) ) )
      = ( inf_inf_set_b @ ( collect_b @ P4 ) @ ( collect_b @ Q2 ) ) ) ).

% Collect_conj_eq
thf(fact_496_Collect__conj__eq,axiom,
    ! [P4: $o > $o,Q2: $o > $o] :
      ( ( collect_o
        @ ^ [X2: $o] :
            ( ( P4 @ X2 )
            & ( Q2 @ X2 ) ) )
      = ( inf_inf_set_o @ ( collect_o @ P4 ) @ ( collect_o @ Q2 ) ) ) ).

% Collect_conj_eq
thf(fact_497_fm_Odistinct_I11_J,axiom,
    ! [X22: list_char,X31: epistemic_fm_b,X32: epistemic_fm_b] :
      ( ( epistemic_Pro_b @ X22 )
     != ( epistemic_Dis_b @ X31 @ X32 ) ) ).

% fm.distinct(11)
thf(fact_498_fm_Odistinct_I11_J,axiom,
    ! [X22: list_char,X31: epistemic_fm_a,X32: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X22 )
     != ( epistemic_Dis_a @ X31 @ X32 ) ) ).

% fm.distinct(11)
thf(fact_499_fm_Odistinct_I11_J,axiom,
    ! [X22: list_char,X31: epistemic_fm_o,X32: epistemic_fm_o] :
      ( ( epistemic_Pro_o @ X22 )
     != ( epistemic_Dis_o @ X31 @ X32 ) ) ).

% fm.distinct(11)
thf(fact_500_inf__sup__ord_I2_J,axiom,
    ! [X3: $o,Y2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_501_inf__sup__ord_I2_J,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_502_inf__sup__ord_I2_J,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_503_inf__sup__ord_I2_J,axiom,
    ! [X3: set_b,Y2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_504_inf__sup__ord_I2_J,axiom,
    ! [X3: b > $o,Y2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_505_inf__sup__ord_I2_J,axiom,
    ! [X3: set_o,Y2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_sup_ord(2)
thf(fact_506_inf__sup__ord_I1_J,axiom,
    ! [X3: $o,Y2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_507_inf__sup__ord_I1_J,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_508_inf__sup__ord_I1_J,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_509_inf__sup__ord_I1_J,axiom,
    ! [X3: set_b,Y2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_510_inf__sup__ord_I1_J,axiom,
    ! [X3: b > $o,Y2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_511_inf__sup__ord_I1_J,axiom,
    ! [X3: set_o,Y2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ X3 ) ).

% inf_sup_ord(1)
thf(fact_512_inf__le1,axiom,
    ! [X3: $o,Y2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_513_inf__le1,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_514_inf__le1,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_515_inf__le1,axiom,
    ! [X3: set_b,Y2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_516_inf__le1,axiom,
    ! [X3: b > $o,Y2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_517_inf__le1,axiom,
    ! [X3: set_o,Y2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ X3 ) ).

% inf_le1
thf(fact_518_inf__le2,axiom,
    ! [X3: $o,Y2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_519_inf__le2,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_520_inf__le2,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_521_inf__le2,axiom,
    ! [X3: set_b,Y2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_522_inf__le2,axiom,
    ! [X3: b > $o,Y2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_523_inf__le2,axiom,
    ! [X3: set_o,Y2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ X3 @ Y2 ) @ Y2 ) ).

% inf_le2
thf(fact_524_le__infE,axiom,
    ! [X3: $o,A: $o,B2: $o] :
      ( ( ord_less_eq_o @ X3 @ ( inf_inf_o @ A @ B2 ) )
     => ~ ( ( ord_less_eq_o @ X3 @ A )
         => ~ ( ord_less_eq_o @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_525_le__infE,axiom,
    ! [X3: epistemic_fm_a > $o,A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) )
     => ~ ( ( ord_le4043730696559282883fm_a_o @ X3 @ A )
         => ~ ( ord_le4043730696559282883fm_a_o @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_526_le__infE,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ X3 @ A )
         => ~ ( ord_le3275665582123262618c_fm_a @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_527_le__infE,axiom,
    ! [X3: set_b,A: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ X3 @ ( inf_inf_set_b @ A @ B2 ) )
     => ~ ( ( ord_less_eq_set_b @ X3 @ A )
         => ~ ( ord_less_eq_set_b @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_528_le__infE,axiom,
    ! [X3: b > $o,A: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ X3 @ ( inf_inf_b_o @ A @ B2 ) )
     => ~ ( ( ord_less_eq_b_o @ X3 @ A )
         => ~ ( ord_less_eq_b_o @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_529_le__infE,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ X3 @ ( inf_inf_set_o @ A @ B2 ) )
     => ~ ( ( ord_less_eq_set_o @ X3 @ A )
         => ~ ( ord_less_eq_set_o @ X3 @ B2 ) ) ) ).

% le_infE
thf(fact_530_le__infI,axiom,
    ! [X3: $o,A: $o,B2: $o] :
      ( ( ord_less_eq_o @ X3 @ A )
     => ( ( ord_less_eq_o @ X3 @ B2 )
       => ( ord_less_eq_o @ X3 @ ( inf_inf_o @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_531_le__infI,axiom,
    ! [X3: epistemic_fm_a > $o,A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ X3 @ B2 )
       => ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_532_le__infI,axiom,
    ! [X3: set_Epistemic_fm_a,A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ X3 @ B2 )
       => ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_533_le__infI,axiom,
    ! [X3: set_b,A: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ X3 @ A )
     => ( ( ord_less_eq_set_b @ X3 @ B2 )
       => ( ord_less_eq_set_b @ X3 @ ( inf_inf_set_b @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_534_le__infI,axiom,
    ! [X3: b > $o,A: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ X3 @ A )
     => ( ( ord_less_eq_b_o @ X3 @ B2 )
       => ( ord_less_eq_b_o @ X3 @ ( inf_inf_b_o @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_535_le__infI,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ X3 @ A )
     => ( ( ord_less_eq_set_o @ X3 @ B2 )
       => ( ord_less_eq_set_o @ X3 @ ( inf_inf_set_o @ A @ B2 ) ) ) ) ).

% le_infI
thf(fact_536_inf__mono,axiom,
    ! [A: $o,C: $o,B2: $o,D: $o] :
      ( ( ord_less_eq_o @ A @ C )
     => ( ( ord_less_eq_o @ B2 @ D )
       => ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ ( inf_inf_o @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_537_inf__mono,axiom,
    ! [A: epistemic_fm_a > $o,C: epistemic_fm_a > $o,B2: epistemic_fm_a > $o,D: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ C )
     => ( ( ord_le4043730696559282883fm_a_o @ B2 @ D )
       => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ ( inf_in3606484609122063093fm_a_o @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_538_inf__mono,axiom,
    ! [A: set_Epistemic_fm_a,C: set_Epistemic_fm_a,B2: set_Epistemic_fm_a,D: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ C )
     => ( ( ord_le3275665582123262618c_fm_a @ B2 @ D )
       => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ ( inf_in2882328776738922472c_fm_a @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_539_inf__mono,axiom,
    ! [A: set_b,C: set_b,B2: set_b,D: set_b] :
      ( ( ord_less_eq_set_b @ A @ C )
     => ( ( ord_less_eq_set_b @ B2 @ D )
       => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ ( inf_inf_set_b @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_540_inf__mono,axiom,
    ! [A: b > $o,C: b > $o,B2: b > $o,D: b > $o] :
      ( ( ord_less_eq_b_o @ A @ C )
     => ( ( ord_less_eq_b_o @ B2 @ D )
       => ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ ( inf_inf_b_o @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_541_inf__mono,axiom,
    ! [A: set_o,C: set_o,B2: set_o,D: set_o] :
      ( ( ord_less_eq_set_o @ A @ C )
     => ( ( ord_less_eq_set_o @ B2 @ D )
       => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ ( inf_inf_set_o @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_542_le__infI1,axiom,
    ! [A: $o,X3: $o,B2: $o] :
      ( ( ord_less_eq_o @ A @ X3 )
     => ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_543_le__infI1,axiom,
    ! [A: epistemic_fm_a > $o,X3: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ X3 )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_544_le__infI1,axiom,
    ! [A: set_Epistemic_fm_a,X3: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ X3 )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_545_le__infI1,axiom,
    ! [A: set_b,X3: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ A @ X3 )
     => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_546_le__infI1,axiom,
    ! [A: b > $o,X3: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ A @ X3 )
     => ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_547_le__infI1,axiom,
    ! [A: set_o,X3: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ A @ X3 )
     => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ X3 ) ) ).

% le_infI1
thf(fact_548_le__infI2,axiom,
    ! [B2: $o,X3: $o,A: $o] :
      ( ( ord_less_eq_o @ B2 @ X3 )
     => ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_549_le__infI2,axiom,
    ! [B2: epistemic_fm_a > $o,X3: epistemic_fm_a > $o,A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B2 @ X3 )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_550_le__infI2,axiom,
    ! [B2: set_Epistemic_fm_a,X3: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B2 @ X3 )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_551_le__infI2,axiom,
    ! [B2: set_b,X3: set_b,A: set_b] :
      ( ( ord_less_eq_set_b @ B2 @ X3 )
     => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_552_le__infI2,axiom,
    ! [B2: b > $o,X3: b > $o,A: b > $o] :
      ( ( ord_less_eq_b_o @ B2 @ X3 )
     => ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_553_le__infI2,axiom,
    ! [B2: set_o,X3: set_o,A: set_o] :
      ( ( ord_less_eq_set_o @ B2 @ X3 )
     => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ X3 ) ) ).

% le_infI2
thf(fact_554_inf_OorderE,axiom,
    ! [A: $o,B2: $o] :
      ( ( ord_less_eq_o @ A @ B2 )
     => ( A
        = ( inf_inf_o @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_555_inf_OorderE,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ B2 )
     => ( A
        = ( inf_in3606484609122063093fm_a_o @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_556_inf_OorderE,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B2 )
     => ( A
        = ( inf_in2882328776738922472c_fm_a @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_557_inf_OorderE,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ A @ B2 )
     => ( A
        = ( inf_inf_set_b @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_558_inf_OorderE,axiom,
    ! [A: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ A @ B2 )
     => ( A
        = ( inf_inf_b_o @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_559_inf_OorderE,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ A @ B2 )
     => ( A
        = ( inf_inf_set_o @ A @ B2 ) ) ) ).

% inf.orderE
thf(fact_560_inf_OorderI,axiom,
    ! [A: $o,B2: $o] :
      ( ( A
        = ( inf_inf_o @ A @ B2 ) )
     => ( ord_less_eq_o @ A @ B2 ) ) ).

% inf.orderI
thf(fact_561_inf_OorderI,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( A
        = ( inf_in3606484609122063093fm_a_o @ A @ B2 ) )
     => ( ord_le4043730696559282883fm_a_o @ A @ B2 ) ) ).

% inf.orderI
thf(fact_562_inf_OorderI,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( A
        = ( inf_in2882328776738922472c_fm_a @ A @ B2 ) )
     => ( ord_le3275665582123262618c_fm_a @ A @ B2 ) ) ).

% inf.orderI
thf(fact_563_inf_OorderI,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( A
        = ( inf_inf_set_b @ A @ B2 ) )
     => ( ord_less_eq_set_b @ A @ B2 ) ) ).

% inf.orderI
thf(fact_564_inf_OorderI,axiom,
    ! [A: b > $o,B2: b > $o] :
      ( ( A
        = ( inf_inf_b_o @ A @ B2 ) )
     => ( ord_less_eq_b_o @ A @ B2 ) ) ).

% inf.orderI
thf(fact_565_inf_OorderI,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( A
        = ( inf_inf_set_o @ A @ B2 ) )
     => ( ord_less_eq_set_o @ A @ B2 ) ) ).

% inf.orderI
thf(fact_566_inf__unique,axiom,
    ! [F2: $o > $o > $o,X3: $o,Y2: $o] :
      ( ! [X: $o,Y3: $o] : ( ord_less_eq_o @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: $o,Y3: $o] : ( ord_less_eq_o @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: $o,Y3: $o,Z3: $o] :
              ( ( ord_less_eq_o @ X @ Y3 )
             => ( ( ord_less_eq_o @ X @ Z3 )
               => ( ord_less_eq_o @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_inf_o @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_567_inf__unique,axiom,
    ! [F2: ( epistemic_fm_a > $o ) > ( epistemic_fm_a > $o ) > epistemic_fm_a > $o,X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
      ( ! [X: epistemic_fm_a > $o,Y3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: epistemic_fm_a > $o,Y3: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: epistemic_fm_a > $o,Y3: epistemic_fm_a > $o,Z3: epistemic_fm_a > $o] :
              ( ( ord_le4043730696559282883fm_a_o @ X @ Y3 )
             => ( ( ord_le4043730696559282883fm_a_o @ X @ Z3 )
               => ( ord_le4043730696559282883fm_a_o @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_568_inf__unique,axiom,
    ! [F2: set_Epistemic_fm_a > set_Epistemic_fm_a > set_Epistemic_fm_a,X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
      ( ! [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a,Z3: set_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ X @ Y3 )
             => ( ( ord_le3275665582123262618c_fm_a @ X @ Z3 )
               => ( ord_le3275665582123262618c_fm_a @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_569_inf__unique,axiom,
    ! [F2: set_b > set_b > set_b,X3: set_b,Y2: set_b] :
      ( ! [X: set_b,Y3: set_b] : ( ord_less_eq_set_b @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: set_b,Y3: set_b] : ( ord_less_eq_set_b @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: set_b,Y3: set_b,Z3: set_b] :
              ( ( ord_less_eq_set_b @ X @ Y3 )
             => ( ( ord_less_eq_set_b @ X @ Z3 )
               => ( ord_less_eq_set_b @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_inf_set_b @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_570_inf__unique,axiom,
    ! [F2: ( b > $o ) > ( b > $o ) > b > $o,X3: b > $o,Y2: b > $o] :
      ( ! [X: b > $o,Y3: b > $o] : ( ord_less_eq_b_o @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: b > $o,Y3: b > $o] : ( ord_less_eq_b_o @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: b > $o,Y3: b > $o,Z3: b > $o] :
              ( ( ord_less_eq_b_o @ X @ Y3 )
             => ( ( ord_less_eq_b_o @ X @ Z3 )
               => ( ord_less_eq_b_o @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_inf_b_o @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_571_inf__unique,axiom,
    ! [F2: set_o > set_o > set_o,X3: set_o,Y2: set_o] :
      ( ! [X: set_o,Y3: set_o] : ( ord_less_eq_set_o @ ( F2 @ X @ Y3 ) @ X )
     => ( ! [X: set_o,Y3: set_o] : ( ord_less_eq_set_o @ ( F2 @ X @ Y3 ) @ Y3 )
       => ( ! [X: set_o,Y3: set_o,Z3: set_o] :
              ( ( ord_less_eq_set_o @ X @ Y3 )
             => ( ( ord_less_eq_set_o @ X @ Z3 )
               => ( ord_less_eq_set_o @ X @ ( F2 @ Y3 @ Z3 ) ) ) )
         => ( ( inf_inf_set_o @ X3 @ Y2 )
            = ( F2 @ X3 @ Y2 ) ) ) ) ) ).

% inf_unique
thf(fact_572_le__iff__inf,axiom,
    ( ord_less_eq_o
    = ( ^ [X2: $o,Y: $o] :
          ( ( inf_inf_o @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_573_le__iff__inf,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [X2: epistemic_fm_a > $o,Y: epistemic_fm_a > $o] :
          ( ( inf_in3606484609122063093fm_a_o @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_574_le__iff__inf,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [X2: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
          ( ( inf_in2882328776738922472c_fm_a @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_575_le__iff__inf,axiom,
    ( ord_less_eq_set_b
    = ( ^ [X2: set_b,Y: set_b] :
          ( ( inf_inf_set_b @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_576_le__iff__inf,axiom,
    ( ord_less_eq_b_o
    = ( ^ [X2: b > $o,Y: b > $o] :
          ( ( inf_inf_b_o @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_577_le__iff__inf,axiom,
    ( ord_less_eq_set_o
    = ( ^ [X2: set_o,Y: set_o] :
          ( ( inf_inf_set_o @ X2 @ Y )
          = X2 ) ) ) ).

% le_iff_inf
thf(fact_578_inf_Oabsorb1,axiom,
    ! [A: $o,B2: $o] :
      ( ( ord_less_eq_o @ A @ B2 )
     => ( ( inf_inf_o @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_579_inf_Oabsorb1,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ B2 )
     => ( ( inf_in3606484609122063093fm_a_o @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_580_inf_Oabsorb1,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B2 )
     => ( ( inf_in2882328776738922472c_fm_a @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_581_inf_Oabsorb1,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ A @ B2 )
     => ( ( inf_inf_set_b @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_582_inf_Oabsorb1,axiom,
    ! [A: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ A @ B2 )
     => ( ( inf_inf_b_o @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_583_inf_Oabsorb1,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ A @ B2 )
     => ( ( inf_inf_set_o @ A @ B2 )
        = A ) ) ).

% inf.absorb1
thf(fact_584_inf_Oabsorb2,axiom,
    ! [B2: $o,A: $o] :
      ( ( ord_less_eq_o @ B2 @ A )
     => ( ( inf_inf_o @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_585_inf_Oabsorb2,axiom,
    ! [B2: epistemic_fm_a > $o,A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B2 @ A )
     => ( ( inf_in3606484609122063093fm_a_o @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_586_inf_Oabsorb2,axiom,
    ! [B2: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B2 @ A )
     => ( ( inf_in2882328776738922472c_fm_a @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_587_inf_Oabsorb2,axiom,
    ! [B2: set_b,A: set_b] :
      ( ( ord_less_eq_set_b @ B2 @ A )
     => ( ( inf_inf_set_b @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_588_inf_Oabsorb2,axiom,
    ! [B2: b > $o,A: b > $o] :
      ( ( ord_less_eq_b_o @ B2 @ A )
     => ( ( inf_inf_b_o @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_589_inf_Oabsorb2,axiom,
    ! [B2: set_o,A: set_o] :
      ( ( ord_less_eq_set_o @ B2 @ A )
     => ( ( inf_inf_set_o @ A @ B2 )
        = B2 ) ) ).

% inf.absorb2
thf(fact_590_inf__absorb1,axiom,
    ! [X3: $o,Y2: $o] :
      ( ( ord_less_eq_o @ X3 @ Y2 )
     => ( ( inf_inf_o @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_591_inf__absorb1,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 )
     => ( ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_592_inf__absorb1,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 )
     => ( ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_593_inf__absorb1,axiom,
    ! [X3: set_b,Y2: set_b] :
      ( ( ord_less_eq_set_b @ X3 @ Y2 )
     => ( ( inf_inf_set_b @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_594_inf__absorb1,axiom,
    ! [X3: b > $o,Y2: b > $o] :
      ( ( ord_less_eq_b_o @ X3 @ Y2 )
     => ( ( inf_inf_b_o @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_595_inf__absorb1,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ord_less_eq_set_o @ X3 @ Y2 )
     => ( ( inf_inf_set_o @ X3 @ Y2 )
        = X3 ) ) ).

% inf_absorb1
thf(fact_596_inf__absorb2,axiom,
    ! [Y2: $o,X3: $o] :
      ( ( ord_less_eq_o @ Y2 @ X3 )
     => ( ( inf_inf_o @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_597_inf__absorb2,axiom,
    ! [Y2: epistemic_fm_a > $o,X3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ Y2 @ X3 )
     => ( ( inf_in3606484609122063093fm_a_o @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_598_inf__absorb2,axiom,
    ! [Y2: set_Epistemic_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ Y2 @ X3 )
     => ( ( inf_in2882328776738922472c_fm_a @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_599_inf__absorb2,axiom,
    ! [Y2: set_b,X3: set_b] :
      ( ( ord_less_eq_set_b @ Y2 @ X3 )
     => ( ( inf_inf_set_b @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_600_inf__absorb2,axiom,
    ! [Y2: b > $o,X3: b > $o] :
      ( ( ord_less_eq_b_o @ Y2 @ X3 )
     => ( ( inf_inf_b_o @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_601_inf__absorb2,axiom,
    ! [Y2: set_o,X3: set_o] :
      ( ( ord_less_eq_set_o @ Y2 @ X3 )
     => ( ( inf_inf_set_o @ X3 @ Y2 )
        = Y2 ) ) ).

% inf_absorb2
thf(fact_602_inf_OboundedE,axiom,
    ! [A: $o,B2: $o,C: $o] :
      ( ( ord_less_eq_o @ A @ ( inf_inf_o @ B2 @ C ) )
     => ~ ( ( ord_less_eq_o @ A @ B2 )
         => ~ ( ord_less_eq_o @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_603_inf_OboundedE,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ ( inf_in3606484609122063093fm_a_o @ B2 @ C ) )
     => ~ ( ( ord_le4043730696559282883fm_a_o @ A @ B2 )
         => ~ ( ord_le4043730696559282883fm_a_o @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_604_inf_OboundedE,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ ( inf_in2882328776738922472c_fm_a @ B2 @ C ) )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ A @ B2 )
         => ~ ( ord_le3275665582123262618c_fm_a @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_605_inf_OboundedE,axiom,
    ! [A: set_b,B2: set_b,C: set_b] :
      ( ( ord_less_eq_set_b @ A @ ( inf_inf_set_b @ B2 @ C ) )
     => ~ ( ( ord_less_eq_set_b @ A @ B2 )
         => ~ ( ord_less_eq_set_b @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_606_inf_OboundedE,axiom,
    ! [A: b > $o,B2: b > $o,C: b > $o] :
      ( ( ord_less_eq_b_o @ A @ ( inf_inf_b_o @ B2 @ C ) )
     => ~ ( ( ord_less_eq_b_o @ A @ B2 )
         => ~ ( ord_less_eq_b_o @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_607_inf_OboundedE,axiom,
    ! [A: set_o,B2: set_o,C: set_o] :
      ( ( ord_less_eq_set_o @ A @ ( inf_inf_set_o @ B2 @ C ) )
     => ~ ( ( ord_less_eq_set_o @ A @ B2 )
         => ~ ( ord_less_eq_set_o @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_608_inf_OboundedI,axiom,
    ! [A: $o,B2: $o,C: $o] :
      ( ( ord_less_eq_o @ A @ B2 )
     => ( ( ord_less_eq_o @ A @ C )
       => ( ord_less_eq_o @ A @ ( inf_inf_o @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_609_inf_OboundedI,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o,C: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ B2 )
     => ( ( ord_le4043730696559282883fm_a_o @ A @ C )
       => ( ord_le4043730696559282883fm_a_o @ A @ ( inf_in3606484609122063093fm_a_o @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_610_inf_OboundedI,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ B2 )
     => ( ( ord_le3275665582123262618c_fm_a @ A @ C )
       => ( ord_le3275665582123262618c_fm_a @ A @ ( inf_in2882328776738922472c_fm_a @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_611_inf_OboundedI,axiom,
    ! [A: set_b,B2: set_b,C: set_b] :
      ( ( ord_less_eq_set_b @ A @ B2 )
     => ( ( ord_less_eq_set_b @ A @ C )
       => ( ord_less_eq_set_b @ A @ ( inf_inf_set_b @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_612_inf_OboundedI,axiom,
    ! [A: b > $o,B2: b > $o,C: b > $o] :
      ( ( ord_less_eq_b_o @ A @ B2 )
     => ( ( ord_less_eq_b_o @ A @ C )
       => ( ord_less_eq_b_o @ A @ ( inf_inf_b_o @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_613_inf_OboundedI,axiom,
    ! [A: set_o,B2: set_o,C: set_o] :
      ( ( ord_less_eq_set_o @ A @ B2 )
     => ( ( ord_less_eq_set_o @ A @ C )
       => ( ord_less_eq_set_o @ A @ ( inf_inf_set_o @ B2 @ C ) ) ) ) ).

% inf.boundedI
thf(fact_614_inf__greatest,axiom,
    ! [X3: $o,Y2: $o,Z2: $o] :
      ( ( ord_less_eq_o @ X3 @ Y2 )
     => ( ( ord_less_eq_o @ X3 @ Z2 )
       => ( ord_less_eq_o @ X3 @ ( inf_inf_o @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_615_inf__greatest,axiom,
    ! [X3: epistemic_fm_a > $o,Y2: epistemic_fm_a > $o,Z2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ X3 @ Y2 )
     => ( ( ord_le4043730696559282883fm_a_o @ X3 @ Z2 )
       => ( ord_le4043730696559282883fm_a_o @ X3 @ ( inf_in3606484609122063093fm_a_o @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_616_inf__greatest,axiom,
    ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Z2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ X3 @ Y2 )
     => ( ( ord_le3275665582123262618c_fm_a @ X3 @ Z2 )
       => ( ord_le3275665582123262618c_fm_a @ X3 @ ( inf_in2882328776738922472c_fm_a @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_617_inf__greatest,axiom,
    ! [X3: set_b,Y2: set_b,Z2: set_b] :
      ( ( ord_less_eq_set_b @ X3 @ Y2 )
     => ( ( ord_less_eq_set_b @ X3 @ Z2 )
       => ( ord_less_eq_set_b @ X3 @ ( inf_inf_set_b @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_618_inf__greatest,axiom,
    ! [X3: b > $o,Y2: b > $o,Z2: b > $o] :
      ( ( ord_less_eq_b_o @ X3 @ Y2 )
     => ( ( ord_less_eq_b_o @ X3 @ Z2 )
       => ( ord_less_eq_b_o @ X3 @ ( inf_inf_b_o @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_619_inf__greatest,axiom,
    ! [X3: set_o,Y2: set_o,Z2: set_o] :
      ( ( ord_less_eq_set_o @ X3 @ Y2 )
     => ( ( ord_less_eq_set_o @ X3 @ Z2 )
       => ( ord_less_eq_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ Z2 ) ) ) ) ).

% inf_greatest
thf(fact_620_inf_Oorder__iff,axiom,
    ( ord_less_eq_o
    = ( ^ [A2: $o,B3: $o] :
          ( A2
          = ( inf_inf_o @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_621_inf_Oorder__iff,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [A2: epistemic_fm_a > $o,B3: epistemic_fm_a > $o] :
          ( A2
          = ( inf_in3606484609122063093fm_a_o @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_622_inf_Oorder__iff,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A2: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( A2
          = ( inf_in2882328776738922472c_fm_a @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_623_inf_Oorder__iff,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A2: set_b,B3: set_b] :
          ( A2
          = ( inf_inf_set_b @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_624_inf_Oorder__iff,axiom,
    ( ord_less_eq_b_o
    = ( ^ [A2: b > $o,B3: b > $o] :
          ( A2
          = ( inf_inf_b_o @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_625_inf_Oorder__iff,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A2: set_o,B3: set_o] :
          ( A2
          = ( inf_inf_set_o @ A2 @ B3 ) ) ) ) ).

% inf.order_iff
thf(fact_626_inf_Ocobounded1,axiom,
    ! [A: $o,B2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_627_inf_Ocobounded1,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_628_inf_Ocobounded1,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_629_inf_Ocobounded1,axiom,
    ! [A: set_b,B2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_630_inf_Ocobounded1,axiom,
    ! [A: b > $o,B2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_631_inf_Ocobounded1,axiom,
    ! [A: set_o,B2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ A ) ).

% inf.cobounded1
thf(fact_632_inf_Ocobounded2,axiom,
    ! [A: $o,B2: $o] : ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_633_inf_Ocobounded2,axiom,
    ! [A: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] : ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_634_inf_Ocobounded2,axiom,
    ! [A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_635_inf_Ocobounded2,axiom,
    ! [A: set_b,B2: set_b] : ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_636_inf_Ocobounded2,axiom,
    ! [A: b > $o,B2: b > $o] : ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_637_inf_Ocobounded2,axiom,
    ! [A: set_o,B2: set_o] : ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ B2 ) ).

% inf.cobounded2
thf(fact_638_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_o
    = ( ^ [A2: $o,B3: $o] :
          ( ( inf_inf_o @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_639_inf_Oabsorb__iff1,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [A2: epistemic_fm_a > $o,B3: epistemic_fm_a > $o] :
          ( ( inf_in3606484609122063093fm_a_o @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_640_inf_Oabsorb__iff1,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A2: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( ( inf_in2882328776738922472c_fm_a @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_641_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A2: set_b,B3: set_b] :
          ( ( inf_inf_set_b @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_642_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_b_o
    = ( ^ [A2: b > $o,B3: b > $o] :
          ( ( inf_inf_b_o @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_643_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A2: set_o,B3: set_o] :
          ( ( inf_inf_set_o @ A2 @ B3 )
          = A2 ) ) ) ).

% inf.absorb_iff1
thf(fact_644_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_o
    = ( ^ [B3: $o,A2: $o] :
          ( ( inf_inf_o @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_645_inf_Oabsorb__iff2,axiom,
    ( ord_le4043730696559282883fm_a_o
    = ( ^ [B3: epistemic_fm_a > $o,A2: epistemic_fm_a > $o] :
          ( ( inf_in3606484609122063093fm_a_o @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_646_inf_Oabsorb__iff2,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [B3: set_Epistemic_fm_a,A2: set_Epistemic_fm_a] :
          ( ( inf_in2882328776738922472c_fm_a @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_647_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_b
    = ( ^ [B3: set_b,A2: set_b] :
          ( ( inf_inf_set_b @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_648_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_b_o
    = ( ^ [B3: b > $o,A2: b > $o] :
          ( ( inf_inf_b_o @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_649_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_o
    = ( ^ [B3: set_o,A2: set_o] :
          ( ( inf_inf_set_o @ A2 @ B3 )
          = B3 ) ) ) ).

% inf.absorb_iff2
thf(fact_650_inf_OcoboundedI1,axiom,
    ! [A: $o,C: $o,B2: $o] :
      ( ( ord_less_eq_o @ A @ C )
     => ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_651_inf_OcoboundedI1,axiom,
    ! [A: epistemic_fm_a > $o,C: epistemic_fm_a > $o,B2: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ A @ C )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_652_inf_OcoboundedI1,axiom,
    ! [A: set_Epistemic_fm_a,C: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A @ C )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_653_inf_OcoboundedI1,axiom,
    ! [A: set_b,C: set_b,B2: set_b] :
      ( ( ord_less_eq_set_b @ A @ C )
     => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_654_inf_OcoboundedI1,axiom,
    ! [A: b > $o,C: b > $o,B2: b > $o] :
      ( ( ord_less_eq_b_o @ A @ C )
     => ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_655_inf_OcoboundedI1,axiom,
    ! [A: set_o,C: set_o,B2: set_o] :
      ( ( ord_less_eq_set_o @ A @ C )
     => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI1
thf(fact_656_inf_OcoboundedI2,axiom,
    ! [B2: $o,C: $o,A: $o] :
      ( ( ord_less_eq_o @ B2 @ C )
     => ( ord_less_eq_o @ ( inf_inf_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_657_inf_OcoboundedI2,axiom,
    ! [B2: epistemic_fm_a > $o,C: epistemic_fm_a > $o,A: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ B2 @ C )
     => ( ord_le4043730696559282883fm_a_o @ ( inf_in3606484609122063093fm_a_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_658_inf_OcoboundedI2,axiom,
    ! [B2: set_Epistemic_fm_a,C: set_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ B2 @ C )
     => ( ord_le3275665582123262618c_fm_a @ ( inf_in2882328776738922472c_fm_a @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_659_inf_OcoboundedI2,axiom,
    ! [B2: set_b,C: set_b,A: set_b] :
      ( ( ord_less_eq_set_b @ B2 @ C )
     => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_660_inf_OcoboundedI2,axiom,
    ! [B2: b > $o,C: b > $o,A: b > $o] :
      ( ( ord_less_eq_b_o @ B2 @ C )
     => ( ord_less_eq_b_o @ ( inf_inf_b_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_661_inf_OcoboundedI2,axiom,
    ! [B2: set_o,C: set_o,A: set_o] :
      ( ( ord_less_eq_set_o @ B2 @ C )
     => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ B2 ) @ C ) ) ).

% inf.coboundedI2
thf(fact_662_fm_Odistinct_I15_J,axiom,
    ! [X22: list_char,X51: epistemic_fm_b,X52: epistemic_fm_b] :
      ( ( epistemic_Pro_b @ X22 )
     != ( epistemic_Imp_b @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_663_fm_Odistinct_I15_J,axiom,
    ! [X22: list_char,X51: epistemic_fm_o,X52: epistemic_fm_o] :
      ( ( epistemic_Pro_o @ X22 )
     != ( epistemic_Imp_o @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_664_fm_Odistinct_I15_J,axiom,
    ! [X22: list_char,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X22 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_665_fm_Odistinct_I21_J,axiom,
    ! [X31: epistemic_fm_b,X32: epistemic_fm_b,X51: epistemic_fm_b,X52: epistemic_fm_b] :
      ( ( epistemic_Dis_b @ X31 @ X32 )
     != ( epistemic_Imp_b @ X51 @ X52 ) ) ).

% fm.distinct(21)
thf(fact_666_fm_Odistinct_I21_J,axiom,
    ! [X31: epistemic_fm_a,X32: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X31 @ X32 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(21)
thf(fact_667_fm_Odistinct_I17_J,axiom,
    ! [X22: list_char,X61: b,X62: epistemic_fm_b] :
      ( ( epistemic_Pro_b @ X22 )
     != ( epistemic_K_b @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_668_fm_Odistinct_I17_J,axiom,
    ! [X22: list_char,X61: $o,X62: epistemic_fm_o] :
      ( ( epistemic_Pro_o @ X22 )
     != ( epistemic_K_o @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_669_fm_Odistinct_I17_J,axiom,
    ! [X22: list_char,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X22 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_670_fm_Odistinct_I23_J,axiom,
    ! [X31: epistemic_fm_o,X32: epistemic_fm_o,X61: $o,X62: epistemic_fm_o] :
      ( ( epistemic_Dis_o @ X31 @ X32 )
     != ( epistemic_K_o @ X61 @ X62 ) ) ).

% fm.distinct(23)
thf(fact_671_fm_Odistinct_I23_J,axiom,
    ! [X31: epistemic_fm_b,X32: epistemic_fm_b,X61: b,X62: epistemic_fm_b] :
      ( ( epistemic_Dis_b @ X31 @ X32 )
     != ( epistemic_K_b @ X61 @ X62 ) ) ).

% fm.distinct(23)
thf(fact_672_fm_Odistinct_I23_J,axiom,
    ! [X31: epistemic_fm_a,X32: epistemic_fm_a,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X31 @ X32 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(23)
thf(fact_673_fm_Odistinct_I1_J,axiom,
    ! [X22: list_char] :
      ( epistemic_FF_o
     != ( epistemic_Pro_o @ X22 ) ) ).

% fm.distinct(1)
thf(fact_674_fm_Odistinct_I1_J,axiom,
    ! [X22: list_char] :
      ( epistemic_FF_a
     != ( epistemic_Pro_a @ X22 ) ) ).

% fm.distinct(1)
thf(fact_675_fm_Odistinct_I3_J,axiom,
    ! [X31: epistemic_fm_o,X32: epistemic_fm_o] :
      ( epistemic_FF_o
     != ( epistemic_Dis_o @ X31 @ X32 ) ) ).

% fm.distinct(3)
thf(fact_676_fm_Odistinct_I3_J,axiom,
    ! [X31: epistemic_fm_b,X32: epistemic_fm_b] :
      ( epistemic_FF_b
     != ( epistemic_Dis_b @ X31 @ X32 ) ) ).

% fm.distinct(3)
thf(fact_677_fm_Odistinct_I3_J,axiom,
    ! [X31: epistemic_fm_a,X32: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_Dis_a @ X31 @ X32 ) ) ).

% fm.distinct(3)
thf(fact_678_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_679_semantics_Osimps_I2_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,X3: list_char] :
      ( ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Pro_a @ X3 ) )
      = ( episte5693316124195166255t_unit @ M @ W @ X3 ) ) ).

% semantics.simps(2)
thf(fact_680_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_681_semantics_Osimps_I3_J,axiom,
    ! [M: episte3224730989885420256t_unit,W: b,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte295617885132580261cs_a_b @ M @ W @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( episte295617885132580261cs_a_b @ M @ W @ P )
        | ( episte295617885132580261cs_a_b @ M @ W @ Q ) ) ) ).

% semantics.simps(3)
thf(fact_682_fm_Odistinct_I13_J,axiom,
    ! [X22: list_char,X41: epistemic_fm_b,X42: epistemic_fm_b] :
      ( ( epistemic_Pro_b @ X22 )
     != ( epistemic_Con_b @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_683_fm_Odistinct_I13_J,axiom,
    ! [X22: list_char,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X22 )
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_684_fm_Odistinct_I13_J,axiom,
    ! [X22: list_char,X41: epistemic_fm_o,X42: epistemic_fm_o] :
      ( ( epistemic_Pro_o @ X22 )
     != ( epistemic_Con_o @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_685_fm_Odistinct_I19_J,axiom,
    ! [X31: epistemic_fm_a,X32: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_Dis_a @ X31 @ X32 )
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(19)
thf(fact_686_fm_Odistinct_I19_J,axiom,
    ! [X31: epistemic_fm_b,X32: epistemic_fm_b,X41: epistemic_fm_b,X42: epistemic_fm_b] :
      ( ( epistemic_Dis_b @ X31 @ X32 )
     != ( epistemic_Con_b @ X41 @ X42 ) ) ).

% fm.distinct(19)
thf(fact_687_eval_Osimps_I2_J,axiom,
    ! [G2: list_char > $o,Uw: epistemic_fm_a > $o,X3: list_char] :
      ( ( epistemic_eval_a @ G2 @ Uw @ ( epistemic_Pro_a @ X3 ) )
      = ( G2 @ X3 ) ) ).

% eval.simps(2)
thf(fact_688_eval_Osimps_I2_J,axiom,
    ! [G2: list_char > $o,Uw: epistemic_fm_o > $o,X3: list_char] :
      ( ( epistemic_eval_o @ G2 @ Uw @ ( epistemic_Pro_o @ X3 ) )
      = ( G2 @ X3 ) ) ).

% eval.simps(2)
thf(fact_689_eval_Osimps_I3_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G2 @ H2 @ P )
        | ( epistemic_eval_a @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_690_eval_Osimps_I3_J,axiom,
    ! [G2: list_char > $o,H2: epistemic_fm_b > $o,P: epistemic_fm_b,Q: epistemic_fm_b] :
      ( ( epistemic_eval_b @ G2 @ H2 @ ( epistemic_Dis_b @ P @ Q ) )
      = ( ( epistemic_eval_b @ G2 @ H2 @ P )
        | ( epistemic_eval_b @ G2 @ H2 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_691_fm_Oexhaust,axiom,
    ! [Y2: epistemic_fm_b] :
      ( ( Y2 != epistemic_FF_b )
     => ( ! [X23: list_char] :
            ( Y2
           != ( epistemic_Pro_b @ X23 ) )
       => ( ! [X312: epistemic_fm_b,X322: epistemic_fm_b] :
              ( Y2
             != ( epistemic_Dis_b @ X312 @ X322 ) )
         => ( ! [X412: epistemic_fm_b,X422: epistemic_fm_b] :
                ( Y2
               != ( epistemic_Con_b @ X412 @ X422 ) )
           => ( ! [X512: epistemic_fm_b,X522: epistemic_fm_b] :
                  ( Y2
                 != ( epistemic_Imp_b @ X512 @ X522 ) )
             => ~ ! [X612: b,X622: epistemic_fm_b] :
                    ( Y2
                   != ( epistemic_K_b @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_692_fm_Oexhaust,axiom,
    ! [Y2: epistemic_fm_o] :
      ( ( Y2 != epistemic_FF_o )
     => ( ! [X23: list_char] :
            ( Y2
           != ( epistemic_Pro_o @ X23 ) )
       => ( ! [X312: epistemic_fm_o,X322: epistemic_fm_o] :
              ( Y2
             != ( epistemic_Dis_o @ X312 @ X322 ) )
         => ( ! [X412: epistemic_fm_o,X422: epistemic_fm_o] :
                ( Y2
               != ( epistemic_Con_o @ X412 @ X422 ) )
           => ( ! [X512: epistemic_fm_o,X522: epistemic_fm_o] :
                  ( Y2
                 != ( epistemic_Imp_o @ X512 @ X522 ) )
             => ~ ! [X612: $o,X622: epistemic_fm_o] :
                    ( Y2
                   != ( epistemic_K_o @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_693_fm_Oexhaust,axiom,
    ! [Y2: epistemic_fm_a] :
      ( ( Y2 != epistemic_FF_a )
     => ( ! [X23: list_char] :
            ( Y2
           != ( epistemic_Pro_a @ X23 ) )
       => ( ! [X312: epistemic_fm_a,X322: epistemic_fm_a] :
              ( Y2
             != ( epistemic_Dis_a @ X312 @ X322 ) )
         => ( ! [X412: epistemic_fm_a,X422: epistemic_fm_a] :
                ( Y2
               != ( epistemic_Con_a @ X412 @ X422 ) )
           => ( ! [X512: epistemic_fm_a,X522: epistemic_fm_a] :
                  ( Y2
                 != ( epistemic_Imp_a @ X512 @ X522 ) )
             => ~ ! [X612: a,X622: epistemic_fm_a] :
                    ( Y2
                   != ( epistemic_K_a @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_694_fm_Orel__induct,axiom,
    ! [R3: b > a > $o,X3: epistemic_fm_b,Y2: epistemic_fm_a,Q2: epistemic_fm_b > epistemic_fm_a > $o] :
      ( ( epistemic_rel_fm_b_a @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_b @ epistemic_FF_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_b @ A22 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_b,A32: epistemic_fm_b,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_b @ A31 @ A32 ) @ ( epistemic_Dis_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_b,A42: epistemic_fm_b,B41: epistemic_fm_a,B42: epistemic_fm_a] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_b @ A41 @ A42 ) @ ( epistemic_Con_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_b,A52: epistemic_fm_b,B51: epistemic_fm_a,B52: epistemic_fm_a] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_b @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: b,A62: epistemic_fm_b,B61: a,B62: epistemic_fm_a] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_b @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_695_fm_Orel__induct,axiom,
    ! [R3: b > $o > $o,X3: epistemic_fm_b,Y2: epistemic_fm_o,Q2: epistemic_fm_b > epistemic_fm_o > $o] :
      ( ( epistemic_rel_fm_b_o @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_b @ epistemic_FF_o )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_b @ A22 ) @ ( epistemic_Pro_o @ B22 ) ) )
         => ( ! [A31: epistemic_fm_b,A32: epistemic_fm_b,B31: epistemic_fm_o,B32: epistemic_fm_o] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_b @ A31 @ A32 ) @ ( epistemic_Dis_o @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_b,A42: epistemic_fm_b,B41: epistemic_fm_o,B42: epistemic_fm_o] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_b @ A41 @ A42 ) @ ( epistemic_Con_o @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_b,A52: epistemic_fm_b,B51: epistemic_fm_o,B52: epistemic_fm_o] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_b @ A51 @ A52 ) @ ( epistemic_Imp_o @ B51 @ B52 ) ) ) )
               => ( ! [A61: b,A62: epistemic_fm_b,B61: $o,B62: epistemic_fm_o] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_b @ A61 @ A62 ) @ ( epistemic_K_o @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_696_fm_Orel__induct,axiom,
    ! [R3: a > b > $o,X3: epistemic_fm_a,Y2: epistemic_fm_b,Q2: epistemic_fm_a > epistemic_fm_b > $o] :
      ( ( epistemic_rel_fm_a_b @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_a @ epistemic_FF_b )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_a @ A22 ) @ ( epistemic_Pro_b @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: epistemic_fm_b,B32: epistemic_fm_b] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_a @ A31 @ A32 ) @ ( epistemic_Dis_b @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_a,A42: epistemic_fm_a,B41: epistemic_fm_b,B42: epistemic_fm_b] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_a @ A41 @ A42 ) @ ( epistemic_Con_b @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_a,A52: epistemic_fm_a,B51: epistemic_fm_b,B52: epistemic_fm_b] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( epistemic_Imp_b @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: b,B62: epistemic_fm_b] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_a @ A61 @ A62 ) @ ( epistemic_K_b @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_697_fm_Orel__induct,axiom,
    ! [R3: a > $o > $o,X3: epistemic_fm_a,Y2: epistemic_fm_o,Q2: epistemic_fm_a > epistemic_fm_o > $o] :
      ( ( epistemic_rel_fm_a_o @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_a @ epistemic_FF_o )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_a @ A22 ) @ ( epistemic_Pro_o @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: epistemic_fm_o,B32: epistemic_fm_o] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_a @ A31 @ A32 ) @ ( epistemic_Dis_o @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_a,A42: epistemic_fm_a,B41: epistemic_fm_o,B42: epistemic_fm_o] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_a @ A41 @ A42 ) @ ( epistemic_Con_o @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_a,A52: epistemic_fm_a,B51: epistemic_fm_o,B52: epistemic_fm_o] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( epistemic_Imp_o @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: $o,B62: epistemic_fm_o] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_a @ A61 @ A62 ) @ ( epistemic_K_o @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_698_fm_Orel__induct,axiom,
    ! [R3: $o > b > $o,X3: epistemic_fm_o,Y2: epistemic_fm_b,Q2: epistemic_fm_o > epistemic_fm_b > $o] :
      ( ( epistemic_rel_fm_o_b @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_o @ epistemic_FF_b )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_o @ A22 ) @ ( epistemic_Pro_b @ B22 ) ) )
         => ( ! [A31: epistemic_fm_o,A32: epistemic_fm_o,B31: epistemic_fm_b,B32: epistemic_fm_b] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_o @ A31 @ A32 ) @ ( epistemic_Dis_b @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_o,A42: epistemic_fm_o,B41: epistemic_fm_b,B42: epistemic_fm_b] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_o @ A41 @ A42 ) @ ( epistemic_Con_b @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_o,A52: epistemic_fm_o,B51: epistemic_fm_b,B52: epistemic_fm_b] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_o @ A51 @ A52 ) @ ( epistemic_Imp_b @ B51 @ B52 ) ) ) )
               => ( ! [A61: $o,A62: epistemic_fm_o,B61: b,B62: epistemic_fm_b] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_o @ A61 @ A62 ) @ ( epistemic_K_b @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_699_fm_Orel__induct,axiom,
    ! [R3: $o > a > $o,X3: epistemic_fm_o,Y2: epistemic_fm_a,Q2: epistemic_fm_o > epistemic_fm_a > $o] :
      ( ( epistemic_rel_fm_o_a @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_o @ epistemic_FF_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_o @ A22 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_o,A32: epistemic_fm_o,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_o @ A31 @ A32 ) @ ( epistemic_Dis_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_o,A42: epistemic_fm_o,B41: epistemic_fm_a,B42: epistemic_fm_a] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_o @ A41 @ A42 ) @ ( epistemic_Con_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_o,A52: epistemic_fm_o,B51: epistemic_fm_a,B52: epistemic_fm_a] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_o @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: $o,A62: epistemic_fm_o,B61: a,B62: epistemic_fm_a] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_o @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_700_fm_Orel__induct,axiom,
    ! [R3: $o > $o > $o,X3: epistemic_fm_o,Y2: epistemic_fm_o,Q2: epistemic_fm_o > epistemic_fm_o > $o] :
      ( ( epistemic_rel_fm_o_o @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_o @ epistemic_FF_o )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_o @ A22 ) @ ( epistemic_Pro_o @ B22 ) ) )
         => ( ! [A31: epistemic_fm_o,A32: epistemic_fm_o,B31: epistemic_fm_o,B32: epistemic_fm_o] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_o @ A31 @ A32 ) @ ( epistemic_Dis_o @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_o,A42: epistemic_fm_o,B41: epistemic_fm_o,B42: epistemic_fm_o] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_o @ A41 @ A42 ) @ ( epistemic_Con_o @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_o,A52: epistemic_fm_o,B51: epistemic_fm_o,B52: epistemic_fm_o] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_o @ A51 @ A52 ) @ ( epistemic_Imp_o @ B51 @ B52 ) ) ) )
               => ( ! [A61: $o,A62: epistemic_fm_o,B61: $o,B62: epistemic_fm_o] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_o @ A61 @ A62 ) @ ( epistemic_K_o @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_701_fm_Orel__induct,axiom,
    ! [R3: b > b > $o,X3: epistemic_fm_b,Y2: epistemic_fm_b,Q2: epistemic_fm_b > epistemic_fm_b > $o] :
      ( ( epistemic_rel_fm_b_b @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_b @ epistemic_FF_b )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_b @ A22 ) @ ( epistemic_Pro_b @ B22 ) ) )
         => ( ! [A31: epistemic_fm_b,A32: epistemic_fm_b,B31: epistemic_fm_b,B32: epistemic_fm_b] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( epistemic_Dis_b @ A31 @ A32 ) @ ( epistemic_Dis_b @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_b,A42: epistemic_fm_b,B41: epistemic_fm_b,B42: epistemic_fm_b] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( epistemic_Con_b @ A41 @ A42 ) @ ( epistemic_Con_b @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_b,A52: epistemic_fm_b,B51: epistemic_fm_b,B52: epistemic_fm_b] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_b @ A51 @ A52 ) @ ( epistemic_Imp_b @ B51 @ B52 ) ) ) )
               => ( ! [A61: b,A62: epistemic_fm_b,B61: b,B62: epistemic_fm_b] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_b @ A61 @ A62 ) @ ( epistemic_K_b @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_702_fm_Orel__induct,axiom,
    ! [R3: a > a > $o,X3: epistemic_fm_a,Y2: epistemic_fm_a,Q2: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( epistemic_rel_fm_a_a @ R3 @ X3 @ Y2 )
     => ( ( Q2 @ epistemic_FF_a @ epistemic_FF_a )
       => ( ! [A22: list_char,B22: list_char] :
              ( ( A22 = B22 )
             => ( Q2 @ ( epistemic_Pro_a @ A22 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q2 @ A31 @ B31 )
               => ( ( Q2 @ A32 @ B32 )
                 => ( Q2 @ ( 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] :
                  ( ( Q2 @ A41 @ B41 )
                 => ( ( Q2 @ A42 @ B42 )
                   => ( Q2 @ ( 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] :
                    ( ( Q2 @ A51 @ B51 )
                   => ( ( Q2 @ A52 @ B52 )
                     => ( Q2 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: a,B62: epistemic_fm_a] :
                      ( ( R3 @ A61 @ B61 )
                     => ( ( Q2 @ A62 @ B62 )
                       => ( Q2 @ ( epistemic_K_a @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q2 @ X3 @ Y2 ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_703_fm_Orel__cases,axiom,
    ! [R3: b > a > $o,A: epistemic_fm_b,B2: epistemic_fm_a] :
      ( ( epistemic_rel_fm_b_a @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_b )
         => ( B2 != epistemic_FF_a ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_b @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_a @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_b,X2a: epistemic_fm_b] :
                ( ( A
                  = ( epistemic_Dis_b @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B2
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_b_a @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_b_a @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_b,X2b: epistemic_fm_b] :
                  ( ( A
                    = ( epistemic_Con_b @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B2
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_b_a @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_b_a @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_b,X2c: epistemic_fm_b] :
                    ( ( A
                      = ( epistemic_Imp_b @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B2
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_b_a @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_b_a @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: b,X2d: epistemic_fm_b] :
                      ( ( A
                        = ( epistemic_K_b @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B2
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_b_a @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_704_fm_Orel__cases,axiom,
    ! [R3: b > $o > $o,A: epistemic_fm_b,B2: epistemic_fm_o] :
      ( ( epistemic_rel_fm_b_o @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_b )
         => ( B2 != epistemic_FF_o ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_b @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_o @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_b,X2a: epistemic_fm_b] :
                ( ( A
                  = ( epistemic_Dis_b @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_o,Y2a: epistemic_fm_o] :
                    ( ( B2
                      = ( epistemic_Dis_o @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_b_o @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_b_o @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_b,X2b: epistemic_fm_b] :
                  ( ( A
                    = ( epistemic_Con_b @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_o,Y2b: epistemic_fm_o] :
                      ( ( B2
                        = ( epistemic_Con_o @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_b_o @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_b_o @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_b,X2c: epistemic_fm_b] :
                    ( ( A
                      = ( epistemic_Imp_b @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_o,Y2c: epistemic_fm_o] :
                        ( ( B2
                          = ( epistemic_Imp_o @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_b_o @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_b_o @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: b,X2d: epistemic_fm_b] :
                      ( ( A
                        = ( epistemic_K_b @ X1c @ X2d ) )
                     => ! [Y1c: $o,Y2d: epistemic_fm_o] :
                          ( ( B2
                            = ( epistemic_K_o @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_b_o @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_705_fm_Orel__cases,axiom,
    ! [R3: a > b > $o,A: epistemic_fm_a,B2: epistemic_fm_b] :
      ( ( epistemic_rel_fm_a_b @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_a )
         => ( B2 != epistemic_FF_b ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_a @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_b @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A
                  = ( epistemic_Dis_a @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_b,Y2a: epistemic_fm_b] :
                    ( ( B2
                      = ( epistemic_Dis_b @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_a_b @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_a_b @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_b,Y2b: epistemic_fm_b] :
                      ( ( B2
                        = ( epistemic_Con_b @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_a_b @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_a_b @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_b,Y2c: epistemic_fm_b] :
                        ( ( B2
                          = ( epistemic_Imp_b @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_a_b @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_a_b @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: b,Y2d: epistemic_fm_b] :
                          ( ( B2
                            = ( epistemic_K_b @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_a_b @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_706_fm_Orel__cases,axiom,
    ! [R3: a > $o > $o,A: epistemic_fm_a,B2: epistemic_fm_o] :
      ( ( epistemic_rel_fm_a_o @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_a )
         => ( B2 != epistemic_FF_o ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_a @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_o @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A
                  = ( epistemic_Dis_a @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_o,Y2a: epistemic_fm_o] :
                    ( ( B2
                      = ( epistemic_Dis_o @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_a_o @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_a_o @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_o,Y2b: epistemic_fm_o] :
                      ( ( B2
                        = ( epistemic_Con_o @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_a_o @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_a_o @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_o,Y2c: epistemic_fm_o] :
                        ( ( B2
                          = ( epistemic_Imp_o @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_a_o @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_a_o @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: $o,Y2d: epistemic_fm_o] :
                          ( ( B2
                            = ( epistemic_K_o @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_a_o @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_707_fm_Orel__cases,axiom,
    ! [R3: $o > b > $o,A: epistemic_fm_o,B2: epistemic_fm_b] :
      ( ( epistemic_rel_fm_o_b @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_o )
         => ( B2 != epistemic_FF_b ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_o @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_b @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_o,X2a: epistemic_fm_o] :
                ( ( A
                  = ( epistemic_Dis_o @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_b,Y2a: epistemic_fm_b] :
                    ( ( B2
                      = ( epistemic_Dis_b @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_o_b @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_o_b @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_o,X2b: epistemic_fm_o] :
                  ( ( A
                    = ( epistemic_Con_o @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_b,Y2b: epistemic_fm_b] :
                      ( ( B2
                        = ( epistemic_Con_b @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_o_b @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_o_b @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_o,X2c: epistemic_fm_o] :
                    ( ( A
                      = ( epistemic_Imp_o @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_b,Y2c: epistemic_fm_b] :
                        ( ( B2
                          = ( epistemic_Imp_b @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_o_b @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_o_b @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: $o,X2d: epistemic_fm_o] :
                      ( ( A
                        = ( epistemic_K_o @ X1c @ X2d ) )
                     => ! [Y1c: b,Y2d: epistemic_fm_b] :
                          ( ( B2
                            = ( epistemic_K_b @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_o_b @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_708_fm_Orel__cases,axiom,
    ! [R3: $o > a > $o,A: epistemic_fm_o,B2: epistemic_fm_a] :
      ( ( epistemic_rel_fm_o_a @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_o )
         => ( B2 != epistemic_FF_a ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_o @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_a @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_o,X2a: epistemic_fm_o] :
                ( ( A
                  = ( epistemic_Dis_o @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B2
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_o_a @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_o_a @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_o,X2b: epistemic_fm_o] :
                  ( ( A
                    = ( epistemic_Con_o @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B2
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_o_a @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_o_a @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_o,X2c: epistemic_fm_o] :
                    ( ( A
                      = ( epistemic_Imp_o @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B2
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_o_a @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_o_a @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: $o,X2d: epistemic_fm_o] :
                      ( ( A
                        = ( epistemic_K_o @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B2
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_o_a @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_709_fm_Orel__cases,axiom,
    ! [R3: $o > $o > $o,A: epistemic_fm_o,B2: epistemic_fm_o] :
      ( ( epistemic_rel_fm_o_o @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_o )
         => ( B2 != epistemic_FF_o ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_o @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_o @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_o,X2a: epistemic_fm_o] :
                ( ( A
                  = ( epistemic_Dis_o @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_o,Y2a: epistemic_fm_o] :
                    ( ( B2
                      = ( epistemic_Dis_o @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_o_o @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_o_o @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_o,X2b: epistemic_fm_o] :
                  ( ( A
                    = ( epistemic_Con_o @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_o,Y2b: epistemic_fm_o] :
                      ( ( B2
                        = ( epistemic_Con_o @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_o_o @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_o_o @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_o,X2c: epistemic_fm_o] :
                    ( ( A
                      = ( epistemic_Imp_o @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_o,Y2c: epistemic_fm_o] :
                        ( ( B2
                          = ( epistemic_Imp_o @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_o_o @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_o_o @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: $o,X2d: epistemic_fm_o] :
                      ( ( A
                        = ( epistemic_K_o @ X1c @ X2d ) )
                     => ! [Y1c: $o,Y2d: epistemic_fm_o] :
                          ( ( B2
                            = ( epistemic_K_o @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_o_o @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_710_fm_Orel__cases,axiom,
    ! [R3: b > b > $o,A: epistemic_fm_b,B2: epistemic_fm_b] :
      ( ( epistemic_rel_fm_b_b @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_b )
         => ( B2 != epistemic_FF_b ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_b @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_b @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_b,X2a: epistemic_fm_b] :
                ( ( A
                  = ( epistemic_Dis_b @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_b,Y2a: epistemic_fm_b] :
                    ( ( B2
                      = ( epistemic_Dis_b @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_b_b @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_b_b @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_b,X2b: epistemic_fm_b] :
                  ( ( A
                    = ( epistemic_Con_b @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_b,Y2b: epistemic_fm_b] :
                      ( ( B2
                        = ( epistemic_Con_b @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_b_b @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_b_b @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_b,X2c: epistemic_fm_b] :
                    ( ( A
                      = ( epistemic_Imp_b @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_b,Y2c: epistemic_fm_b] :
                        ( ( B2
                          = ( epistemic_Imp_b @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_b_b @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_b_b @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: b,X2d: epistemic_fm_b] :
                      ( ( A
                        = ( epistemic_K_b @ X1c @ X2d ) )
                     => ! [Y1c: b,Y2d: epistemic_fm_b] :
                          ( ( B2
                            = ( epistemic_K_b @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_b_b @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_711_fm_Orel__cases,axiom,
    ! [R3: a > a > $o,A: epistemic_fm_a,B2: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R3 @ A @ B2 )
     => ( ( ( A = epistemic_FF_a )
         => ( B2 != epistemic_FF_a ) )
       => ( ! [X: list_char] :
              ( ( A
                = ( epistemic_Pro_a @ X ) )
             => ! [Y3: list_char] :
                  ( ( B2
                    = ( epistemic_Pro_a @ Y3 ) )
                 => ( X != Y3 ) ) )
         => ( ! [X1: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A
                  = ( epistemic_Dis_a @ X1 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B2
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_a_a @ R3 @ X1 @ Y1 )
                     => ~ ( epistemic_rel_fm_a_a @ R3 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B2
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_a_a @ R3 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_a_a @ R3 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B2
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_a_a @ R3 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_a_a @ R3 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B2
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R3 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_a_a @ R3 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_712_inf__Int__eq,axiom,
    ! [R3: set_se5208064806568342746c_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( inf_in5938521974262266133fm_a_o
        @ ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ R3 )
        @ ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ S ) )
      = ( ^ [X2: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X2 @ ( inf_in1884693029477671368c_fm_a @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_713_inf__Int__eq,axiom,
    ! [R3: set_set_o,S: set_set_o] :
      ( ( inf_inf_set_o_o
        @ ^ [X2: set_o] : ( member_set_o @ X2 @ R3 )
        @ ^ [X2: set_o] : ( member_set_o @ X2 @ S ) )
      = ( ^ [X2: set_o] : ( member_set_o @ X2 @ ( inf_inf_set_set_o @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_714_inf__Int__eq,axiom,
    ! [R3: set_set_b,S: set_set_b] :
      ( ( inf_inf_set_b_o
        @ ^ [X2: set_b] : ( member_set_b @ X2 @ R3 )
        @ ^ [X2: set_b] : ( member_set_b @ X2 @ S ) )
      = ( ^ [X2: set_b] : ( member_set_b @ X2 @ ( inf_inf_set_set_b @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_715_inf__Int__eq,axiom,
    ! [R3: set_a,S: set_a] :
      ( ( inf_inf_a_o
        @ ^ [X2: a] : ( member_a @ X2 @ R3 )
        @ ^ [X2: a] : ( member_a @ X2 @ S ) )
      = ( ^ [X2: a] : ( member_a @ X2 @ ( inf_inf_set_a @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_716_inf__Int__eq,axiom,
    ! [R3: set_o,S: set_o] :
      ( ( inf_inf_o_o
        @ ^ [X2: $o] : ( member_o @ X2 @ R3 )
        @ ^ [X2: $o] : ( member_o @ X2 @ S ) )
      = ( ^ [X2: $o] : ( member_o @ X2 @ ( inf_inf_set_o @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_717_inf__Int__eq,axiom,
    ! [R3: set_b,S: set_b] :
      ( ( inf_inf_b_o
        @ ^ [X2: b] : ( member_b @ X2 @ R3 )
        @ ^ [X2: b] : ( member_b @ X2 @ S ) )
      = ( ^ [X2: b] : ( member_b @ X2 @ ( inf_inf_set_b @ R3 @ S ) ) ) ) ).

% inf_Int_eq
thf(fact_718_fm_Oset__cases,axiom,
    ! [E: set_Epistemic_fm_a,A: episte5999154429349999510c_fm_a] :
      ( ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ A ) )
     => ( ! [Z1: episte5999154429349999510c_fm_a] :
            ( ? [Z22: episte5999154429349999510c_fm_a] :
                ( A
                = ( episte9190102072588321003c_fm_a @ Z1 @ Z22 ) )
           => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
       => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
              ( ( A
                = ( episte9190102072588321003c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
         => ( ! [Z1: episte5999154429349999510c_fm_a] :
                ( ? [Z22: episte5999154429349999510c_fm_a] :
                    ( A
                    = ( episte8719284489194433015c_fm_a @ Z1 @ Z22 ) )
               => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
           => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
                  ( ( A
                    = ( episte8719284489194433015c_fm_a @ Z1 @ Z22 ) )
                 => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
             => ( ! [Z1: episte5999154429349999510c_fm_a] :
                    ( ? [Z22: episte5999154429349999510c_fm_a] :
                        ( A
                        = ( episte5200161025749276397c_fm_a @ Z1 @ Z22 ) )
                   => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z1 ) ) )
               => ( ! [Z1: episte5999154429349999510c_fm_a,Z22: episte5999154429349999510c_fm_a] :
                      ( ( A
                        = ( episte5200161025749276397c_fm_a @ Z1 @ Z22 ) )
                     => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) )
                 => ( ! [Z22: episte5999154429349999510c_fm_a] :
                        ( A
                       != ( episte3013695276341575662c_fm_a @ E @ Z22 ) )
                   => ~ ! [Z1: set_Epistemic_fm_a,Z22: episte5999154429349999510c_fm_a] :
                          ( ( A
                            = ( episte3013695276341575662c_fm_a @ Z1 @ Z22 ) )
                         => ~ ( member536094252920883875c_fm_a @ E @ ( episte6227279731293865264c_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_719_fm_Oset__cases,axiom,
    ! [E: set_o,A: epistemic_fm_set_o] :
      ( ( member_set_o @ E @ ( episte5067851541165005998_set_o @ A ) )
     => ( ! [Z1: epistemic_fm_set_o] :
            ( ? [Z22: epistemic_fm_set_o] :
                ( A
                = ( epistemic_Dis_set_o @ Z1 @ Z22 ) )
           => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_set_o,Z22: epistemic_fm_set_o] :
              ( ( A
                = ( epistemic_Dis_set_o @ Z1 @ Z22 ) )
             => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_set_o] :
                ( ? [Z22: epistemic_fm_set_o] :
                    ( A
                    = ( epistemic_Con_set_o @ Z1 @ Z22 ) )
               => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_set_o,Z22: epistemic_fm_set_o] :
                  ( ( A
                    = ( epistemic_Con_set_o @ Z1 @ Z22 ) )
                 => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_set_o] :
                    ( ? [Z22: epistemic_fm_set_o] :
                        ( A
                        = ( epistemic_Imp_set_o @ Z1 @ Z22 ) )
                   => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_set_o,Z22: epistemic_fm_set_o] :
                      ( ( A
                        = ( epistemic_Imp_set_o @ Z1 @ Z22 ) )
                     => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_set_o] :
                        ( A
                       != ( epistemic_K_set_o @ E @ Z22 ) )
                   => ~ ! [Z1: set_o,Z22: epistemic_fm_set_o] :
                          ( ( A
                            = ( epistemic_K_set_o @ Z1 @ Z22 ) )
                         => ~ ( member_set_o @ E @ ( episte5067851541165005998_set_o @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_720_fm_Oset__cases,axiom,
    ! [E: set_b,A: epistemic_fm_set_b] :
      ( ( member_set_b @ E @ ( episte1019240489619528469_set_b @ A ) )
     => ( ! [Z1: epistemic_fm_set_b] :
            ( ? [Z22: epistemic_fm_set_b] :
                ( A
                = ( epistemic_Dis_set_b @ Z1 @ Z22 ) )
           => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_set_b,Z22: epistemic_fm_set_b] :
              ( ( A
                = ( epistemic_Dis_set_b @ Z1 @ Z22 ) )
             => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_set_b] :
                ( ? [Z22: epistemic_fm_set_b] :
                    ( A
                    = ( epistemic_Con_set_b @ Z1 @ Z22 ) )
               => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_set_b,Z22: epistemic_fm_set_b] :
                  ( ( A
                    = ( epistemic_Con_set_b @ Z1 @ Z22 ) )
                 => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_set_b] :
                    ( ? [Z22: epistemic_fm_set_b] :
                        ( A
                        = ( epistemic_Imp_set_b @ Z1 @ Z22 ) )
                   => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_set_b,Z22: epistemic_fm_set_b] :
                      ( ( A
                        = ( epistemic_Imp_set_b @ Z1 @ Z22 ) )
                     => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_set_b] :
                        ( A
                       != ( epistemic_K_set_b @ E @ Z22 ) )
                   => ~ ! [Z1: set_b,Z22: epistemic_fm_set_b] :
                          ( ( A
                            = ( epistemic_K_set_b @ Z1 @ Z22 ) )
                         => ~ ( member_set_b @ E @ ( episte1019240489619528469_set_b @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_721_fm_Oset__cases,axiom,
    ! [E: $o,A: epistemic_fm_o] :
      ( ( member_o @ E @ ( epistemic_set_fm_o @ A ) )
     => ( ! [Z1: epistemic_fm_o] :
            ( ? [Z22: epistemic_fm_o] :
                ( A
                = ( epistemic_Dis_o @ Z1 @ Z22 ) )
           => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_o,Z22: epistemic_fm_o] :
              ( ( A
                = ( epistemic_Dis_o @ Z1 @ Z22 ) )
             => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_o] :
                ( ? [Z22: epistemic_fm_o] :
                    ( A
                    = ( epistemic_Con_o @ Z1 @ Z22 ) )
               => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_o,Z22: epistemic_fm_o] :
                  ( ( A
                    = ( epistemic_Con_o @ Z1 @ Z22 ) )
                 => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_o] :
                    ( ? [Z22: epistemic_fm_o] :
                        ( A
                        = ( epistemic_Imp_o @ Z1 @ Z22 ) )
                   => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_o,Z22: epistemic_fm_o] :
                      ( ( A
                        = ( epistemic_Imp_o @ Z1 @ Z22 ) )
                     => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_o] :
                        ( A
                       != ( epistemic_K_o @ E @ Z22 ) )
                   => ~ ! [Z1: $o,Z22: epistemic_fm_o] :
                          ( ( A
                            = ( epistemic_K_o @ Z1 @ Z22 ) )
                         => ~ ( member_o @ E @ ( epistemic_set_fm_o @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_722_fm_Oset__cases,axiom,
    ! [E: b,A: epistemic_fm_b] :
      ( ( member_b @ E @ ( epistemic_set_fm_b @ A ) )
     => ( ! [Z1: epistemic_fm_b] :
            ( ? [Z22: epistemic_fm_b] :
                ( A
                = ( epistemic_Dis_b @ Z1 @ Z22 ) )
           => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_b,Z22: epistemic_fm_b] :
              ( ( A
                = ( epistemic_Dis_b @ Z1 @ Z22 ) )
             => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_b] :
                ( ? [Z22: epistemic_fm_b] :
                    ( A
                    = ( epistemic_Con_b @ Z1 @ Z22 ) )
               => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_b,Z22: epistemic_fm_b] :
                  ( ( A
                    = ( epistemic_Con_b @ Z1 @ Z22 ) )
                 => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_b] :
                    ( ? [Z22: epistemic_fm_b] :
                        ( A
                        = ( epistemic_Imp_b @ Z1 @ Z22 ) )
                   => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_b,Z22: epistemic_fm_b] :
                      ( ( A
                        = ( epistemic_Imp_b @ Z1 @ Z22 ) )
                     => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_b] :
                        ( A
                       != ( epistemic_K_b @ E @ Z22 ) )
                   => ~ ! [Z1: b,Z22: epistemic_fm_b] :
                          ( ( A
                            = ( epistemic_K_b @ Z1 @ Z22 ) )
                         => ~ ( member_b @ E @ ( epistemic_set_fm_b @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_723_fm_Oset__cases,axiom,
    ! [E: a,A: epistemic_fm_a] :
      ( ( member_a @ E @ ( epistemic_set_fm_a @ A ) )
     => ( ! [Z1: epistemic_fm_a] :
            ( ? [Z22: epistemic_fm_a] :
                ( A
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
           => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
              ( ( A
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_a] :
                ( ? [Z22: epistemic_fm_a] :
                    ( A
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
               => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                  ( ( A
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
                 => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_a] :
                    ( ? [Z22: epistemic_fm_a] :
                        ( A
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                   => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                      ( ( A
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                     => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_a] :
                        ( A
                       != ( epistemic_K_a @ E @ Z22 ) )
                   => ~ ! [Z1: a,Z22: epistemic_fm_a] :
                          ( ( A
                            = ( epistemic_K_a @ Z1 @ Z22 ) )
                         => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_724_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_AxB_a @ P3 )
                | ( epistemic_Ax4_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M4 )
            & ( episte5478016696552465318t_unit @ M4 )
            & ( episte8364071018013720454t_unit @ M4 ) )
         => ! [X4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5
thf(fact_725_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_AxB_a @ P3 )
                | ( epistemic_Ax4_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( ( episte3426825378771607259t_unit @ M4 )
            & ( episte4899516349225340390t_unit @ M4 )
            & ( episte9018110198556821958t_unit @ M4 ) )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5
thf(fact_726_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_Ax5_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M4 )
            & ( episte5478016696552465318t_unit @ M4 )
            & ( episte8364071018013720454t_unit @ M4 ) )
         => ! [X4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5'
thf(fact_727_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_Ax5_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( ( episte3426825378771607259t_unit @ M4 )
            & ( episte4899516349225340390t_unit @ M4 )
            & ( episte9018110198556821958t_unit @ M4 ) )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>5'
thf(fact_728_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_729_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_730_fm_Opred__mono,axiom,
    ! [P4: b > $o,Pa: b > $o] :
      ( ( ord_less_eq_b_o @ P4 @ Pa )
     => ( ord_le1256275114586606850fm_b_o @ ( epistemic_pred_fm_b @ P4 ) @ ( epistemic_pred_fm_b @ Pa ) ) ) ).

% fm.pred_mono
thf(fact_731_eval__semantics,axiom,
    ! [Pi4: set_Epistemic_fm_a > list_char > $o,W: set_Epistemic_fm_a,W6: 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 @ W6 @ R @ ( episte8239586592105053771t_unit @ Pi4 @ product_Unity ) ) @ W ) @ P )
      = ( episte7081087998767065248c_fm_a @ ( episte2888590659910966568t_unit @ W6 @ R @ ( episte8239586592105053771t_unit @ Pi4 @ product_Unity ) ) @ W @ P ) ) ).

% eval_semantics
thf(fact_732_eval__semantics,axiom,
    ! [Pi4: b > list_char > $o,W: b,W6: set_b,R: a > b > set_b,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ ( Pi4 @ W ) @ ( episte295617885132580261cs_a_b @ ( episte4938218340073005086t_unit @ W6 @ R @ ( episte6143282164508887558t_unit @ Pi4 @ product_Unity ) ) @ W ) @ P )
      = ( episte295617885132580261cs_a_b @ ( episte4938218340073005086t_unit @ W6 @ R @ ( episte6143282164508887558t_unit @ Pi4 @ product_Unity ) ) @ W @ P ) ) ).

% eval_semantics
thf(fact_733_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_Ax4_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte1560738328020401952t_unit] :
          ( ( ( episte5648423998891577755t_unit @ M4 )
            & ( episte8364071018013720454t_unit @ M4 ) )
         => ! [X4: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ Xa ) )
               => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>4
thf(fact_734_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
            @ ^ [P3: epistemic_fm_a] :
                ( ( epistemic_AxT_a @ P3 )
                | ( epistemic_Ax4_a @ P3 ) )
            @ ( epistemic_imply_a @ Qs @ P ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( ( episte3426825378771607259t_unit @ M4 )
            & ( episte9018110198556821958t_unit @ M4 ) )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>S\<^sub>4
thf(fact_735_subset__antisym,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A3 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ A3 )
       => ( A3 = B ) ) ) ).

% subset_antisym
thf(fact_736_subset__antisym,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( ord_less_eq_set_b @ A3 @ B )
     => ( ( ord_less_eq_set_b @ B @ A3 )
       => ( A3 = B ) ) ) ).

% subset_antisym
thf(fact_737_subset__antisym,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ B )
     => ( ( ord_less_eq_set_o @ B @ A3 )
       => ( A3 = B ) ) ) ).

% subset_antisym
thf(fact_738_subsetI,axiom,
    ! [A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a] :
      ( ! [X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ A3 )
         => ( member536094252920883875c_fm_a @ X @ B ) )
     => ( ord_le7112219575281605754c_fm_a @ A3 @ B ) ) ).

% subsetI
thf(fact_739_subsetI,axiom,
    ! [A3: set_set_o,B: set_set_o] :
      ( ! [X: set_o] :
          ( ( member_set_o @ X @ A3 )
         => ( member_set_o @ X @ B ) )
     => ( ord_le4374716579403074808_set_o @ A3 @ B ) ) ).

% subsetI
thf(fact_740_subsetI,axiom,
    ! [A3: set_set_b,B: set_set_b] :
      ( ! [X: set_b] :
          ( ( member_set_b @ X @ A3 )
         => ( member_set_b @ X @ B ) )
     => ( ord_le3795704787696855135_set_b @ A3 @ B ) ) ).

% subsetI
thf(fact_741_subsetI,axiom,
    ! [A3: set_a,B: set_a] :
      ( ! [X: a] :
          ( ( member_a @ X @ A3 )
         => ( member_a @ X @ B ) )
     => ( ord_less_eq_set_a @ A3 @ B ) ) ).

% subsetI
thf(fact_742_subsetI,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ! [X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ A3 )
         => ( member6642669571620171971c_fm_a @ X @ B ) )
     => ( ord_le3275665582123262618c_fm_a @ A3 @ B ) ) ).

% subsetI
thf(fact_743_subsetI,axiom,
    ! [A3: set_o,B: set_o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A3 )
         => ( member_o @ X @ B ) )
     => ( ord_less_eq_set_o @ A3 @ B ) ) ).

% subsetI
thf(fact_744_subsetI,axiom,
    ! [A3: set_b,B: set_b] :
      ( ! [X: b] :
          ( ( member_b @ X @ A3 )
         => ( member_b @ X @ B ) )
     => ( ord_less_eq_set_b @ A3 @ B ) ) ).

% subsetI
thf(fact_745_inf1I,axiom,
    ! [A3: b > $o,X3: b,B: b > $o] :
      ( ( A3 @ X3 )
     => ( ( B @ X3 )
       => ( inf_inf_b_o @ A3 @ B @ X3 ) ) ) ).

% inf1I
thf(fact_746_Int__subset__iff,axiom,
    ! [C2: set_Epistemic_fm_a,A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ C2 @ ( inf_in2882328776738922472c_fm_a @ A3 @ B ) )
      = ( ( ord_le3275665582123262618c_fm_a @ C2 @ A3 )
        & ( ord_le3275665582123262618c_fm_a @ C2 @ B ) ) ) ).

% Int_subset_iff
thf(fact_747_Int__subset__iff,axiom,
    ! [C2: set_b,A3: set_b,B: set_b] :
      ( ( ord_less_eq_set_b @ C2 @ ( inf_inf_set_b @ A3 @ B ) )
      = ( ( ord_less_eq_set_b @ C2 @ A3 )
        & ( ord_less_eq_set_b @ C2 @ B ) ) ) ).

% Int_subset_iff
thf(fact_748_Int__subset__iff,axiom,
    ! [C2: set_o,A3: set_o,B: set_o] :
      ( ( ord_less_eq_set_o @ C2 @ ( inf_inf_set_o @ A3 @ B ) )
      = ( ( ord_less_eq_set_o @ C2 @ A3 )
        & ( ord_less_eq_set_o @ C2 @ B ) ) ) ).

% Int_subset_iff
thf(fact_749_fm_Opred__inject_I5_J,axiom,
    ! [P4: b > $o,A: epistemic_fm_b,Aa2: epistemic_fm_b] :
      ( ( epistemic_pred_fm_b @ P4 @ ( epistemic_Imp_b @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_b @ P4 @ A )
        & ( epistemic_pred_fm_b @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(5)
thf(fact_750_fm_Opred__inject_I5_J,axiom,
    ! [P4: a > $o,A: epistemic_fm_a,Aa2: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Imp_a @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A )
        & ( epistemic_pred_fm_a @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(5)
thf(fact_751_fm_Opred__inject_I6_J,axiom,
    ! [P4: $o > $o,A: $o,Aa2: epistemic_fm_o] :
      ( ( epistemic_pred_fm_o @ P4 @ ( epistemic_K_o @ A @ Aa2 ) )
      = ( ( P4 @ A )
        & ( epistemic_pred_fm_o @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(6)
thf(fact_752_fm_Opred__inject_I6_J,axiom,
    ! [P4: b > $o,A: b,Aa2: epistemic_fm_b] :
      ( ( epistemic_pred_fm_b @ P4 @ ( epistemic_K_b @ A @ Aa2 ) )
      = ( ( P4 @ A )
        & ( epistemic_pred_fm_b @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(6)
thf(fact_753_fm_Opred__inject_I6_J,axiom,
    ! [P4: a > $o,A: a,Aa2: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_K_a @ A @ Aa2 ) )
      = ( ( P4 @ A )
        & ( epistemic_pred_fm_a @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(6)
thf(fact_754_fm_Opred__inject_I4_J,axiom,
    ! [P4: a > $o,A: epistemic_fm_a,Aa2: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Con_a @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A )
        & ( epistemic_pred_fm_a @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(4)
thf(fact_755_fm_Opred__inject_I4_J,axiom,
    ! [P4: b > $o,A: epistemic_fm_b,Aa2: epistemic_fm_b] :
      ( ( epistemic_pred_fm_b @ P4 @ ( epistemic_Con_b @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_b @ P4 @ A )
        & ( epistemic_pred_fm_b @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(4)
thf(fact_756_fm_Opred__inject_I3_J,axiom,
    ! [P4: a > $o,A: epistemic_fm_a,Aa2: epistemic_fm_a] :
      ( ( epistemic_pred_fm_a @ P4 @ ( epistemic_Dis_a @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_a @ P4 @ A )
        & ( epistemic_pred_fm_a @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(3)
thf(fact_757_fm_Opred__inject_I3_J,axiom,
    ! [P4: b > $o,A: epistemic_fm_b,Aa2: epistemic_fm_b] :
      ( ( epistemic_pred_fm_b @ P4 @ ( epistemic_Dis_b @ A @ Aa2 ) )
      = ( ( epistemic_pred_fm_b @ P4 @ A )
        & ( epistemic_pred_fm_b @ P4 @ Aa2 ) ) ) ).

% fm.pred_inject(3)
thf(fact_758_strong__completeness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
         => ( ! [Xa2: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
               => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
           => ( episte7081087998767065248c_fm_a @ M2 @ 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 ) ) ) ) ).

% strong_completeness\<^sub>K
thf(fact_759_main_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M3: episte1560738328020401952t_unit,X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
           => ( ! [Y: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ Y @ G5 )
                 => ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Y ) )
             => ( episte7081087998767065248c_fm_a @ M3 @ 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 ) ) ) ) ) ).

% main\<^sub>K
thf(fact_760_K__imply__weaken,axiom,
    ! [A3: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,Ps2: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps @ Q ) )
     => ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Ps2 ) )
       => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps2 @ Q ) ) ) ) ).

% K_imply_weaken
thf(fact_761_Collect__mono__iff,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q2: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q2 ) )
      = ( ! [X2: set_Epistemic_fm_a] :
            ( ( P4 @ X2 )
           => ( Q2 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_762_Collect__mono__iff,axiom,
    ! [P4: epistemic_fm_a > $o,Q2: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q2 ) )
      = ( ! [X2: epistemic_fm_a] :
            ( ( P4 @ X2 )
           => ( Q2 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_763_Collect__mono__iff,axiom,
    ! [P4: b > $o,Q2: b > $o] :
      ( ( ord_less_eq_set_b @ ( collect_b @ P4 ) @ ( collect_b @ Q2 ) )
      = ( ! [X2: b] :
            ( ( P4 @ X2 )
           => ( Q2 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_764_Collect__mono__iff,axiom,
    ! [P4: $o > $o,Q2: $o > $o] :
      ( ( ord_less_eq_set_o @ ( collect_o @ P4 ) @ ( collect_o @ Q2 ) )
      = ( ! [X2: $o] :
            ( ( P4 @ X2 )
           => ( Q2 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_765_Collect__subset,axiom,
    ! [A3: set_set_o,P4: set_o > $o] :
      ( ord_le4374716579403074808_set_o
      @ ( collect_set_o
        @ ^ [X2: set_o] :
            ( ( member_set_o @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_766_Collect__subset,axiom,
    ! [A3: set_set_b,P4: set_b > $o] :
      ( ord_le3795704787696855135_set_b
      @ ( collect_set_b
        @ ^ [X2: set_b] :
            ( ( member_set_b @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_767_Collect__subset,axiom,
    ! [A3: set_a,P4: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X2: a] :
            ( ( member_a @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_768_Collect__subset,axiom,
    ! [A3: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ord_le7112219575281605754c_fm_a
      @ ( collec2519470961442302949c_fm_a
        @ ^ [X2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_769_Collect__subset,axiom,
    ! [A3: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ord_le3275665582123262618c_fm_a
      @ ( collec4904205152690461189c_fm_a
        @ ^ [X2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_770_Collect__subset,axiom,
    ! [A3: set_o,P4: $o > $o] :
      ( ord_less_eq_set_o
      @ ( collect_o
        @ ^ [X2: $o] :
            ( ( member_o @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_771_Collect__subset,axiom,
    ! [A3: set_b,P4: b > $o] :
      ( ord_less_eq_set_b
      @ ( collect_b
        @ ^ [X2: b] :
            ( ( member_b @ X2 @ A3 )
            & ( P4 @ X2 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_772_set__eq__subset,axiom,
    ( ( ^ [Y4: set_Epistemic_fm_a,Z4: set_Epistemic_fm_a] : ( Y4 = Z4 ) )
    = ( ^ [A4: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
          ( ( ord_le3275665582123262618c_fm_a @ A4 @ B4 )
          & ( ord_le3275665582123262618c_fm_a @ B4 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_773_set__eq__subset,axiom,
    ( ( ^ [Y4: set_b,Z4: set_b] : ( Y4 = Z4 ) )
    = ( ^ [A4: set_b,B4: set_b] :
          ( ( ord_less_eq_set_b @ A4 @ B4 )
          & ( ord_less_eq_set_b @ B4 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_774_set__eq__subset,axiom,
    ( ( ^ [Y4: set_o,Z4: set_o] : ( Y4 = Z4 ) )
    = ( ^ [A4: set_o,B4: set_o] :
          ( ( ord_less_eq_set_o @ A4 @ B4 )
          & ( ord_less_eq_set_o @ B4 @ A4 ) ) ) ) ).

% set_eq_subset
thf(fact_775_subset__trans,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A3 @ B )
     => ( ( ord_le3275665582123262618c_fm_a @ B @ C2 )
       => ( ord_le3275665582123262618c_fm_a @ A3 @ C2 ) ) ) ).

% subset_trans
thf(fact_776_subset__trans,axiom,
    ! [A3: set_b,B: set_b,C2: set_b] :
      ( ( ord_less_eq_set_b @ A3 @ B )
     => ( ( ord_less_eq_set_b @ B @ C2 )
       => ( ord_less_eq_set_b @ A3 @ C2 ) ) ) ).

% subset_trans
thf(fact_777_subset__trans,axiom,
    ! [A3: set_o,B: set_o,C2: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ B )
     => ( ( ord_less_eq_set_o @ B @ C2 )
       => ( ord_less_eq_set_o @ A3 @ C2 ) ) ) ).

% subset_trans
thf(fact_778_Collect__mono,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q2: set_Epistemic_fm_a > $o] :
      ( ! [X: set_Epistemic_fm_a] :
          ( ( P4 @ X )
         => ( Q2 @ X ) )
     => ( ord_le7112219575281605754c_fm_a @ ( collec2519470961442302949c_fm_a @ P4 ) @ ( collec2519470961442302949c_fm_a @ Q2 ) ) ) ).

% Collect_mono
thf(fact_779_Collect__mono,axiom,
    ! [P4: epistemic_fm_a > $o,Q2: epistemic_fm_a > $o] :
      ( ! [X: epistemic_fm_a] :
          ( ( P4 @ X )
         => ( Q2 @ X ) )
     => ( ord_le3275665582123262618c_fm_a @ ( collec4904205152690461189c_fm_a @ P4 ) @ ( collec4904205152690461189c_fm_a @ Q2 ) ) ) ).

% Collect_mono
thf(fact_780_Collect__mono,axiom,
    ! [P4: b > $o,Q2: b > $o] :
      ( ! [X: b] :
          ( ( P4 @ X )
         => ( Q2 @ X ) )
     => ( ord_less_eq_set_b @ ( collect_b @ P4 ) @ ( collect_b @ Q2 ) ) ) ).

% Collect_mono
thf(fact_781_Collect__mono,axiom,
    ! [P4: $o > $o,Q2: $o > $o] :
      ( ! [X: $o] :
          ( ( P4 @ X )
         => ( Q2 @ X ) )
     => ( ord_less_eq_set_o @ ( collect_o @ P4 ) @ ( collect_o @ Q2 ) ) ) ).

% Collect_mono
thf(fact_782_subset__refl,axiom,
    ! [A3: set_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ A3 @ A3 ) ).

% subset_refl
thf(fact_783_subset__refl,axiom,
    ! [A3: set_b] : ( ord_less_eq_set_b @ A3 @ A3 ) ).

% subset_refl
thf(fact_784_subset__refl,axiom,
    ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ A3 ) ).

% subset_refl
thf(fact_785_subset__iff,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A4: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
        ! [T: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ T @ A4 )
         => ( member536094252920883875c_fm_a @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_786_subset__iff,axiom,
    ( ord_le4374716579403074808_set_o
    = ( ^ [A4: set_set_o,B4: set_set_o] :
        ! [T: set_o] :
          ( ( member_set_o @ T @ A4 )
         => ( member_set_o @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_787_subset__iff,axiom,
    ( ord_le3795704787696855135_set_b
    = ( ^ [A4: set_set_b,B4: set_set_b] :
        ! [T: set_b] :
          ( ( member_set_b @ T @ A4 )
         => ( member_set_b @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_788_subset__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B4: set_a] :
        ! [T: a] :
          ( ( member_a @ T @ A4 )
         => ( member_a @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_789_subset__iff,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
        ! [T: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ T @ A4 )
         => ( member6642669571620171971c_fm_a @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_790_subset__iff,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A4: set_o,B4: set_o] :
        ! [T: $o] :
          ( ( member_o @ T @ A4 )
         => ( member_o @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_791_subset__iff,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A4: set_b,B4: set_b] :
        ! [T: b] :
          ( ( member_b @ T @ A4 )
         => ( member_b @ T @ B4 ) ) ) ) ).

% subset_iff
thf(fact_792_equalityD2,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( A3 = B )
     => ( ord_le3275665582123262618c_fm_a @ B @ A3 ) ) ).

% equalityD2
thf(fact_793_equalityD2,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( A3 = B )
     => ( ord_less_eq_set_b @ B @ A3 ) ) ).

% equalityD2
thf(fact_794_equalityD2,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( A3 = B )
     => ( ord_less_eq_set_o @ B @ A3 ) ) ).

% equalityD2
thf(fact_795_equalityD1,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( A3 = B )
     => ( ord_le3275665582123262618c_fm_a @ A3 @ B ) ) ).

% equalityD1
thf(fact_796_equalityD1,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( A3 = B )
     => ( ord_less_eq_set_b @ A3 @ B ) ) ).

% equalityD1
thf(fact_797_equalityD1,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( A3 = B )
     => ( ord_less_eq_set_o @ A3 @ B ) ) ).

% equalityD1
thf(fact_798_subset__eq,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A4: set_se5208064806568342746c_fm_a,B4: set_se5208064806568342746c_fm_a] :
        ! [X2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X2 @ A4 )
         => ( member536094252920883875c_fm_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_799_subset__eq,axiom,
    ( ord_le4374716579403074808_set_o
    = ( ^ [A4: set_set_o,B4: set_set_o] :
        ! [X2: set_o] :
          ( ( member_set_o @ X2 @ A4 )
         => ( member_set_o @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_800_subset__eq,axiom,
    ( ord_le3795704787696855135_set_b
    = ( ^ [A4: set_set_b,B4: set_set_b] :
        ! [X2: set_b] :
          ( ( member_set_b @ X2 @ A4 )
         => ( member_set_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_801_subset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A4: set_a,B4: set_a] :
        ! [X2: a] :
          ( ( member_a @ X2 @ A4 )
         => ( member_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_802_subset__eq,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A4: set_Epistemic_fm_a,B4: set_Epistemic_fm_a] :
        ! [X2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X2 @ A4 )
         => ( member6642669571620171971c_fm_a @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_803_subset__eq,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A4: set_o,B4: set_o] :
        ! [X2: $o] :
          ( ( member_o @ X2 @ A4 )
         => ( member_o @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_804_subset__eq,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A4: set_b,B4: set_b] :
        ! [X2: b] :
          ( ( member_b @ X2 @ A4 )
         => ( member_b @ X2 @ B4 ) ) ) ) ).

% subset_eq
thf(fact_805_equalityE,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a] :
      ( ( A3 = B )
     => ~ ( ( ord_le3275665582123262618c_fm_a @ A3 @ B )
         => ~ ( ord_le3275665582123262618c_fm_a @ B @ A3 ) ) ) ).

% equalityE
thf(fact_806_equalityE,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( A3 = B )
     => ~ ( ( ord_less_eq_set_b @ A3 @ B )
         => ~ ( ord_less_eq_set_b @ B @ A3 ) ) ) ).

% equalityE
thf(fact_807_equalityE,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( A3 = B )
     => ~ ( ( ord_less_eq_set_o @ A3 @ B )
         => ~ ( ord_less_eq_set_o @ B @ A3 ) ) ) ).

% equalityE
thf(fact_808_subsetD,axiom,
    ! [A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a,C: set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A3 @ B )
     => ( ( member536094252920883875c_fm_a @ C @ A3 )
       => ( member536094252920883875c_fm_a @ C @ B ) ) ) ).

% subsetD
thf(fact_809_subsetD,axiom,
    ! [A3: set_set_o,B: set_set_o,C: set_o] :
      ( ( ord_le4374716579403074808_set_o @ A3 @ B )
     => ( ( member_set_o @ C @ A3 )
       => ( member_set_o @ C @ B ) ) ) ).

% subsetD
thf(fact_810_subsetD,axiom,
    ! [A3: set_set_b,B: set_set_b,C: set_b] :
      ( ( ord_le3795704787696855135_set_b @ A3 @ B )
     => ( ( member_set_b @ C @ A3 )
       => ( member_set_b @ C @ B ) ) ) ).

% subsetD
thf(fact_811_subsetD,axiom,
    ! [A3: set_a,B: set_a,C: a] :
      ( ( ord_less_eq_set_a @ A3 @ B )
     => ( ( member_a @ C @ A3 )
       => ( member_a @ C @ B ) ) ) ).

% subsetD
thf(fact_812_subsetD,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a,C: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A3 @ B )
     => ( ( member6642669571620171971c_fm_a @ C @ A3 )
       => ( member6642669571620171971c_fm_a @ C @ B ) ) ) ).

% subsetD
thf(fact_813_subsetD,axiom,
    ! [A3: set_o,B: set_o,C: $o] :
      ( ( ord_less_eq_set_o @ A3 @ B )
     => ( ( member_o @ C @ A3 )
       => ( member_o @ C @ B ) ) ) ).

% subsetD
thf(fact_814_subsetD,axiom,
    ! [A3: set_b,B: set_b,C: b] :
      ( ( ord_less_eq_set_b @ A3 @ B )
     => ( ( member_b @ C @ A3 )
       => ( member_b @ C @ B ) ) ) ).

% subsetD
thf(fact_815_in__mono,axiom,
    ! [A3: set_se5208064806568342746c_fm_a,B: set_se5208064806568342746c_fm_a,X3: set_Epistemic_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ A3 @ B )
     => ( ( member536094252920883875c_fm_a @ X3 @ A3 )
       => ( member536094252920883875c_fm_a @ X3 @ B ) ) ) ).

% in_mono
thf(fact_816_in__mono,axiom,
    ! [A3: set_set_o,B: set_set_o,X3: set_o] :
      ( ( ord_le4374716579403074808_set_o @ A3 @ B )
     => ( ( member_set_o @ X3 @ A3 )
       => ( member_set_o @ X3 @ B ) ) ) ).

% in_mono
thf(fact_817_in__mono,axiom,
    ! [A3: set_set_b,B: set_set_b,X3: set_b] :
      ( ( ord_le3795704787696855135_set_b @ A3 @ B )
     => ( ( member_set_b @ X3 @ A3 )
       => ( member_set_b @ X3 @ B ) ) ) ).

% in_mono
thf(fact_818_in__mono,axiom,
    ! [A3: set_a,B: set_a,X3: a] :
      ( ( ord_less_eq_set_a @ A3 @ B )
     => ( ( member_a @ X3 @ A3 )
       => ( member_a @ X3 @ B ) ) ) ).

% in_mono
thf(fact_819_in__mono,axiom,
    ! [A3: set_Epistemic_fm_a,B: set_Epistemic_fm_a,X3: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ A3 @ B )
     => ( ( member6642669571620171971c_fm_a @ X3 @ A3 )
       => ( member6642669571620171971c_fm_a @ X3 @ B ) ) ) ).

% in_mono
thf(fact_820_in__mono,axiom,
    ! [A3: set_o,B: set_o,X3: $o] :
      ( ( ord_less_eq_set_o @ A3 @ B )
     => ( ( member_o @ X3 @ A3 )
       => ( member_o @ X3 @ B ) ) ) ).

% in_mono
thf(fact_821_in__mono,axiom,
    ! [A3: set_b,B: set_b,X3: b] :
      ( ( ord_less_eq_set_b @ A3 @ B )
     => ( ( member_b @ X3 @ A3 )
       => ( member_b @ X3 @ B ) ) ) ).

% in_mono
thf(fact_822_fm_Orel__mono,axiom,
    ! [R3: a > a > $o,Ra: a > a > $o] :
      ( ( ord_less_eq_a_a_o @ R3 @ Ra )
     => ( ord_le3934200179093585166fm_a_o @ ( epistemic_rel_fm_a_a @ R3 ) @ ( epistemic_rel_fm_a_a @ Ra ) ) ) ).

% fm.rel_mono
thf(fact_823_fm_Orel__mono,axiom,
    ! [R3: b > b > $o,Ra: b > b > $o] :
      ( ( ord_less_eq_b_b_o @ R3 @ Ra )
     => ( ord_le7238499765113434702fm_b_o @ ( epistemic_rel_fm_b_b @ R3 ) @ ( epistemic_rel_fm_b_b @ Ra ) ) ) ).

% fm.rel_mono
thf(fact_824_inf1E,axiom,
    ! [A3: b > $o,B: b > $o,X3: b] :
      ( ( inf_inf_b_o @ A3 @ B @ X3 )
     => ~ ( ( A3 @ X3 )
         => ~ ( B @ X3 ) ) ) ).

% inf1E
thf(fact_825_inf1D1,axiom,
    ! [A3: b > $o,B: b > $o,X3: b] :
      ( ( inf_inf_b_o @ A3 @ B @ X3 )
     => ( A3 @ X3 ) ) ).

% inf1D1
thf(fact_826_inf1D2,axiom,
    ! [A3: b > $o,B: b > $o,X3: b] :
      ( ( inf_inf_b_o @ A3 @ B @ X3 )
     => ( B @ X3 ) ) ).

% inf1D2
thf(fact_827_fm_Orel__eq,axiom,
    ( ( epistemic_rel_fm_a_a
      @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 ) )
    = ( ^ [Y4: epistemic_fm_a,Z4: epistemic_fm_a] : ( Y4 = Z4 ) ) ) ).

% fm.rel_eq
thf(fact_828_fm_Orel__eq,axiom,
    ( ( epistemic_rel_fm_b_b
      @ ^ [Y4: b,Z4: b] : ( Y4 = Z4 ) )
    = ( ^ [Y4: epistemic_fm_b,Z4: epistemic_fm_b] : ( Y4 = Z4 ) ) ) ).

% fm.rel_eq
thf(fact_829_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_b,Ya: epistemic_fm_b,Y2: epistemic_fm_b,Xa3: epistemic_fm_b,R3: b > b > $o,Ra: b > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: b,Yb: b] :
              ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ Ya ) )
             => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_b_b @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_b_b @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_830_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y2: epistemic_fm_a,Xa3: epistemic_fm_a,R3: a > a > $o,Ra: a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: a,Yb: a] :
              ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_a_a @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_a_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_831_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y2: epistemic_fm_b,Xa3: epistemic_fm_b,R3: a > b > $o,Ra: a > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: a,Yb: b] :
              ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_a_b @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_a_b @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_832_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,Y2: epistemic_fm_o,Xa3: epistemic_fm_o,R3: a > $o > $o,Ra: a > $o > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: a,Yb: $o] :
              ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ Ya ) )
             => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_a_o @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_a_o @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_833_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_b,Ya: epistemic_fm_b,Y2: epistemic_fm_a,Xa3: epistemic_fm_a,R3: b > a > $o,Ra: b > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: b,Yb: a] :
              ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_b_a @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_b_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_834_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_b,Ya: epistemic_fm_b,Y2: epistemic_fm_o,Xa3: epistemic_fm_o,R3: b > $o > $o,Ra: b > $o > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: b,Yb: $o] :
              ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ Ya ) )
             => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_b_o @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_b_o @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_835_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_o,Ya: epistemic_fm_o,Y2: epistemic_fm_a,Xa3: epistemic_fm_a,R3: $o > a > $o,Ra: $o > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: $o,Yb: a] :
              ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_o_a @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_o_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_836_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_o,Ya: epistemic_fm_o,Y2: epistemic_fm_b,Xa3: epistemic_fm_b,R3: $o > b > $o,Ra: $o > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: $o,Yb: b] :
              ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ Ya ) )
             => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_o_b @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_o_b @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_837_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_o,Ya: epistemic_fm_o,Y2: epistemic_fm_o,Xa3: epistemic_fm_o,R3: $o > $o > $o,Ra: $o > $o > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: $o,Yb: $o] :
              ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ Ya ) )
             => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( epistemic_rel_fm_o_o @ R3 @ X3 @ Y2 )
            = ( epistemic_rel_fm_o_o @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_838_fm_Orel__cong,axiom,
    ! [X3: epistemic_fm_set_o,Ya: epistemic_fm_set_o,Y2: epistemic_fm_a,Xa3: epistemic_fm_a,R3: set_o > a > $o,Ra: set_o > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y2 = Xa3 )
       => ( ! [Z3: set_o,Yb: a] :
              ( ( member_set_o @ Z3 @ ( episte5067851541165005998_set_o @ Ya ) )
             => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Xa3 ) )
               => ( ( R3 @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( episte1442162560295717094et_o_a @ R3 @ X3 @ Y2 )
            = ( episte1442162560295717094et_o_a @ Ra @ Ya @ Xa3 ) ) ) ) ) ).

% fm.rel_cong
thf(fact_839_fm_Orel__refl,axiom,
    ! [Ra: a > a > $o,X3: epistemic_fm_a] :
      ( ! [X: a] : ( Ra @ X @ X )
     => ( epistemic_rel_fm_a_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl
thf(fact_840_fm_Orel__refl,axiom,
    ! [Ra: b > b > $o,X3: epistemic_fm_b] :
      ( ! [X: b] : ( Ra @ X @ X )
     => ( epistemic_rel_fm_b_b @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl
thf(fact_841_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 )
     => ( ! [Z3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z3 @ ( episte6227279731293865264c_fm_a @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( episte1367365995573110961c_fm_a @ P4 @ X3 )
          = ( episte1367365995573110961c_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_842_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_set_o,Ya: epistemic_fm_set_o,P4: set_o > $o,Pa: set_o > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: set_o] :
            ( ( member_set_o @ Z3 @ ( episte5067851541165005998_set_o @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( episte2463951554458028079_set_o @ P4 @ X3 )
          = ( episte2463951554458028079_set_o @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_843_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_set_b,Ya: epistemic_fm_set_b,P4: set_b > $o,Pa: set_b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: set_b] :
            ( ( member_set_b @ Z3 @ ( episte1019240489619528469_set_b @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( episte1592375260622591510_set_b @ P4 @ X3 )
          = ( episte1592375260622591510_set_b @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_844_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_o,Ya: epistemic_fm_o,P4: $o > $o,Pa: $o > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: $o] :
            ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( epistemic_pred_fm_o @ P4 @ X3 )
          = ( epistemic_pred_fm_o @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_845_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_a,Ya: epistemic_fm_a,P4: a > $o,Pa: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: a] :
            ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( epistemic_pred_fm_a @ P4 @ X3 )
          = ( epistemic_pred_fm_a @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_846_fm_Opred__cong,axiom,
    ! [X3: epistemic_fm_b,Ya: epistemic_fm_b,P4: b > $o,Pa: b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: b] :
            ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ Ya ) )
           => ( ( P4 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( epistemic_pred_fm_b @ P4 @ X3 )
          = ( epistemic_pred_fm_b @ Pa @ Ya ) ) ) ) ).

% fm.pred_cong
thf(fact_847_fm_Orel__mono__strong,axiom,
    ! [R3: b > b > $o,X3: epistemic_fm_b,Y2: epistemic_fm_b,Ra: b > b > $o] :
      ( ( epistemic_rel_fm_b_b @ R3 @ X3 @ Y2 )
     => ( ! [Z3: b,Yb: b] :
            ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ X3 ) )
           => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_b_b @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_848_fm_Orel__mono__strong,axiom,
    ! [R3: a > a > $o,X3: epistemic_fm_a,Y2: epistemic_fm_a,Ra: a > a > $o] :
      ( ( epistemic_rel_fm_a_a @ R3 @ X3 @ Y2 )
     => ( ! [Z3: a,Yb: a] :
            ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_a_a @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_849_fm_Orel__mono__strong,axiom,
    ! [R3: a > b > $o,X3: epistemic_fm_a,Y2: epistemic_fm_b,Ra: a > b > $o] :
      ( ( epistemic_rel_fm_a_b @ R3 @ X3 @ Y2 )
     => ( ! [Z3: a,Yb: b] :
            ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_a_b @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_850_fm_Orel__mono__strong,axiom,
    ! [R3: a > $o > $o,X3: epistemic_fm_a,Y2: epistemic_fm_o,Ra: a > $o > $o] :
      ( ( epistemic_rel_fm_a_o @ R3 @ X3 @ Y2 )
     => ( ! [Z3: a,Yb: $o] :
            ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_a_o @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_851_fm_Orel__mono__strong,axiom,
    ! [R3: b > a > $o,X3: epistemic_fm_b,Y2: epistemic_fm_a,Ra: b > a > $o] :
      ( ( epistemic_rel_fm_b_a @ R3 @ X3 @ Y2 )
     => ( ! [Z3: b,Yb: a] :
            ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_b_a @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_852_fm_Orel__mono__strong,axiom,
    ! [R3: b > $o > $o,X3: epistemic_fm_b,Y2: epistemic_fm_o,Ra: b > $o > $o] :
      ( ( epistemic_rel_fm_b_o @ R3 @ X3 @ Y2 )
     => ( ! [Z3: b,Yb: $o] :
            ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ X3 ) )
           => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_b_o @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_853_fm_Orel__mono__strong,axiom,
    ! [R3: $o > a > $o,X3: epistemic_fm_o,Y2: epistemic_fm_a,Ra: $o > a > $o] :
      ( ( epistemic_rel_fm_o_a @ R3 @ X3 @ Y2 )
     => ( ! [Z3: $o,Yb: a] :
            ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_o_a @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_854_fm_Orel__mono__strong,axiom,
    ! [R3: $o > b > $o,X3: epistemic_fm_o,Y2: epistemic_fm_b,Ra: $o > b > $o] :
      ( ( epistemic_rel_fm_o_b @ R3 @ X3 @ Y2 )
     => ( ! [Z3: $o,Yb: b] :
            ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ X3 ) )
           => ( ( member_b @ Yb @ ( epistemic_set_fm_b @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_o_b @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_855_fm_Orel__mono__strong,axiom,
    ! [R3: $o > $o > $o,X3: epistemic_fm_o,Y2: epistemic_fm_o,Ra: $o > $o > $o] :
      ( ( epistemic_rel_fm_o_o @ R3 @ X3 @ Y2 )
     => ( ! [Z3: $o,Yb: $o] :
            ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ X3 ) )
           => ( ( member_o @ Yb @ ( epistemic_set_fm_o @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( epistemic_rel_fm_o_o @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_856_fm_Orel__mono__strong,axiom,
    ! [R3: set_o > a > $o,X3: epistemic_fm_set_o,Y2: epistemic_fm_a,Ra: set_o > a > $o] :
      ( ( episte1442162560295717094et_o_a @ R3 @ X3 @ Y2 )
     => ( ! [Z3: set_o,Yb: a] :
            ( ( member_set_o @ Z3 @ ( episte5067851541165005998_set_o @ X3 ) )
           => ( ( member_a @ Yb @ ( epistemic_set_fm_a @ Y2 ) )
             => ( ( R3 @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( episte1442162560295717094et_o_a @ Ra @ X3 @ Y2 ) ) ) ).

% fm.rel_mono_strong
thf(fact_857_fm_Orel__refl__strong,axiom,
    ! [X3: episte5999154429349999510c_fm_a,Ra: set_Epistemic_fm_a > set_Epistemic_fm_a > $o] :
      ( ! [Z3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ Z3 @ ( episte6227279731293865264c_fm_a @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( episte8246226516352692192c_fm_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_858_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_set_o,Ra: set_o > set_o > $o] :
      ( ! [Z3: set_o] :
          ( ( member_set_o @ Z3 @ ( episte5067851541165005998_set_o @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( episte5145029844727815264_set_o @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_859_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_set_b,Ra: set_b > set_b > $o] :
      ( ! [Z3: set_b] :
          ( ( member_set_b @ Z3 @ ( episte1019240489619528469_set_b @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( episte6429547790201822112_set_b @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_860_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_a,Ra: a > a > $o] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( epistemic_rel_fm_a_a @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_861_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_o,Ra: $o > $o > $o] :
      ( ! [Z3: $o] :
          ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( epistemic_rel_fm_o_o @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_862_fm_Orel__refl__strong,axiom,
    ! [X3: epistemic_fm_b,Ra: b > b > $o] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( epistemic_rel_fm_b_b @ Ra @ X3 @ X3 ) ) ).

% fm.rel_refl_strong
thf(fact_863_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 )
     => ( ! [Z3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z3 @ ( episte6227279731293865264c_fm_a @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( episte1367365995573110961c_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_864_fm_Opred__mono__strong,axiom,
    ! [P4: set_o > $o,X3: epistemic_fm_set_o,Pa: set_o > $o] :
      ( ( episte2463951554458028079_set_o @ P4 @ X3 )
     => ( ! [Z3: set_o] :
            ( ( member_set_o @ Z3 @ ( episte5067851541165005998_set_o @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( episte2463951554458028079_set_o @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_865_fm_Opred__mono__strong,axiom,
    ! [P4: set_b > $o,X3: epistemic_fm_set_b,Pa: set_b > $o] :
      ( ( episte1592375260622591510_set_b @ P4 @ X3 )
     => ( ! [Z3: set_b] :
            ( ( member_set_b @ Z3 @ ( episte1019240489619528469_set_b @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( episte1592375260622591510_set_b @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_866_fm_Opred__mono__strong,axiom,
    ! [P4: $o > $o,X3: epistemic_fm_o,Pa: $o > $o] :
      ( ( epistemic_pred_fm_o @ P4 @ X3 )
     => ( ! [Z3: $o] :
            ( ( member_o @ Z3 @ ( epistemic_set_fm_o @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( epistemic_pred_fm_o @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_867_fm_Opred__mono__strong,axiom,
    ! [P4: a > $o,X3: epistemic_fm_a,Pa: a > $o] :
      ( ( epistemic_pred_fm_a @ P4 @ X3 )
     => ( ! [Z3: a] :
            ( ( member_a @ Z3 @ ( epistemic_set_fm_a @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( epistemic_pred_fm_a @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_868_fm_Opred__mono__strong,axiom,
    ! [P4: b > $o,X3: epistemic_fm_b,Pa: b > $o] :
      ( ( epistemic_pred_fm_b @ P4 @ X3 )
     => ( ! [Z3: b] :
            ( ( member_b @ Z3 @ ( epistemic_set_fm_b @ X3 ) )
           => ( ( P4 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( epistemic_pred_fm_b @ Pa @ X3 ) ) ) ).

% fm.pred_mono_strong
thf(fact_869_kripke_Ocases,axiom,
    ! [R: episte3224730989885420256t_unit] :
      ~ ! [W4: set_b,K3: a > b > set_b,Pi3: b > list_char > $o] :
          ( R
         != ( episte4938218340073005086t_unit @ W4 @ K3 @ ( episte6143282164508887558t_unit @ Pi3 @ product_Unity ) ) ) ).

% kripke.cases
thf(fact_870_kripke_Ocases,axiom,
    ! [R: episte1560738328020401952t_unit] :
      ~ ! [W4: set_se5208064806568342746c_fm_a,K3: a > set_Epistemic_fm_a > set_se5208064806568342746c_fm_a,Pi3: set_Epistemic_fm_a > list_char > $o] :
          ( R
         != ( episte2888590659910966568t_unit @ W4 @ K3 @ ( episte8239586592105053771t_unit @ Pi3 @ product_Unity ) ) ) ).

% kripke.cases
thf(fact_871_strong__completeness_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( episte5648423998891577755t_unit @ M2 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ 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 ) ) ) ) ).

% strong_completeness\<^sub>T
thf(fact_872_main_092_060_094sub_062T,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M3: episte1560738328020401952t_unit] :
            ( ( episte5648423998891577755t_unit @ M3 )
           => ! [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Y: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Y ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ 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 ) ) ) ) ) ).

% main\<^sub>T
thf(fact_873_tautology__imply__superset,axiom,
    ! [Ps: list_Epistemic_fm_b,Qs4: list_Epistemic_fm_b,R: epistemic_fm_b] :
      ( ( ord_le3346699622169608603c_fm_b @ ( set_Epistemic_fm_b2 @ Ps ) @ ( set_Epistemic_fm_b2 @ Qs4 ) )
     => ! [G: list_char > $o,H: epistemic_fm_b > $o] : ( epistemic_eval_b @ G @ H @ ( epistemic_Imp_b @ ( epistemic_imply_b @ Ps @ R ) @ ( epistemic_imply_b @ Qs4 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_874_tautology__imply__superset,axiom,
    ! [Ps: list_Epistemic_fm_a,Qs4: list_Epistemic_fm_a,R: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Qs4 ) )
     => ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ Ps @ R ) @ ( epistemic_imply_a @ Qs4 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_875_fm_Opred__True,axiom,
    ( ( epistemic_pred_fm_a
      @ ^ [Uu2: a] : $true )
    = ( ^ [Uu2: epistemic_fm_a] : $true ) ) ).

% fm.pred_True
thf(fact_876_fm_Opred__True,axiom,
    ( ( epistemic_pred_fm_b
      @ ^ [Uu2: b] : $true )
    = ( ^ [Uu2: epistemic_fm_b] : $true ) ) ).

% fm.pred_True
thf(fact_877_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 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ 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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>4
thf(fact_878_main_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M3: episte1560738328020401952t_unit] :
            ( ( episte8364071018013720454t_unit @ M3 )
           => ! [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Y: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Y ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ 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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>4
thf(fact_879_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 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ 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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>5
thf(fact_880_main_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M3: episte1560738328020401952t_unit] :
            ( ( episte2449151000174023629t_unit @ M3 )
           => ! [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Y: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Y ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ 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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>5
thf(fact_881_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 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ 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 ) ) ) ) ).

% strong_completeness\<^sub>K\<^sub>B
thf(fact_882_main_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ! [M3: episte1560738328020401952t_unit] :
            ( ( episte5478016696552465318t_unit @ M3 )
           => ! [X2: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X2 @ ( episte8072386903178013299t_unit @ M3 ) )
               => ( ! [Y: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Y @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M3 @ X2 @ Y ) )
                 => ( episte7081087998767065248c_fm_a @ M3 @ 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 ) ) ) ) ) ).

% main\<^sub>K\<^sub>B
thf(fact_883_strong__soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte8559422309061589728t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte8559422309061589728t_unit,W5: set_b,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_set_b @ W5 @ ( episte2726209618768418739t_unit @ M2 ) )
             => ( episte586216548244424325_set_b @ M2 @ W5 @ P2 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M4: episte8559422309061589728t_unit] :
            ( ( P4 @ M4 )
           => ! [X4: set_b] :
                ( ( member_set_b @ X4 @ ( episte2726209618768418739t_unit @ M4 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte586216548244424325_set_b @ M4 @ X4 @ Xa ) )
                 => ( episte586216548244424325_set_b @ M4 @ X4 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_884_strong__soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte6182337868402532512t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte6182337868402532512t_unit,W5: a,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_a @ W5 @ ( episte6926715892928323059t_unit @ M2 ) )
             => ( episte295617885132580260cs_a_a @ M2 @ W5 @ P2 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M4: episte6182337868402532512t_unit] :
            ( ( P4 @ M4 )
           => ! [X4: a] :
                ( ( member_a @ X4 @ ( episte6926715892928323059t_unit @ M4 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte295617885132580260cs_a_a @ M4 @ X4 @ Xa ) )
                 => ( episte295617885132580260cs_a_a @ M4 @ X4 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_885_strong__soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte1560738328020401952t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte1560738328020401952t_unit,W5: set_Epistemic_fm_a,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member536094252920883875c_fm_a @ W5 @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( episte7081087998767065248c_fm_a @ M2 @ W5 @ P2 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M4: episte1560738328020401952t_unit] :
            ( ( P4 @ M4 )
           => ! [X4: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X4 @ ( episte8072386903178013299t_unit @ M4 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ Xa ) )
                 => ( episte7081087998767065248c_fm_a @ M4 @ X4 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_886_strong__soundness,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte3224730989885420256t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte3224730989885420256t_unit,W5: b,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_b @ W5 @ ( episte1782384855165018035t_unit @ M2 ) )
             => ( episte295617885132580261cs_a_b @ M2 @ W5 @ P2 ) ) ) )
     => ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ P ) ) )
       => ! [M4: episte3224730989885420256t_unit] :
            ( ( P4 @ M4 )
           => ! [X4: b] :
                ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                     => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
                 => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ) ).

% strong_soundness
thf(fact_887_fm_Orel__inject_I5_J,axiom,
    ! [R3: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) )
      = ( ( epistemic_rel_fm_a_a @ R3 @ X51 @ Y51 )
        & ( epistemic_rel_fm_a_a @ R3 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_888_fm_Orel__intros_I5_J,axiom,
    ! [R3: a > a > $o,X51: epistemic_fm_a,Y51: epistemic_fm_a,X52: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R3 @ X51 @ Y51 )
     => ( ( epistemic_rel_fm_a_a @ R3 @ X52 @ Y52 )
       => ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_889_fm_Orel__inject_I6_J,axiom,
    ! [R3: a > a > $o,X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) )
      = ( ( R3 @ X61 @ Y61 )
        & ( epistemic_rel_fm_a_a @ R3 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_890_fm_Orel__intros_I6_J,axiom,
    ! [R3: a > a > $o,X61: a,Y61: a,X62: epistemic_fm_a,Y62: epistemic_fm_a] :
      ( ( R3 @ X61 @ Y61 )
     => ( ( epistemic_rel_fm_a_a @ R3 @ X62 @ Y62 )
       => ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_891_fm_Octr__transfer_I1_J,axiom,
    ! [R3: a > a > $o] : ( epistemic_rel_fm_a_a @ R3 @ epistemic_FF_a @ epistemic_FF_a ) ).

% fm.ctr_transfer(1)
thf(fact_892_strong__soundness_092_060_094sub_062K,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a,P4: episte3224730989885420256t_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 ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( P4 @ M4 )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K
thf(fact_893_Int__Collect__mono,axiom,
    ! [A3: set_b,B: set_b,P4: b > $o,Q2: b > $o] :
      ( ( ord_less_eq_set_b @ A3 @ B )
     => ( ! [X: b] :
            ( ( member_b @ X @ A3 )
           => ( ( P4 @ X )
             => ( Q2 @ X ) ) )
       => ( ord_less_eq_set_b @ ( inf_inf_set_b @ A3 @ ( collect_b @ P4 ) ) @ ( inf_inf_set_b @ B @ ( collect_b @ Q2 ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_894_fm_Oset__intros_I6_J,axiom,
    ! [Yf: b,X52: epistemic_fm_b,X51: epistemic_fm_b] :
      ( ( member_b @ Yf @ ( epistemic_set_fm_b @ X52 ) )
     => ( member_b @ Yf @ ( epistemic_set_fm_b @ ( epistemic_Imp_b @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(6)
thf(fact_895_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_896_fm_Oset__intros_I5_J,axiom,
    ! [Ye: b,X51: epistemic_fm_b,X52: epistemic_fm_b] :
      ( ( member_b @ Ye @ ( epistemic_set_fm_b @ X51 ) )
     => ( member_b @ Ye @ ( epistemic_set_fm_b @ ( epistemic_Imp_b @ X51 @ X52 ) ) ) ) ).

% fm.set_intros(5)
thf(fact_897_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_898_fm_Oset__intros_I8_J,axiom,
    ! [Yg: b,X62: epistemic_fm_b,X61: b] :
      ( ( member_b @ Yg @ ( epistemic_set_fm_b @ X62 ) )
     => ( member_b @ Yg @ ( epistemic_set_fm_b @ ( epistemic_K_b @ X61 @ X62 ) ) ) ) ).

% fm.set_intros(8)
thf(fact_899_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_900_fm_Oset__intros_I7_J,axiom,
    ! [X61: b,X62: epistemic_fm_b] : ( member_b @ X61 @ ( epistemic_set_fm_b @ ( epistemic_K_b @ X61 @ X62 ) ) ) ).

% fm.set_intros(7)
thf(fact_901_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_902_fm_Oset__intros_I4_J,axiom,
    ! [Yd: b,X42: epistemic_fm_b,X41: epistemic_fm_b] :
      ( ( member_b @ Yd @ ( epistemic_set_fm_b @ X42 ) )
     => ( member_b @ Yd @ ( epistemic_set_fm_b @ ( epistemic_Con_b @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_903_fm_Oset__intros_I3_J,axiom,
    ! [Yc: b,X41: epistemic_fm_b,X42: epistemic_fm_b] :
      ( ( member_b @ Yc @ ( epistemic_set_fm_b @ X41 ) )
     => ( member_b @ Yc @ ( epistemic_set_fm_b @ ( epistemic_Con_b @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_904_fm_Oset__intros_I2_J,axiom,
    ! [Yb2: b,X32: epistemic_fm_b,X31: epistemic_fm_b] :
      ( ( member_b @ Yb2 @ ( epistemic_set_fm_b @ X32 ) )
     => ( member_b @ Yb2 @ ( epistemic_set_fm_b @ ( epistemic_Dis_b @ X31 @ X32 ) ) ) ) ).

% fm.set_intros(2)
thf(fact_905_fm_Oset__intros_I1_J,axiom,
    ! [Ya: b,X31: epistemic_fm_b,X32: epistemic_fm_b] :
      ( ( member_b @ Ya @ ( epistemic_set_fm_b @ X31 ) )
     => ( member_b @ Ya @ ( epistemic_set_fm_b @ ( epistemic_Dis_b @ X31 @ X32 ) ) ) ) ).

% fm.set_intros(1)
thf(fact_906_fm_Opred__inject_I1_J,axiom,
    ! [P4: a > $o] : ( epistemic_pred_fm_a @ P4 @ epistemic_FF_a ) ).

% fm.pred_inject(1)
thf(fact_907_soundness__imply,axiom,
    ! [A3: epistemic_fm_a > $o,P4: episte3224730989885420256t_unit > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ! [M2: episte3224730989885420256t_unit,W5: b,P2: epistemic_fm_a] :
          ( ( A3 @ P2 )
         => ( ( P4 @ M2 )
           => ( ( member_b @ W5 @ ( episte1782384855165018035t_unit @ M2 ) )
             => ( episte295617885132580261cs_a_b @ M2 @ W5 @ P2 ) ) ) )
     => ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps @ P ) )
       => ! [M4: episte3224730989885420256t_unit] :
            ( ( P4 @ M4 )
           => ! [X4: b] :
                ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
               => ( ! [Xa: epistemic_fm_a] :
                      ( ( member6642669571620171971c_fm_a @ Xa @ ( set_Epistemic_fm_a2 @ Ps ) )
                     => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
                 => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ) ).

% soundness_imply
thf(fact_908_less__eq__set__def,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( ord_less_eq_b_o
          @ ^ [X2: b] : ( member_b @ X2 @ A4 )
          @ ^ [X2: b] : ( member_b @ X2 @ B4 ) ) ) ) ).

% less_eq_set_def
thf(fact_909_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 ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( episte3426825378771607259t_unit @ M4 )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>T
thf(fact_910_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 ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( episte9018110198556821958t_unit @ M4 )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>4
thf(fact_911_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 ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( episte4899516349225340390t_unit @ M4 )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>B
thf(fact_912_fm_Orel__distinct_I30_J,axiom,
    ! [R3: a > a > $o,Y61: a,Y62: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_913_fm_Orel__distinct_I29_J,axiom,
    ! [R3: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_914_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 ) ) )
     => ! [M4: episte3224730989885420256t_unit] :
          ( ( episte6418945320598494989t_unit @ M4 )
         => ! [X4: b] :
              ( ( member_b @ X4 @ ( episte1782384855165018035t_unit @ M4 ) )
             => ( ! [Xa: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa @ G5 )
                   => ( episte295617885132580261cs_a_b @ M4 @ X4 @ Xa ) )
               => ( episte295617885132580261cs_a_b @ M4 @ X4 @ P ) ) ) ) ) ).

% strong_soundness\<^sub>K\<^sub>5
thf(fact_915_fm_Orel__distinct_I8_J,axiom,
    ! [R3: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(8)
thf(fact_916_fm_Orel__distinct_I7_J,axiom,
    ! [R3: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ epistemic_FF_a @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(7)
thf(fact_917_fm_Orel__distinct_I10_J,axiom,
    ! [R3: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ ( epistemic_K_a @ Y61 @ Y62 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(10)
thf(fact_918_fm_Orel__distinct_I9_J,axiom,
    ! [R3: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R3 @ epistemic_FF_a @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(9)
thf(fact_919_K__right__mp,axiom,
    ! [A3: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps @ P ) )
     => ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps @ ( epistemic_Imp_a @ P @ Q ) ) )
       => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Ps @ Q ) ) ) ) ).

% K_right_mp
thf(fact_920_imply__conjunct,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_imply_a @ G5 @ P ) @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% imply_conjunct
thf(fact_921_conjunct__imply,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% conjunct_imply
thf(fact_922_K__conjunct__imply,axiom,
    ! [A3: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_conjunct_imply
thf(fact_923_K__imply__conjunct,axiom,
    ! [A3: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ G5 @ P ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% K_imply_conjunct
thf(fact_924_consistent__def,axiom,
    ( episte2285483198712856226tent_a
    = ( ^ [A4: epistemic_fm_a > $o,S2: set_Epistemic_fm_a] :
          ~ ? [Qs3: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs3 ) @ S2 )
              & ( epistemic_AK_a @ A4 @ ( epistemic_imply_a @ Qs3 @ epistemic_FF_a ) ) ) ) ) ).

% consistent_def
thf(fact_925_K__Boole,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ G5 ) @ epistemic_FF_a ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_Boole
thf(fact_926_strong__completeness,axiom,
    ! [P4: episte1560738328020401952t_unit > $o,G5: set_Epistemic_fm_a,P: epistemic_fm_a,A3: epistemic_fm_a > $o] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( P4 @ M2 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ G5 )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X @ P ) ) ) )
     => ( ( P4
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W7: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
            @ ^ [I2: a,V3: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
              @ product_Unity ) ) )
       => ? [Qs2: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs2 ) @ G5 )
            & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs2 @ P ) ) ) ) ) ).

% strong_completeness
thf(fact_927_symmetric_092_060_094sub_062K_092_060_094sub_062B,axiom,
    ! [A3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A3 )
     => ( episte5478016696552465318t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W7: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
          @ ^ [I2: a,V3: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
            @ product_Unity ) ) ) ) ).

% symmetric\<^sub>K\<^sub>B
thf(fact_928_consequent__in__maximal,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
       => ( ( member6642669571620171971c_fm_a @ P @ V4 )
         => ( ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ V4 )
           => ( member6642669571620171971c_fm_a @ Q @ V4 ) ) ) ) ) ).

% consequent_in_maximal
thf(fact_929_exactly__one__in__maximal,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
       => ( ( member6642669571620171971c_fm_a @ P @ V4 )
          = ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ V4 ) ) ) ) ) ).

% exactly_one_in_maximal
thf(fact_930_dual__reach,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,I3: a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
       => ( ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ V4 )
         => ? [W8: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ W8
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) )
              & ( member6642669571620171971c_fm_a @ P @ W8 ) ) ) ) ) ).

% dual_reach
thf(fact_931_reach__dualK,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,W6: set_Epistemic_fm_a,I3: a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
       => ( ( episte2285483198712856226tent_a @ A3 @ W6 )
         => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W6 )
           => ( ( member536094252920883875c_fm_a @ W6
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) )
             => ! [P5: epistemic_fm_a] :
                  ( ( member6642669571620171971c_fm_a @ P5 @ W6 )
                 => ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P5 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ V4 ) ) ) ) ) ) ) ).

% reach_dualK
thf(fact_932_truth__lemma,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
       => ( ( member6642669571620171971c_fm_a @ P @ V4 )
          = ( episte7081087998767065248c_fm_a
            @ ( episte2888590659910966568t_unit
              @ ( collec2519470961442302949c_fm_a
                @ ^ [W7: set_Epistemic_fm_a] :
                    ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                    & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
              @ ^ [I2: a,V3: set_Epistemic_fm_a] :
                  ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
              @ ( episte8239586592105053771t_unit
                @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
                @ product_Unity ) )
            @ V4
            @ P ) ) ) ) ).

% truth_lemma
thf(fact_933_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_934_AxT__reflexive,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,I3: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A3 )
     => ( ( episte2285483198712856226tent_a @ A3 @ V4 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
         => ( member536094252920883875c_fm_a @ V4
            @ ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) ) ) ) ) ).

% AxT_reflexive
thf(fact_935_Ax4__transitive,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,W6: set_Epistemic_fm_a,I3: a,U: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A3 )
     => ( ( episte2285483198712856226tent_a @ A3 @ V4 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
         => ( ( member536094252920883875c_fm_a @ W6
              @ ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) )
           => ( ( member536094252920883875c_fm_a @ U
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ W6 ) ) ) ) )
             => ( member536094252920883875c_fm_a @ U
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) ) ) ) ) ) ) ).

% Ax4_transitive
thf(fact_936_Ax5__Euclidean,axiom,
    ! [A3: epistemic_fm_a > $o,U: set_Epistemic_fm_a,V4: set_Epistemic_fm_a,W6: set_Epistemic_fm_a,I3: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A3 )
     => ( ( episte2285483198712856226tent_a @ A3 @ U )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ U )
         => ( ( episte2285483198712856226tent_a @ A3 @ V4 )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
             => ( ( episte2285483198712856226tent_a @ A3 @ W6 )
               => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W6 )
                 => ( ( member536094252920883875c_fm_a @ V4
                      @ ( collec2519470961442302949c_fm_a
                        @ ( ord_le3275665582123262618c_fm_a
                          @ ( collec4904205152690461189c_fm_a
                            @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ U ) ) ) ) )
                   => ( ( member536094252920883875c_fm_a @ W6
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ U ) ) ) ) )
                     => ( member536094252920883875c_fm_a @ W6
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% Ax5_Euclidean
thf(fact_937_AxB__symmetric_H,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,W6: set_Epistemic_fm_a,I3: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A3 )
     => ( ( episte2285483198712856226tent_a @ A3 @ V4 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ V4 )
         => ( ( episte2285483198712856226tent_a @ A3 @ W6 )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W6 )
             => ( ( member536094252920883875c_fm_a @ W6
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ V4 ) ) ) ) )
               => ( member536094252920883875c_fm_a @ V4
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I3 @ P3 ) @ W6 ) ) ) ) ) ) ) ) ) ) ) ).

% AxB_symmetric'
thf(fact_938_K__ImpI,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G5 ) @ Q ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ G5 @ ( epistemic_Imp_a @ P @ Q ) ) ) ) ).

% K_ImpI
thf(fact_939_K__mp,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ G5 ) ) @ Q ) ) ).

% K_mp
thf(fact_940_reflexive_092_060_094sub_062T,axiom,
    ! [A3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A3 )
     => ( episte5648423998891577755t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W7: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
          @ ^ [I2: a,V3: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
            @ product_Unity ) ) ) ) ).

% reflexive\<^sub>T
thf(fact_941_transitive_092_060_094sub_062K_092_060_094sub_0624,axiom,
    ! [A3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A3 )
     => ( episte8364071018013720454t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W7: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
          @ ^ [I2: a,V3: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
            @ product_Unity ) ) ) ) ).

% transitive\<^sub>K\<^sub>4
thf(fact_942_Euclidean_092_060_094sub_062K_092_060_094sub_0625,axiom,
    ! [A3: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A3 )
     => ( episte2449151000174023629t_unit
        @ ( episte2888590659910966568t_unit
          @ ( collec2519470961442302949c_fm_a
            @ ^ [W7: set_Epistemic_fm_a] :
                ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
          @ ^ [I2: a,V3: set_Epistemic_fm_a] :
              ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
          @ ( episte8239586592105053771t_unit
            @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
            @ product_Unity ) ) ) ) ).

% Euclidean\<^sub>K\<^sub>5
thf(fact_943_completeness,axiom,
    ! [P4: episte1560738328020401952t_unit > $o,P: epistemic_fm_a,A3: epistemic_fm_a > $o] :
      ( ! [M2: episte1560738328020401952t_unit] :
          ( ( P4 @ M2 )
         => ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ ( episte8072386903178013299t_unit @ M2 ) )
             => ( ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ bot_bo3626323581529592678c_fm_a )
                   => ( episte7081087998767065248c_fm_a @ M2 @ X @ Xa2 ) )
               => ( episte7081087998767065248c_fm_a @ M2 @ X @ P ) ) ) )
     => ( ( P4
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W7: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
            @ ^ [I2: a,V3: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
              @ product_Unity ) ) )
       => ( epistemic_AK_a @ A3 @ P ) ) ) ).

% completeness
thf(fact_944_K__conjunction__out__mult,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I3 ) @ G5 ) ) @ ( epistemic_K_a @ I3 @ ( stalnaker_conjunct_a @ G5 ) ) ) ) ).

% K_conjunction_out_mult
thf(fact_945_K__conjunction__in__mult,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( stalnaker_conjunct_a @ G5 ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I3 ) @ G5 ) ) ) ) ).

% K_conjunction_in_mult
thf(fact_946_canonical__model_I1_J,axiom,
    ! [A3: epistemic_fm_a > $o,S: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ S )
     => ( ( member6642669571620171971c_fm_a @ P @ S )
       => ( episte7081087998767065248c_fm_a
          @ ( episte2888590659910966568t_unit
            @ ( collec2519470961442302949c_fm_a
              @ ^ [W7: set_Epistemic_fm_a] :
                  ( ( episte2285483198712856226tent_a @ A3 @ W7 )
                  & ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A3 ) @ W7 ) ) )
            @ ^ [I2: a,V3: set_Epistemic_fm_a] :
                ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P3: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I2 @ P3 ) @ V3 ) ) ) )
            @ ( episte8239586592105053771t_unit
              @ ^ [V3: set_Epistemic_fm_a,X2: list_char] : ( member6642669571620171971c_fm_a @ ( epistemic_Pro_a @ X2 ) @ V3 )
              @ product_Unity ) )
          @ ( maxima2580775624958445067c_fm_a @ ( bNF_Ca1305897159876240246c_fm_a @ top_to7796028867103199306c_fm_a ) @ ( episte2285483198712856226tent_a @ A3 ) @ S )
          @ P ) ) ) ).

% canonical_model(1)
thf(fact_947_UNIV__I,axiom,
    ! [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).

% UNIV_I
thf(fact_948_UNIV__I,axiom,
    ! [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ).

% UNIV_I
thf(fact_949_empty__iff,axiom,
    ! [C: b] :
      ~ ( member_b @ C @ bot_bot_set_b ) ).

% empty_iff
thf(fact_950_empty__iff,axiom,
    ! [C: $o] :
      ~ ( member_o @ C @ bot_bot_set_o ) ).

% empty_iff
thf(fact_951_all__not__in__conv,axiom,
    ! [A3: set_b] :
      ( ( ! [X2: b] :
            ~ ( member_b @ X2 @ A3 ) )
      = ( A3 = bot_bot_set_b ) ) ).

% all_not_in_conv
thf(fact_952_all__not__in__conv,axiom,
    ! [A3: set_o] :
      ( ( ! [X2: $o] :
            ~ ( member_o @ X2 @ A3 ) )
      = ( A3 = bot_bot_set_o ) ) ).

% all_not_in_conv
thf(fact_953_Collect__empty__eq,axiom,
    ! [P4: $o > $o] :
      ( ( ( collect_o @ P4 )
        = bot_bot_set_o )
      = ( ! [X2: $o] :
            ~ ( P4 @ X2 ) ) ) ).

% Collect_empty_eq
thf(fact_954_empty__Collect__eq,axiom,
    ! [P4: $o > $o] :
      ( ( bot_bot_set_o
        = ( collect_o @ P4 ) )
      = ( ! [X2: $o] :
            ~ ( P4 @ X2 ) ) ) ).

% empty_Collect_eq
thf(fact_955_empty__subsetI,axiom,
    ! [A3: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A3 ) ).

% empty_subsetI
thf(fact_956_subset__empty,axiom,
    ! [A3: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ bot_bot_set_o )
      = ( A3 = bot_bot_set_o ) ) ).

% subset_empty
thf(fact_957_inf__bot__right,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ bot_bot_set_o )
      = bot_bot_set_o ) ).

% inf_bot_right
thf(fact_958_inf__bot__left,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ bot_bot_set_o @ X3 )
      = bot_bot_set_o ) ).

% inf_bot_left
thf(fact_959_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ bot_bot_set_o )
      = bot_bot_set_o ) ).

% boolean_algebra.conj_zero_right
thf(fact_960_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ bot_bot_set_o @ X3 )
      = bot_bot_set_o ) ).

% boolean_algebra.conj_zero_left
thf(fact_961_inf__top_Oright__neutral,axiom,
    ! [A: set_o] :
      ( ( inf_inf_set_o @ A @ top_top_set_o )
      = A ) ).

% inf_top.right_neutral
thf(fact_962_inf__top_Oneutr__eq__iff,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( top_top_set_o
        = ( inf_inf_set_o @ A @ B2 ) )
      = ( ( A = top_top_set_o )
        & ( B2 = top_top_set_o ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_963_inf__top_Oleft__neutral,axiom,
    ! [A: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ A )
      = A ) ).

% inf_top.left_neutral
thf(fact_964_inf__top_Oeq__neutr__iff,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( ( inf_inf_set_o @ A @ B2 )
        = top_top_set_o )
      = ( ( A = top_top_set_o )
        & ( B2 = top_top_set_o ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_965_top__eq__inf__iff,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( top_top_set_o
        = ( inf_inf_set_o @ X3 @ Y2 ) )
      = ( ( X3 = top_top_set_o )
        & ( Y2 = top_top_set_o ) ) ) ).

% top_eq_inf_iff
thf(fact_966_inf__eq__top__iff,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( inf_inf_set_o @ X3 @ Y2 )
        = top_top_set_o )
      = ( ( X3 = top_top_set_o )
        & ( Y2 = top_top_set_o ) ) ) ).

% inf_eq_top_iff
thf(fact_967_inf__top__right,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ top_top_set_o )
      = X3 ) ).

% inf_top_right
thf(fact_968_inf__top__left,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ X3 )
      = X3 ) ).

% inf_top_left
thf(fact_969_Int__UNIV,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = top_top_set_o )
      = ( ( A3 = top_top_set_o )
        & ( B = top_top_set_o ) ) ) ).

% Int_UNIV
thf(fact_970_Collect__const,axiom,
    ! [P4: $o] :
      ( ( P4
       => ( ( collect_o
            @ ^ [S3: $o] : P4 )
          = top_top_set_o ) )
      & ( ~ P4
       => ( ( collect_o
            @ ^ [S3: $o] : P4 )
          = bot_bot_set_o ) ) ) ).

% Collect_const
thf(fact_971_empty__def,axiom,
    ( bot_bot_set_o
    = ( collect_o
      @ ^ [X2: $o] : $false ) ) ).

% empty_def
thf(fact_972_UNIV__def,axiom,
    ( top_top_set_o
    = ( collect_o
      @ ^ [X2: $o] : $true ) ) ).

% UNIV_def
thf(fact_973_emptyE,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ) ).

% emptyE
thf(fact_974_emptyE,axiom,
    ! [A: $o] :
      ~ ( member_o @ A @ bot_bot_set_o ) ).

% emptyE
thf(fact_975_equals0D,axiom,
    ! [A3: set_b,A: b] :
      ( ( A3 = bot_bot_set_b )
     => ~ ( member_b @ A @ A3 ) ) ).

% equals0D
thf(fact_976_equals0D,axiom,
    ! [A3: set_o,A: $o] :
      ( ( A3 = bot_bot_set_o )
     => ~ ( member_o @ A @ A3 ) ) ).

% equals0D
thf(fact_977_equals0I,axiom,
    ! [A3: set_b] :
      ( ! [Y3: b] :
          ~ ( member_b @ Y3 @ A3 )
     => ( A3 = bot_bot_set_b ) ) ).

% equals0I
thf(fact_978_equals0I,axiom,
    ! [A3: set_o] :
      ( ! [Y3: $o] :
          ~ ( member_o @ Y3 @ A3 )
     => ( A3 = bot_bot_set_o ) ) ).

% equals0I
thf(fact_979_UNIV__eq__I,axiom,
    ! [A3: set_b] :
      ( ! [X: b] : ( member_b @ X @ A3 )
     => ( top_top_set_b = A3 ) ) ).

% UNIV_eq_I
thf(fact_980_UNIV__eq__I,axiom,
    ! [A3: set_o] :
      ( ! [X: $o] : ( member_o @ X @ A3 )
     => ( top_top_set_o = A3 ) ) ).

% UNIV_eq_I
thf(fact_981_ex__in__conv,axiom,
    ! [A3: set_b] :
      ( ( ? [X2: b] : ( member_b @ X2 @ A3 ) )
      = ( A3 != bot_bot_set_b ) ) ).

% ex_in_conv
thf(fact_982_ex__in__conv,axiom,
    ! [A3: set_o] :
      ( ( ? [X2: $o] : ( member_o @ X2 @ A3 ) )
      = ( A3 != bot_bot_set_o ) ) ).

% ex_in_conv
thf(fact_983_UNIV__witness,axiom,
    ? [X: b] : ( member_b @ X @ top_top_set_b ) ).

% UNIV_witness
thf(fact_984_UNIV__witness,axiom,
    ? [X: $o] : ( member_o @ X @ top_top_set_o ) ).

% UNIV_witness
thf(fact_985_empty__not__UNIV,axiom,
    bot_bot_set_o != top_top_set_o ).

% empty_not_UNIV
thf(fact_986_boolean__algebra_Oconj__one__right,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ top_top_set_o )
      = X3 ) ).

% boolean_algebra.conj_one_right
thf(fact_987_subset__UNIV,axiom,
    ! [A3: set_o] : ( ord_less_eq_set_o @ A3 @ top_top_set_o ) ).

% subset_UNIV
thf(fact_988_Int__UNIV__right,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ A3 @ top_top_set_o )
      = A3 ) ).

% Int_UNIV_right
thf(fact_989_Int__UNIV__left,axiom,
    ! [B: set_o] :
      ( ( inf_inf_set_o @ top_top_set_o @ B )
      = B ) ).

% Int_UNIV_left
thf(fact_990_disjoint__iff__not__equal,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = bot_bot_set_o )
      = ( ! [X2: $o] :
            ( ( member_o @ X2 @ A3 )
           => ! [Y: $o] :
                ( ( member_o @ Y @ B )
               => ( X2 = (~ Y) ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_991_Int__empty__right,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ A3 @ bot_bot_set_o )
      = bot_bot_set_o ) ).

% Int_empty_right
thf(fact_992_Int__empty__left,axiom,
    ! [B: set_o] :
      ( ( inf_inf_set_o @ bot_bot_set_o @ B )
      = bot_bot_set_o ) ).

% Int_empty_left
thf(fact_993_disjoint__iff,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ A3 @ B )
        = bot_bot_set_b )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ A3 )
           => ~ ( member_b @ X2 @ B ) ) ) ) ).

% disjoint_iff
thf(fact_994_disjoint__iff,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = bot_bot_set_o )
      = ( ! [X2: $o] :
            ( ( member_o @ X2 @ A3 )
           => ~ ( member_o @ X2 @ B ) ) ) ) ).

% disjoint_iff
thf(fact_995_Int__emptyI,axiom,
    ! [A3: set_b,B: set_b] :
      ( ! [X: b] :
          ( ( member_b @ X @ A3 )
         => ~ ( member_b @ X @ B ) )
     => ( ( inf_inf_set_b @ A3 @ B )
        = bot_bot_set_b ) ) ).

% Int_emptyI
thf(fact_996_Int__emptyI,axiom,
    ! [A3: set_o,B: set_o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A3 )
         => ~ ( member_o @ X @ B ) )
     => ( ( inf_inf_set_o @ A3 @ B )
        = bot_bot_set_o ) ) ).

% Int_emptyI
thf(fact_997_fm_Osimps_I90_J,axiom,
    ( ( epistemic_set_fm_a @ epistemic_FF_a )
    = bot_bot_set_a ) ).

% fm.simps(90)
thf(fact_998_fm_Osimps_I90_J,axiom,
    ( ( epistemic_set_fm_o @ epistemic_FF_o )
    = bot_bot_set_o ) ).

% fm.simps(90)
thf(fact_999_fm_Osimps_I91_J,axiom,
    ! [X22: list_char] :
      ( ( epistemic_set_fm_o @ ( epistemic_Pro_o @ X22 ) )
      = bot_bot_set_o ) ).

% fm.simps(91)
thf(fact_1000_K__distrib__K__imp,axiom,
    ! [A3: epistemic_fm_a > $o,I3: a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A3 @ ( epistemic_K_a @ I3 @ ( epistemic_imply_a @ G5 @ Q ) ) )
     => ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I3 ) @ G5 ) @ ( epistemic_K_a @ I3 @ Q ) ) ) ) ).

% K_distrib_K_imp
thf(fact_1001_Set_Ois__empty__def,axiom,
    ( is_empty_o
    = ( ^ [A4: set_o] : ( A4 = bot_bot_set_o ) ) ) ).

% Set.is_empty_def
thf(fact_1002_bot__set__def,axiom,
    ( bot_bot_set_o
    = ( collect_o @ bot_bot_o_o ) ) ).

% bot_set_def
thf(fact_1003_top__set__def,axiom,
    ( top_top_set_o
    = ( collect_o @ top_top_o_o ) ) ).

% top_set_def
thf(fact_1004_inter__Set__filter,axiom,
    ! [B: set_b,A3: set_b] :
      ( ( finite_finite_b @ B )
     => ( ( inf_inf_set_b @ A3 @ B )
        = ( filter_b
          @ ^ [X2: b] : ( member_b @ X2 @ A3 )
          @ B ) ) ) ).

% inter_Set_filter
thf(fact_1005_member__filter,axiom,
    ! [X3: b,P4: b > $o,A3: set_b] :
      ( ( member_b @ X3 @ ( filter_b @ P4 @ A3 ) )
      = ( ( member_b @ X3 @ A3 )
        & ( P4 @ X3 ) ) ) ).

% member_filter
thf(fact_1006_Set_Ofilter__def,axiom,
    ( filter_b
    = ( ^ [P6: b > $o,A4: set_b] :
          ( collect_b
          @ ^ [A2: b] :
              ( ( member_b @ A2 @ A4 )
              & ( P6 @ A2 ) ) ) ) ) ).

% Set.filter_def
thf(fact_1007_inconsistent__subset,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ~ ( episte2285483198712856226tent_a @ A3 @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P @ bot_bo3626323581529592678c_fm_a ) @ V4 ) )
       => ~ ! [V5: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ V5 ) @ V4 )
             => ~ ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ V5 ) @ epistemic_FF_a ) ) ) ) ) ).

% inconsistent_subset
thf(fact_1008_insert__absorb2,axiom,
    ! [X3: $o,A3: set_o] :
      ( ( insert_o @ X3 @ ( insert_o @ X3 @ A3 ) )
      = ( insert_o @ X3 @ A3 ) ) ).

% insert_absorb2
thf(fact_1009_insert__iff,axiom,
    ! [A: $o,B2: $o,A3: set_o] :
      ( ( member_o @ A @ ( insert_o @ B2 @ A3 ) )
      = ( ( A = B2 )
        | ( member_o @ A @ A3 ) ) ) ).

% insert_iff
thf(fact_1010_insert__iff,axiom,
    ! [A: b,B2: b,A3: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A3 ) )
      = ( ( A = B2 )
        | ( member_b @ A @ A3 ) ) ) ).

% insert_iff
thf(fact_1011_insertCI,axiom,
    ! [A: $o,B: set_o,B2: $o] :
      ( ( ~ ( member_o @ A @ B )
       => ( A = B2 ) )
     => ( member_o @ A @ ( insert_o @ B2 @ B ) ) ) ).

% insertCI
thf(fact_1012_insertCI,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( ~ ( member_b @ A @ B )
       => ( A = B2 ) )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertCI
thf(fact_1013_Un__iff,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( sup_sup_set_b @ A3 @ B ) )
      = ( ( member_b @ C @ A3 )
        | ( member_b @ C @ B ) ) ) ).

% Un_iff
thf(fact_1014_UnCI,axiom,
    ! [C: b,B: set_b,A3: set_b] :
      ( ( ~ ( member_b @ C @ B )
       => ( member_b @ C @ A3 ) )
     => ( member_b @ C @ ( sup_sup_set_b @ A3 @ B ) ) ) ).

% UnCI
thf(fact_1015_sup__bot_Oright__neutral,axiom,
    ! [A: set_o] :
      ( ( sup_sup_set_o @ A @ bot_bot_set_o )
      = A ) ).

% sup_bot.right_neutral
thf(fact_1016_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( bot_bot_set_o
        = ( sup_sup_set_o @ A @ B2 ) )
      = ( ( A = bot_bot_set_o )
        & ( B2 = bot_bot_set_o ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_1017_sup__bot_Oleft__neutral,axiom,
    ! [A: set_o] :
      ( ( sup_sup_set_o @ bot_bot_set_o @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_1018_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_o,B2: set_o] :
      ( ( ( sup_sup_set_o @ A @ B2 )
        = bot_bot_set_o )
      = ( ( A = bot_bot_set_o )
        & ( B2 = bot_bot_set_o ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_1019_sup__eq__bot__iff,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( sup_sup_set_o @ X3 @ Y2 )
        = bot_bot_set_o )
      = ( ( X3 = bot_bot_set_o )
        & ( Y2 = bot_bot_set_o ) ) ) ).

% sup_eq_bot_iff
thf(fact_1020_bot__eq__sup__iff,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( bot_bot_set_o
        = ( sup_sup_set_o @ X3 @ Y2 ) )
      = ( ( X3 = bot_bot_set_o )
        & ( Y2 = bot_bot_set_o ) ) ) ).

% bot_eq_sup_iff
thf(fact_1021_sup__bot__right,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ X3 @ bot_bot_set_o )
      = X3 ) ).

% sup_bot_right
thf(fact_1022_sup__bot__left,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ bot_bot_set_o @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_1023_sup__top__right,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ X3 @ top_top_set_o )
      = top_top_set_o ) ).

% sup_top_right
thf(fact_1024_sup__top__left,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ top_top_set_o @ X3 )
      = top_top_set_o ) ).

% sup_top_left
thf(fact_1025_boolean__algebra_Odisj__one__right,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ X3 @ top_top_set_o )
      = top_top_set_o ) ).

% boolean_algebra.disj_one_right
thf(fact_1026_boolean__algebra_Odisj__one__left,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ top_top_set_o @ X3 )
      = top_top_set_o ) ).

% boolean_algebra.disj_one_left
thf(fact_1027_singletonI,axiom,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ) ).

% singletonI
thf(fact_1028_singletonI,axiom,
    ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).

% singletonI
thf(fact_1029_insert__subset,axiom,
    ! [X3: $o,A3: set_o,B: set_o] :
      ( ( ord_less_eq_set_o @ ( insert_o @ X3 @ A3 ) @ B )
      = ( ( member_o @ X3 @ B )
        & ( ord_less_eq_set_o @ A3 @ B ) ) ) ).

% insert_subset
thf(fact_1030_insert__subset,axiom,
    ! [X3: b,A3: set_b,B: set_b] :
      ( ( ord_less_eq_set_b @ ( insert_b @ X3 @ A3 ) @ B )
      = ( ( member_b @ X3 @ B )
        & ( ord_less_eq_set_b @ A3 @ B ) ) ) ).

% insert_subset
thf(fact_1031_Un__empty,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( sup_sup_set_o @ A3 @ B )
        = bot_bot_set_o )
      = ( ( A3 = bot_bot_set_o )
        & ( B = bot_bot_set_o ) ) ) ).

% Un_empty
thf(fact_1032_Int__insert__left__if0,axiom,
    ! [A: $o,C2: set_o,B: set_o] :
      ( ~ ( member_o @ A @ C2 )
     => ( ( inf_inf_set_o @ ( insert_o @ A @ B ) @ C2 )
        = ( inf_inf_set_o @ B @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1033_Int__insert__left__if0,axiom,
    ! [A: b,C2: set_b,B: set_b] :
      ( ~ ( member_b @ A @ C2 )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C2 )
        = ( inf_inf_set_b @ B @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1034_Int__insert__left__if1,axiom,
    ! [A: $o,C2: set_o,B: set_o] :
      ( ( member_o @ A @ C2 )
     => ( ( inf_inf_set_o @ ( insert_o @ A @ B ) @ C2 )
        = ( insert_o @ A @ ( inf_inf_set_o @ B @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1035_Int__insert__left__if1,axiom,
    ! [A: b,C2: set_b,B: set_b] :
      ( ( member_b @ A @ C2 )
     => ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C2 )
        = ( insert_b @ A @ ( inf_inf_set_b @ B @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1036_insert__inter__insert,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ( inf_inf_set_o @ ( insert_o @ A @ A3 ) @ ( insert_o @ A @ B ) )
      = ( insert_o @ A @ ( inf_inf_set_o @ A3 @ B ) ) ) ).

% insert_inter_insert
thf(fact_1037_Int__insert__right__if0,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ~ ( member_o @ A @ A3 )
     => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A @ B ) )
        = ( inf_inf_set_o @ A3 @ B ) ) ) ).

% Int_insert_right_if0
thf(fact_1038_Int__insert__right__if0,axiom,
    ! [A: b,A3: set_b,B: set_b] :
      ( ~ ( member_b @ A @ A3 )
     => ( ( inf_inf_set_b @ A3 @ ( insert_b @ A @ B ) )
        = ( inf_inf_set_b @ A3 @ B ) ) ) ).

% Int_insert_right_if0
thf(fact_1039_Int__insert__right__if1,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ( member_o @ A @ A3 )
     => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A @ B ) )
        = ( insert_o @ A @ ( inf_inf_set_o @ A3 @ B ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1040_Int__insert__right__if1,axiom,
    ! [A: b,A3: set_b,B: set_b] :
      ( ( member_b @ A @ A3 )
     => ( ( inf_inf_set_b @ A3 @ ( insert_b @ A @ B ) )
        = ( insert_b @ A @ ( inf_inf_set_b @ A3 @ B ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1041_Un__insert__right,axiom,
    ! [A3: set_o,A: $o,B: set_o] :
      ( ( sup_sup_set_o @ A3 @ ( insert_o @ A @ B ) )
      = ( insert_o @ A @ ( sup_sup_set_o @ A3 @ B ) ) ) ).

% Un_insert_right
thf(fact_1042_Un__insert__left,axiom,
    ! [A: $o,B: set_o,C2: set_o] :
      ( ( sup_sup_set_o @ ( insert_o @ A @ B ) @ C2 )
      = ( insert_o @ A @ ( sup_sup_set_o @ B @ C2 ) ) ) ).

% Un_insert_left
thf(fact_1043_singleton__conv,axiom,
    ! [A: $o] :
      ( ( collect_o
        @ ^ [X2: $o] : ( X2 = A ) )
      = ( insert_o @ A @ bot_bot_set_o ) ) ).

% singleton_conv
thf(fact_1044_singleton__conv2,axiom,
    ! [A: $o] :
      ( ( collect_o
        @ ( ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
          @ A ) )
      = ( insert_o @ A @ bot_bot_set_o ) ) ).

% singleton_conv2
thf(fact_1045_singleton__insert__inj__eq,axiom,
    ! [B2: $o,A: $o,A3: set_o] :
      ( ( ( insert_o @ B2 @ bot_bot_set_o )
        = ( insert_o @ A @ A3 ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_o @ A3 @ ( insert_o @ B2 @ bot_bot_set_o ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_1046_singleton__insert__inj__eq_H,axiom,
    ! [A: $o,A3: set_o,B2: $o] :
      ( ( ( insert_o @ A @ A3 )
        = ( insert_o @ B2 @ bot_bot_set_o ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_o @ A3 @ ( insert_o @ B2 @ bot_bot_set_o ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_1047_insert__disjoint_I1_J,axiom,
    ! [A: b,A3: set_b,B: set_b] :
      ( ( ( inf_inf_set_b @ ( insert_b @ A @ A3 ) @ B )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ B )
        & ( ( inf_inf_set_b @ A3 @ B )
          = bot_bot_set_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1048_insert__disjoint_I1_J,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ ( insert_o @ A @ A3 ) @ B )
        = bot_bot_set_o )
      = ( ~ ( member_o @ A @ B )
        & ( ( inf_inf_set_o @ A3 @ B )
          = bot_bot_set_o ) ) ) ).

% insert_disjoint(1)
thf(fact_1049_insert__disjoint_I2_J,axiom,
    ! [A: b,A3: set_b,B: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ ( insert_b @ A @ A3 ) @ B ) )
      = ( ~ ( member_b @ A @ B )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ A3 @ B ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1050_insert__disjoint_I2_J,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ( bot_bot_set_o
        = ( inf_inf_set_o @ ( insert_o @ A @ A3 ) @ B ) )
      = ( ~ ( member_o @ A @ B )
        & ( bot_bot_set_o
          = ( inf_inf_set_o @ A3 @ B ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1051_disjoint__insert_I1_J,axiom,
    ! [B: set_b,A: b,A3: set_b] :
      ( ( ( inf_inf_set_b @ B @ ( insert_b @ A @ A3 ) )
        = bot_bot_set_b )
      = ( ~ ( member_b @ A @ B )
        & ( ( inf_inf_set_b @ B @ A3 )
          = bot_bot_set_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1052_disjoint__insert_I1_J,axiom,
    ! [B: set_o,A: $o,A3: set_o] :
      ( ( ( inf_inf_set_o @ B @ ( insert_o @ A @ A3 ) )
        = bot_bot_set_o )
      = ( ~ ( member_o @ A @ B )
        & ( ( inf_inf_set_o @ B @ A3 )
          = bot_bot_set_o ) ) ) ).

% disjoint_insert(1)
thf(fact_1053_disjoint__insert_I2_J,axiom,
    ! [A3: set_b,B2: b,B: set_b] :
      ( ( bot_bot_set_b
        = ( inf_inf_set_b @ A3 @ ( insert_b @ B2 @ B ) ) )
      = ( ~ ( member_b @ B2 @ A3 )
        & ( bot_bot_set_b
          = ( inf_inf_set_b @ A3 @ B ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1054_disjoint__insert_I2_J,axiom,
    ! [A3: set_o,B2: $o,B: set_o] :
      ( ( bot_bot_set_o
        = ( inf_inf_set_o @ A3 @ ( insert_o @ B2 @ B ) ) )
      = ( ~ ( member_o @ B2 @ A3 )
        & ( bot_bot_set_o
          = ( inf_inf_set_o @ A3 @ B ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1055_fm_Osimps_I95_J,axiom,
    ! [X61: $o,X62: epistemic_fm_o] :
      ( ( epistemic_set_fm_o @ ( epistemic_K_o @ X61 @ X62 ) )
      = ( insert_o @ X61 @ ( epistemic_set_fm_o @ X62 ) ) ) ).

% fm.simps(95)
thf(fact_1056_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_1057_boolean__algebra_Odisj__zero__right,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ X3 @ bot_bot_set_o )
      = X3 ) ).

% boolean_algebra.disj_zero_right
thf(fact_1058_insert__is__Un,axiom,
    ( insert_o
    = ( ^ [A2: $o] : ( sup_sup_set_o @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ).

% insert_is_Un
thf(fact_1059_Un__singleton__iff,axiom,
    ! [A3: set_o,B: set_o,X3: $o] :
      ( ( ( sup_sup_set_o @ A3 @ B )
        = ( insert_o @ X3 @ bot_bot_set_o ) )
      = ( ( ( A3 = bot_bot_set_o )
          & ( B
            = ( insert_o @ X3 @ bot_bot_set_o ) ) )
        | ( ( A3
            = ( insert_o @ X3 @ bot_bot_set_o ) )
          & ( B = bot_bot_set_o ) )
        | ( ( A3
            = ( insert_o @ X3 @ bot_bot_set_o ) )
          & ( B
            = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1060_singleton__Un__iff,axiom,
    ! [X3: $o,A3: set_o,B: set_o] :
      ( ( ( insert_o @ X3 @ bot_bot_set_o )
        = ( sup_sup_set_o @ A3 @ B ) )
      = ( ( ( A3 = bot_bot_set_o )
          & ( B
            = ( insert_o @ X3 @ bot_bot_set_o ) ) )
        | ( ( A3
            = ( insert_o @ X3 @ bot_bot_set_o ) )
          & ( B = bot_bot_set_o ) )
        | ( ( A3
            = ( insert_o @ X3 @ bot_bot_set_o ) )
          & ( B
            = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1061_Un__UNIV__right,axiom,
    ! [A3: set_o] :
      ( ( sup_sup_set_o @ A3 @ top_top_set_o )
      = top_top_set_o ) ).

% Un_UNIV_right
thf(fact_1062_Un__UNIV__left,axiom,
    ! [B: set_o] :
      ( ( sup_sup_set_o @ top_top_set_o @ B )
      = top_top_set_o ) ).

% Un_UNIV_left
thf(fact_1063_Un__empty__right,axiom,
    ! [A3: set_o] :
      ( ( sup_sup_set_o @ A3 @ bot_bot_set_o )
      = A3 ) ).

% Un_empty_right
thf(fact_1064_Un__empty__left,axiom,
    ! [B: set_o] :
      ( ( sup_sup_set_o @ bot_bot_set_o @ B )
      = B ) ).

% Un_empty_left
thf(fact_1065_insert__UNIV,axiom,
    ! [X3: $o] :
      ( ( insert_o @ X3 @ top_top_set_o )
      = top_top_set_o ) ).

% insert_UNIV
thf(fact_1066_singleton__inject,axiom,
    ! [A: $o,B2: $o] :
      ( ( ( insert_o @ A @ bot_bot_set_o )
        = ( insert_o @ B2 @ bot_bot_set_o ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_1067_insert__not__empty,axiom,
    ! [A: $o,A3: set_o] :
      ( ( insert_o @ A @ A3 )
     != bot_bot_set_o ) ).

% insert_not_empty
thf(fact_1068_doubleton__eq__iff,axiom,
    ! [A: $o,B2: $o,C: $o,D: $o] :
      ( ( ( insert_o @ A @ ( insert_o @ B2 @ bot_bot_set_o ) )
        = ( insert_o @ C @ ( insert_o @ D @ bot_bot_set_o ) ) )
      = ( ( ( A = C )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_1069_singleton__iff,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1070_singleton__iff,axiom,
    ! [B2: $o,A: $o] :
      ( ( member_o @ B2 @ ( insert_o @ A @ bot_bot_set_o ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1071_singletonD,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1072_singletonD,axiom,
    ! [B2: $o,A: $o] :
      ( ( member_o @ B2 @ ( insert_o @ A @ bot_bot_set_o ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1073_mk__disjoint__insert,axiom,
    ! [A: $o,A3: set_o] :
      ( ( member_o @ A @ A3 )
     => ? [B5: set_o] :
          ( ( A3
            = ( insert_o @ A @ B5 ) )
          & ~ ( member_o @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1074_mk__disjoint__insert,axiom,
    ! [A: b,A3: set_b] :
      ( ( member_b @ A @ A3 )
     => ? [B5: set_b] :
          ( ( A3
            = ( insert_b @ A @ B5 ) )
          & ~ ( member_b @ A @ B5 ) ) ) ).

% mk_disjoint_insert
thf(fact_1075_insert__commute,axiom,
    ! [X3: $o,Y2: $o,A3: set_o] :
      ( ( insert_o @ X3 @ ( insert_o @ Y2 @ A3 ) )
      = ( insert_o @ Y2 @ ( insert_o @ X3 @ A3 ) ) ) ).

% insert_commute
thf(fact_1076_insert__eq__iff,axiom,
    ! [A: $o,A3: set_o,B2: $o,B: set_o] :
      ( ~ ( member_o @ A @ A3 )
     => ( ~ ( member_o @ B2 @ B )
       => ( ( ( insert_o @ A @ A3 )
            = ( insert_o @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A3 = B ) )
            & ( ( A = (~ B2) )
             => ? [C3: set_o] :
                  ( ( A3
                    = ( insert_o @ B2 @ C3 ) )
                  & ~ ( member_o @ B2 @ C3 )
                  & ( B
                    = ( insert_o @ A @ C3 ) )
                  & ~ ( member_o @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1077_insert__eq__iff,axiom,
    ! [A: b,A3: set_b,B2: b,B: set_b] :
      ( ~ ( member_b @ A @ A3 )
     => ( ~ ( member_b @ B2 @ B )
       => ( ( ( insert_b @ A @ A3 )
            = ( insert_b @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A3 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_b] :
                  ( ( A3
                    = ( insert_b @ B2 @ C3 ) )
                  & ~ ( member_b @ B2 @ C3 )
                  & ( B
                    = ( insert_b @ A @ C3 ) )
                  & ~ ( member_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1078_insert__absorb,axiom,
    ! [A: $o,A3: set_o] :
      ( ( member_o @ A @ A3 )
     => ( ( insert_o @ A @ A3 )
        = A3 ) ) ).

% insert_absorb
thf(fact_1079_insert__absorb,axiom,
    ! [A: b,A3: set_b] :
      ( ( member_b @ A @ A3 )
     => ( ( insert_b @ A @ A3 )
        = A3 ) ) ).

% insert_absorb
thf(fact_1080_insert__ident,axiom,
    ! [X3: $o,A3: set_o,B: set_o] :
      ( ~ ( member_o @ X3 @ A3 )
     => ( ~ ( member_o @ X3 @ B )
       => ( ( ( insert_o @ X3 @ A3 )
            = ( insert_o @ X3 @ B ) )
          = ( A3 = B ) ) ) ) ).

% insert_ident
thf(fact_1081_insert__ident,axiom,
    ! [X3: b,A3: set_b,B: set_b] :
      ( ~ ( member_b @ X3 @ A3 )
     => ( ~ ( member_b @ X3 @ B )
       => ( ( ( insert_b @ X3 @ A3 )
            = ( insert_b @ X3 @ B ) )
          = ( A3 = B ) ) ) ) ).

% insert_ident
thf(fact_1082_Set_Oset__insert,axiom,
    ! [X3: $o,A3: set_o] :
      ( ( member_o @ X3 @ A3 )
     => ~ ! [B5: set_o] :
            ( ( A3
              = ( insert_o @ X3 @ B5 ) )
           => ( member_o @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1083_Set_Oset__insert,axiom,
    ! [X3: b,A3: set_b] :
      ( ( member_b @ X3 @ A3 )
     => ~ ! [B5: set_b] :
            ( ( A3
              = ( insert_b @ X3 @ B5 ) )
           => ( member_b @ X3 @ B5 ) ) ) ).

% Set.set_insert
thf(fact_1084_insertI2,axiom,
    ! [A: $o,B: set_o,B2: $o] :
      ( ( member_o @ A @ B )
     => ( member_o @ A @ ( insert_o @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1085_insertI2,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( member_b @ A @ B )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1086_insertI1,axiom,
    ! [A: $o,B: set_o] : ( member_o @ A @ ( insert_o @ A @ B ) ) ).

% insertI1
thf(fact_1087_insertI1,axiom,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ) ).

% insertI1
thf(fact_1088_insertE,axiom,
    ! [A: $o,B2: $o,A3: set_o] :
      ( ( member_o @ A @ ( insert_o @ B2 @ A3 ) )
     => ( ( A = (~ B2) )
       => ( member_o @ A @ A3 ) ) ) ).

% insertE
thf(fact_1089_insertE,axiom,
    ! [A: b,B2: b,A3: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A3 ) )
     => ( ( A != B2 )
       => ( member_b @ A @ A3 ) ) ) ).

% insertE
thf(fact_1090_UnI2,axiom,
    ! [C: b,B: set_b,A3: set_b] :
      ( ( member_b @ C @ B )
     => ( member_b @ C @ ( sup_sup_set_b @ A3 @ B ) ) ) ).

% UnI2
thf(fact_1091_UnI1,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ A3 )
     => ( member_b @ C @ ( sup_sup_set_b @ A3 @ B ) ) ) ).

% UnI1
thf(fact_1092_UnE,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( sup_sup_set_b @ A3 @ B ) )
     => ( ~ ( member_b @ C @ A3 )
       => ( member_b @ C @ B ) ) ) ).

% UnE
thf(fact_1093_Un__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ A4 )
              | ( member_b @ X2 @ B4 ) ) ) ) ) ).

% Un_def
thf(fact_1094_insert__def,axiom,
    ( insert_o
    = ( ^ [A2: $o] :
          ( sup_sup_set_o
          @ ( collect_o
            @ ^ [X2: $o] : ( X2 = A2 ) ) ) ) ) ).

% insert_def
thf(fact_1095_insert__compr,axiom,
    ( insert_o
    = ( ^ [A2: $o,B4: set_o] :
          ( collect_o
          @ ^ [X2: $o] :
              ( ( X2 = A2 )
              | ( member_o @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1096_insert__compr,axiom,
    ( insert_b
    = ( ^ [A2: b,B4: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( X2 = A2 )
              | ( member_b @ X2 @ B4 ) ) ) ) ) ).

% insert_compr
thf(fact_1097_insert__Collect,axiom,
    ! [A: $o,P4: $o > $o] :
      ( ( insert_o @ A @ ( collect_o @ P4 ) )
      = ( collect_o
        @ ^ [U2: $o] :
            ( ( U2 != A )
           => ( P4 @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_1098_Int__insert__right,axiom,
    ! [A: $o,A3: set_o,B: set_o] :
      ( ( ( member_o @ A @ A3 )
       => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A @ B ) )
          = ( insert_o @ A @ ( inf_inf_set_o @ A3 @ B ) ) ) )
      & ( ~ ( member_o @ A @ A3 )
       => ( ( inf_inf_set_o @ A3 @ ( insert_o @ A @ B ) )
          = ( inf_inf_set_o @ A3 @ B ) ) ) ) ).

% Int_insert_right
thf(fact_1099_Int__insert__right,axiom,
    ! [A: b,A3: set_b,B: set_b] :
      ( ( ( member_b @ A @ A3 )
       => ( ( inf_inf_set_b @ A3 @ ( insert_b @ A @ B ) )
          = ( insert_b @ A @ ( inf_inf_set_b @ A3 @ B ) ) ) )
      & ( ~ ( member_b @ A @ A3 )
       => ( ( inf_inf_set_b @ A3 @ ( insert_b @ A @ B ) )
          = ( inf_inf_set_b @ A3 @ B ) ) ) ) ).

% Int_insert_right
thf(fact_1100_Int__insert__left,axiom,
    ! [A: $o,C2: set_o,B: set_o] :
      ( ( ( member_o @ A @ C2 )
       => ( ( inf_inf_set_o @ ( insert_o @ A @ B ) @ C2 )
          = ( insert_o @ A @ ( inf_inf_set_o @ B @ C2 ) ) ) )
      & ( ~ ( member_o @ A @ C2 )
       => ( ( inf_inf_set_o @ ( insert_o @ A @ B ) @ C2 )
          = ( inf_inf_set_o @ B @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1101_Int__insert__left,axiom,
    ! [A: b,C2: set_b,B: set_b] :
      ( ( ( member_b @ A @ C2 )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C2 )
          = ( insert_b @ A @ ( inf_inf_set_b @ B @ C2 ) ) ) )
      & ( ~ ( member_b @ A @ C2 )
       => ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C2 )
          = ( inf_inf_set_b @ B @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_1102_subset__insertI2,axiom,
    ! [A3: set_o,B: set_o,B2: $o] :
      ( ( ord_less_eq_set_o @ A3 @ B )
     => ( ord_less_eq_set_o @ A3 @ ( insert_o @ B2 @ B ) ) ) ).

% subset_insertI2
thf(fact_1103_subset__insertI,axiom,
    ! [B: set_o,A: $o] : ( ord_less_eq_set_o @ B @ ( insert_o @ A @ B ) ) ).

% subset_insertI
thf(fact_1104_subset__insert,axiom,
    ! [X3: $o,A3: set_o,B: set_o] :
      ( ~ ( member_o @ X3 @ A3 )
     => ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X3 @ B ) )
        = ( ord_less_eq_set_o @ A3 @ B ) ) ) ).

% subset_insert
thf(fact_1105_subset__insert,axiom,
    ! [X3: b,A3: set_b,B: set_b] :
      ( ~ ( member_b @ X3 @ A3 )
     => ( ( ord_less_eq_set_b @ A3 @ ( insert_b @ X3 @ B ) )
        = ( ord_less_eq_set_b @ A3 @ B ) ) ) ).

% subset_insert
thf(fact_1106_insert__mono,axiom,
    ! [C2: set_o,D2: set_o,A: $o] :
      ( ( ord_less_eq_set_o @ C2 @ D2 )
     => ( ord_less_eq_set_o @ ( insert_o @ A @ C2 ) @ ( insert_o @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_1107_Collect__conv__if,axiom,
    ! [P4: $o > $o,A: $o] :
      ( ( ( P4 @ A )
       => ( ( collect_o
            @ ^ [X2: $o] :
                ( ( X2 = A )
                & ( P4 @ X2 ) ) )
          = ( insert_o @ A @ bot_bot_set_o ) ) )
      & ( ~ ( P4 @ A )
       => ( ( collect_o
            @ ^ [X2: $o] :
                ( ( X2 = A )
                & ( P4 @ X2 ) ) )
          = bot_bot_set_o ) ) ) ).

% Collect_conv_if
thf(fact_1108_Collect__conv__if2,axiom,
    ! [P4: $o > $o,A: $o] :
      ( ( ( P4 @ A )
       => ( ( collect_o
            @ ^ [X2: $o] :
                ( ( A = X2 )
                & ( P4 @ X2 ) ) )
          = ( insert_o @ A @ bot_bot_set_o ) ) )
      & ( ~ ( P4 @ A )
       => ( ( collect_o
            @ ^ [X2: $o] :
                ( ( A = X2 )
                & ( P4 @ X2 ) ) )
          = bot_bot_set_o ) ) ) ).

% Collect_conv_if2
thf(fact_1109_subset__singletonD,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) )
     => ( ( A3 = bot_bot_set_o )
        | ( A3
          = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).

% subset_singletonD
thf(fact_1110_subset__singleton__iff,axiom,
    ! [X5: set_o,A: $o] :
      ( ( ord_less_eq_set_o @ X5 @ ( insert_o @ A @ bot_bot_set_o ) )
      = ( ( X5 = bot_bot_set_o )
        | ( X5
          = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).

% subset_singleton_iff
thf(fact_1111_consistent__consequent,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( member6642669571620171971c_fm_a @ P @ V4 )
       => ( ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A3 @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V4 ) ) ) ) ) ).

% consistent_consequent
thf(fact_1112_consistent__consequent_H,axiom,
    ! [A3: epistemic_fm_a > $o,V4: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A3 @ V4 )
     => ( ( member6642669571620171971c_fm_a @ P @ V4 )
       => ( ! [G3: list_char > $o,H3: epistemic_fm_a > $o] : ( epistemic_eval_a @ G3 @ H3 @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A3 @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V4 ) ) ) ) ) ).

% consistent_consequent'
thf(fact_1113_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_1114_boolean__algebra_Ocomplement__unique,axiom,
    ! [A: set_o,X3: set_o,Y2: set_o] :
      ( ( ( inf_inf_set_o @ A @ X3 )
        = bot_bot_set_o )
     => ( ( ( sup_sup_set_o @ A @ X3 )
          = top_top_set_o )
       => ( ( ( inf_inf_set_o @ A @ Y2 )
            = bot_bot_set_o )
         => ( ( ( sup_sup_set_o @ A @ Y2 )
              = top_top_set_o )
           => ( X3 = Y2 ) ) ) ) ) ).

% boolean_algebra.complement_unique
thf(fact_1115_exists__finite__inconsistent,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,V4: set_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A3 @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V4 ) )
     => ~ ! [W8: 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 ) @ W8 ) @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V4 ) )
           => ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ W8 )
             => ( ( finite3304564945125563331c_fm_a @ W8 )
               => ( episte2285483198712856226tent_a @ A3 @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W8 ) ) ) ) ) ) ).

% exists_finite_inconsistent
thf(fact_1116_inconsistent__imply,axiom,
    ! [A3: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A3 @ ( 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 @ A3 @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% inconsistent_imply
thf(fact_1117_the__elem__eq,axiom,
    ! [X3: $o] :
      ( ( the_elem_o @ ( insert_o @ X3 @ bot_bot_set_o ) )
      = X3 ) ).

% the_elem_eq
thf(fact_1118_is__singletonI,axiom,
    ! [X3: $o] : ( is_singleton_o @ ( insert_o @ X3 @ bot_bot_set_o ) ) ).

% is_singletonI
thf(fact_1119_subset__singleton__iff__Uniq,axiom,
    ! [A3: set_b] :
      ( ( ? [A2: b] : ( ord_less_eq_set_b @ A3 @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
      = ( uniq_b
        @ ^ [X2: b] : ( member_b @ X2 @ A3 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1120_subset__singleton__iff__Uniq,axiom,
    ! [A3: set_o] :
      ( ( ? [A2: $o] : ( ord_less_eq_set_o @ A3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
      = ( uniq_o
        @ ^ [X2: $o] : ( member_o @ X2 @ A3 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1121_is__singletonE,axiom,
    ! [A3: set_o] :
      ( ( is_singleton_o @ A3 )
     => ~ ! [X: $o] :
            ( A3
           != ( insert_o @ X @ bot_bot_set_o ) ) ) ).

% is_singletonE
thf(fact_1122_sup__set__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ( sup_sup_b_o
            @ ^ [X2: b] : ( member_b @ X2 @ A4 )
            @ ^ [X2: b] : ( member_b @ X2 @ B4 ) ) ) ) ) ).

% sup_set_def
thf(fact_1123_is__singleton__the__elem,axiom,
    ( is_singleton_o
    = ( ^ [A4: set_o] :
          ( A4
          = ( insert_o @ ( the_elem_o @ A4 ) @ bot_bot_set_o ) ) ) ) ).

% is_singleton_the_elem
thf(fact_1124_is__singletonI_H,axiom,
    ! [A3: set_b] :
      ( ( A3 != bot_bot_set_b )
     => ( ! [X: b,Y3: b] :
            ( ( member_b @ X @ A3 )
           => ( ( member_b @ Y3 @ A3 )
             => ( X = Y3 ) ) )
       => ( is_singleton_b @ A3 ) ) ) ).

% is_singletonI'
thf(fact_1125_is__singletonI_H,axiom,
    ! [A3: set_o] :
      ( ( A3 != bot_bot_set_o )
     => ( ! [X: $o,Y3: $o] :
            ( ( member_o @ X @ A3 )
           => ( ( member_o @ Y3 @ A3 )
             => ( X = Y3 ) ) )
       => ( is_singleton_o @ A3 ) ) ) ).

% is_singletonI'
thf(fact_1126_is__singleton__def,axiom,
    ( is_singleton_o
    = ( ^ [A4: set_o] :
        ? [X2: $o] :
          ( A4
          = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).

% is_singleton_def
thf(fact_1127_the__elem__def,axiom,
    ( the_elem_o
    = ( ^ [X6: set_o] :
          ( the_o
          @ ^ [X2: $o] :
              ( X6
              = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) ).

% the_elem_def
thf(fact_1128_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( inf_inf_set_o @ X3 @ Y2 )
        = bot_bot_set_o )
     => ( ( ( sup_sup_set_o @ X3 @ Y2 )
          = top_top_set_o )
       => ( ( uminus_uminus_set_o @ X3 )
          = Y2 ) ) ) ).

% boolean_algebra_class.boolean_algebra.compl_unique
thf(fact_1129_Compl__disjoint2,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A3 ) @ A3 )
      = bot_bot_set_o ) ).

% Compl_disjoint2
thf(fact_1130_Compl__disjoint,axiom,
    ! [A3: set_o] :
      ( ( inf_inf_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
      = bot_bot_set_o ) ).

% Compl_disjoint
thf(fact_1131_boolean__algebra_Ocompl__zero,axiom,
    ( ( uminus_uminus_set_o @ bot_bot_set_o )
    = top_top_set_o ) ).

% boolean_algebra.compl_zero
thf(fact_1132_boolean__algebra_Ocompl__one,axiom,
    ( ( uminus_uminus_set_o @ top_top_set_o )
    = bot_bot_set_o ) ).

% boolean_algebra.compl_one
thf(fact_1133_inf__compl__bot__left1,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X3 ) @ ( inf_inf_set_o @ X3 @ Y2 ) )
      = bot_bot_set_o ) ).

% inf_compl_bot_left1
thf(fact_1134_inf__compl__bot__left2,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X3 ) @ Y2 ) )
      = bot_bot_set_o ) ).

% inf_compl_bot_left2
thf(fact_1135_inf__compl__bot__right,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( inf_inf_set_o @ Y2 @ ( uminus_uminus_set_o @ X3 ) ) )
      = bot_bot_set_o ) ).

% inf_compl_bot_right
thf(fact_1136_boolean__algebra_Oconj__cancel__left,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X3 ) @ X3 )
      = bot_bot_set_o ) ).

% boolean_algebra.conj_cancel_left
thf(fact_1137_boolean__algebra_Oconj__cancel__right,axiom,
    ! [X3: set_o] :
      ( ( inf_inf_set_o @ X3 @ ( uminus_uminus_set_o @ X3 ) )
      = bot_bot_set_o ) ).

% boolean_algebra.conj_cancel_right
thf(fact_1138_subset__Compl__singleton,axiom,
    ! [A3: set_b,B2: b] :
      ( ( ord_less_eq_set_b @ A3 @ ( uminus_uminus_set_b @ ( insert_b @ B2 @ bot_bot_set_b ) ) )
      = ( ~ ( member_b @ B2 @ A3 ) ) ) ).

% subset_Compl_singleton
thf(fact_1139_subset__Compl__singleton,axiom,
    ! [A3: set_o,B2: $o] :
      ( ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ ( insert_o @ B2 @ bot_bot_set_o ) ) )
      = ( ~ ( member_o @ B2 @ A3 ) ) ) ).

% subset_Compl_singleton
thf(fact_1140_sup__compl__top__left1,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X3 ) @ ( sup_sup_set_o @ X3 @ Y2 ) )
      = top_top_set_o ) ).

% sup_compl_top_left1
thf(fact_1141_sup__compl__top__left2,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( sup_sup_set_o @ X3 @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X3 ) @ Y2 ) )
      = top_top_set_o ) ).

% sup_compl_top_left2
thf(fact_1142_boolean__algebra_Odisj__cancel__left,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X3 ) @ X3 )
      = top_top_set_o ) ).

% boolean_algebra.disj_cancel_left
thf(fact_1143_boolean__algebra_Odisj__cancel__right,axiom,
    ! [X3: set_o] :
      ( ( sup_sup_set_o @ X3 @ ( uminus_uminus_set_o @ X3 ) )
      = top_top_set_o ) ).

% boolean_algebra.disj_cancel_right
thf(fact_1144_Compl__empty__eq,axiom,
    ( ( uminus_uminus_set_o @ bot_bot_set_o )
    = top_top_set_o ) ).

% Compl_empty_eq
thf(fact_1145_Compl__UNIV__eq,axiom,
    ( ( uminus_uminus_set_o @ top_top_set_o )
    = bot_bot_set_o ) ).

% Compl_UNIV_eq
thf(fact_1146_inf__cancel__left1,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ X3 @ A ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X3 ) @ B2 ) )
      = bot_bot_set_o ) ).

% inf_cancel_left1
thf(fact_1147_inf__cancel__left2,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X3 ) @ A ) @ ( inf_inf_set_o @ X3 @ B2 ) )
      = bot_bot_set_o ) ).

% inf_cancel_left2
thf(fact_1148_sup__cancel__left1,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( sup_sup_set_o @ ( sup_sup_set_o @ X3 @ A ) @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X3 ) @ B2 ) )
      = top_top_set_o ) ).

% sup_cancel_left1
thf(fact_1149_sup__cancel__left2,axiom,
    ! [X3: set_o,A: set_o,B2: set_o] :
      ( ( sup_sup_set_o @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X3 ) @ A ) @ ( sup_sup_set_o @ X3 @ B2 ) )
      = top_top_set_o ) ).

% sup_cancel_left2
thf(fact_1150_subset__Compl__self__eq,axiom,
    ! [A3: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
      = ( A3 = bot_bot_set_o ) ) ).

% subset_Compl_self_eq
thf(fact_1151_Compl__partition,axiom,
    ! [A3: set_o] :
      ( ( sup_sup_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
      = top_top_set_o ) ).

% Compl_partition
thf(fact_1152_Compl__partition2,axiom,
    ! [A3: set_o] :
      ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ A3 ) @ A3 )
      = top_top_set_o ) ).

% Compl_partition2
thf(fact_1153_inf__shunt,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( inf_inf_set_o @ X3 @ Y2 )
        = bot_bot_set_o )
      = ( ord_less_eq_set_o @ X3 @ ( uminus_uminus_set_o @ Y2 ) ) ) ).

% inf_shunt
thf(fact_1154_sup__shunt,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( sup_sup_set_o @ X3 @ Y2 )
        = top_top_set_o )
      = ( ord_less_eq_set_o @ ( uminus_uminus_set_o @ X3 ) @ Y2 ) ) ).

% sup_shunt
thf(fact_1155_disjoint__eq__subset__Compl,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = bot_bot_set_o )
      = ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ B ) ) ) ).

% disjoint_eq_subset_Compl
thf(fact_1156_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
    boolea379910186789422830_set_o @ inf_inf_set_o @ sup_sup_set_o @ uminus_uminus_set_o @ bot_bot_set_o @ top_top_set_o ).

% boolean_algebra.abstract_boolean_algebra_axioms
thf(fact_1157_range__constant,axiom,
    ! [X3: $o] :
      ( ( image_o_o
        @ ^ [Uu2: $o] : X3
        @ top_top_set_o )
      = ( insert_o @ X3 @ bot_bot_set_o ) ) ).

% range_constant
thf(fact_1158_image__eqI,axiom,
    ! [B2: b,F2: b > b,X3: b,A3: set_b] :
      ( ( B2
        = ( F2 @ X3 ) )
     => ( ( member_b @ X3 @ A3 )
       => ( member_b @ B2 @ ( image_b_b @ F2 @ A3 ) ) ) ) ).

% image_eqI
thf(fact_1159_Compl__iff,axiom,
    ! [C: b,A3: set_b] :
      ( ( member_b @ C @ ( uminus_uminus_set_b @ A3 ) )
      = ( ~ ( member_b @ C @ A3 ) ) ) ).

% Compl_iff
thf(fact_1160_ComplI,axiom,
    ! [C: b,A3: set_b] :
      ( ~ ( member_b @ C @ A3 )
     => ( member_b @ C @ ( uminus_uminus_set_b @ A3 ) ) ) ).

% ComplI
thf(fact_1161_image__is__empty,axiom,
    ! [F2: $o > $o,A3: set_o] :
      ( ( ( image_o_o @ F2 @ A3 )
        = bot_bot_set_o )
      = ( A3 = bot_bot_set_o ) ) ).

% image_is_empty
thf(fact_1162_empty__is__image,axiom,
    ! [F2: $o > $o,A3: set_o] :
      ( ( bot_bot_set_o
        = ( image_o_o @ F2 @ A3 ) )
      = ( A3 = bot_bot_set_o ) ) ).

% empty_is_image
thf(fact_1163_image__empty,axiom,
    ! [F2: $o > $o] :
      ( ( image_o_o @ F2 @ bot_bot_set_o )
      = bot_bot_set_o ) ).

% image_empty
thf(fact_1164_insert__image,axiom,
    ! [X3: b,A3: set_b,F2: b > $o] :
      ( ( member_b @ X3 @ A3 )
     => ( ( insert_o @ ( F2 @ X3 ) @ ( image_b_o @ F2 @ A3 ) )
        = ( image_b_o @ F2 @ A3 ) ) ) ).

% insert_image
thf(fact_1165_image__insert,axiom,
    ! [F2: $o > $o,A: $o,B: set_o] :
      ( ( image_o_o @ F2 @ ( insert_o @ A @ B ) )
      = ( insert_o @ ( F2 @ A ) @ ( image_o_o @ F2 @ B ) ) ) ).

% image_insert
thf(fact_1166_ComplD,axiom,
    ! [C: b,A3: set_b] :
      ( ( member_b @ C @ ( uminus_uminus_set_b @ A3 ) )
     => ~ ( member_b @ C @ A3 ) ) ).

% ComplD
thf(fact_1167_Compl__eq,axiom,
    ( uminus_uminus_set_b
    = ( ^ [A4: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ~ ( member_b @ X2 @ A4 ) ) ) ) ).

% Compl_eq
thf(fact_1168_uminus__set__def,axiom,
    ( uminus_uminus_set_b
    = ( ^ [A4: set_b] :
          ( collect_b
          @ ( uminus_uminus_b_o
            @ ^ [X2: b] : ( member_b @ X2 @ A4 ) ) ) ) ) ).

% uminus_set_def
thf(fact_1169_Compr__image__eq,axiom,
    ! [F2: b > b,A3: set_b,P4: b > $o] :
      ( ( collect_b
        @ ^ [X2: b] :
            ( ( member_b @ X2 @ ( image_b_b @ F2 @ A3 ) )
            & ( P4 @ X2 ) ) )
      = ( image_b_b @ F2
        @ ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ A3 )
              & ( P4 @ ( F2 @ X2 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_1170_imageE,axiom,
    ! [B2: b,F2: b > b,A3: set_b] :
      ( ( member_b @ B2 @ ( image_b_b @ F2 @ A3 ) )
     => ~ ! [X: b] :
            ( ( B2
              = ( F2 @ X ) )
           => ~ ( member_b @ X @ A3 ) ) ) ).

% imageE
thf(fact_1171_imageI,axiom,
    ! [X3: b,A3: set_b,F2: b > b] :
      ( ( member_b @ X3 @ A3 )
     => ( member_b @ ( F2 @ X3 ) @ ( image_b_b @ F2 @ A3 ) ) ) ).

% imageI
thf(fact_1172_rev__image__eqI,axiom,
    ! [X3: b,A3: set_b,B2: b,F2: b > b] :
      ( ( member_b @ X3 @ A3 )
     => ( ( B2
          = ( F2 @ X3 ) )
       => ( member_b @ B2 @ ( image_b_b @ F2 @ A3 ) ) ) ) ).

% rev_image_eqI
thf(fact_1173_image__subsetI,axiom,
    ! [A3: set_b,F2: b > b,B: set_b] :
      ( ! [X: b] :
          ( ( member_b @ X @ A3 )
         => ( member_b @ ( F2 @ X ) @ B ) )
     => ( ord_less_eq_set_b @ ( image_b_b @ F2 @ A3 ) @ B ) ) ).

% image_subsetI
thf(fact_1174_range__eqI,axiom,
    ! [B2: b,F2: $o > b,X3: $o] :
      ( ( B2
        = ( F2 @ X3 ) )
     => ( member_b @ B2 @ ( image_o_b @ F2 @ top_top_set_o ) ) ) ).

% range_eqI
thf(fact_1175_rangeI,axiom,
    ! [F2: $o > b,X3: $o] : ( member_b @ ( F2 @ X3 ) @ ( image_o_b @ F2 @ top_top_set_o ) ) ).

% rangeI
thf(fact_1176_rangeE,axiom,
    ! [B2: b,F2: $o > b] :
      ( ( member_b @ B2 @ ( image_o_b @ F2 @ top_top_set_o ) )
     => ~ ! [X: $o] :
            ( B2
           != ( F2 @ X ) ) ) ).

% rangeE
thf(fact_1177_range__subsetD,axiom,
    ! [F2: $o > b,B: set_b,I3: $o] :
      ( ( ord_less_eq_set_b @ ( image_o_b @ F2 @ top_top_set_o ) @ B )
     => ( member_b @ ( F2 @ I3 ) @ B ) ) ).

% range_subsetD
thf(fact_1178_image__constant,axiom,
    ! [X3: b,A3: set_b,C: $o] :
      ( ( member_b @ X3 @ A3 )
     => ( ( image_b_o
          @ ^ [X2: b] : C
          @ A3 )
        = ( insert_o @ C @ bot_bot_set_o ) ) ) ).

% image_constant
thf(fact_1179_image__constant__conv,axiom,
    ! [A3: set_o,C: $o] :
      ( ( ( A3 = bot_bot_set_o )
       => ( ( image_o_o
            @ ^ [X2: $o] : C
            @ A3 )
          = bot_bot_set_o ) )
      & ( ( A3 != bot_bot_set_o )
       => ( ( image_o_o
            @ ^ [X2: $o] : C
            @ A3 )
          = ( insert_o @ C @ bot_bot_set_o ) ) ) ) ).

% image_constant_conv
thf(fact_1180_range__eq__singletonD,axiom,
    ! [F2: $o > $o,A: $o,X3: $o] :
      ( ( ( image_o_o @ F2 @ top_top_set_o )
        = ( insert_o @ A @ bot_bot_set_o ) )
     => ( ( F2 @ X3 )
        = A ) ) ).

% range_eq_singletonD
thf(fact_1181_empty__bind,axiom,
    ! [F2: $o > set_o] :
      ( ( bind_o_o @ bot_bot_set_o @ F2 )
      = bot_bot_set_o ) ).

% empty_bind
thf(fact_1182_insert__partition,axiom,
    ! [X3: set_o,F4: set_set_o] :
      ( ~ ( member_set_o @ X3 @ F4 )
     => ( ! [X: set_o] :
            ( ( member_set_o @ X @ ( insert_set_o @ X3 @ F4 ) )
           => ! [Xa: set_o] :
                ( ( member_set_o @ Xa @ ( insert_set_o @ X3 @ F4 ) )
               => ( ( X != Xa )
                 => ( ( inf_inf_set_o @ X @ Xa )
                    = bot_bot_set_o ) ) ) )
       => ( ( inf_inf_set_o @ X3 @ ( comple90263536869209701_set_o @ F4 ) )
          = bot_bot_set_o ) ) ) ).

% insert_partition
thf(fact_1183_bind__const,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( A3 = bot_bot_set_o )
       => ( ( bind_o_o @ A3
            @ ^ [Uu2: $o] : B )
          = bot_bot_set_o ) )
      & ( ( A3 != bot_bot_set_o )
       => ( ( bind_o_o @ A3
            @ ^ [Uu2: $o] : B )
          = B ) ) ) ).

% bind_const
thf(fact_1184_Union__disjoint,axiom,
    ! [C2: set_set_o,A3: set_o] :
      ( ( ( inf_inf_set_o @ ( comple90263536869209701_set_o @ C2 ) @ A3 )
        = bot_bot_set_o )
      = ( ! [X2: set_o] :
            ( ( member_set_o @ X2 @ C2 )
           => ( ( inf_inf_set_o @ X2 @ A3 )
              = bot_bot_set_o ) ) ) ) ).

% Union_disjoint
thf(fact_1185_Sup__inf__eq__bot__iff,axiom,
    ! [B: set_set_o,A: set_o] :
      ( ( ( inf_inf_set_o @ ( comple90263536869209701_set_o @ B ) @ A )
        = bot_bot_set_o )
      = ( ! [X2: set_o] :
            ( ( member_set_o @ X2 @ B )
           => ( ( inf_inf_set_o @ X2 @ A )
              = bot_bot_set_o ) ) ) ) ).

% Sup_inf_eq_bot_iff
thf(fact_1186_INT__simps_I1_J,axiom,
    ! [C2: set_o,A3: $o > set_o,B: set_o] :
      ( ( ( C2 = bot_bot_set_o )
       => ( ( comple3063163877087187839_set_o
            @ ( image_o_set_o
              @ ^ [X2: $o] : ( inf_inf_set_o @ ( A3 @ X2 ) @ B )
              @ C2 ) )
          = top_top_set_o ) )
      & ( ( C2 != bot_bot_set_o )
       => ( ( comple3063163877087187839_set_o
            @ ( image_o_set_o
              @ ^ [X2: $o] : ( inf_inf_set_o @ ( A3 @ X2 ) @ B )
              @ C2 ) )
          = ( inf_inf_set_o @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ A3 @ C2 ) ) @ B ) ) ) ) ).

% INT_simps(1)
thf(fact_1187_INT__simps_I2_J,axiom,
    ! [C2: set_o,A3: set_o,B: $o > set_o] :
      ( ( ( C2 = bot_bot_set_o )
       => ( ( comple3063163877087187839_set_o
            @ ( image_o_set_o
              @ ^ [X2: $o] : ( inf_inf_set_o @ A3 @ ( B @ X2 ) )
              @ C2 ) )
          = top_top_set_o ) )
      & ( ( C2 != bot_bot_set_o )
       => ( ( comple3063163877087187839_set_o
            @ ( image_o_set_o
              @ ^ [X2: $o] : ( inf_inf_set_o @ A3 @ ( B @ X2 ) )
              @ C2 ) )
          = ( inf_inf_set_o @ A3 @ ( comple3063163877087187839_set_o @ ( image_o_set_o @ B @ C2 ) ) ) ) ) ) ).

% INT_simps(2)
thf(fact_1188_Inf__insert,axiom,
    ! [A: $o,A3: set_o] :
      ( ( complete_Inf_Inf_o @ ( insert_o @ A @ A3 ) )
      = ( inf_inf_o @ A @ ( complete_Inf_Inf_o @ A3 ) ) ) ).

% Inf_insert
thf(fact_1189_finite__Inf__in,axiom,
    ! [A3: set_o] :
      ( ( finite_finite_o @ A3 )
     => ( ( A3 != bot_bot_set_o )
       => ( ! [X: $o,Y3: $o] :
              ( ( member_o @ X @ A3 )
             => ( ( member_o @ Y3 @ A3 )
               => ( member_o @ ( inf_inf_o @ X @ Y3 ) @ A3 ) ) )
         => ( member_o @ ( complete_Inf_Inf_o @ A3 ) @ A3 ) ) ) ) ).

% finite_Inf_in
thf(fact_1190_vimage__eq,axiom,
    ! [A: b,F2: b > b,B: set_b] :
      ( ( member_b @ A @ ( vimage_b_b @ F2 @ B ) )
      = ( member_b @ ( F2 @ A ) @ B ) ) ).

% vimage_eq
thf(fact_1191_vimageI,axiom,
    ! [F2: b > b,A: b,B2: b,B: set_b] :
      ( ( ( F2 @ A )
        = B2 )
     => ( ( member_b @ B2 @ B )
       => ( member_b @ A @ ( vimage_b_b @ F2 @ B ) ) ) ) ).

% vimageI
thf(fact_1192_vimage__UNIV,axiom,
    ! [F2: $o > $o] :
      ( ( vimage_o_o @ F2 @ top_top_set_o )
      = top_top_set_o ) ).

% vimage_UNIV
thf(fact_1193_vimage__empty,axiom,
    ! [F2: $o > $o] :
      ( ( vimage_o_o @ F2 @ bot_bot_set_o )
      = bot_bot_set_o ) ).

% vimage_empty
thf(fact_1194_vimage__const,axiom,
    ! [C: b,A3: set_b] :
      ( ( ( member_b @ C @ A3 )
       => ( ( vimage_o_b
            @ ^ [X2: $o] : C
            @ A3 )
          = top_top_set_o ) )
      & ( ~ ( member_b @ C @ A3 )
       => ( ( vimage_o_b
            @ ^ [X2: $o] : C
            @ A3 )
          = bot_bot_set_o ) ) ) ).

% vimage_const
thf(fact_1195_vimage__if,axiom,
    ! [C: b,A3: set_b,D: b,B: set_b] :
      ( ( ( member_b @ C @ A3 )
       => ( ( ( member_b @ D @ A3 )
           => ( ( vimage_b_b
                @ ^ [X2: b] : ( if_b @ ( member_b @ X2 @ B ) @ C @ D )
                @ A3 )
              = top_top_set_b ) )
          & ( ~ ( member_b @ D @ A3 )
           => ( ( vimage_b_b
                @ ^ [X2: b] : ( if_b @ ( member_b @ X2 @ B ) @ C @ D )
                @ A3 )
              = B ) ) ) )
      & ( ~ ( member_b @ C @ A3 )
       => ( ( ( member_b @ D @ A3 )
           => ( ( vimage_b_b
                @ ^ [X2: b] : ( if_b @ ( member_b @ X2 @ B ) @ C @ D )
                @ A3 )
              = ( uminus_uminus_set_b @ B ) ) )
          & ( ~ ( member_b @ D @ A3 )
           => ( ( vimage_b_b
                @ ^ [X2: b] : ( if_b @ ( member_b @ X2 @ B ) @ C @ D )
                @ A3 )
              = bot_bot_set_b ) ) ) ) ) ).

% vimage_if
thf(fact_1196_vimage__if,axiom,
    ! [C: b,A3: set_b,D: b,B: set_o] :
      ( ( ( member_b @ C @ A3 )
       => ( ( ( member_b @ D @ A3 )
           => ( ( vimage_o_b
                @ ^ [X2: $o] : ( if_b @ ( member_o @ X2 @ B ) @ C @ D )
                @ A3 )
              = top_top_set_o ) )
          & ( ~ ( member_b @ D @ A3 )
           => ( ( vimage_o_b
                @ ^ [X2: $o] : ( if_b @ ( member_o @ X2 @ B ) @ C @ D )
                @ A3 )
              = B ) ) ) )
      & ( ~ ( member_b @ C @ A3 )
       => ( ( ( member_b @ D @ A3 )
           => ( ( vimage_o_b
                @ ^ [X2: $o] : ( if_b @ ( member_o @ X2 @ B ) @ C @ D )
                @ A3 )
              = ( uminus_uminus_set_o @ B ) ) )
          & ( ~ ( member_b @ D @ A3 )
           => ( ( vimage_o_b
                @ ^ [X2: $o] : ( if_b @ ( member_o @ X2 @ B ) @ C @ D )
                @ A3 )
              = bot_bot_set_o ) ) ) ) ) ).

% vimage_if
thf(fact_1197_UNIV__bool,axiom,
    ( top_top_set_o
    = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).

% UNIV_bool
thf(fact_1198_vimage__singleton__eq,axiom,
    ! [A: b,F2: b > $o,B2: $o] :
      ( ( member_b @ A @ ( vimage_b_o @ F2 @ ( insert_o @ B2 @ bot_bot_set_o ) ) )
      = ( ( F2 @ A )
        = B2 ) ) ).

% vimage_singleton_eq
thf(fact_1199_vimageI2,axiom,
    ! [F2: b > b,A: b,A3: set_b] :
      ( ( member_b @ ( F2 @ A ) @ A3 )
     => ( member_b @ A @ ( vimage_b_b @ F2 @ A3 ) ) ) ).

% vimageI2
thf(fact_1200_vimageE,axiom,
    ! [A: b,F2: b > b,B: set_b] :
      ( ( member_b @ A @ ( vimage_b_b @ F2 @ B ) )
     => ( member_b @ ( F2 @ A ) @ B ) ) ).

% vimageE
thf(fact_1201_vimageD,axiom,
    ! [A: b,F2: b > b,A3: set_b] :
      ( ( member_b @ A @ ( vimage_b_b @ F2 @ A3 ) )
     => ( member_b @ ( F2 @ A ) @ A3 ) ) ).

% vimageD
thf(fact_1202_inj__on__vimage__singleton,axiom,
    ! [F2: b > $o,A3: set_b,A: $o] :
      ( ( inj_on_b_o @ F2 @ A3 )
     => ( ord_less_eq_set_b @ ( inf_inf_set_b @ ( vimage_b_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ A3 )
        @ ( insert_b
          @ ( the_b
            @ ^ [X2: b] :
                ( ( member_b @ X2 @ A3 )
                & ( ( F2 @ X2 )
                  = A ) ) )
          @ bot_bot_set_b ) ) ) ).

% inj_on_vimage_singleton
thf(fact_1203_inj__on__vimage__singleton,axiom,
    ! [F2: $o > $o,A3: set_o,A: $o] :
      ( ( inj_on_o_o @ F2 @ A3 )
     => ( ord_less_eq_set_o @ ( inf_inf_set_o @ ( vimage_o_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ A3 )
        @ ( insert_o
          @ ( the_o
            @ ^ [X2: $o] :
                ( ( member_o @ X2 @ A3 )
                & ( ( F2 @ X2 )
                  = A ) ) )
          @ bot_bot_set_o ) ) ) ).

% inj_on_vimage_singleton
thf(fact_1204_Pow__empty,axiom,
    ( ( pow_o @ bot_bot_set_o )
    = ( insert_set_o @ bot_bot_set_o @ bot_bot_set_set_o ) ) ).

% Pow_empty
thf(fact_1205_Pow__UNIV,axiom,
    ( ( pow_o @ top_top_set_o )
    = top_top_set_set_o ) ).

% Pow_UNIV
thf(fact_1206_Pow__singleton__iff,axiom,
    ! [X5: set_o,Y5: set_o] :
      ( ( ( pow_o @ X5 )
        = ( insert_set_o @ Y5 @ bot_bot_set_set_o ) )
      = ( ( X5 = bot_bot_set_o )
        & ( Y5 = bot_bot_set_o ) ) ) ).

% Pow_singleton_iff
thf(fact_1207_Pow__bottom,axiom,
    ! [B: set_o] : ( member_set_o @ bot_bot_set_o @ ( pow_o @ B ) ) ).

% Pow_bottom
thf(fact_1208_inj__on__disjoint__Un,axiom,
    ! [F2: b > $o,A3: set_b,G2: b > $o,B: set_b] :
      ( ( inj_on_b_o @ F2 @ A3 )
     => ( ( inj_on_b_o @ G2 @ B )
       => ( ( ( inf_inf_set_o @ ( image_b_o @ F2 @ A3 ) @ ( image_b_o @ G2 @ B ) )
            = bot_bot_set_o )
         => ( inj_on_b_o
            @ ^ [X2: b] :
                ( ( ( member_b @ X2 @ A3 )
                 => ( F2 @ X2 ) )
                & ( ~ ( member_b @ X2 @ A3 )
                 => ( G2 @ X2 ) ) )
            @ ( sup_sup_set_b @ A3 @ B ) ) ) ) ) ).

% inj_on_disjoint_Un
thf(fact_1209_Pow__insert,axiom,
    ! [A: $o,A3: set_o] :
      ( ( pow_o @ ( insert_o @ A @ A3 ) )
      = ( sup_sup_set_set_o @ ( pow_o @ A3 ) @ ( image_set_o_set_o @ ( insert_o @ A ) @ ( pow_o @ A3 ) ) ) ) ).

% Pow_insert
thf(fact_1210_Inf__fold__inf,axiom,
    ! [A3: set_set_o] :
      ( ( finite_finite_set_o @ A3 )
     => ( ( comple3063163877087187839_set_o @ A3 )
        = ( finite4337638375924247368_set_o @ inf_inf_set_o @ top_top_set_o @ A3 ) ) ) ).

% Inf_fold_inf
thf(fact_1211_Diff__iff,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A3 @ B ) )
      = ( ( member_b @ C @ A3 )
        & ~ ( member_b @ C @ B ) ) ) ).

% Diff_iff
thf(fact_1212_DiffI,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ A3 )
     => ( ~ ( member_b @ C @ B )
       => ( member_b @ C @ ( minus_minus_set_b @ A3 @ B ) ) ) ) ).

% DiffI
thf(fact_1213_Diff__empty,axiom,
    ! [A3: set_o] :
      ( ( minus_minus_set_o @ A3 @ bot_bot_set_o )
      = A3 ) ).

% Diff_empty
thf(fact_1214_empty__Diff,axiom,
    ! [A3: set_o] :
      ( ( minus_minus_set_o @ bot_bot_set_o @ A3 )
      = bot_bot_set_o ) ).

% empty_Diff
thf(fact_1215_Diff__cancel,axiom,
    ! [A3: set_o] :
      ( ( minus_minus_set_o @ A3 @ A3 )
      = bot_bot_set_o ) ).

% Diff_cancel
thf(fact_1216_Diff__insert0,axiom,
    ! [X3: $o,A3: set_o,B: set_o] :
      ( ~ ( member_o @ X3 @ A3 )
     => ( ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ B ) )
        = ( minus_minus_set_o @ A3 @ B ) ) ) ).

% Diff_insert0
thf(fact_1217_Diff__insert0,axiom,
    ! [X3: b,A3: set_b,B: set_b] :
      ( ~ ( member_b @ X3 @ A3 )
     => ( ( minus_minus_set_b @ A3 @ ( insert_b @ X3 @ B ) )
        = ( minus_minus_set_b @ A3 @ B ) ) ) ).

% Diff_insert0
thf(fact_1218_insert__Diff1,axiom,
    ! [X3: $o,B: set_o,A3: set_o] :
      ( ( member_o @ X3 @ B )
     => ( ( minus_minus_set_o @ ( insert_o @ X3 @ A3 ) @ B )
        = ( minus_minus_set_o @ A3 @ B ) ) ) ).

% insert_Diff1
thf(fact_1219_insert__Diff1,axiom,
    ! [X3: b,B: set_b,A3: set_b] :
      ( ( member_b @ X3 @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A3 ) @ B )
        = ( minus_minus_set_b @ A3 @ B ) ) ) ).

% insert_Diff1
thf(fact_1220_Diff__UNIV,axiom,
    ! [A3: set_o] :
      ( ( minus_minus_set_o @ A3 @ top_top_set_o )
      = bot_bot_set_o ) ).

% Diff_UNIV
thf(fact_1221_Diff__eq__empty__iff,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( minus_minus_set_o @ A3 @ B )
        = bot_bot_set_o )
      = ( ord_less_eq_set_o @ A3 @ B ) ) ).

% Diff_eq_empty_iff
thf(fact_1222_insert__Diff__single,axiom,
    ! [A: $o,A3: set_o] :
      ( ( insert_o @ A @ ( minus_minus_set_o @ A3 @ ( insert_o @ A @ bot_bot_set_o ) ) )
      = ( insert_o @ A @ A3 ) ) ).

% insert_Diff_single
thf(fact_1223_Diff__disjoint,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( inf_inf_set_o @ A3 @ ( minus_minus_set_o @ B @ A3 ) )
      = bot_bot_set_o ) ).

% Diff_disjoint
thf(fact_1224_Diff__insert,axiom,
    ! [A3: set_o,A: $o,B: set_o] :
      ( ( minus_minus_set_o @ A3 @ ( insert_o @ A @ B ) )
      = ( minus_minus_set_o @ ( minus_minus_set_o @ A3 @ B ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).

% Diff_insert
thf(fact_1225_insert__Diff,axiom,
    ! [A: b,A3: set_b] :
      ( ( member_b @ A @ A3 )
     => ( ( insert_b @ A @ ( minus_minus_set_b @ A3 @ ( insert_b @ A @ bot_bot_set_b ) ) )
        = A3 ) ) ).

% insert_Diff
thf(fact_1226_insert__Diff,axiom,
    ! [A: $o,A3: set_o] :
      ( ( member_o @ A @ A3 )
     => ( ( insert_o @ A @ ( minus_minus_set_o @ A3 @ ( insert_o @ A @ bot_bot_set_o ) ) )
        = A3 ) ) ).

% insert_Diff
thf(fact_1227_Diff__insert2,axiom,
    ! [A3: set_o,A: $o,B: set_o] :
      ( ( minus_minus_set_o @ A3 @ ( insert_o @ A @ B ) )
      = ( minus_minus_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B ) ) ).

% Diff_insert2
thf(fact_1228_Diff__insert__absorb,axiom,
    ! [X3: b,A3: set_b] :
      ( ~ ( member_b @ X3 @ A3 )
     => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A3 ) @ ( insert_b @ X3 @ bot_bot_set_b ) )
        = A3 ) ) ).

% Diff_insert_absorb
thf(fact_1229_Diff__insert__absorb,axiom,
    ! [X3: $o,A3: set_o] :
      ( ~ ( member_o @ X3 @ A3 )
     => ( ( minus_minus_set_o @ ( insert_o @ X3 @ A3 ) @ ( insert_o @ X3 @ bot_bot_set_o ) )
        = A3 ) ) ).

% Diff_insert_absorb
thf(fact_1230_diff__shunt__var,axiom,
    ! [X3: set_o,Y2: set_o] :
      ( ( ( minus_minus_set_o @ X3 @ Y2 )
        = bot_bot_set_o )
      = ( ord_less_eq_set_o @ X3 @ Y2 ) ) ).

% diff_shunt_var
thf(fact_1231_Int__Diff__disjoint,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( inf_inf_set_o @ ( inf_inf_set_o @ A3 @ B ) @ ( minus_minus_set_o @ A3 @ B ) )
      = bot_bot_set_o ) ).

% Int_Diff_disjoint
thf(fact_1232_Diff__triv,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( ( inf_inf_set_o @ A3 @ B )
        = bot_bot_set_o )
     => ( ( minus_minus_set_o @ A3 @ B )
        = A3 ) ) ).

% Diff_triv
thf(fact_1233_insert__Diff__if,axiom,
    ! [X3: $o,B: set_o,A3: set_o] :
      ( ( ( member_o @ X3 @ B )
       => ( ( minus_minus_set_o @ ( insert_o @ X3 @ A3 ) @ B )
          = ( minus_minus_set_o @ A3 @ B ) ) )
      & ( ~ ( member_o @ X3 @ B )
       => ( ( minus_minus_set_o @ ( insert_o @ X3 @ A3 ) @ B )
          = ( insert_o @ X3 @ ( minus_minus_set_o @ A3 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1234_insert__Diff__if,axiom,
    ! [X3: b,B: set_b,A3: set_b] :
      ( ( ( member_b @ X3 @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A3 ) @ B )
          = ( minus_minus_set_b @ A3 @ B ) ) )
      & ( ~ ( member_b @ X3 @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A3 ) @ B )
          = ( insert_b @ X3 @ ( minus_minus_set_b @ A3 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1235_subset__Diff__insert,axiom,
    ! [A3: set_o,B: set_o,X3: $o,C2: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ ( minus_minus_set_o @ B @ ( insert_o @ X3 @ C2 ) ) )
      = ( ( ord_less_eq_set_o @ A3 @ ( minus_minus_set_o @ B @ C2 ) )
        & ~ ( member_o @ X3 @ A3 ) ) ) ).

% subset_Diff_insert
thf(fact_1236_subset__Diff__insert,axiom,
    ! [A3: set_b,B: set_b,X3: b,C2: set_b] :
      ( ( ord_less_eq_set_b @ A3 @ ( minus_minus_set_b @ B @ ( insert_b @ X3 @ C2 ) ) )
      = ( ( ord_less_eq_set_b @ A3 @ ( minus_minus_set_b @ B @ C2 ) )
        & ~ ( member_b @ X3 @ A3 ) ) ) ).

% subset_Diff_insert
thf(fact_1237_DiffD2,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A3 @ B ) )
     => ~ ( member_b @ C @ B ) ) ).

% DiffD2
thf(fact_1238_DiffD1,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A3 @ B ) )
     => ( member_b @ C @ A3 ) ) ).

% DiffD1
thf(fact_1239_DiffE,axiom,
    ! [C: b,A3: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A3 @ B ) )
     => ~ ( ( member_b @ C @ A3 )
         => ( member_b @ C @ B ) ) ) ).

% DiffE
thf(fact_1240_set__diff__eq,axiom,
    ( minus_minus_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ A4 )
              & ~ ( member_b @ X2 @ B4 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1241_Compl__eq__Diff__UNIV,axiom,
    ( uminus_uminus_set_o
    = ( minus_minus_set_o @ top_top_set_o ) ) ).

% Compl_eq_Diff_UNIV
thf(fact_1242_Diff__single__insert,axiom,
    ! [A3: set_o,X3: $o,B: set_o] :
      ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ B )
     => ( ord_less_eq_set_o @ A3 @ ( insert_o @ X3 @ B ) ) ) ).

% Diff_single_insert
thf(fact_1243_subset__insert__iff,axiom,
    ! [A3: set_b,X3: b,B: set_b] :
      ( ( ord_less_eq_set_b @ A3 @ ( insert_b @ X3 @ B ) )
      = ( ( ( member_b @ X3 @ A3 )
         => ( ord_less_eq_set_b @ ( minus_minus_set_b @ A3 @ ( insert_b @ X3 @ bot_bot_set_b ) ) @ B ) )
        & ( ~ ( member_b @ X3 @ A3 )
         => ( ord_less_eq_set_b @ A3 @ B ) ) ) ) ).

% subset_insert_iff
thf(fact_1244_subset__insert__iff,axiom,
    ! [A3: set_o,X3: $o,B: set_o] :
      ( ( ord_less_eq_set_o @ A3 @ ( insert_o @ X3 @ B ) )
      = ( ( ( member_o @ X3 @ A3 )
         => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ B ) )
        & ( ~ ( member_o @ X3 @ A3 )
         => ( ord_less_eq_set_o @ A3 @ B ) ) ) ) ).

% subset_insert_iff
thf(fact_1245_Compl__insert,axiom,
    ! [X3: $o,A3: set_o] :
      ( ( uminus_uminus_set_o @ ( insert_o @ X3 @ A3 ) )
      = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A3 ) @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).

% Compl_insert
thf(fact_1246_in__image__insert__iff,axiom,
    ! [B: set_set_b,X3: b,A3: set_b] :
      ( ! [C4: set_b] :
          ( ( member_set_b @ C4 @ B )
         => ~ ( member_b @ X3 @ C4 ) )
     => ( ( member_set_b @ A3 @ ( image_set_b_set_b @ ( insert_b @ X3 ) @ B ) )
        = ( ( member_b @ X3 @ A3 )
          & ( member_set_b @ ( minus_minus_set_b @ A3 @ ( insert_b @ X3 @ bot_bot_set_b ) ) @ B ) ) ) ) ).

% in_image_insert_iff
thf(fact_1247_in__image__insert__iff,axiom,
    ! [B: set_set_o,X3: $o,A3: set_o] :
      ( ! [C4: set_o] :
          ( ( member_set_o @ C4 @ B )
         => ~ ( member_o @ X3 @ C4 ) )
     => ( ( member_set_o @ A3 @ ( image_set_o_set_o @ ( insert_o @ X3 ) @ B ) )
        = ( ( member_o @ X3 @ A3 )
          & ( member_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ B ) ) ) ) ).

% in_image_insert_iff
thf(fact_1248_remove__def,axiom,
    ( remove_o
    = ( ^ [X2: $o,A4: set_o] : ( minus_minus_set_o @ A4 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).

% remove_def
thf(fact_1249_member__remove,axiom,
    ! [X3: b,Y2: b,A3: set_b] :
      ( ( member_b @ X3 @ ( remove_b @ Y2 @ A3 ) )
      = ( ( member_b @ X3 @ A3 )
        & ( X3 != Y2 ) ) ) ).

% member_remove
thf(fact_1250_minus__set__def,axiom,
    ( minus_minus_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( collect_b
          @ ( minus_minus_b_o
            @ ^ [X2: b] : ( member_b @ X2 @ A4 )
            @ ^ [X2: b] : ( member_b @ X2 @ B4 ) ) ) ) ) ).

% minus_set_def
thf(fact_1251_pairwise__alt,axiom,
    ( pairwise_o
    = ( ^ [R4: $o > $o > $o,S2: set_o] :
        ! [X2: $o] :
          ( ( member_o @ X2 @ S2 )
         => ! [Y: $o] :
              ( ( member_o @ Y @ ( minus_minus_set_o @ S2 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
             => ( R4 @ X2 @ Y ) ) ) ) ) ).

% pairwise_alt
thf(fact_1252_pairwiseD,axiom,
    ! [R3: b > b > $o,S: set_b,X3: b,Y2: b] :
      ( ( pairwise_b @ R3 @ S )
     => ( ( member_b @ X3 @ S )
       => ( ( member_b @ Y2 @ S )
         => ( ( X3 != Y2 )
           => ( R3 @ X3 @ Y2 ) ) ) ) ) ).

% pairwiseD
thf(fact_1253_pairwiseI,axiom,
    ! [S: set_b,R3: b > b > $o] :
      ( ! [X: b,Y3: b] :
          ( ( member_b @ X @ S )
         => ( ( member_b @ Y3 @ S )
           => ( ( X != Y3 )
             => ( R3 @ X @ Y3 ) ) ) )
     => ( pairwise_b @ R3 @ S ) ) ).

% pairwiseI
thf(fact_1254_pairwise__insert,axiom,
    ! [R: $o > $o > $o,X3: $o,S4: set_o] :
      ( ( pairwise_o @ R @ ( insert_o @ X3 @ S4 ) )
      = ( ! [Y: $o] :
            ( ( ( member_o @ Y @ S4 )
              & ( Y != X3 ) )
           => ( ( R @ X3 @ Y )
              & ( R @ Y @ X3 ) ) )
        & ( pairwise_o @ R @ S4 ) ) ) ).

% pairwise_insert
thf(fact_1255_pairwise__insert,axiom,
    ! [R: b > b > $o,X3: b,S4: set_b] :
      ( ( pairwise_b @ R @ ( insert_b @ X3 @ S4 ) )
      = ( ! [Y: b] :
            ( ( ( member_b @ Y @ S4 )
              & ( Y != X3 ) )
           => ( ( R @ X3 @ Y )
              & ( R @ Y @ X3 ) ) )
        & ( pairwise_b @ R @ S4 ) ) ) ).

% pairwise_insert
thf(fact_1256_pairwise__empty,axiom,
    ! [P4: $o > $o > $o] : ( pairwise_o @ P4 @ bot_bot_set_o ) ).

% pairwise_empty
thf(fact_1257_Inf__set__fold,axiom,
    ! [Xs: list_set_o] :
      ( ( comple3063163877087187839_set_o @ ( set_set_o2 @ Xs ) )
      = ( fold_set_o_set_o @ inf_inf_set_o @ Xs @ top_top_set_o ) ) ).

% Inf_set_fold
thf(fact_1258_pairwise__singleton,axiom,
    ! [P4: $o > $o > $o,A3: $o] : ( pairwise_o @ P4 @ ( insert_o @ A3 @ bot_bot_set_o ) ) ).

% pairwise_singleton
thf(fact_1259_Inf__fin_Oinsert,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( finite_finite_o @ A3 )
     => ( ( A3 != bot_bot_set_o )
       => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X3 @ A3 ) )
          = ( inf_inf_o @ X3 @ ( lattic4107685809792843317_fin_o @ A3 ) ) ) ) ) ).

% Inf_fin.insert
thf(fact_1260_Inf__fin_Oinsert__remove,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( finite_finite_o @ A3 )
     => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X3 @ A3 ) )
        = ( ( ( ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) )
              = bot_bot_set_o )
           => X3 )
          & ( ( ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) )
             != bot_bot_set_o )
           => ( inf_inf_o @ X3 @ ( lattic4107685809792843317_fin_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ) ) ) ).

% Inf_fin.insert_remove
thf(fact_1261_Inf__fin_Ohom__commute,axiom,
    ! [H2: $o > $o,N: set_o] :
      ( ! [X: $o,Y3: $o] :
          ( ( H2 @ ( inf_inf_o @ X @ Y3 ) )
          = ( inf_inf_o @ ( H2 @ X ) @ ( H2 @ Y3 ) ) )
     => ( ( finite_finite_o @ N )
       => ( ( N != bot_bot_set_o )
         => ( ( H2 @ ( lattic4107685809792843317_fin_o @ N ) )
            = ( lattic4107685809792843317_fin_o @ ( image_o_o @ H2 @ N ) ) ) ) ) ) ).

% Inf_fin.hom_commute
thf(fact_1262_Inf__fin_Osubset,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( finite_finite_o @ A3 )
     => ( ( B != bot_bot_set_o )
       => ( ( ord_less_eq_set_o @ B @ A3 )
         => ( ( inf_inf_o @ ( lattic4107685809792843317_fin_o @ B ) @ ( lattic4107685809792843317_fin_o @ A3 ) )
            = ( lattic4107685809792843317_fin_o @ A3 ) ) ) ) ) ).

% Inf_fin.subset
thf(fact_1263_Inf__fin_Oclosed,axiom,
    ! [A3: set_o] :
      ( ( finite_finite_o @ A3 )
     => ( ( A3 != bot_bot_set_o )
       => ( ! [X: $o,Y3: $o] : ( member_o @ ( inf_inf_o @ X @ Y3 ) @ ( insert_o @ X @ ( insert_o @ Y3 @ bot_bot_set_o ) ) )
         => ( member_o @ ( lattic4107685809792843317_fin_o @ A3 ) @ A3 ) ) ) ) ).

% Inf_fin.closed
thf(fact_1264_Inf__fin_Oinsert__not__elem,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( finite_finite_o @ A3 )
     => ( ~ ( member_o @ X3 @ A3 )
       => ( ( A3 != bot_bot_set_o )
         => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X3 @ A3 ) )
            = ( inf_inf_o @ X3 @ ( lattic4107685809792843317_fin_o @ A3 ) ) ) ) ) ) ).

% Inf_fin.insert_not_elem
thf(fact_1265_Inf__fin_Ounion,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( finite_finite_o @ A3 )
     => ( ( A3 != bot_bot_set_o )
       => ( ( finite_finite_o @ B )
         => ( ( B != bot_bot_set_o )
           => ( ( lattic4107685809792843317_fin_o @ ( sup_sup_set_o @ A3 @ B ) )
              = ( inf_inf_o @ ( lattic4107685809792843317_fin_o @ A3 ) @ ( lattic4107685809792843317_fin_o @ B ) ) ) ) ) ) ) ).

% Inf_fin.union
thf(fact_1266_Inf__fin_Oeq__fold,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( finite_finite_o @ A3 )
     => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X3 @ A3 ) )
        = ( finite_fold_o_o @ inf_inf_o @ X3 @ A3 ) ) ) ).

% Inf_fin.eq_fold
thf(fact_1267_Inf__fin_Oremove,axiom,
    ! [A3: set_o,X3: $o] :
      ( ( finite_finite_o @ A3 )
     => ( ( member_o @ X3 @ A3 )
       => ( ( lattic4107685809792843317_fin_o @ A3 )
          = ( ( ( ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) )
                = bot_bot_set_o )
             => X3 )
            & ( ( ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) )
               != bot_bot_set_o )
             => ( inf_inf_o @ X3 @ ( lattic4107685809792843317_fin_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).

% Inf_fin.remove
thf(fact_1268_psubset__insert__iff,axiom,
    ! [A3: set_b,X3: b,B: set_b] :
      ( ( ord_less_set_b @ A3 @ ( insert_b @ X3 @ B ) )
      = ( ( ( member_b @ X3 @ B )
         => ( ord_less_set_b @ A3 @ B ) )
        & ( ~ ( member_b @ X3 @ B )
         => ( ( ( member_b @ X3 @ A3 )
             => ( ord_less_set_b @ ( minus_minus_set_b @ A3 @ ( insert_b @ X3 @ bot_bot_set_b ) ) @ B ) )
            & ( ~ ( member_b @ X3 @ A3 )
             => ( ord_less_eq_set_b @ A3 @ B ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1269_psubset__insert__iff,axiom,
    ! [A3: set_o,X3: $o,B: set_o] :
      ( ( ord_less_set_o @ A3 @ ( insert_o @ X3 @ B ) )
      = ( ( ( member_o @ X3 @ B )
         => ( ord_less_set_o @ A3 @ B ) )
        & ( ~ ( member_o @ X3 @ B )
         => ( ( ( member_o @ X3 @ A3 )
             => ( ord_less_set_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ B ) )
            & ( ~ ( member_o @ X3 @ A3 )
             => ( ord_less_eq_set_o @ A3 @ B ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1270_not__psubset__empty,axiom,
    ! [A3: set_o] :
      ~ ( ord_less_set_o @ A3 @ bot_bot_set_o ) ).

% not_psubset_empty
thf(fact_1271_psubsetD,axiom,
    ! [A3: set_b,B: set_b,C: b] :
      ( ( ord_less_set_b @ A3 @ B )
     => ( ( member_b @ C @ A3 )
       => ( member_b @ C @ B ) ) ) ).

% psubsetD
thf(fact_1272_psubset__imp__ex__mem,axiom,
    ! [A3: set_b,B: set_b] :
      ( ( ord_less_set_b @ A3 @ B )
     => ? [B6: b] : ( member_b @ B6 @ ( minus_minus_set_b @ B @ A3 ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1273_sup__bot_Osemilattice__neutr__order__axioms,axiom,
    ( semila2554085542299052326_set_o @ sup_sup_set_o @ bot_bot_set_o
    @ ^ [X2: set_o,Y: set_o] : ( ord_less_eq_set_o @ Y @ X2 )
    @ ^ [X2: set_o,Y: set_o] : ( ord_less_set_o @ Y @ X2 ) ) ).

% sup_bot.semilattice_neutr_order_axioms
thf(fact_1274_inf__top_Osemilattice__neutr__order__axioms,axiom,
    semila2554085542299052326_set_o @ inf_inf_set_o @ top_top_set_o @ ord_less_eq_set_o @ ord_less_set_o ).

% inf_top.semilattice_neutr_order_axioms
thf(fact_1275_less__set__def,axiom,
    ( ord_less_set_b
    = ( ^ [A4: set_b,B4: set_b] :
          ( ord_less_b_o
          @ ^ [X2: b] : ( member_b @ X2 @ A4 )
          @ ^ [X2: b] : ( member_b @ X2 @ B4 ) ) ) ) ).

% less_set_def
thf(fact_1276_card__partition,axiom,
    ! [C2: set_set_o,K4: nat] :
      ( ( finite_finite_set_o @ C2 )
     => ( ( finite_finite_o @ ( comple90263536869209701_set_o @ C2 ) )
       => ( ! [C5: set_o] :
              ( ( member_set_o @ C5 @ C2 )
             => ( ( finite_card_o @ C5 )
                = K4 ) )
         => ( ! [C1: set_o,C22: set_o] :
                ( ( member_set_o @ C1 @ C2 )
               => ( ( member_set_o @ C22 @ C2 )
                 => ( ( C1 != C22 )
                   => ( ( inf_inf_set_o @ C1 @ C22 )
                      = bot_bot_set_o ) ) ) )
           => ( ( times_times_nat @ K4 @ ( finite_card_set_o @ C2 ) )
              = ( finite_card_o @ ( comple90263536869209701_set_o @ C2 ) ) ) ) ) ) ) ).

% card_partition
thf(fact_1277_card__Un__disjoint,axiom,
    ! [A3: set_o,B: set_o] :
      ( ( finite_finite_o @ A3 )
     => ( ( finite_finite_o @ B )
       => ( ( ( inf_inf_set_o @ A3 @ B )
            = bot_bot_set_o )
         => ( ( finite_card_o @ ( sup_sup_set_o @ A3 @ B ) )
            = ( plus_plus_nat @ ( finite_card_o @ A3 ) @ ( finite_card_o @ B ) ) ) ) ) ) ).

% card_Un_disjoint
thf(fact_1278_dvd__partition,axiom,
    ! [C2: set_set_o,K4: nat] :
      ( ( finite_finite_o @ ( comple90263536869209701_set_o @ C2 ) )
     => ( ! [X: set_o] :
            ( ( member_set_o @ X @ C2 )
           => ( dvd_dvd_nat @ K4 @ ( finite_card_o @ X ) ) )
       => ( ! [X: set_o] :
              ( ( member_set_o @ X @ C2 )
             => ! [Xa: set_o] :
                  ( ( member_set_o @ Xa @ C2 )
                 => ( ( X != Xa )
                   => ( ( inf_inf_set_o @ X @ Xa )
                      = bot_bot_set_o ) ) ) )
         => ( dvd_dvd_nat @ K4 @ ( finite_card_o @ ( comple90263536869209701_set_o @ C2 ) ) ) ) ) ) ).

% dvd_partition

% Helper facts (3)
thf(help_If_3_1_If_001tf__b_T,axiom,
    ! [P4: $o] :
      ( ( P4 = $true )
      | ( P4 = $false ) ) ).

thf(help_If_2_1_If_001tf__b_T,axiom,
    ! [X3: b,Y2: b] :
      ( ( if_b @ $false @ X3 @ Y2 )
      = Y2 ) ).

thf(help_If_1_1_If_001tf__b_T,axiom,
    ! [X3: b,Y2: b] :
      ( ( if_b @ $true @ X3 @ Y2 )
      = X3 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    episte295617885132580261cs_a_b @ m @ w @ ( 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 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( epistemic_Imp_a @ p @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ).

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