TPTP Problem File: SLH0139^1.p

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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Stalnaker_Logic/0000_Stalnaker_Logic/prob_00171_005474__6271442_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1649 ( 758 unt; 362 typ;   0 def)
%            Number of atoms       : 3568 (2184 equ;   0 cnn)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives : 12707 ( 575   ~;  73   |; 402   &;10275   @)
%                                         (   0 <=>;1382  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Number of types       :   29 (  28 usr)
%            Number of type conns  : 1823 (1823   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  337 ( 334 usr;  19 con; 0-3 aty)
%            Number of variables   : 4254 ( 368   ^;3515   !; 371   ?;4254   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 16:11:49.694
%------------------------------------------------------------------------------
% Could-be-implicit typings (28)
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% Explicit typings (334)
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    accp_l5045591749613577993c_fm_a: ( list_s580375451141968640c_fm_a > list_s580375451141968640c_fm_a > $o ) > list_s580375451141968640c_fm_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_062_It__Epistemic____Logic__Ofm_Itf__a_J_M_Eo_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    accp_P8153917284782618338c_fm_a: ( produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o ) > produc7493720319326827993c_fm_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J,type,
    accp_P3999429264564614062c_fm_a: ( produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o ) > produc3921445516396586231c_fm_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    accp_P1207204058359408560c_fm_a: ( produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o ) > produc5756089960658898087c_fm_a > $o ).

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

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

thf(sy_c_member_001t__List__Olist_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member7465314387053329231c_fm_a: list_l6083326122719238310c_fm_a > set_li1092409891198325638c_fm_a > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member914871927696214614c_fm_a: list_P3099032918374241197c_fm_a > set_li5400946639045803789c_fm_a > $o ).

thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J,type,
    member2056814488595083094c_fm_a: list_P7917480606449584557c_fm_a > set_li5579717781341779981c_fm_a > $o ).

thf(sy_c_member_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member2328277852289759785c_fm_a: list_s580375451141968640c_fm_a > set_li4204741992506657632c_fm_a > $o ).

thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
    member_list_a: list_a > set_list_a > $o ).

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

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J,type,
    member3265983909902097104c_fm_a: produc5756089960658898087c_fm_a > set_Pr3219225162411408519c_fm_a > $o ).

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

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

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

thf(sy_v_Ga____,type,
    ga: list_Epistemic_fm_a ).

thf(sy_v_a____,type,
    a3: epistemic_fm_a ).

thf(sy_v_i,type,
    i: a ).

% Relevant facts (1273)
thf(fact_0__092_060open_062A_A_092_060turnstile_062_AK_Ai_Aa_A_092_060_094bold_062_092_060and_062_AK_Ai_A_Iconjunct_AG_J_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_Aa_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) ) @ ( epistemic_K_a @ i @ a3 ) ) ).

% \<open>A \<turnstile> K i a \<^bold>\<and> K i (conjunct G) \<^bold>\<longrightarrow> K i a\<close>
thf(fact_1_o2,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ i ) @ ga ) ) ) ).

% o2
thf(fact_2__092_060open_062A_A_092_060turnstile_062_AK_Ai_A_Ia_A_092_060_094bold_062_092_060and_062_Aconjunct_AG_J_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_Aa_A_092_060_094bold_062_092_060and_062_AK_Ai_A_Iconjunct_AG_J_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( epistemic_Con_a @ a3 @ ( stalnaker_conjunct_a @ ga ) ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) ) ) ).

% \<open>A \<turnstile> K i (a \<^bold>\<and> conjunct G) \<^bold>\<longrightarrow> K i a \<^bold>\<and> K i (conjunct G)\<close>
thf(fact_3_K__imp__trans,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans
thf(fact_4_K__imp__trans_H,axiom,
    ! [A: epistemic_fm_a > $o,Q: epistemic_fm_a,R: epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ Q @ R ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_imp_trans'
thf(fact_5_K__imply__multi,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ B ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ C ) )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Con_a @ B @ C ) ) ) ) ) ).

% K_imply_multi
thf(fact_6_K__multi__imply,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a,B: epistemic_fm_a,C: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ A2 @ ( epistemic_Imp_a @ B @ C ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ A2 @ B ) @ C ) ) ) ).

% K_multi_imply
thf(fact_7_K__conjunction__in,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_conjunction_in
thf(fact_8_K__conj__imply__factor,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) @ R ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Con_a @ P @ Q ) ) @ R ) ) ) ).

% K_conj_imply_factor
thf(fact_9__092_060open_062A_A_092_060turnstile_062_AK_Ai_A_Iconjunct_A_Ia_A_D_AG_J_J_A_092_060_094bold_062_092_060longrightarrow_062_AK_Ai_A_Ia_A_092_060_094bold_062_092_060and_062_Aconjunct_AG_J_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ( cons_Epistemic_fm_a @ a3 @ ga ) ) ) @ ( epistemic_K_a @ i @ ( epistemic_Con_a @ a3 @ ( stalnaker_conjunct_a @ ga ) ) ) ) ).

% \<open>A \<turnstile> K i (conjunct (a # G)) \<^bold>\<longrightarrow> K i (a \<^bold>\<and> conjunct G)\<close>
thf(fact_10_o1,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ( cons_Epistemic_fm_a @ a3 @ ga ) ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) ) ) ).

% o1
thf(fact_11_A2,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) ) @ ( epistemic_K_a @ I @ Q ) ) ) ).

% A2
thf(fact_12_local_OCons,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ i ) @ ga ) ) ) ).

% local.Cons
thf(fact_13_K__A2_H,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ Q ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_A2'
thf(fact_14_K__map,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,I: a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_map
thf(fact_15_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_16_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_17_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_18_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_19_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_20_R2,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( epistemic_AK_a @ A @ P )
     => ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ P ) ) ) ).

% R2
thf(fact_21_conjunct_Osimps_I2_J,axiom,
    ! [P: epistemic_fm_a,Ps: list_Epistemic_fm_a] :
      ( ( stalnaker_conjunct_a @ ( cons_Epistemic_fm_a @ P @ Ps ) )
      = ( epistemic_Con_a @ P @ ( stalnaker_conjunct_a @ Ps ) ) ) ).

% conjunct.simps(2)
thf(fact_22_Ax,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a] :
      ( ( A @ P )
     => ( epistemic_AK_a @ A @ P ) ) ).

% Ax
thf(fact_23_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_24_K__trans,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,R: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ Q ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ Q @ R ) @ ( epistemic_Imp_a @ P @ R ) ) ) ) ).

% K_trans
thf(fact_25_R1,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ P )
     => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
       => ( epistemic_AK_a @ A @ Q ) ) ) ).

% R1
thf(fact_26__092_060open_062A_A_092_060turnstile_062_AK_Ai_A_Iconjunct_A_091_093_J_A_092_060_094bold_062_092_060longrightarrow_062_Aconjunct_A_Imap_A_IK_Ai_J_A_091_093_J_092_060close_062,axiom,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ nil_Epistemic_fm_a ) ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ i ) @ nil_Epistemic_fm_a ) ) ) ).

% \<open>A \<turnstile> K i (conjunct []) \<^bold>\<longrightarrow> conjunct (map (K i) [])\<close>
thf(fact_27_map__ident,axiom,
    ( ( map_li3080774272885743684c_fm_a
      @ ^ [X: list_Epistemic_fm_a] : X )
    = ( ^ [Xs: list_l6083326122719238310c_fm_a] : Xs ) ) ).

% map_ident
thf(fact_28_map__ident,axiom,
    ( ( map_Ep7084560364594560580c_fm_a
      @ ^ [X: epistemic_fm_a] : X )
    = ( ^ [Xs: list_Epistemic_fm_a] : Xs ) ) ).

% map_ident
thf(fact_29_list_Oinject,axiom,
    ! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a,Y21: list_Epistemic_fm_a,Y22: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X21 @ X22 )
        = ( cons_l8134865115577406678c_fm_a @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_30_list_Oinject,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a,Y21: epistemic_fm_a,Y22: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X21 @ X22 )
        = ( cons_Epistemic_fm_a @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_31_map__eq__Cons__conv,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,Y: list_l6083326122719238310c_fm_a,Ys: list_l3671048651222332332c_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = ( cons_l2479501935080859996c_fm_a @ Y @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_Ep4939040189629079504c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_32_map__eq__Cons__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a,Ys: list_l3671048651222332332c_fm_a] :
      ( ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
        = ( cons_l2479501935080859996c_fm_a @ Y @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_li3858915945532548554c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_33_map__eq__Cons__conv,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = ( cons_Epistemic_fm_a @ Y @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_li5516866612190465598c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_34_map__eq__Cons__conv,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_Ep1988204514693272906c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_35_map__eq__Cons__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_li3080774272885743684c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_36_map__eq__Cons__conv,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( cons_Epistemic_fm_a @ Y @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( ( F @ Z )
              = Y )
            & ( ( map_Ep7084560364594560580c_fm_a @ F @ Zs )
              = Ys ) ) ) ) ).

% map_eq_Cons_conv
thf(fact_37_Cons__eq__map__conv,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_l2479501935080859996c_fm_a @ X2 @ Xs2 )
        = ( map_Ep4939040189629079504c_fm_a @ F @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Ys
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_Ep4939040189629079504c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_38_Cons__eq__map__conv,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l2479501935080859996c_fm_a @ X2 @ Xs2 )
        = ( map_li3858915945532548554c_fm_a @ F @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_li3858915945532548554c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_39_Cons__eq__map__conv,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( map_li5516866612190465598c_fm_a @ F @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_li5516866612190465598c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_40_Cons__eq__map__conv,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( map_Ep1988204514693272906c_fm_a @ F @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Ys
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_Ep1988204514693272906c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_41_Cons__eq__map__conv,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( map_li3080774272885743684c_fm_a @ F @ Ys ) )
      = ( ? [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( cons_l8134865115577406678c_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_li3080774272885743684c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_42_Cons__eq__map__conv,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( map_Ep7084560364594560580c_fm_a @ F @ Ys ) )
      = ( ? [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Ys
              = ( cons_Epistemic_fm_a @ Z @ Zs ) )
            & ( X2
              = ( F @ Z ) )
            & ( Xs2
              = ( map_Ep7084560364594560580c_fm_a @ F @ Zs ) ) ) ) ) ).

% Cons_eq_map_conv
thf(fact_43_map__eq__Cons__D,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,Y: list_l6083326122719238310c_fm_a,Ys: list_l3671048651222332332c_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = ( cons_l2479501935080859996c_fm_a @ Y @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_Ep4939040189629079504c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_44_map__eq__Cons__D,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a,Ys: list_l3671048651222332332c_fm_a] :
      ( ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
        = ( cons_l2479501935080859996c_fm_a @ Y @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_li3858915945532548554c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_45_map__eq__Cons__D,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = ( cons_Epistemic_fm_a @ Y @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_li5516866612190465598c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_46_map__eq__Cons__D,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_Ep1988204514693272906c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_47_map__eq__Cons__D,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_li3080774272885743684c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_48_map__eq__Cons__D,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( cons_Epistemic_fm_a @ Y @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( ( F @ Z2 )
            = Y )
          & ( ( map_Ep7084560364594560580c_fm_a @ F @ Zs2 )
            = Ys ) ) ) ).

% map_eq_Cons_D
thf(fact_49_Cons__eq__map__D,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_l2479501935080859996c_fm_a @ X2 @ Xs2 )
        = ( map_Ep4939040189629079504c_fm_a @ F @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Ys
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_Ep4939040189629079504c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_50_Cons__eq__map__D,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l2479501935080859996c_fm_a @ X2 @ Xs2 )
        = ( map_li3858915945532548554c_fm_a @ F @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Ys
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_li3858915945532548554c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_51_Cons__eq__map__D,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( map_li5516866612190465598c_fm_a @ F @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Ys
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_li5516866612190465598c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_52_Cons__eq__map__D,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( map_Ep1988204514693272906c_fm_a @ F @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Ys
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_Ep1988204514693272906c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_53_Cons__eq__map__D,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( map_li3080774272885743684c_fm_a @ F @ Ys ) )
     => ? [Z2: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Ys
            = ( cons_l8134865115577406678c_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_li3080774272885743684c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_54_Cons__eq__map__D,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( map_Ep7084560364594560580c_fm_a @ F @ Ys ) )
     => ? [Z2: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Ys
            = ( cons_Epistemic_fm_a @ Z2 @ Zs2 ) )
          & ( X2
            = ( F @ Z2 ) )
          & ( Xs2
            = ( map_Ep7084560364594560580c_fm_a @ F @ Zs2 ) ) ) ) ).

% Cons_eq_map_D
thf(fact_55_list_Osimps_I9_J,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( map_Ep4939040189629079504c_fm_a @ F @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( cons_l2479501935080859996c_fm_a @ ( F @ X21 ) @ ( map_Ep4939040189629079504c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_56_list_Osimps_I9_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( map_Ep1988204514693272906c_fm_a @ F @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( cons_l8134865115577406678c_fm_a @ ( F @ X21 ) @ ( map_Ep1988204514693272906c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_57_list_Osimps_I9_J,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( map_li3858915945532548554c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
      = ( cons_l2479501935080859996c_fm_a @ ( F @ X21 ) @ ( map_li3858915945532548554c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_58_list_Osimps_I9_J,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( map_li5516866612190465598c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
      = ( cons_Epistemic_fm_a @ ( F @ X21 ) @ ( map_li5516866612190465598c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_59_list_Osimps_I9_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( map_li3080774272885743684c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
      = ( cons_l8134865115577406678c_fm_a @ ( F @ X21 ) @ ( map_li3080774272885743684c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_60_list_Osimps_I9_J,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( cons_Epistemic_fm_a @ ( F @ X21 ) @ ( map_Ep7084560364594560580c_fm_a @ F @ X22 ) ) ) ).

% list.simps(9)
thf(fact_61_AK_Osimps,axiom,
    ( epistemic_AK_a
    = ( ^ [A3: epistemic_fm_a > $o,A4: epistemic_fm_a] :
          ( ? [P2: epistemic_fm_a] :
              ( ( A4 = P2 )
              & ! [G: list_char > $o,H: epistemic_fm_a > $o] : ( epistemic_eval_a @ G @ H @ P2 ) )
          | ? [I2: a,P2: epistemic_fm_a,Q2: epistemic_fm_a] :
              ( A4
              = ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I2 @ P2 ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ Q2 ) ) ) @ ( epistemic_K_a @ I2 @ Q2 ) ) )
          | ? [P2: epistemic_fm_a] :
              ( ( A4 = P2 )
              & ( A3 @ P2 ) )
          | ? [P2: epistemic_fm_a,Q2: epistemic_fm_a] :
              ( ( A4 = Q2 )
              & ( epistemic_AK_a @ A3 @ P2 )
              & ( epistemic_AK_a @ A3 @ ( epistemic_Imp_a @ P2 @ Q2 ) ) )
          | ? [P2: epistemic_fm_a,I2: a] :
              ( ( A4
                = ( epistemic_K_a @ I2 @ P2 ) )
              & ( epistemic_AK_a @ A3 @ P2 ) ) ) ) ) ).

% AK.simps
thf(fact_62_AK_Ocases,axiom,
    ! [A: epistemic_fm_a > $o,A2: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ A2 )
     => ( ~ ! [G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ A2 )
       => ( ! [I3: a,P3: epistemic_fm_a,Q3: epistemic_fm_a] :
              ( A2
             != ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I3 @ P3 ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ Q3 ) ) ) @ ( epistemic_K_a @ I3 @ Q3 ) ) )
         => ( ~ ( A @ A2 )
           => ( ! [P3: epistemic_fm_a] :
                  ( ( epistemic_AK_a @ A @ P3 )
                 => ~ ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P3 @ A2 ) ) )
             => ~ ! [P3: epistemic_fm_a] :
                    ( ? [I3: a] :
                        ( A2
                        = ( epistemic_K_a @ I3 @ P3 ) )
                   => ~ ( epistemic_AK_a @ A @ P3 ) ) ) ) ) ) ) ).

% AK.cases
thf(fact_63_list_Omap__disc__iff,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A2: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ A2 )
        = nil_Epistemic_fm_a )
      = ( A2 = nil_Epistemic_fm_a ) ) ).

% list.map_disc_iff
thf(fact_64_list_Omap__disc__iff,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se8248101584983471204c_fm_a @ F @ A2 )
        = nil_Epistemic_fm_a )
      = ( A2 = nil_se102576565402781184c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_65_list_Omap__disc__iff,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,A2: list_Epistemic_fm_a] :
      ( ( ( map_Ep6135353274472911908c_fm_a @ F @ A2 )
        = nil_se102576565402781184c_fm_a )
      = ( A2 = nil_Epistemic_fm_a ) ) ).

% list.map_disc_iff
thf(fact_66_list_Omap__disc__iff,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,A2: list_Epistemic_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ A2 )
        = nil_li2451196919128234278c_fm_a )
      = ( A2 = nil_Epistemic_fm_a ) ) ).

% list.map_disc_iff
thf(fact_67_list_Omap__disc__iff,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ A2 )
        = nil_Epistemic_fm_a )
      = ( A2 = nil_li2451196919128234278c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_68_list_Omap__disc__iff,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se6909769656262425450c_fm_a @ F @ A2 )
        = nil_li2451196919128234278c_fm_a )
      = ( A2 = nil_se102576565402781184c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_69_list_Omap__disc__iff,axiom,
    ! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li6596013992111160350c_fm_a @ F @ A2 )
        = nil_se102576565402781184c_fm_a )
      = ( A2 = nil_li2451196919128234278c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_70_list_Omap__disc__iff,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se7333198834109155908c_fm_a @ F @ A2 )
        = nil_se102576565402781184c_fm_a )
      = ( A2 = nil_se102576565402781184c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_71_list_Omap__disc__iff,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ A2 )
        = nil_li2451196919128234278c_fm_a )
      = ( A2 = nil_li2451196919128234278c_fm_a ) ) ).

% list.map_disc_iff
thf(fact_72_list_Omap__disc__iff,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,A2: list_Epistemic_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ A2 )
        = nil_li5178944226519631276c_fm_a )
      = ( A2 = nil_Epistemic_fm_a ) ) ).

% list.map_disc_iff
thf(fact_73_Nil__is__map__conv,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_74_Nil__is__map__conv,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( map_se8248101584983471204c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_75_Nil__is__map__conv,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( map_Ep6135353274472911908c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_76_Nil__is__map__conv,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_77_Nil__is__map__conv,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_78_Nil__is__map__conv,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( map_se6909769656262425450c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_79_Nil__is__map__conv,axiom,
    ! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( map_li6596013992111160350c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_80_Nil__is__map__conv,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( map_se7333198834109155908c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_81_Nil__is__map__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_82_Nil__is__map__conv,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( nil_li5178944226519631276c_fm_a
        = ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% Nil_is_map_conv
thf(fact_83_map__is__Nil__conv,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_84_map__is__Nil__conv,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se8248101584983471204c_fm_a @ F @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_85_map__is__Nil__conv,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( map_Ep6135353274472911908c_fm_a @ F @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_86_map__is__Nil__conv,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_87_map__is__Nil__conv,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_88_map__is__Nil__conv,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se6909769656262425450c_fm_a @ F @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_89_map__is__Nil__conv,axiom,
    ! [F: list_Epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li6596013992111160350c_fm_a @ F @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_90_map__is__Nil__conv,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( map_se7333198834109155908c_fm_a @ F @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_91_map__is__Nil__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_92_map__is__Nil__conv,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = nil_li5178944226519631276c_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% map_is_Nil_conv
thf(fact_93_transpose_Ocases,axiom,
    ! [X2: list_l985973790606564998c_fm_a] :
      ( ( X2 != nil_li5433889876484989702c_fm_a )
     => ( ! [Xss: list_l985973790606564998c_fm_a] :
            ( X2
           != ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
       => ~ ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
              ( X2
             != ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_94_transpose_Ocases,axiom,
    ! [X2: list_l3671048651222332332c_fm_a] :
      ( ( X2 != nil_li5178944226519631276c_fm_a )
     => ( ! [Xss: list_l3671048651222332332c_fm_a] :
            ( X2
           != ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
       => ~ ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
              ( X2
             != ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_95_transpose_Ocases,axiom,
    ! [X2: list_l6083326122719238310c_fm_a] :
      ( ( X2 != nil_li2451196919128234278c_fm_a )
     => ( ! [Xss: list_l6083326122719238310c_fm_a] :
            ( X2
           != ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
       => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
              ( X2
             != ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_96_list__nonempty__induct,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,P4: list_s580375451141968640c_fm_a > $o] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a] : ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
       => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
              ( ( Xs3 != nil_se102576565402781184c_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_97_list__nonempty__induct,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a] : ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
       => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
              ( ( Xs3 != nil_li2451196919128234278c_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_98_list__nonempty__induct,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ! [X3: epistemic_fm_a] : ( P4 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
       => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( Xs3 != nil_Epistemic_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% list_nonempty_induct
thf(fact_99_list__induct2_H,axiom,
    ! [P4: list_s580375451141968640c_fm_a > list_s580375451141968640c_fm_a > $o,Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( P4 @ nil_se102576565402781184c_fm_a @ nil_se102576565402781184c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
       => ( ! [Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] : ( P4 @ nil_se102576565402781184c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_100_list__induct2_H,axiom,
    ! [P4: list_s580375451141968640c_fm_a > list_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( P4 @ nil_se102576565402781184c_fm_a @ nil_Epistemic_fm_a )
     => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ nil_Epistemic_fm_a )
       => ( ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] : ( P4 @ nil_se102576565402781184c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_101_list__induct2_H,axiom,
    ! [P4: list_s580375451141968640c_fm_a > list_l6083326122719238310c_fm_a > $o,Xs2: list_s580375451141968640c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( P4 @ nil_se102576565402781184c_fm_a @ nil_li2451196919128234278c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] : ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
       => ( ! [Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] : ( P4 @ nil_se102576565402781184c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_102_list__induct2_H,axiom,
    ! [P4: list_Epistemic_fm_a > list_s580375451141968640c_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( P4 @ nil_Epistemic_fm_a @ nil_se102576565402781184c_fm_a )
     => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
       => ( ! [Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] : ( P4 @ nil_Epistemic_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_103_list__induct2_H,axiom,
    ! [P4: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( P4 @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a )
     => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
       => ( ! [Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] : ( P4 @ nil_Epistemic_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_104_list__induct2_H,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > list_s580375451141968640c_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( P4 @ nil_li2451196919128234278c_fm_a @ nil_se102576565402781184c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ nil_se102576565402781184c_fm_a )
       => ( ! [Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] : ( P4 @ nil_li2451196919128234278c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: set_Epistemic_fm_a,Ys2: list_s580375451141968640c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_105_list__induct2_H,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( P4 @ nil_li2451196919128234278c_fm_a @ nil_Epistemic_fm_a )
     => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ nil_Epistemic_fm_a )
       => ( ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] : ( P4 @ nil_li2451196919128234278c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_106_list__induct2_H,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( P4 @ nil_li2451196919128234278c_fm_a @ nil_li2451196919128234278c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] : ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ nil_li2451196919128234278c_fm_a )
       => ( ! [Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] : ( P4 @ nil_li2451196919128234278c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Y2: list_Epistemic_fm_a,Ys2: list_l6083326122719238310c_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_107_list__induct2_H,axiom,
    ! [P4: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( P4 @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a )
     => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] : ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ nil_Epistemic_fm_a )
       => ( ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] : ( P4 @ nil_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
         => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                ( ( P4 @ Xs3 @ Ys2 )
               => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) )
           => ( P4 @ Xs2 @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_108_mem__Collect__eq,axiom,
    ! [A2: produc2203834439629243303c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( member5029746173879296720c_fm_a @ A2 @ ( collec7391038856303340306c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_109_mem__Collect__eq,axiom,
    ! [A2: produc5756089960658898087c_fm_a,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( member3265983909902097104c_fm_a @ A2 @ ( collec6124610372686893330c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_110_mem__Collect__eq,axiom,
    ! [A2: a,P4: a > $o] :
      ( ( member_a @ A2 @ ( collect_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_111_mem__Collect__eq,axiom,
    ! [A2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( member5906877432388582473c_fm_a @ A2 @ ( collec5191077796991884427c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_112_mem__Collect__eq,axiom,
    ! [A2: epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( member6642669571620171971c_fm_a @ A2 @ ( collec4904205152690461189c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_113_mem__Collect__eq,axiom,
    ! [A2: set_Epistemic_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( member536094252920883875c_fm_a @ A2 @ ( collec2519470961442302949c_fm_a @ P4 ) )
      = ( P4 @ A2 ) ) ).

% mem_Collect_eq
thf(fact_114_Collect__mem__eq,axiom,
    ! [A: set_Pr8948481099588399239c_fm_a] :
      ( ( collec7391038856303340306c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_115_Collect__mem__eq,axiom,
    ! [A: set_Pr3219225162411408519c_fm_a] :
      ( ( collec6124610372686893330c_fm_a
        @ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_116_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X: a] : ( member_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_117_Collect__mem__eq,axiom,
    ! [A: set_li769143395467472256c_fm_a] :
      ( ( collec5191077796991884427c_fm_a
        @ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_118_Collect__mem__eq,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_119_Collect__mem__eq,axiom,
    ! [A: set_se5208064806568342746c_fm_a] :
      ( ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_120_Collect__cong,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Q4: list_Epistemic_fm_a > $o] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( P4 @ X3 )
          = ( Q4 @ X3 ) )
     => ( ( collec5191077796991884427c_fm_a @ P4 )
        = ( collec5191077796991884427c_fm_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_121_Collect__cong,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ! [X3: epistemic_fm_a] :
          ( ( P4 @ X3 )
          = ( Q4 @ X3 ) )
     => ( ( collec4904205152690461189c_fm_a @ P4 )
        = ( collec4904205152690461189c_fm_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_122_Collect__cong,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ! [X3: set_Epistemic_fm_a] :
          ( ( P4 @ X3 )
          = ( Q4 @ X3 ) )
     => ( ( collec2519470961442302949c_fm_a @ P4 )
        = ( collec2519470961442302949c_fm_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_123_neq__Nil__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
      = ( ? [Y3: set_Epistemic_fm_a,Ys3: list_s580375451141968640c_fm_a] :
            ( Xs2
            = ( cons_s4394448069393209776c_fm_a @ Y3 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_124_neq__Nil__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
      = ( ? [Y3: list_Epistemic_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
            ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ Y3 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_125_neq__Nil__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
      = ( ? [Y3: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
            ( Xs2
            = ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_126_remdups__adj_Ocases,axiom,
    ! [X2: list_s580375451141968640c_fm_a] :
      ( ( X2 != nil_se102576565402781184c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a] :
            ( X2
           != ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
       => ~ ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
              ( X2
             != ( cons_s4394448069393209776c_fm_a @ X3 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_127_remdups__adj_Ocases,axiom,
    ! [X2: list_l6083326122719238310c_fm_a] :
      ( ( X2 != nil_li2451196919128234278c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( X2
           != ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
       => ~ ! [X3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
              ( X2
             != ( cons_l8134865115577406678c_fm_a @ X3 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_128_remdups__adj_Ocases,axiom,
    ! [X2: list_Epistemic_fm_a] :
      ( ( X2 != nil_Epistemic_fm_a )
     => ( ! [X3: epistemic_fm_a] :
            ( X2
           != ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
       => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( X2
             != ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_129_min__list_Ocases,axiom,
    ! [X2: list_s580375451141968640c_fm_a] :
      ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
          ( X2
         != ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) )
     => ( X2 = nil_se102576565402781184c_fm_a ) ) ).

% min_list.cases
thf(fact_130_list_Oexhaust,axiom,
    ! [Y: list_s580375451141968640c_fm_a] :
      ( ( Y != nil_se102576565402781184c_fm_a )
     => ~ ! [X212: set_Epistemic_fm_a,X222: list_s580375451141968640c_fm_a] :
            ( Y
           != ( cons_s4394448069393209776c_fm_a @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_131_list_Oexhaust,axiom,
    ! [Y: list_l6083326122719238310c_fm_a] :
      ( ( Y != nil_li2451196919128234278c_fm_a )
     => ~ ! [X212: list_Epistemic_fm_a,X222: list_l6083326122719238310c_fm_a] :
            ( Y
           != ( cons_l8134865115577406678c_fm_a @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_132_list_Oexhaust,axiom,
    ! [Y: list_Epistemic_fm_a] :
      ( ( Y != nil_Epistemic_fm_a )
     => ~ ! [X212: epistemic_fm_a,X222: list_Epistemic_fm_a] :
            ( Y
           != ( cons_Epistemic_fm_a @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_133_list_OdiscI,axiom,
    ! [List: list_s580375451141968640c_fm_a,X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] :
      ( ( List
        = ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) )
     => ( List != nil_se102576565402781184c_fm_a ) ) ).

% list.discI
thf(fact_134_list_OdiscI,axiom,
    ! [List: list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( List
        = ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
     => ( List != nil_li2451196919128234278c_fm_a ) ) ).

% list.discI
thf(fact_135_list_OdiscI,axiom,
    ! [List: list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( List
        = ( cons_Epistemic_fm_a @ X21 @ X22 ) )
     => ( List != nil_Epistemic_fm_a ) ) ).

% list.discI
thf(fact_136_list_Odistinct_I1_J,axiom,
    ! [X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] :
      ( nil_se102576565402781184c_fm_a
     != ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_137_list_Odistinct_I1_J,axiom,
    ! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( nil_li2451196919128234278c_fm_a
     != ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_138_list_Odistinct_I1_J,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( nil_Epistemic_fm_a
     != ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_139_list_Osimps_I8_J,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% list.simps(8)
thf(fact_140_list_Osimps_I8_J,axiom,
    ! [F: epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( map_Ep6135353274472911908c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% list.simps(8)
thf(fact_141_list_Osimps_I8_J,axiom,
    ! [F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( map_se8248101584983471204c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_Epistemic_fm_a ) ).

% list.simps(8)
thf(fact_142_list_Osimps_I8_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( map_Ep1988204514693272906c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% list.simps(8)
thf(fact_143_list_Osimps_I8_J,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( map_li5516866612190465598c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_Epistemic_fm_a ) ).

% list.simps(8)
thf(fact_144_list_Osimps_I8_J,axiom,
    ! [F: list_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( map_li6596013992111160350c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% list.simps(8)
thf(fact_145_list_Osimps_I8_J,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( map_se6909769656262425450c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% list.simps(8)
thf(fact_146_list_Osimps_I8_J,axiom,
    ! [F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ( map_se7333198834109155908c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% list.simps(8)
thf(fact_147_list_Osimps_I8_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( map_li3080774272885743684c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% list.simps(8)
thf(fact_148_list_Osimps_I8_J,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( map_Ep4939040189629079504c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_li5178944226519631276c_fm_a ) ).

% list.simps(8)
thf(fact_149_eval_Osimps_I5_J,axiom,
    ! [G3: list_char > $o,H3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G3 @ H3 @ ( epistemic_Imp_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G3 @ H3 @ P )
       => ( epistemic_eval_a @ G3 @ H3 @ Q ) ) ) ).

% eval.simps(5)
thf(fact_150_eval_Osimps_I6_J,axiom,
    ! [Ux: list_char > $o,H3: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( epistemic_eval_a @ Ux @ H3 @ ( epistemic_K_a @ I @ P ) )
      = ( H3 @ ( epistemic_K_a @ I @ P ) ) ) ).

% eval.simps(6)
thf(fact_151_A1,axiom,
    ! [P: epistemic_fm_a,A: epistemic_fm_a > $o] :
      ( ! [G4: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G4 @ H4 @ P )
     => ( epistemic_AK_a @ A @ P ) ) ).

% A1
thf(fact_152_eval_Osimps_I4_J,axiom,
    ! [G3: list_char > $o,H3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G3 @ H3 @ ( epistemic_Con_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G3 @ H3 @ P )
        & ( epistemic_eval_a @ G3 @ H3 @ Q ) ) ) ).

% eval.simps(4)
thf(fact_153_not__Cons__self2,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_154_not__Cons__self2,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
     != Xs2 ) ).

% not_Cons_self2
thf(fact_155_list_Omap__ident,axiom,
    ! [T: list_l6083326122719238310c_fm_a] :
      ( ( map_li3080774272885743684c_fm_a
        @ ^ [X: list_Epistemic_fm_a] : X
        @ T )
      = T ) ).

% list.map_ident
thf(fact_156_list_Omap__ident,axiom,
    ! [T: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a
        @ ^ [X: epistemic_fm_a] : X
        @ T )
      = T ) ).

% list.map_ident
thf(fact_157_map__rec,axiom,
    ( map_Ep4939040189629079504c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
          ( rec_li3857189064575089956c_fm_a @ nil_li5178944226519631276c_fm_a
          @ ^ [X: epistemic_fm_a,Uu: list_Epistemic_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_158_map__rec,axiom,
    ( map_li3858915945532548554c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
          ( rec_li4767119888041796650c_fm_a @ nil_li5178944226519631276c_fm_a
          @ ^ [X: list_Epistemic_fm_a,Uu: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_159_map__rec,axiom,
    ( map_li5516866612190465598c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > epistemic_fm_a] :
          ( rec_li2845402903074671286c_fm_a @ nil_Epistemic_fm_a
          @ ^ [X: list_Epistemic_fm_a,Uu: list_l6083326122719238310c_fm_a] : ( cons_Epistemic_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_160_map__rec,axiom,
    ( map_Ep1988204514693272906c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_Epistemic_fm_a] :
          ( rec_li2622076421192168746c_fm_a @ nil_li2451196919128234278c_fm_a
          @ ^ [X: epistemic_fm_a,Uu: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_161_map__rec,axiom,
    ( map_li3080774272885743684c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_Epistemic_fm_a] :
          ( rec_li5579148116651729200c_fm_a @ nil_li2451196919128234278c_fm_a
          @ ^ [X: list_Epistemic_fm_a,Uu: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_162_map__rec,axiom,
    ( map_Ep7084560364594560580c_fm_a
    = ( ^ [F2: epistemic_fm_a > epistemic_fm_a] :
          ( rec_li4360243526537435568c_fm_a @ nil_Epistemic_fm_a
          @ ^ [X: epistemic_fm_a,Uu: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F2 @ X ) ) ) ) ) ).

% map_rec
thf(fact_163_insert__Nil,axiom,
    ! [X2: set_Epistemic_fm_a] :
      ( ( insert1868103382419917334c_fm_a @ X2 @ nil_se102576565402781184c_fm_a )
      = ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ).

% insert_Nil
thf(fact_164_insert__Nil,axiom,
    ! [X2: list_Epistemic_fm_a] :
      ( ( insert335162795743670844c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a )
      = ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ).

% insert_Nil
thf(fact_165_insert__Nil,axiom,
    ! [X2: epistemic_fm_a] :
      ( ( insert177310161492556854c_fm_a @ X2 @ nil_Epistemic_fm_a )
      = ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ).

% insert_Nil
thf(fact_166_map__eq__map__tailrec,axiom,
    map_Ep1988204514693272906c_fm_a = map_ta2019361550626295956c_fm_a ).

% map_eq_map_tailrec
thf(fact_167_map__eq__map__tailrec,axiom,
    map_li3080774272885743684c_fm_a = map_ta7821446597547650702c_fm_a ).

% map_eq_map_tailrec
thf(fact_168_map__eq__map__tailrec,axiom,
    map_Ep4939040189629079504c_fm_a = map_ta456340477436210714c_fm_a ).

% map_eq_map_tailrec
thf(fact_169_map__eq__map__tailrec,axiom,
    map_li3858915945532548554c_fm_a = map_ta6463483919923529492c_fm_a ).

% map_eq_map_tailrec
thf(fact_170_map__eq__map__tailrec,axiom,
    map_li5516866612190465598c_fm_a = map_ta5548023648123488648c_fm_a ).

% map_eq_map_tailrec
thf(fact_171_map__eq__map__tailrec,axiom,
    map_Ep7084560364594560580c_fm_a = map_ta875960198429730446c_fm_a ).

% map_eq_map_tailrec
thf(fact_172_concat__map__singleton,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( concat5652308878773863783c_fm_a
        @ ( map_Ep4245182426433019350c_fm_a
          @ ^ [X: epistemic_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F @ X ) @ nil_li5178944226519631276c_fm_a )
          @ Xs2 ) )
      = ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_173_concat__map__singleton,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat5652308878773863783c_fm_a
        @ ( map_li5567427098789011152c_fm_a
          @ ^ [X: list_Epistemic_fm_a] : ( cons_l2479501935080859996c_fm_a @ ( F @ X ) @ nil_li5178944226519631276c_fm_a )
          @ Xs2 ) )
      = ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_174_concat__map__singleton,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat2780896542826320603c_fm_a
        @ ( map_li3080774272885743684c_fm_a
          @ ^ [X: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F @ X ) @ nil_Epistemic_fm_a )
          @ Xs2 ) )
      = ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_175_concat__map__singleton,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( concat6109960377493484129c_fm_a
        @ ( map_Ep4939040189629079504c_fm_a
          @ ^ [X: epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F @ X ) @ nil_li2451196919128234278c_fm_a )
          @ Xs2 ) )
      = ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_176_concat__map__singleton,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat6109960377493484129c_fm_a
        @ ( map_li3858915945532548554c_fm_a
          @ ^ [X: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ ( F @ X ) @ nil_li2451196919128234278c_fm_a )
          @ Xs2 ) )
      = ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_177_concat__map__singleton,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( concat2780896542826320603c_fm_a
        @ ( map_Ep1988204514693272906c_fm_a
          @ ^ [X: epistemic_fm_a] : ( cons_Epistemic_fm_a @ ( F @ X ) @ nil_Epistemic_fm_a )
          @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) ) ).

% concat_map_singleton
thf(fact_178_list__ex1__simps_I1_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o] :
      ~ ( list_e1371837923195959913c_fm_a @ P4 @ nil_li2451196919128234278c_fm_a ) ).

% list_ex1_simps(1)
thf(fact_179_list__ex1__simps_I1_J,axiom,
    ! [P4: set_Epistemic_fm_a > $o] :
      ~ ( list_e3415556844334454979c_fm_a @ P4 @ nil_se102576565402781184c_fm_a ) ).

% list_ex1_simps(1)
thf(fact_180_list__ex1__simps_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ~ ( list_e2031426293596896995c_fm_a @ P4 @ nil_Epistemic_fm_a ) ).

% list_ex1_simps(1)
thf(fact_181_K__thm,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a,Q: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Con_a @ P @ Q ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ).

% K_thm
thf(fact_182_conjunct_Osimps_I1_J,axiom,
    ( ( stalnaker_conjunct_a @ nil_Epistemic_fm_a )
    = ( epistemic_Imp_a @ epistemic_FF_a @ epistemic_FF_a ) ) ).

% conjunct.simps(1)
thf(fact_183_K__distrib__K__imp,axiom,
    ! [A: epistemic_fm_a > $o,I: a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_K_a @ I @ ( epistemic_imply_a @ G5 @ Q ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ I ) @ G5 ) @ ( epistemic_K_a @ I @ Q ) ) ) ) ).

% K_distrib_K_imp
thf(fact_184_map__tailrec__rev_Oelims,axiom,
    ! [X2: set_Epistemic_fm_a > epistemic_fm_a,Xa: list_s580375451141968640c_fm_a,Xb: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( map_ta3870718651422774037c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_se102576565402781184c_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: set_Epistemic_fm_a,As: list_s580375451141968640c_fm_a] :
              ( ( Xa
                = ( cons_s4394448069393209776c_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta3870718651422774037c_fm_a @ X2 @ As @ ( cons_Epistemic_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_185_map__tailrec__rev_Oelims,axiom,
    ! [X2: set_Epistemic_fm_a > list_Epistemic_fm_a,Xa: list_s580375451141968640c_fm_a,Xb: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( map_ta7115970949835247003c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_se102576565402781184c_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: set_Epistemic_fm_a,As: list_s580375451141968640c_fm_a] :
              ( ( Xa
                = ( cons_s4394448069393209776c_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta7115970949835247003c_fm_a @ X2 @ As @ ( cons_l8134865115577406678c_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_186_map__tailrec__rev_Oelims,axiom,
    ! [X2: epistemic_fm_a > list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Xb: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( map_ta3940434083879480187c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_Epistemic_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: epistemic_fm_a,As: list_Epistemic_fm_a] :
              ( ( Xa
                = ( cons_Epistemic_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta3940434083879480187c_fm_a @ X2 @ As @ ( cons_l8134865115577406678c_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_187_map__tailrec__rev_Oelims,axiom,
    ! [X2: list_Epistemic_fm_a > epistemic_fm_a,Xa: list_l6083326122719238310c_fm_a,Xb: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( map_ta7469096181376672879c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_li2451196919128234278c_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: list_Epistemic_fm_a,As: list_l6083326122719238310c_fm_a] :
              ( ( Xa
                = ( cons_l8134865115577406678c_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta7469096181376672879c_fm_a @ X2 @ As @ ( cons_Epistemic_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_188_map__tailrec__rev_Oelims,axiom,
    ! [X2: list_Epistemic_fm_a > list_Epistemic_fm_a,Xa: list_l6083326122719238310c_fm_a,Xb: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( map_ta5197791105168353781c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_li2451196919128234278c_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: list_Epistemic_fm_a,As: list_l6083326122719238310c_fm_a] :
              ( ( Xa
                = ( cons_l8134865115577406678c_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta5197791105168353781c_fm_a @ X2 @ As @ ( cons_l8134865115577406678c_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_189_map__tailrec__rev_Oelims,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a,Xa: list_Epistemic_fm_a,Xb: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( map_ta6565535454553546997c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( ( Xa = nil_Epistemic_fm_a )
         => ( Y != Xb ) )
       => ~ ! [A5: epistemic_fm_a,As: list_Epistemic_fm_a] :
              ( ( Xa
                = ( cons_Epistemic_fm_a @ A5 @ As ) )
             => ( Y
               != ( map_ta6565535454553546997c_fm_a @ X2 @ As @ ( cons_Epistemic_fm_a @ ( X2 @ A5 ) @ Xb ) ) ) ) ) ) ).

% map_tailrec_rev.elims
thf(fact_190_ord_Olexordp__eq__simps_I3_J,axiom,
    ! [Less: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ~ ( lexord2449210163466708806c_fm_a @ Less @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) @ nil_se102576565402781184c_fm_a ) ).

% ord.lexordp_eq_simps(3)
thf(fact_191_ord_Olexordp__eq__simps_I3_J,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ~ ( lexord3118506718869075820c_fm_a @ Less @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ nil_li2451196919128234278c_fm_a ) ).

% ord.lexordp_eq_simps(3)
thf(fact_192_ord_Olexordp__eq__simps_I3_J,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ~ ( lexord491902619044731238c_fm_a @ Less @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ nil_Epistemic_fm_a ) ).

% ord.lexordp_eq_simps(3)
thf(fact_193_ord_Olexordp__eq__simps_I4_J,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( lexord3118506718869075820c_fm_a @ Less @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
      = ( ( Less @ X2 @ Y )
        | ( ~ ( Less @ Y @ X2 )
          & ( lexord3118506718869075820c_fm_a @ Less @ Xs2 @ Ys ) ) ) ) ).

% ord.lexordp_eq_simps(4)
thf(fact_194_ord_Olexordp__eq__simps_I4_J,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( lexord491902619044731238c_fm_a @ Less @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) )
      = ( ( Less @ X2 @ Y )
        | ( ~ ( Less @ Y @ X2 )
          & ( lexord491902619044731238c_fm_a @ Less @ Xs2 @ Ys ) ) ) ) ).

% ord.lexordp_eq_simps(4)
thf(fact_195_ord_Olexordp__eq__simps_I2_J,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( lexord3118506718869075820c_fm_a @ Less @ Xs2 @ nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% ord.lexordp_eq_simps(2)
thf(fact_196_ord_Olexordp__eq__simps_I2_J,axiom,
    ! [Less: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
      ( ( lexord2449210163466708806c_fm_a @ Less @ Xs2 @ nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% ord.lexordp_eq_simps(2)
thf(fact_197_ord_Olexordp__eq__simps_I2_J,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( lexord491902619044731238c_fm_a @ Less @ Xs2 @ nil_Epistemic_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% ord.lexordp_eq_simps(2)
thf(fact_198_ord_Olexordp__eq__simps_I1_J,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a] : ( lexord3118506718869075820c_fm_a @ Less @ nil_li2451196919128234278c_fm_a @ Ys ) ).

% ord.lexordp_eq_simps(1)
thf(fact_199_ord_Olexordp__eq__simps_I1_J,axiom,
    ! [Less: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,Ys: list_s580375451141968640c_fm_a] : ( lexord2449210163466708806c_fm_a @ Less @ nil_se102576565402781184c_fm_a @ Ys ) ).

% ord.lexordp_eq_simps(1)
thf(fact_200_ord_Olexordp__eq__simps_I1_J,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,Ys: list_Epistemic_fm_a] : ( lexord491902619044731238c_fm_a @ Less @ nil_Epistemic_fm_a @ Ys ) ).

% ord.lexordp_eq_simps(1)
thf(fact_201_ord_Olexordp__eq__refl,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] : ( lexord491902619044731238c_fm_a @ Less @ Xs2 @ Xs2 ) ).

% ord.lexordp_eq_refl
thf(fact_202_ord_Olexordp__eq_Ocong,axiom,
    lexord491902619044731238c_fm_a = lexord491902619044731238c_fm_a ).

% ord.lexordp_eq.cong
thf(fact_203_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_204_fm_Odistinct_I9_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( epistemic_FF_a
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(9)
thf(fact_205_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_206_concat_Osimps_I1_J,axiom,
    ( ( concat6109960377493484129c_fm_a @ nil_li5178944226519631276c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% concat.simps(1)
thf(fact_207_concat_Osimps_I1_J,axiom,
    ( ( concat2941956077894552763c_fm_a @ nil_li5433889876484989702c_fm_a )
    = nil_se102576565402781184c_fm_a ) ).

% concat.simps(1)
thf(fact_208_concat_Osimps_I1_J,axiom,
    ( ( concat2780896542826320603c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_Epistemic_fm_a ) ).

% concat.simps(1)
thf(fact_209_map__concat,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_Ep1988204514693272906c_fm_a @ F @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
      = ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_210_map__concat,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( map_li3080774272885743684c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
      = ( concat6109960377493484129c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_211_map__concat,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_Ep4939040189629079504c_fm_a @ F @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
      = ( concat5652308878773863783c_fm_a @ ( map_li5567427098789011152c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_212_map__concat,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( map_li3858915945532548554c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
      = ( concat5652308878773863783c_fm_a @ ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_213_map__concat,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( map_li5516866612190465598c_fm_a @ F @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
      = ( concat2780896542826320603c_fm_a @ ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_214_map__concat,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
      = ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ Xs2 ) ) ) ).

% map_concat
thf(fact_215_eval_Osimps_I1_J,axiom,
    ! [Uu2: list_char > $o,Uv: epistemic_fm_a > $o] :
      ~ ( epistemic_eval_a @ Uu2 @ Uv @ epistemic_FF_a ) ).

% eval.simps(1)
thf(fact_216_ord_Olexordp__eq_OCons,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( Less @ X2 @ Y )
     => ( lexord3118506718869075820c_fm_a @ Less @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) ) ) ).

% ord.lexordp_eq.Cons
thf(fact_217_ord_Olexordp__eq_OCons,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Less @ X2 @ Y )
     => ( lexord491902619044731238c_fm_a @ Less @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) ).

% ord.lexordp_eq.Cons
thf(fact_218_ord_Olexordp__eq_OCons__eq,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ~ ( Less @ X2 @ Y )
     => ( ~ ( Less @ Y @ X2 )
       => ( ( lexord3118506718869075820c_fm_a @ Less @ Xs2 @ Ys )
         => ( lexord3118506718869075820c_fm_a @ Less @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) ) ) ) ) ).

% ord.lexordp_eq.Cons_eq
thf(fact_219_ord_Olexordp__eq_OCons__eq,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ~ ( Less @ X2 @ Y )
     => ( ~ ( Less @ Y @ X2 )
       => ( ( lexord491902619044731238c_fm_a @ Less @ Xs2 @ Ys )
         => ( lexord491902619044731238c_fm_a @ Less @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) ) ) ).

% ord.lexordp_eq.Cons_eq
thf(fact_220_ord_Olexordp__eq_ONil,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a] : ( lexord3118506718869075820c_fm_a @ Less @ nil_li2451196919128234278c_fm_a @ Ys ) ).

% ord.lexordp_eq.Nil
thf(fact_221_ord_Olexordp__eq_ONil,axiom,
    ! [Less: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,Ys: list_s580375451141968640c_fm_a] : ( lexord2449210163466708806c_fm_a @ Less @ nil_se102576565402781184c_fm_a @ Ys ) ).

% ord.lexordp_eq.Nil
thf(fact_222_ord_Olexordp__eq_ONil,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,Ys: list_Epistemic_fm_a] : ( lexord491902619044731238c_fm_a @ Less @ nil_Epistemic_fm_a @ Ys ) ).

% ord.lexordp_eq.Nil
thf(fact_223_K__Boole,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ G5 ) @ epistemic_FF_a ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_Boole
thf(fact_224_imply_Osimps_I1_J,axiom,
    ! [Q: epistemic_fm_a] :
      ( ( epistemic_imply_a @ nil_Epistemic_fm_a @ Q )
      = Q ) ).

% imply.simps(1)
thf(fact_225_list_Osimps_I7_J,axiom,
    ! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( F22 @ X21 @ X22 @ ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ X22 ) ) ) ).

% list.simps(7)
thf(fact_226_map__tailrec__rev_Osimps_I2_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,A2: epistemic_fm_a,As2: list_Epistemic_fm_a,Bs: list_l6083326122719238310c_fm_a] :
      ( ( map_ta3940434083879480187c_fm_a @ F @ ( cons_Epistemic_fm_a @ A2 @ As2 ) @ Bs )
      = ( map_ta3940434083879480187c_fm_a @ F @ As2 @ ( cons_l8134865115577406678c_fm_a @ ( F @ A2 ) @ Bs ) ) ) ).

% map_tailrec_rev.simps(2)
thf(fact_227_map__tailrec__rev_Osimps_I2_J,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,A2: list_Epistemic_fm_a,As2: list_l6083326122719238310c_fm_a,Bs: list_Epistemic_fm_a] :
      ( ( map_ta7469096181376672879c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ A2 @ As2 ) @ Bs )
      = ( map_ta7469096181376672879c_fm_a @ F @ As2 @ ( cons_Epistemic_fm_a @ ( F @ A2 ) @ Bs ) ) ) ).

% map_tailrec_rev.simps(2)
thf(fact_228_map__tailrec__rev_Osimps_I2_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,A2: list_Epistemic_fm_a,As2: list_l6083326122719238310c_fm_a,Bs: list_l6083326122719238310c_fm_a] :
      ( ( map_ta5197791105168353781c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ A2 @ As2 ) @ Bs )
      = ( map_ta5197791105168353781c_fm_a @ F @ As2 @ ( cons_l8134865115577406678c_fm_a @ ( F @ A2 ) @ Bs ) ) ) ).

% map_tailrec_rev.simps(2)
thf(fact_229_map__tailrec__rev_Osimps_I2_J,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A2: epistemic_fm_a,As2: list_Epistemic_fm_a,Bs: list_Epistemic_fm_a] :
      ( ( map_ta6565535454553546997c_fm_a @ F @ ( cons_Epistemic_fm_a @ A2 @ As2 ) @ Bs )
      = ( map_ta6565535454553546997c_fm_a @ F @ As2 @ ( cons_Epistemic_fm_a @ ( F @ A2 ) @ Bs ) ) ) ).

% map_tailrec_rev.simps(2)
thf(fact_230_list_Osimps_I6_J,axiom,
    ! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( rec_li4360243526537435568c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
      = F1 ) ).

% list.simps(6)
thf(fact_231_map__tailrec__rev_Osimps_I1_J,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Bs: list_Epistemic_fm_a] :
      ( ( map_ta6565535454553546997c_fm_a @ F @ nil_Epistemic_fm_a @ Bs )
      = Bs ) ).

% map_tailrec_rev.simps(1)
thf(fact_232_K__right__mp,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ P ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ ( epistemic_Imp_a @ P @ Q ) ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) ) ) ) ).

% K_right_mp
thf(fact_233_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_234_K__swap,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G5: list_Epistemic_fm_a,R: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ Q @ G5 ) ) @ R ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ ( cons_Epistemic_fm_a @ P @ G5 ) ) @ R ) ) ) ).

% K_swap
thf(fact_235_K__imply__Cons,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) ) ) ).

% K_imply_Cons
thf(fact_236_K__imply__head,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ P ) ) ).

% K_imply_head
thf(fact_237_ord_Olexordp__eq_Osimps,axiom,
    ( lexord2449210163466708806c_fm_a
    = ( ^ [Less2: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,A1: list_s580375451141968640c_fm_a,A22: list_s580375451141968640c_fm_a] :
          ( ? [Ys3: list_s580375451141968640c_fm_a] :
              ( ( A1 = nil_se102576565402781184c_fm_a )
              & ( A22 = Ys3 ) )
          | ? [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a,Ys3: list_s580375451141968640c_fm_a] :
              ( ( A1
                = ( cons_s4394448069393209776c_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_s4394448069393209776c_fm_a @ Y3 @ Ys3 ) )
              & ( Less2 @ X @ Y3 ) )
          | ? [X: set_Epistemic_fm_a,Y3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a,Ys3: list_s580375451141968640c_fm_a] :
              ( ( A1
                = ( cons_s4394448069393209776c_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_s4394448069393209776c_fm_a @ Y3 @ Ys3 ) )
              & ~ ( Less2 @ X @ Y3 )
              & ~ ( Less2 @ Y3 @ X )
              & ( lexord2449210163466708806c_fm_a @ Less2 @ Xs @ Ys3 ) ) ) ) ) ).

% ord.lexordp_eq.simps
thf(fact_238_ord_Olexordp__eq_Osimps,axiom,
    ( lexord3118506718869075820c_fm_a
    = ( ^ [Less2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A1: list_l6083326122719238310c_fm_a,A22: list_l6083326122719238310c_fm_a] :
          ( ? [Ys3: list_l6083326122719238310c_fm_a] :
              ( ( A1 = nil_li2451196919128234278c_fm_a )
              & ( A22 = Ys3 ) )
          | ? [X: list_Epistemic_fm_a,Y3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
              ( ( A1
                = ( cons_l8134865115577406678c_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_l8134865115577406678c_fm_a @ Y3 @ Ys3 ) )
              & ( Less2 @ X @ Y3 ) )
          | ? [X: list_Epistemic_fm_a,Y3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a,Ys3: list_l6083326122719238310c_fm_a] :
              ( ( A1
                = ( cons_l8134865115577406678c_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_l8134865115577406678c_fm_a @ Y3 @ Ys3 ) )
              & ~ ( Less2 @ X @ Y3 )
              & ~ ( Less2 @ Y3 @ X )
              & ( lexord3118506718869075820c_fm_a @ Less2 @ Xs @ Ys3 ) ) ) ) ) ).

% ord.lexordp_eq.simps
thf(fact_239_ord_Olexordp__eq_Osimps,axiom,
    ( lexord491902619044731238c_fm_a
    = ( ^ [Less2: epistemic_fm_a > epistemic_fm_a > $o,A1: list_Epistemic_fm_a,A22: list_Epistemic_fm_a] :
          ( ? [Ys3: list_Epistemic_fm_a] :
              ( ( A1 = nil_Epistemic_fm_a )
              & ( A22 = Ys3 ) )
          | ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
              ( ( A1
                = ( cons_Epistemic_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) )
              & ( Less2 @ X @ Y3 ) )
          | ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
              ( ( A1
                = ( cons_Epistemic_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) )
              & ~ ( Less2 @ X @ Y3 )
              & ~ ( Less2 @ Y3 @ X )
              & ( lexord491902619044731238c_fm_a @ Less2 @ Xs @ Ys3 ) ) ) ) ) ).

% ord.lexordp_eq.simps
thf(fact_240_ord_Olexordp__eq_Ocases,axiom,
    ! [Less: set_Epistemic_fm_a > set_Epistemic_fm_a > $o,A12: list_s580375451141968640c_fm_a,A23: list_s580375451141968640c_fm_a] :
      ( ( lexord2449210163466708806c_fm_a @ Less @ A12 @ A23 )
     => ( ( A12 != nil_se102576565402781184c_fm_a )
       => ( ! [X3: set_Epistemic_fm_a] :
              ( ? [Xs3: list_s580375451141968640c_fm_a] :
                  ( A12
                  = ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) )
             => ! [Y2: set_Epistemic_fm_a] :
                  ( ? [Ys2: list_s580375451141968640c_fm_a] :
                      ( A23
                      = ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) )
                 => ~ ( Less @ X3 @ Y2 ) ) )
         => ~ ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
                ( ( A12
                  = ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) )
               => ! [Ys2: list_s580375451141968640c_fm_a] :
                    ( ( A23
                      = ( cons_s4394448069393209776c_fm_a @ Y2 @ Ys2 ) )
                   => ( ~ ( Less @ X3 @ Y2 )
                     => ( ~ ( Less @ Y2 @ X3 )
                       => ~ ( lexord2449210163466708806c_fm_a @ Less @ Xs3 @ Ys2 ) ) ) ) ) ) ) ) ).

% ord.lexordp_eq.cases
thf(fact_241_ord_Olexordp__eq_Ocases,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A12: list_l6083326122719238310c_fm_a,A23: list_l6083326122719238310c_fm_a] :
      ( ( lexord3118506718869075820c_fm_a @ Less @ A12 @ A23 )
     => ( ( A12 != nil_li2451196919128234278c_fm_a )
       => ( ! [X3: list_Epistemic_fm_a] :
              ( ? [Xs3: list_l6083326122719238310c_fm_a] :
                  ( A12
                  = ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) )
             => ! [Y2: list_Epistemic_fm_a] :
                  ( ? [Ys2: list_l6083326122719238310c_fm_a] :
                      ( A23
                      = ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) )
                 => ~ ( Less @ X3 @ Y2 ) ) )
         => ~ ! [X3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
                ( ( A12
                  = ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) )
               => ! [Ys2: list_l6083326122719238310c_fm_a] :
                    ( ( A23
                      = ( cons_l8134865115577406678c_fm_a @ Y2 @ Ys2 ) )
                   => ( ~ ( Less @ X3 @ Y2 )
                     => ( ~ ( Less @ Y2 @ X3 )
                       => ~ ( lexord3118506718869075820c_fm_a @ Less @ Xs3 @ Ys2 ) ) ) ) ) ) ) ) ).

% ord.lexordp_eq.cases
thf(fact_242_ord_Olexordp__eq_Ocases,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,A12: list_Epistemic_fm_a,A23: list_Epistemic_fm_a] :
      ( ( lexord491902619044731238c_fm_a @ Less @ A12 @ A23 )
     => ( ( A12 != nil_Epistemic_fm_a )
       => ( ! [X3: epistemic_fm_a] :
              ( ? [Xs3: list_Epistemic_fm_a] :
                  ( A12
                  = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
             => ! [Y2: epistemic_fm_a] :
                  ( ? [Ys2: list_Epistemic_fm_a] :
                      ( A23
                      = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                 => ~ ( Less @ X3 @ Y2 ) ) )
         => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( A12
                  = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
               => ! [Ys2: list_Epistemic_fm_a] :
                    ( ( A23
                      = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                   => ( ~ ( Less @ X3 @ Y2 )
                     => ( ~ ( Less @ Y2 @ X3 )
                       => ~ ( lexord491902619044731238c_fm_a @ Less @ Xs3 @ Ys2 ) ) ) ) ) ) ) ) ).

% ord.lexordp_eq.cases
thf(fact_243_K__L__dual,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ).

% K_L_dual
thf(fact_244_K__LK,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ).

% K_LK
thf(fact_245_duality__taut,axiom,
    ! [I: a,P: epistemic_fm_a,Q: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) ) @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ Q @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) ) ) ).

% duality_taut
thf(fact_246_K__ImpI,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G5 ) @ Q ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ ( epistemic_Imp_a @ P @ Q ) ) ) ) ).

% K_ImpI
thf(fact_247_K__mp,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a,G5: list_Epistemic_fm_a] : ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ ( cons_Epistemic_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ G5 ) ) @ Q ) ) ).

% K_mp
thf(fact_248_K__imply__conjunct,axiom,
    ! [A: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% K_imply_conjunct
thf(fact_249_K__conjunct__imply,axiom,
    ! [A: epistemic_fm_a > $o,G5: list_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% K_conjunct_imply
thf(fact_250_imply__conjunct,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_imply_a @ G5 @ P ) @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) ) ) ).

% imply_conjunct
thf(fact_251_conjunct__imply,axiom,
    ! [G5: list_Epistemic_fm_a,P: epistemic_fm_a,G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( stalnaker_conjunct_a @ G5 ) @ P ) @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% conjunct_imply
thf(fact_252_rec__list__Nil__imp,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( F
        = ( rec_li4360243526537435568c_fm_a @ F1 @ F22 ) )
     => ( ( F @ nil_Epistemic_fm_a )
        = F1 ) ) ).

% rec_list_Nil_imp
thf(fact_253_rec__list__Cons__imp,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( F
        = ( rec_li4360243526537435568c_fm_a @ F1 @ F22 ) )
     => ( ( F @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
        = ( F22 @ X2 @ Xs2 @ ( F @ Xs2 ) ) ) ) ).

% rec_list_Cons_imp
thf(fact_254_product__lists_Osimps_I1_J,axiom,
    ( ( produc4433783857981728015c_fm_a @ nil_li5178944226519631276c_fm_a )
    = ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ nil_li5178944226519631276c_fm_a ) ) ).

% product_lists.simps(1)
thf(fact_255_product__lists_Osimps_I1_J,axiom,
    ( ( produc3894803040673298025c_fm_a @ nil_li5433889876484989702c_fm_a )
    = ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ nil_li5433889876484989702c_fm_a ) ) ).

% product_lists.simps(1)
thf(fact_256_product__lists_Osimps_I1_J,axiom,
    ( ( produc1391074687832863881c_fm_a @ nil_li2451196919128234278c_fm_a )
    = ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a ) ) ).

% product_lists.simps(1)
thf(fact_257_concat__map__maps,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
      = ( maps_E6072454603808916545c_fm_a @ F @ Xs2 ) ) ).

% concat_map_maps
thf(fact_258_concat__map__maps,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
      = ( maps_l2078986973461115323c_fm_a @ F @ Xs2 ) ) ).

% concat_map_maps
thf(fact_259_concat__map__maps,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( concat6109960377493484129c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
      = ( maps_E7773696912818698439c_fm_a @ F @ Xs2 ) ) ).

% concat_map_maps
thf(fact_260_concat__map__maps,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) )
      = ( maps_l3685687229838205249c_fm_a @ F @ Xs2 ) ) ).

% concat_map_maps
thf(fact_261_maps__def,axiom,
    ( maps_E6072454603808916545c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_Epistemic_fm_a,Xs: list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F2 @ Xs ) ) ) ) ).

% maps_def
thf(fact_262_maps__def,axiom,
    ( maps_l2078986973461115323c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F2 @ Xs ) ) ) ) ).

% maps_def
thf(fact_263_maps__def,axiom,
    ( maps_E7773696912818698439c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_Epistemic_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F2 @ Xs ) ) ) ) ).

% maps_def
thf(fact_264_maps__def,axiom,
    ( maps_l3685687229838205249c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs: list_l6083326122719238310c_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F2 @ Xs ) ) ) ) ).

% maps_def
thf(fact_265_subseqs_Osimps_I1_J,axiom,
    ( ( subseq3170398737635186805c_fm_a @ nil_li2451196919128234278c_fm_a )
    = ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ nil_li5178944226519631276c_fm_a ) ) ).

% subseqs.simps(1)
thf(fact_266_subseqs_Osimps_I1_J,axiom,
    ( ( subseq7171631445414591695c_fm_a @ nil_se102576565402781184c_fm_a )
    = ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ nil_li5433889876484989702c_fm_a ) ) ).

% subseqs.simps(1)
thf(fact_267_subseqs_Osimps_I1_J,axiom,
    ( ( subseq859285839621985007c_fm_a @ nil_Epistemic_fm_a )
    = ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ nil_li2451196919128234278c_fm_a ) ) ).

% subseqs.simps(1)
thf(fact_268_product__lists_Osimps_I2_J,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
      ( ( produc4433783857981728015c_fm_a @ ( cons_l2479501935080859996c_fm_a @ Xs2 @ Xss2 ) )
      = ( concat5652308878773863783c_fm_a
        @ ( map_li5567427098789011152c_fm_a
          @ ^ [X: list_Epistemic_fm_a] : ( map_li8347733892191492164c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X ) @ ( produc4433783857981728015c_fm_a @ Xss2 ) )
          @ Xs2 ) ) ) ).

% product_lists.simps(2)
thf(fact_269_product__lists_Osimps_I2_J,axiom,
    ! [Xs2: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
      ( ( produc1391074687832863881c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Xs2 @ Xss2 ) )
      = ( concat6109960377493484129c_fm_a
        @ ( map_Ep4939040189629079504c_fm_a
          @ ^ [X: epistemic_fm_a] : ( map_li3080774272885743684c_fm_a @ ( cons_Epistemic_fm_a @ X ) @ ( produc1391074687832863881c_fm_a @ Xss2 ) )
          @ Xs2 ) ) ) ).

% product_lists.simps(2)
thf(fact_270_List_Obind__def,axiom,
    ( bind_E8451893407412458119c_fm_a
    = ( ^ [Xs: list_Epistemic_fm_a,F2: epistemic_fm_a > list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F2 @ Xs ) ) ) ) ).

% List.bind_def
thf(fact_271_List_Obind__def,axiom,
    ( bind_l9085712471134790913c_fm_a
    = ( ^ [Xs: list_l6083326122719238310c_fm_a,F2: list_Epistemic_fm_a > list_Epistemic_fm_a] : ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ F2 @ Xs ) ) ) ) ).

% List.bind_def
thf(fact_272_List_Obind__def,axiom,
    ( bind_E5557050373637598221c_fm_a
    = ( ^ [Xs: list_Epistemic_fm_a,F2: epistemic_fm_a > list_l6083326122719238310c_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F2 @ Xs ) ) ) ) ).

% List.bind_def
thf(fact_273_List_Obind__def,axiom,
    ( bind_l6536575428307499399c_fm_a
    = ( ^ [Xs: list_l6083326122719238310c_fm_a,F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] : ( concat6109960377493484129c_fm_a @ ( map_li3858915945532548554c_fm_a @ F2 @ Xs ) ) ) ) ).

% List.bind_def
thf(fact_274_bind__simps_I1_J,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( bind_E5557050373637598221c_fm_a @ nil_Epistemic_fm_a @ F )
      = nil_li2451196919128234278c_fm_a ) ).

% bind_simps(1)
thf(fact_275_bind__simps_I1_J,axiom,
    ! [F: epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( bind_E2618557688023538791c_fm_a @ nil_Epistemic_fm_a @ F )
      = nil_se102576565402781184c_fm_a ) ).

% bind_simps(1)
thf(fact_276_bind__simps_I1_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( bind_l9085712471134790913c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
      = nil_Epistemic_fm_a ) ).

% bind_simps(1)
thf(fact_277_bind__simps_I1_J,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( bind_l6536575428307499399c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
      = nil_li2451196919128234278c_fm_a ) ).

% bind_simps(1)
thf(fact_278_bind__simps_I1_J,axiom,
    ! [F: list_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( bind_l1363406430957618913c_fm_a @ nil_li2451196919128234278c_fm_a @ F )
      = nil_se102576565402781184c_fm_a ) ).

% bind_simps(1)
thf(fact_279_bind__simps_I1_J,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( bind_s4731305998534098087c_fm_a @ nil_se102576565402781184c_fm_a @ F )
      = nil_Epistemic_fm_a ) ).

% bind_simps(1)
thf(fact_280_bind__simps_I1_J,axiom,
    ! [F: set_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( bind_s1677162095108884013c_fm_a @ nil_se102576565402781184c_fm_a @ F )
      = nil_li2451196919128234278c_fm_a ) ).

% bind_simps(1)
thf(fact_281_bind__simps_I1_J,axiom,
    ! [F: set_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( bind_s3527534645263337095c_fm_a @ nil_se102576565402781184c_fm_a @ F )
      = nil_se102576565402781184c_fm_a ) ).

% bind_simps(1)
thf(fact_282_bind__simps_I1_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( bind_E8451893407412458119c_fm_a @ nil_Epistemic_fm_a @ F )
      = nil_Epistemic_fm_a ) ).

% bind_simps(1)
thf(fact_283_list_Ocase__distrib,axiom,
    ! [H3: list_Epistemic_fm_a > list_Epistemic_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_284_list_Ocase__distrib,axiom,
    ! [H3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_285_list_Ocase__distrib,axiom,
    ! [H3: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_286_list_Ocase__distrib,axiom,
    ! [H3: list_l6083326122719238310c_fm_a > list_Epistemic_fm_a,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_287_list_Ocase__distrib,axiom,
    ! [H3: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_288_list_Ocase__distrib,axiom,
    ! [H3: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_289_list_Ocase__distrib,axiom,
    ! [H3: $o > list_Epistemic_fm_a,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l8442927312758267104c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_290_list_Ocase__distrib,axiom,
    ! [H3: $o > list_l6083326122719238310c_fm_a,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l5707353781634818138c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_291_list_Ocase__distrib,axiom,
    ! [H3: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
      ( ( H3 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
      = ( case_l2021589626981272552c_fm_a @ ( H3 @ F1 )
        @ ^ [X1: epistemic_fm_a,X23: list_Epistemic_fm_a] : ( H3 @ ( F22 @ X1 @ X23 ) )
        @ List ) ) ).

% list.case_distrib
thf(fact_292_list_Osimps_I5_J,axiom,
    ! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( F22 @ X21 @ X22 ) ) ).

% list.simps(5)
thf(fact_293_list_Osimps_I5_J,axiom,
    ! [F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( F22 @ X21 @ X22 ) ) ).

% list.simps(5)
thf(fact_294_list_Osimps_I5_J,axiom,
    ! [F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( F22 @ X21 @ X22 ) ) ).

% list.simps(5)
thf(fact_295_list_Osimps_I4_J,axiom,
    ! [F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
      = F1 ) ).

% list.simps(4)
thf(fact_296_list_Osimps_I4_J,axiom,
    ! [F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
      = F1 ) ).

% list.simps(4)
thf(fact_297_list_Osimps_I4_J,axiom,
    ! [F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o] :
      ( ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ nil_Epistemic_fm_a )
      = F1 ) ).

% list.simps(4)
thf(fact_298_maps__simps_I2_J,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( maps_E7773696912818698439c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% maps_simps(2)
thf(fact_299_maps__simps_I2_J,axiom,
    ! [F: epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( maps_E2162433029970929185c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% maps_simps(2)
thf(fact_300_maps__simps_I2_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( maps_l2078986973461115323c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_Epistemic_fm_a ) ).

% maps_simps(2)
thf(fact_301_maps__simps_I2_J,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( maps_l3685687229838205249c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% maps_simps(2)
thf(fact_302_maps__simps_I2_J,axiom,
    ! [F: list_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( maps_l5051011768039730075c_fm_a @ F @ nil_li2451196919128234278c_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% maps_simps(2)
thf(fact_303_maps__simps_I2_J,axiom,
    ! [F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( maps_s4275181340481488481c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_Epistemic_fm_a ) ).

% maps_simps(2)
thf(fact_304_maps__simps_I2_J,axiom,
    ! [F: set_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( maps_s5364767432190995175c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% maps_simps(2)
thf(fact_305_maps__simps_I2_J,axiom,
    ! [F: set_Epistemic_fm_a > list_s580375451141968640c_fm_a] :
      ( ( maps_s148483366175664193c_fm_a @ F @ nil_se102576565402781184c_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% maps_simps(2)
thf(fact_306_maps__simps_I2_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( maps_E6072454603808916545c_fm_a @ F @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% maps_simps(2)
thf(fact_307_AxB_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_AxB_a @ A2 )
     => ~ ! [P3: epistemic_fm_a,I3: a] :
            ( A2
           != ( epistemic_Imp_a @ P3 @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% AxB.cases
thf(fact_308_AxB_Osimps,axiom,
    ( epistemic_AxB_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [P2: epistemic_fm_a,I2: a] :
          ( A4
          = ( epistemic_Imp_a @ P2 @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% AxB.simps
thf(fact_309_AxB_Ointros,axiom,
    ! [P: epistemic_fm_a,I: a] : ( epistemic_AxB_a @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% AxB.intros
thf(fact_310_transpose_Osimps_I3_J,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a,Xss2: list_l985973790606564998c_fm_a] :
      ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
      = ( cons_l1626872963913326262c_fm_a
        @ ( cons_s4394448069393209776c_fm_a @ X2
          @ ( concat2941956077894552763c_fm_a
            @ ( map_li1341364954853471300c_fm_a
              @ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
                @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H @ nil_se102576565402781184c_fm_a ) )
              @ Xss2 ) ) )
        @ ( transp493887097527820938c_fm_a
          @ ( cons_l1626872963913326262c_fm_a @ Xs2
            @ ( concat4130251116320034881c_fm_a
              @ ( map_li7441020096712412618c_fm_a
                @ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
                  @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
                @ Xss2 ) ) ) ) ) ) ).

% transpose.simps(3)
thf(fact_311_transpose_Osimps_I3_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
      ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
      = ( cons_l2479501935080859996c_fm_a
        @ ( cons_l8134865115577406678c_fm_a @ X2
          @ ( concat6109960377493484129c_fm_a
            @ ( map_li8347733892191492164c_fm_a
              @ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
                @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H @ nil_li2451196919128234278c_fm_a ) )
              @ Xss2 ) ) )
        @ ( transp7189280393105805488c_fm_a
          @ ( cons_l2479501935080859996c_fm_a @ Xs2
            @ ( concat5652308878773863783c_fm_a
              @ ( map_li3568483382057536586c_fm_a
                @ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
                  @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
                @ Xss2 ) ) ) ) ) ) ).

% transpose.simps(3)
thf(fact_312_transpose_Osimps_I3_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
      ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
      = ( cons_l8134865115577406678c_fm_a
        @ ( cons_Epistemic_fm_a @ X2
          @ ( concat2780896542826320603c_fm_a
            @ ( map_li3080774272885743684c_fm_a
              @ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
                @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H @ nil_Epistemic_fm_a ) )
              @ Xss2 ) ) )
        @ ( transp2882070860200649898c_fm_a
          @ ( cons_l8134865115577406678c_fm_a @ Xs2
            @ ( concat6109960377493484129c_fm_a
              @ ( map_li3858915945532548554c_fm_a
                @ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
                  @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
                @ Xss2 ) ) ) ) ) ) ).

% transpose.simps(3)
thf(fact_313_transpose_Oelims,axiom,
    ! [X2: list_l985973790606564998c_fm_a,Y: list_l985973790606564998c_fm_a] :
      ( ( ( transp493887097527820938c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_li5433889876484989702c_fm_a )
         => ( Y != nil_li5433889876484989702c_fm_a ) )
       => ( ! [Xss: list_l985973790606564998c_fm_a] :
              ( ( X2
                = ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
             => ( Y
               != ( transp493887097527820938c_fm_a @ Xss ) ) )
         => ~ ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
                ( ( X2
                  = ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( Y
                 != ( cons_l1626872963913326262c_fm_a
                    @ ( cons_s4394448069393209776c_fm_a @ X3
                      @ ( concat2941956077894552763c_fm_a
                        @ ( map_li1341364954853471300c_fm_a
                          @ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
                            @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H @ nil_se102576565402781184c_fm_a ) )
                          @ Xss ) ) )
                    @ ( transp493887097527820938c_fm_a
                      @ ( cons_l1626872963913326262c_fm_a @ Xs3
                        @ ( concat4130251116320034881c_fm_a
                          @ ( map_li7441020096712412618c_fm_a
                            @ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
                              @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
                            @ Xss ) ) ) ) ) ) ) ) ) ) ).

% transpose.elims
thf(fact_314_transpose_Oelims,axiom,
    ! [X2: list_l3671048651222332332c_fm_a,Y: list_l3671048651222332332c_fm_a] :
      ( ( ( transp7189280393105805488c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_li5178944226519631276c_fm_a )
         => ( Y != nil_li5178944226519631276c_fm_a ) )
       => ( ! [Xss: list_l3671048651222332332c_fm_a] :
              ( ( X2
                = ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
             => ( Y
               != ( transp7189280393105805488c_fm_a @ Xss ) ) )
         => ~ ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
                ( ( X2
                  = ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( Y
                 != ( cons_l2479501935080859996c_fm_a
                    @ ( cons_l8134865115577406678c_fm_a @ X3
                      @ ( concat6109960377493484129c_fm_a
                        @ ( map_li8347733892191492164c_fm_a
                          @ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
                            @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H @ nil_li2451196919128234278c_fm_a ) )
                          @ Xss ) ) )
                    @ ( transp7189280393105805488c_fm_a
                      @ ( cons_l2479501935080859996c_fm_a @ Xs3
                        @ ( concat5652308878773863783c_fm_a
                          @ ( map_li3568483382057536586c_fm_a
                            @ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
                              @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
                            @ Xss ) ) ) ) ) ) ) ) ) ) ).

% transpose.elims
thf(fact_315_transpose_Oelims,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( transp2882070860200649898c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_li2451196919128234278c_fm_a )
         => ( Y != nil_li2451196919128234278c_fm_a ) )
       => ( ! [Xss: list_l6083326122719238310c_fm_a] :
              ( ( X2
                = ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
             => ( Y
               != ( transp2882070860200649898c_fm_a @ Xss ) ) )
         => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
                ( ( X2
                  = ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( Y
                 != ( cons_l8134865115577406678c_fm_a
                    @ ( cons_Epistemic_fm_a @ X3
                      @ ( concat2780896542826320603c_fm_a
                        @ ( map_li3080774272885743684c_fm_a
                          @ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
                            @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H @ nil_Epistemic_fm_a ) )
                          @ Xss ) ) )
                    @ ( transp2882070860200649898c_fm_a
                      @ ( cons_l8134865115577406678c_fm_a @ Xs3
                        @ ( concat6109960377493484129c_fm_a
                          @ ( map_li3858915945532548554c_fm_a
                            @ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
                              @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
                            @ Xss ) ) ) ) ) ) ) ) ) ) ).

% transpose.elims
thf(fact_316_transpose_Opinduct,axiom,
    ! [A0: list_l985973790606564998c_fm_a,P4: list_l985973790606564998c_fm_a > $o] :
      ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ A0 )
     => ( ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ nil_li5433889876484989702c_fm_a )
         => ( P4 @ nil_li5433889876484989702c_fm_a ) )
       => ( ! [Xss: list_l985973790606564998c_fm_a] :
              ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) )
             => ( ( P4 @ Xss )
               => ( P4 @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss ) ) ) )
         => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a,Xss: list_l985973790606564998c_fm_a] :
                ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( ( P4
                    @ ( cons_l1626872963913326262c_fm_a @ Xs3
                      @ ( concat4130251116320034881c_fm_a
                        @ ( map_li7441020096712412618c_fm_a
                          @ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
                            @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
                          @ Xss ) ) ) )
                 => ( P4 @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) )
           => ( P4 @ A0 ) ) ) ) ) ).

% transpose.pinduct
thf(fact_317_transpose_Opinduct,axiom,
    ! [A0: list_l3671048651222332332c_fm_a,P4: list_l3671048651222332332c_fm_a > $o] :
      ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ A0 )
     => ( ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ nil_li5178944226519631276c_fm_a )
         => ( P4 @ nil_li5178944226519631276c_fm_a ) )
       => ( ! [Xss: list_l3671048651222332332c_fm_a] :
              ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) )
             => ( ( P4 @ Xss )
               => ( P4 @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss ) ) ) )
         => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xss: list_l3671048651222332332c_fm_a] :
                ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( ( P4
                    @ ( cons_l2479501935080859996c_fm_a @ Xs3
                      @ ( concat5652308878773863783c_fm_a
                        @ ( map_li3568483382057536586c_fm_a
                          @ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
                            @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
                          @ Xss ) ) ) )
                 => ( P4 @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) )
           => ( P4 @ A0 ) ) ) ) ) ).

% transpose.pinduct
thf(fact_318_transpose_Opinduct,axiom,
    ! [A0: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ A0 )
     => ( ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ nil_li2451196919128234278c_fm_a )
         => ( P4 @ nil_li2451196919128234278c_fm_a ) )
       => ( ! [Xss: list_l6083326122719238310c_fm_a] :
              ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) )
             => ( ( P4 @ Xss )
               => ( P4 @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss ) ) ) )
         => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Xss: list_l6083326122719238310c_fm_a] :
                ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Xss ) )
               => ( ( P4
                    @ ( cons_l8134865115577406678c_fm_a @ Xs3
                      @ ( concat6109960377493484129c_fm_a
                        @ ( map_li3858915945532548554c_fm_a
                          @ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
                            @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
                          @ Xss ) ) ) )
                 => ( P4 @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Xss ) ) ) )
           => ( P4 @ A0 ) ) ) ) ) ).

% transpose.pinduct
thf(fact_319_transpose_Opsimps_I3_J,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a,Xss2: list_l985973790606564998c_fm_a] :
      ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
     => ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
        = ( cons_l1626872963913326262c_fm_a
          @ ( cons_s4394448069393209776c_fm_a @ X2
            @ ( concat2941956077894552763c_fm_a
              @ ( map_li1341364954853471300c_fm_a
                @ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
                  @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H @ nil_se102576565402781184c_fm_a ) )
                @ Xss2 ) ) )
          @ ( transp493887097527820938c_fm_a
            @ ( cons_l1626872963913326262c_fm_a @ Xs2
              @ ( concat4130251116320034881c_fm_a
                @ ( map_li7441020096712412618c_fm_a
                  @ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
                    @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
                  @ Xss2 ) ) ) ) ) ) ) ).

% transpose.psimps(3)
thf(fact_320_transpose_Opsimps_I3_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Xss2: list_l3671048651222332332c_fm_a] :
      ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
     => ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
        = ( cons_l2479501935080859996c_fm_a
          @ ( cons_l8134865115577406678c_fm_a @ X2
            @ ( concat6109960377493484129c_fm_a
              @ ( map_li8347733892191492164c_fm_a
                @ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
                  @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H @ nil_li2451196919128234278c_fm_a ) )
                @ Xss2 ) ) )
          @ ( transp7189280393105805488c_fm_a
            @ ( cons_l2479501935080859996c_fm_a @ Xs2
              @ ( concat5652308878773863783c_fm_a
                @ ( map_li3568483382057536586c_fm_a
                  @ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
                    @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
                  @ Xss2 ) ) ) ) ) ) ) ).

% transpose.psimps(3)
thf(fact_321_transpose_Opsimps_I3_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Xss2: list_l6083326122719238310c_fm_a] :
      ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
     => ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Xss2 ) )
        = ( cons_l8134865115577406678c_fm_a
          @ ( cons_Epistemic_fm_a @ X2
            @ ( concat2780896542826320603c_fm_a
              @ ( map_li3080774272885743684c_fm_a
                @ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
                  @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H @ nil_Epistemic_fm_a ) )
                @ Xss2 ) ) )
          @ ( transp2882070860200649898c_fm_a
            @ ( cons_l8134865115577406678c_fm_a @ Xs2
              @ ( concat6109960377493484129c_fm_a
                @ ( map_li3858915945532548554c_fm_a
                  @ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
                    @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
                  @ Xss2 ) ) ) ) ) ) ) ).

% transpose.psimps(3)
thf(fact_322_Ax5_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_Ax5_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ ( epistemic_Imp_a @ P3 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ).

% Ax5.cases
thf(fact_323_Ax5_Osimps,axiom,
    ( epistemic_Ax5_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ ( epistemic_Imp_a @ P2 @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% Ax5.simps
thf(fact_324_Ax5_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_Ax5_a @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% Ax5.intros
thf(fact_325_transpose_Opsimps_I1_J,axiom,
    ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ nil_li2451196919128234278c_fm_a )
   => ( ( transp2882070860200649898c_fm_a @ nil_li2451196919128234278c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ) ).

% transpose.psimps(1)
thf(fact_326_transpose_Opsimps_I2_J,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( accp_l8971127668057225909c_fm_a @ transp5805013372743109973c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
     => ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
        = ( transp7189280393105805488c_fm_a @ Xss2 ) ) ) ).

% transpose.psimps(2)
thf(fact_327_transpose_Opsimps_I2_J,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( accp_l1289336314643896847c_fm_a @ transp578517656548729263c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
     => ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
        = ( transp493887097527820938c_fm_a @ Xss2 ) ) ) ).

% transpose.psimps(2)
thf(fact_328_transpose_Opsimps_I2_J,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( accp_l7472382826029824047c_fm_a @ transp597054356388329423c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
     => ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
        = ( transp2882070860200649898c_fm_a @ Xss2 ) ) ) ).

% transpose.psimps(2)
thf(fact_329_transpose_Osimps_I1_J,axiom,
    ( ( transp2882070860200649898c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% transpose.simps(1)
thf(fact_330_list_Odisc__eq__case_I1_J,axiom,
    ! [List: list_l6083326122719238310c_fm_a] :
      ( ( List = nil_li2451196919128234278c_fm_a )
      = ( case_l3589819172248781038c_fm_a @ $true
        @ ^ [Uu: list_Epistemic_fm_a,Uv2: list_l6083326122719238310c_fm_a] : $false
        @ List ) ) ).

% list.disc_eq_case(1)
thf(fact_331_list_Odisc__eq__case_I1_J,axiom,
    ! [List: list_s580375451141968640c_fm_a] :
      ( ( List = nil_se102576565402781184c_fm_a )
      = ( case_l4166027460215902664c_fm_a @ $true
        @ ^ [Uu: set_Epistemic_fm_a,Uv2: list_s580375451141968640c_fm_a] : $false
        @ List ) ) ).

% list.disc_eq_case(1)
thf(fact_332_list_Odisc__eq__case_I1_J,axiom,
    ! [List: list_Epistemic_fm_a] :
      ( ( List = nil_Epistemic_fm_a )
      = ( case_l2021589626981272552c_fm_a @ $true
        @ ^ [Uu: epistemic_fm_a,Uv2: list_Epistemic_fm_a] : $false
        @ List ) ) ).

% list.disc_eq_case(1)
thf(fact_333_list_Odisc__eq__case_I2_J,axiom,
    ! [List: list_l6083326122719238310c_fm_a] :
      ( ( List != nil_li2451196919128234278c_fm_a )
      = ( case_l3589819172248781038c_fm_a @ $false
        @ ^ [Uu: list_Epistemic_fm_a,Uv2: list_l6083326122719238310c_fm_a] : $true
        @ List ) ) ).

% list.disc_eq_case(2)
thf(fact_334_list_Odisc__eq__case_I2_J,axiom,
    ! [List: list_s580375451141968640c_fm_a] :
      ( ( List != nil_se102576565402781184c_fm_a )
      = ( case_l4166027460215902664c_fm_a @ $false
        @ ^ [Uu: set_Epistemic_fm_a,Uv2: list_s580375451141968640c_fm_a] : $true
        @ List ) ) ).

% list.disc_eq_case(2)
thf(fact_335_list_Odisc__eq__case_I2_J,axiom,
    ! [List: list_Epistemic_fm_a] :
      ( ( List != nil_Epistemic_fm_a )
      = ( case_l2021589626981272552c_fm_a @ $false
        @ ^ [Uu: epistemic_fm_a,Uv2: list_Epistemic_fm_a] : $true
        @ List ) ) ).

% list.disc_eq_case(2)
thf(fact_336_transpose_Osimps_I2_J,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( transp7189280393105805488c_fm_a @ ( cons_l2479501935080859996c_fm_a @ nil_li2451196919128234278c_fm_a @ Xss2 ) )
      = ( transp7189280393105805488c_fm_a @ Xss2 ) ) ).

% transpose.simps(2)
thf(fact_337_transpose_Osimps_I2_J,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( transp493887097527820938c_fm_a @ ( cons_l1626872963913326262c_fm_a @ nil_se102576565402781184c_fm_a @ Xss2 ) )
      = ( transp493887097527820938c_fm_a @ Xss2 ) ) ).

% transpose.simps(2)
thf(fact_338_transpose_Osimps_I2_J,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( transp2882070860200649898c_fm_a @ ( cons_l8134865115577406678c_fm_a @ nil_Epistemic_fm_a @ Xss2 ) )
      = ( transp2882070860200649898c_fm_a @ Xss2 ) ) ).

% transpose.simps(2)
thf(fact_339_transpose__map__map,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( transp7189280393105805488c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ Xs2 ) )
      = ( map_li8347733892191492164c_fm_a @ ( map_li3080774272885743684c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_340_transpose__map__map,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( transp9220707655006416950c_fm_a @ ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ Xs2 ) )
      = ( map_li3568483382057536586c_fm_a @ ( map_li3858915945532548554c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_341_transpose__map__map,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( transp9220707655006416950c_fm_a @ ( map_li5567427098789011152c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F ) @ Xs2 ) )
      = ( map_li5567427098789011152c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F ) @ ( transp2882070860200649898c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_342_transpose__map__map,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( transp7189280393105805488c_fm_a @ ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ Xs2 ) )
      = ( map_li3858915945532548554c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F ) @ ( transp2882070860200649898c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_343_transpose__map__map,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( transp2882070860200649898c_fm_a @ ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ Xs2 ) )
      = ( map_li8743910666895923134c_fm_a @ ( map_li5516866612190465598c_fm_a @ F ) @ ( transp7189280393105805488c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_344_transpose__map__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( transp2882070860200649898c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ Xs2 ) )
      = ( map_li3080774272885743684c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( transp2882070860200649898c_fm_a @ Xs2 ) ) ) ).

% transpose_map_map
thf(fact_345_K5__L,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% K5_L
thf(fact_346_map__tailrec__def,axiom,
    ( map_ta875960198429730446c_fm_a
    = ( ^ [F2: epistemic_fm_a > epistemic_fm_a,As3: list_Epistemic_fm_a] : ( rev_Epistemic_fm_a @ ( map_ta6565535454553546997c_fm_a @ F2 @ As3 @ nil_Epistemic_fm_a ) ) ) ) ).

% map_tailrec_def
thf(fact_347_list__ex1__simps_I2_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( list_e1371837923195959913c_fm_a @ P4 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( ( ( P4 @ X2 )
         => ( list_a5890043570083025364c_fm_a
            @ ^ [Y3: list_Epistemic_fm_a] :
                ( ~ ( P4 @ Y3 )
                | ( X2 = Y3 ) )
            @ Xs2 ) )
        & ( ~ ( P4 @ X2 )
         => ( list_e1371837923195959913c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% list_ex1_simps(2)
thf(fact_348_list__ex1__simps_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( list_e2031426293596896995c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ( ( P4 @ X2 )
         => ( list_a5841931967666341838c_fm_a
            @ ^ [Y3: epistemic_fm_a] :
                ( ~ ( P4 @ Y3 )
                | ( X2 = Y3 ) )
            @ Xs2 ) )
        & ( ~ ( P4 @ X2 )
         => ( list_e2031426293596896995c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% list_ex1_simps(2)
thf(fact_349_transpose__aux__filter__tail,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( concat5652308878773863783c_fm_a
        @ ( map_li3568483382057536586c_fm_a
          @ ( case_l7601246044141707098c_fm_a @ nil_li5178944226519631276c_fm_a
            @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l2479501935080859996c_fm_a @ T2 @ nil_li5178944226519631276c_fm_a ) )
          @ Xss2 ) )
      = ( map_li8347733892191492164c_fm_a @ tl_lis3363300823944467983c_fm_a
        @ ( filter389827114350055331c_fm_a
          @ ^ [Ys3: list_l6083326122719238310c_fm_a] : ( Ys3 != nil_li2451196919128234278c_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_tail
thf(fact_350_transpose__aux__filter__tail,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( concat4130251116320034881c_fm_a
        @ ( map_li7441020096712412618c_fm_a
          @ ( case_l4953383812495590490c_fm_a @ nil_li5433889876484989702c_fm_a
            @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_l1626872963913326262c_fm_a @ T2 @ nil_li5433889876484989702c_fm_a ) )
          @ Xss2 ) )
      = ( map_li1341364954853471300c_fm_a @ tl_set2007602089164433257c_fm_a
        @ ( filter1974008165531859069c_fm_a
          @ ^ [Ys3: list_s580375451141968640c_fm_a] : ( Ys3 != nil_se102576565402781184c_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_tail
thf(fact_351_transpose__aux__filter__tail,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( concat6109960377493484129c_fm_a
        @ ( map_li3858915945532548554c_fm_a
          @ ( case_l5707353781634818138c_fm_a @ nil_li2451196919128234278c_fm_a
            @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_l8134865115577406678c_fm_a @ T2 @ nil_li2451196919128234278c_fm_a ) )
          @ Xss2 ) )
      = ( map_li3080774272885743684c_fm_a @ tl_Epistemic_fm_a
        @ ( filter441479637125139101c_fm_a
          @ ^ [Ys3: list_Epistemic_fm_a] : ( Ys3 != nil_Epistemic_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_tail
thf(fact_352_Shift__def,axiom,
    ( bNF_Gr2321306230395443647c_fm_a
    = ( ^ [Kl: set_li1092409891198325638c_fm_a,K: list_Epistemic_fm_a] :
          ( collec1112116247058879121c_fm_a
          @ ^ [Kl2: list_l6083326122719238310c_fm_a] : ( member7465314387053329231c_fm_a @ ( cons_l8134865115577406678c_fm_a @ K @ Kl2 ) @ Kl ) ) ) ) ).

% Shift_def
thf(fact_353_Shift__def,axiom,
    ( bNF_Gr8437504134799245625c_fm_a
    = ( ^ [Kl: set_li769143395467472256c_fm_a,K: epistemic_fm_a] :
          ( collec5191077796991884427c_fm_a
          @ ^ [Kl2: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ K @ Kl2 ) @ Kl ) ) ) ) ).

% Shift_def
thf(fact_354_subseqs_Osimps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( subseq3170398737635186805c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append9013695642829458881c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 ) @ ( subseq3170398737635186805c_fm_a @ Xs2 ) ) @ ( subseq3170398737635186805c_fm_a @ Xs2 ) ) ) ).

% subseqs.simps(2)
thf(fact_355_subseqs_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( subseq859285839621985007c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( subseq859285839621985007c_fm_a @ Xs2 ) ) @ ( subseq859285839621985007c_fm_a @ Xs2 ) ) ) ).

% subseqs.simps(2)
thf(fact_356_K__DisE,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a,R: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ G5 ) @ R ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ Q @ G5 ) @ R ) )
       => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ ( epistemic_Dis_a @ P @ Q ) ) )
         => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ R ) ) ) ) ) ).

% K_DisE
thf(fact_357_K__DisL,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,P5: epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ Ps ) @ Q ) )
     => ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P5 @ Ps ) @ Q ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ ( epistemic_Dis_a @ P @ P5 ) @ Ps ) @ Q ) ) ) ) ).

% K_DisL
thf(fact_358_remdups__adj__Cons,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) )
      = ( case_l6572946392233364704c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a )
        @ ^ [Y3: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] : ( if_lis3811715425919989702c_fm_a @ ( X2 = Y3 ) @ ( cons_s4394448069393209776c_fm_a @ Y3 @ Xs ) @ ( cons_s4394448069393209776c_fm_a @ X2 @ ( cons_s4394448069393209776c_fm_a @ Y3 @ Xs ) ) )
        @ ( remdup2256950222776403766c_fm_a @ Xs2 ) ) ) ).

% remdups_adj_Cons
thf(fact_359_remdups__adj__Cons,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( case_l116314299590685792c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a )
        @ ^ [Y3: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] : ( if_lis342421823373228652c_fm_a @ ( X2 = Y3 ) @ ( cons_l8134865115577406678c_fm_a @ Y3 @ Xs ) @ ( cons_l8134865115577406678c_fm_a @ X2 @ ( cons_l8134865115577406678c_fm_a @ Y3 @ Xs ) ) )
        @ ( remdup8355899821003448156c_fm_a @ Xs2 ) ) ) ).

% remdups_adj_Cons
thf(fact_360_remdups__adj__Cons,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( case_l8442927312758267104c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a )
        @ ^ [Y3: epistemic_fm_a,Xs: list_Epistemic_fm_a] : ( if_lis2878681784746929638c_fm_a @ ( X2 = Y3 ) @ ( cons_Epistemic_fm_a @ Y3 @ Xs ) @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y3 @ Xs ) ) )
        @ ( remdup1727679340039403862c_fm_a @ Xs2 ) ) ) ).

% remdups_adj_Cons
thf(fact_361_append_Oassoc,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,B: list_l6083326122719238310c_fm_a,C: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ ( append1384085151619559355c_fm_a @ A2 @ B ) @ C )
      = ( append1384085151619559355c_fm_a @ A2 @ ( append1384085151619559355c_fm_a @ B @ C ) ) ) ).

% append.assoc
thf(fact_362_append_Oassoc,axiom,
    ! [A2: list_Epistemic_fm_a,B: list_Epistemic_fm_a,C: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ ( append9179727413925872949c_fm_a @ A2 @ B ) @ C )
      = ( append9179727413925872949c_fm_a @ A2 @ ( append9179727413925872949c_fm_a @ B @ C ) ) ) ).

% append.assoc
thf(fact_363_append__assoc,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) @ Zs3 )
      = ( append1384085151619559355c_fm_a @ Xs2 @ ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) ) ) ).

% append_assoc
thf(fact_364_append__assoc,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) @ Zs3 )
      = ( append9179727413925872949c_fm_a @ Xs2 @ ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) ) ) ).

% append_assoc
thf(fact_365_append__same__eq,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Ys @ Xs2 )
        = ( append1384085151619559355c_fm_a @ Zs3 @ Xs2 ) )
      = ( Ys = Zs3 ) ) ).

% append_same_eq
thf(fact_366_append__same__eq,axiom,
    ! [Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Ys @ Xs2 )
        = ( append9179727413925872949c_fm_a @ Zs3 @ Xs2 ) )
      = ( Ys = Zs3 ) ) ).

% append_same_eq
thf(fact_367_same__append__eq,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
        = ( append1384085151619559355c_fm_a @ Xs2 @ Zs3 ) )
      = ( Ys = Zs3 ) ) ).

% same_append_eq
thf(fact_368_same__append__eq,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
        = ( append9179727413925872949c_fm_a @ Xs2 @ Zs3 ) )
      = ( Ys = Zs3 ) ) ).

% same_append_eq
thf(fact_369_rev__rev__ident,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( rev_Epistemic_fm_a @ Xs2 ) )
      = Xs2 ) ).

% rev_rev_ident
thf(fact_370_rev__is__rev__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( rev_Epistemic_fm_a @ Xs2 )
        = ( rev_Epistemic_fm_a @ Ys ) )
      = ( Xs2 = Ys ) ) ).

% rev_is_rev_conv
thf(fact_371_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_372_filter__filter,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Q4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( filter441479637125139101c_fm_a @ P4 @ ( filter441479637125139101c_fm_a @ Q4 @ Xs2 ) )
      = ( filter441479637125139101c_fm_a
        @ ^ [X: list_Epistemic_fm_a] :
            ( ( Q4 @ X )
            & ( P4 @ X ) )
        @ Xs2 ) ) ).

% filter_filter
thf(fact_373_filter__filter,axiom,
    ! [P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( filter7636273809395300631c_fm_a @ P4 @ ( filter7636273809395300631c_fm_a @ Q4 @ Xs2 ) )
      = ( filter7636273809395300631c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( Q4 @ X )
            & ( P4 @ X ) )
        @ Xs2 ) ) ).

% filter_filter
thf(fact_374_append__is__Nil__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
        = nil_li2451196919128234278c_fm_a )
      = ( ( Xs2 = nil_li2451196919128234278c_fm_a )
        & ( Ys = nil_li2451196919128234278c_fm_a ) ) ) ).

% append_is_Nil_conv
thf(fact_375_append__is__Nil__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( append5257919162946131733c_fm_a @ Xs2 @ Ys )
        = nil_se102576565402781184c_fm_a )
      = ( ( Xs2 = nil_se102576565402781184c_fm_a )
        & ( Ys = nil_se102576565402781184c_fm_a ) ) ) ).

% append_is_Nil_conv
thf(fact_376_append__is__Nil__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
        = nil_Epistemic_fm_a )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        & ( Ys = nil_Epistemic_fm_a ) ) ) ).

% append_is_Nil_conv
thf(fact_377_Nil__is__append__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( ( Xs2 = nil_li2451196919128234278c_fm_a )
        & ( Ys = nil_li2451196919128234278c_fm_a ) ) ) ).

% Nil_is_append_conv
thf(fact_378_Nil__is__append__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
      = ( ( Xs2 = nil_se102576565402781184c_fm_a )
        & ( Ys = nil_se102576565402781184c_fm_a ) ) ) ).

% Nil_is_append_conv
thf(fact_379_Nil__is__append__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        & ( Ys = nil_Epistemic_fm_a ) ) ) ).

% Nil_is_append_conv
thf(fact_380_self__append__conv2,axiom,
    ! [Y: list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Y
        = ( append1384085151619559355c_fm_a @ Xs2 @ Y ) )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% self_append_conv2
thf(fact_381_self__append__conv2,axiom,
    ! [Y: list_s580375451141968640c_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( Y
        = ( append5257919162946131733c_fm_a @ Xs2 @ Y ) )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% self_append_conv2
thf(fact_382_self__append__conv2,axiom,
    ! [Y: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( Y
        = ( append9179727413925872949c_fm_a @ Xs2 @ Y ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% self_append_conv2
thf(fact_383_append__self__conv2,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
        = Ys )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% append_self_conv2
thf(fact_384_append__self__conv2,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( append5257919162946131733c_fm_a @ Xs2 @ Ys )
        = Ys )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% append_self_conv2
thf(fact_385_append__self__conv2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
        = Ys )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% append_self_conv2
thf(fact_386_self__append__conv,axiom,
    ! [Y: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( Y
        = ( append1384085151619559355c_fm_a @ Y @ Ys ) )
      = ( Ys = nil_li2451196919128234278c_fm_a ) ) ).

% self_append_conv
thf(fact_387_self__append__conv,axiom,
    ! [Y: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( Y
        = ( append5257919162946131733c_fm_a @ Y @ Ys ) )
      = ( Ys = nil_se102576565402781184c_fm_a ) ) ).

% self_append_conv
thf(fact_388_self__append__conv,axiom,
    ! [Y: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Y
        = ( append9179727413925872949c_fm_a @ Y @ Ys ) )
      = ( Ys = nil_Epistemic_fm_a ) ) ).

% self_append_conv
thf(fact_389_append__self__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
        = Xs2 )
      = ( Ys = nil_li2451196919128234278c_fm_a ) ) ).

% append_self_conv
thf(fact_390_append__self__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( append5257919162946131733c_fm_a @ Xs2 @ Ys )
        = Xs2 )
      = ( Ys = nil_se102576565402781184c_fm_a ) ) ).

% append_self_conv
thf(fact_391_append__self__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
        = Xs2 )
      = ( Ys = nil_Epistemic_fm_a ) ) ).

% append_self_conv
thf(fact_392_append__Nil2,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ Xs2 @ nil_li2451196919128234278c_fm_a )
      = Xs2 ) ).

% append_Nil2
thf(fact_393_append__Nil2,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( append5257919162946131733c_fm_a @ Xs2 @ nil_se102576565402781184c_fm_a )
      = Xs2 ) ).

% append_Nil2
thf(fact_394_append__Nil2,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ Xs2 @ nil_Epistemic_fm_a )
      = Xs2 ) ).

% append_Nil2
thf(fact_395_append_Oright__neutral,axiom,
    ! [A2: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ A2 @ nil_li2451196919128234278c_fm_a )
      = A2 ) ).

% append.right_neutral
thf(fact_396_append_Oright__neutral,axiom,
    ! [A2: list_s580375451141968640c_fm_a] :
      ( ( append5257919162946131733c_fm_a @ A2 @ nil_se102576565402781184c_fm_a )
      = A2 ) ).

% append.right_neutral
thf(fact_397_append_Oright__neutral,axiom,
    ! [A2: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ A2 @ nil_Epistemic_fm_a )
      = A2 ) ).

% append.right_neutral
thf(fact_398_map__append,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( map_Ep1988204514693272906c_fm_a @ F @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( append1384085151619559355c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) @ ( map_Ep1988204514693272906c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_399_map__append,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( map_li3080774272885743684c_fm_a @ F @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append1384085151619559355c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) @ ( map_li3080774272885743684c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_400_map__append,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( map_Ep4939040189629079504c_fm_a @ F @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( append9013695642829458881c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) @ ( map_Ep4939040189629079504c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_401_map__append,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( map_li3858915945532548554c_fm_a @ F @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append9013695642829458881c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) @ ( map_li3858915945532548554c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_402_map__append,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( map_li5516866612190465598c_fm_a @ F @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append9179727413925872949c_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) @ ( map_li5516866612190465598c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_403_map__append,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( append9179727413925872949c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) @ ( map_Ep7084560364594560580c_fm_a @ F @ Ys ) ) ) ).

% map_append
thf(fact_404_rev__is__Nil__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( rev_li1443896382544221062c_fm_a @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% rev_is_Nil_conv
thf(fact_405_rev__is__Nil__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( rev_se1616163181097742432c_fm_a @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% rev_is_Nil_conv
thf(fact_406_rev__is__Nil__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( rev_Epistemic_fm_a @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% rev_is_Nil_conv
thf(fact_407_Nil__is__rev__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( rev_li1443896382544221062c_fm_a @ Xs2 ) )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% Nil_is_rev_conv
thf(fact_408_Nil__is__rev__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( rev_se1616163181097742432c_fm_a @ Xs2 ) )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% Nil_is_rev_conv
thf(fact_409_Nil__is__rev__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( rev_Epistemic_fm_a @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% Nil_is_rev_conv
thf(fact_410_filter__append,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( filter441479637125139101c_fm_a @ P4 @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append1384085151619559355c_fm_a @ ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) @ ( filter441479637125139101c_fm_a @ P4 @ Ys ) ) ) ).

% filter_append
thf(fact_411_filter__append,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( filter7636273809395300631c_fm_a @ P4 @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( append9179727413925872949c_fm_a @ ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) @ ( filter7636273809395300631c_fm_a @ P4 @ Ys ) ) ) ).

% filter_append
thf(fact_412_rev__append,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append1384085151619559355c_fm_a @ ( rev_li1443896382544221062c_fm_a @ Ys ) @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ).

% rev_append
thf(fact_413_rev__append,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ Ys ) @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% rev_append
thf(fact_414_remdups__adj__Nil__iff,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( remdup8355899821003448156c_fm_a @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% remdups_adj_Nil_iff
thf(fact_415_remdups__adj__Nil__iff,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( remdup2256950222776403766c_fm_a @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% remdups_adj_Nil_iff
thf(fact_416_remdups__adj__Nil__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( remdup1727679340039403862c_fm_a @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% remdups_adj_Nil_iff
thf(fact_417_list_Opred__inject_I2_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o,A2: list_Epistemic_fm_a,Aa: list_l6083326122719238310c_fm_a] :
      ( ( list_a5890043570083025364c_fm_a @ P4 @ ( cons_l8134865115577406678c_fm_a @ A2 @ Aa ) )
      = ( ( P4 @ A2 )
        & ( list_a5890043570083025364c_fm_a @ P4 @ Aa ) ) ) ).

% list.pred_inject(2)
thf(fact_418_list_Opred__inject_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o,A2: epistemic_fm_a,Aa: list_Epistemic_fm_a] :
      ( ( list_a5841931967666341838c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ A2 @ Aa ) )
      = ( ( P4 @ A2 )
        & ( list_a5841931967666341838c_fm_a @ P4 @ Aa ) ) ) ).

% list.pred_inject(2)
thf(fact_419_list__all__simps_I1_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( list_a5890043570083025364c_fm_a @ P4 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( ( P4 @ X2 )
        & ( list_a5890043570083025364c_fm_a @ P4 @ Xs2 ) ) ) ).

% list_all_simps(1)
thf(fact_420_list__all__simps_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( list_a5841931967666341838c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ( P4 @ X2 )
        & ( list_a5841931967666341838c_fm_a @ P4 @ Xs2 ) ) ) ).

% list_all_simps(1)
thf(fact_421_list__all__simps_I2_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o] : ( list_a5890043570083025364c_fm_a @ P4 @ nil_li2451196919128234278c_fm_a ) ).

% list_all_simps(2)
thf(fact_422_list__all__simps_I2_J,axiom,
    ! [P4: set_Epistemic_fm_a > $o] : ( list_a5130230249644717486c_fm_a @ P4 @ nil_se102576565402781184c_fm_a ) ).

% list_all_simps(2)
thf(fact_423_list__all__simps_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o] : ( list_a5841931967666341838c_fm_a @ P4 @ nil_Epistemic_fm_a ) ).

% list_all_simps(2)
thf(fact_424_list__all__append,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( list_a5890043570083025364c_fm_a @ P4 @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( ( list_a5890043570083025364c_fm_a @ P4 @ Xs2 )
        & ( list_a5890043570083025364c_fm_a @ P4 @ Ys ) ) ) ).

% list_all_append
thf(fact_425_list__all__append,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( list_a5841931967666341838c_fm_a @ P4 @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( ( list_a5841931967666341838c_fm_a @ P4 @ Xs2 )
        & ( list_a5841931967666341838c_fm_a @ P4 @ Ys ) ) ) ).

% list_all_append
thf(fact_426_remdups__adj__rev,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( rev_Epistemic_fm_a @ Xs2 ) )
      = ( rev_Epistemic_fm_a @ ( remdup1727679340039403862c_fm_a @ Xs2 ) ) ) ).

% remdups_adj_rev
thf(fact_427_list__all__rev,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( list_a5841931967666341838c_fm_a @ P4 @ ( rev_Epistemic_fm_a @ Xs2 ) )
      = ( list_a5841931967666341838c_fm_a @ P4 @ Xs2 ) ) ).

% list_all_rev
thf(fact_428_append1__eq__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a,Ys: list_s580375451141968640c_fm_a,Y: set_Epistemic_fm_a] :
      ( ( ( append5257919162946131733c_fm_a @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) )
        = ( append5257919162946131733c_fm_a @ Ys @ ( cons_s4394448069393209776c_fm_a @ Y @ nil_se102576565402781184c_fm_a ) ) )
      = ( ( Xs2 = Ys )
        & ( X2 = Y ) ) ) ).

% append1_eq_conv
thf(fact_429_append1__eq__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) )
        = ( append1384085151619559355c_fm_a @ Ys @ ( cons_l8134865115577406678c_fm_a @ Y @ nil_li2451196919128234278c_fm_a ) ) )
      = ( ( Xs2 = Ys )
        & ( X2 = Y ) ) ) ).

% append1_eq_conv
thf(fact_430_append1__eq__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a,Ys: list_Epistemic_fm_a,Y: epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
        = ( append9179727413925872949c_fm_a @ Ys @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) )
      = ( ( Xs2 = Ys )
        & ( X2 = Y ) ) ) ).

% append1_eq_conv
thf(fact_431_rev__singleton__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a] :
      ( ( ( rev_se1616163181097742432c_fm_a @ Xs2 )
        = ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) )
      = ( Xs2
        = ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ) ).

% rev_singleton_conv
thf(fact_432_rev__singleton__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a] :
      ( ( ( rev_li1443896382544221062c_fm_a @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) )
      = ( Xs2
        = ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ) ).

% rev_singleton_conv
thf(fact_433_rev__singleton__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( ( rev_Epistemic_fm_a @ Xs2 )
        = ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
      = ( Xs2
        = ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) ).

% rev_singleton_conv
thf(fact_434_singleton__rev__conv,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a )
        = ( rev_se1616163181097742432c_fm_a @ Xs2 ) )
      = ( ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a )
        = Xs2 ) ) ).

% singleton_rev_conv
thf(fact_435_singleton__rev__conv,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a )
        = ( rev_li1443896382544221062c_fm_a @ Xs2 ) )
      = ( ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a )
        = Xs2 ) ) ).

% singleton_rev_conv
thf(fact_436_singleton__rev__conv,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a )
        = ( rev_Epistemic_fm_a @ Xs2 ) )
      = ( ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a )
        = Xs2 ) ) ).

% singleton_rev_conv
thf(fact_437_tl__append2,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( tl_lis3363300823944467983c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
        = ( append1384085151619559355c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) @ Ys ) ) ) ).

% tl_append2
thf(fact_438_tl__append2,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( tl_set2007602089164433257c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
        = ( append5257919162946131733c_fm_a @ ( tl_set2007602089164433257c_fm_a @ Xs2 ) @ Ys ) ) ) ).

% tl_append2
thf(fact_439_tl__append2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs2 ) @ Ys ) ) ) ).

% tl_append2
thf(fact_440_remdups__adj__Cons__alt,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( cons_l8134865115577406678c_fm_a @ X2 @ ( tl_lis3363300823944467983c_fm_a @ ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) ) )
      = ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) ) ).

% remdups_adj_Cons_alt
thf(fact_441_remdups__adj__Cons__alt,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( cons_Epistemic_fm_a @ X2 @ ( tl_Epistemic_fm_a @ ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) )
      = ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) ).

% remdups_adj_Cons_alt
thf(fact_442_bind__simps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( bind_E5557050373637598221c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ F )
      = ( append1384085151619559355c_fm_a @ ( F @ X2 ) @ ( bind_E5557050373637598221c_fm_a @ Xs2 @ F ) ) ) ).

% bind_simps(2)
thf(fact_443_bind__simps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( bind_E8451893407412458119c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ F )
      = ( append9179727413925872949c_fm_a @ ( F @ X2 ) @ ( bind_E8451893407412458119c_fm_a @ Xs2 @ F ) ) ) ).

% bind_simps(2)
thf(fact_444_bind__simps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( bind_l6536575428307499399c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ F )
      = ( append1384085151619559355c_fm_a @ ( F @ X2 ) @ ( bind_l6536575428307499399c_fm_a @ Xs2 @ F ) ) ) ).

% bind_simps(2)
thf(fact_445_bind__simps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( bind_l9085712471134790913c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ F )
      = ( append9179727413925872949c_fm_a @ ( F @ X2 ) @ ( bind_l9085712471134790913c_fm_a @ Xs2 @ F ) ) ) ).

% bind_simps(2)
thf(fact_446_concat__append,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( concat2780896542826320603c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( append9179727413925872949c_fm_a @ ( concat2780896542826320603c_fm_a @ Xs2 ) @ ( concat2780896542826320603c_fm_a @ Ys ) ) ) ).

% concat_append
thf(fact_447_concat__append,axiom,
    ! [Xs2: list_l3671048651222332332c_fm_a,Ys: list_l3671048651222332332c_fm_a] :
      ( ( concat6109960377493484129c_fm_a @ ( append9013695642829458881c_fm_a @ Xs2 @ Ys ) )
      = ( append1384085151619559355c_fm_a @ ( concat6109960377493484129c_fm_a @ Xs2 ) @ ( concat6109960377493484129c_fm_a @ Ys ) ) ) ).

% concat_append
thf(fact_448_rev__eq__Cons__iff,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Y: set_Epistemic_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( rev_se1616163181097742432c_fm_a @ Xs2 )
        = ( cons_s4394448069393209776c_fm_a @ Y @ Ys ) )
      = ( Xs2
        = ( append5257919162946131733c_fm_a @ ( rev_se1616163181097742432c_fm_a @ Ys ) @ ( cons_s4394448069393209776c_fm_a @ Y @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% rev_eq_Cons_iff
thf(fact_449_rev__eq__Cons__iff,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Y: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( rev_li1443896382544221062c_fm_a @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ Y @ Ys ) )
      = ( Xs2
        = ( append1384085151619559355c_fm_a @ ( rev_li1443896382544221062c_fm_a @ Ys ) @ ( cons_l8134865115577406678c_fm_a @ Y @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% rev_eq_Cons_iff
thf(fact_450_rev__eq__Cons__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( rev_Epistemic_fm_a @ Xs2 )
        = ( cons_Epistemic_fm_a @ Y @ Ys ) )
      = ( Xs2
        = ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ Ys ) @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) ) ) ).

% rev_eq_Cons_iff
thf(fact_451_remdups__adj__append,axiom,
    ! [Xs_1: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a,Xs_2: list_s580375451141968640c_fm_a] :
      ( ( remdup2256950222776403766c_fm_a @ ( append5257919162946131733c_fm_a @ Xs_1 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs_2 ) ) )
      = ( append5257919162946131733c_fm_a @ ( remdup2256950222776403766c_fm_a @ ( append5257919162946131733c_fm_a @ Xs_1 @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ) @ ( tl_set2007602089164433257c_fm_a @ ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs_2 ) ) ) ) ) ).

% remdups_adj_append
thf(fact_452_remdups__adj__append,axiom,
    ! [Xs_1: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Xs_2: list_l6083326122719238310c_fm_a] :
      ( ( remdup8355899821003448156c_fm_a @ ( append1384085151619559355c_fm_a @ Xs_1 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs_2 ) ) )
      = ( append1384085151619559355c_fm_a @ ( remdup8355899821003448156c_fm_a @ ( append1384085151619559355c_fm_a @ Xs_1 @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ) @ ( tl_lis3363300823944467983c_fm_a @ ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs_2 ) ) ) ) ) ).

% remdups_adj_append
thf(fact_453_remdups__adj__append,axiom,
    ! [Xs_1: list_Epistemic_fm_a,X2: epistemic_fm_a,Xs_2: list_Epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs_1 @ ( cons_Epistemic_fm_a @ X2 @ Xs_2 ) ) )
      = ( append9179727413925872949c_fm_a @ ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs_1 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) @ ( tl_Epistemic_fm_a @ ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs_2 ) ) ) ) ) ).

% remdups_adj_append
thf(fact_454_tl__append__if,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( Xs2 = nil_li2451196919128234278c_fm_a )
       => ( ( tl_lis3363300823944467983c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
          = ( tl_lis3363300823944467983c_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_li2451196919128234278c_fm_a )
       => ( ( tl_lis3363300823944467983c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
          = ( append1384085151619559355c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) @ Ys ) ) ) ) ).

% tl_append_if
thf(fact_455_tl__append__if,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( Xs2 = nil_se102576565402781184c_fm_a )
       => ( ( tl_set2007602089164433257c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
          = ( tl_set2007602089164433257c_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_se102576565402781184c_fm_a )
       => ( ( tl_set2007602089164433257c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
          = ( append5257919162946131733c_fm_a @ ( tl_set2007602089164433257c_fm_a @ Xs2 ) @ Ys ) ) ) ) ).

% tl_append_if
thf(fact_456_tl__append__if,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
       => ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( tl_Epistemic_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_Epistemic_fm_a )
       => ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs2 ) @ Ys ) ) ) ) ).

% tl_append_if
thf(fact_457_list_Opred__mono,axiom,
    ! [P4: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ P4 @ Pa )
     => ( ord_le5289359451089373629fm_a_o @ ( list_a5841931967666341838c_fm_a @ P4 ) @ ( list_a5841931967666341838c_fm_a @ Pa ) ) ) ).

% list.pred_mono
thf(fact_458_rev__swap,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( rev_Epistemic_fm_a @ Xs2 )
        = Ys )
      = ( Xs2
        = ( rev_Epistemic_fm_a @ Ys ) ) ) ).

% rev_swap
thf(fact_459_rev__filter,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) )
      = ( filter441479637125139101c_fm_a @ P4 @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ).

% rev_filter
thf(fact_460_rev__filter,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) )
      = ( filter7636273809395300631c_fm_a @ P4 @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% rev_filter
thf(fact_461_append__eq__appendI,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Xs1: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Us: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Xs1 )
        = Zs3 )
     => ( ( Ys
          = ( append1384085151619559355c_fm_a @ Xs1 @ Us ) )
       => ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
          = ( append1384085151619559355c_fm_a @ Zs3 @ Us ) ) ) ) ).

% append_eq_appendI
thf(fact_462_append__eq__appendI,axiom,
    ! [Xs2: list_Epistemic_fm_a,Xs1: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Us: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Xs1 )
        = Zs3 )
     => ( ( Ys
          = ( append9179727413925872949c_fm_a @ Xs1 @ Us ) )
       => ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
          = ( append9179727413925872949c_fm_a @ Zs3 @ Us ) ) ) ) ).

% append_eq_appendI
thf(fact_463_append__eq__append__conv2,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a,Ts: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Ys )
        = ( append1384085151619559355c_fm_a @ Zs3 @ Ts ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a] :
            ( ( ( Xs2
                = ( append1384085151619559355c_fm_a @ Zs3 @ Us2 ) )
              & ( ( append1384085151619559355c_fm_a @ Us2 @ Ys )
                = Ts ) )
            | ( ( ( append1384085151619559355c_fm_a @ Xs2 @ Us2 )
                = Zs3 )
              & ( Ys
                = ( append1384085151619559355c_fm_a @ Us2 @ Ts ) ) ) ) ) ) ).

% append_eq_append_conv2
thf(fact_464_append__eq__append__conv2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,Ts: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Ys )
        = ( append9179727413925872949c_fm_a @ Zs3 @ Ts ) )
      = ( ? [Us2: list_Epistemic_fm_a] :
            ( ( ( Xs2
                = ( append9179727413925872949c_fm_a @ Zs3 @ Us2 ) )
              & ( ( append9179727413925872949c_fm_a @ Us2 @ Ys )
                = Ts ) )
            | ( ( ( append9179727413925872949c_fm_a @ Xs2 @ Us2 )
                = Zs3 )
              & ( Ys
                = ( append9179727413925872949c_fm_a @ Us2 @ Ts ) ) ) ) ) ) ).

% append_eq_append_conv2
thf(fact_465_list_Opred__True,axiom,
    ( ( list_a5841931967666341838c_fm_a
      @ ^ [Uu: epistemic_fm_a] : $true )
    = ( ^ [Uu: list_Epistemic_fm_a] : $true ) ) ).

% list.pred_True
thf(fact_466_tl__append,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( tl_lis3363300823944467983c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
      = ( case_l116314299590685792c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ Ys )
        @ ^ [Z: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] : ( append1384085151619559355c_fm_a @ Zs @ Ys )
        @ Xs2 ) ) ).

% tl_append
thf(fact_467_tl__append,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( tl_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( case_l8442927312758267104c_fm_a @ ( tl_Epistemic_fm_a @ Ys )
        @ ^ [Z: epistemic_fm_a,Zs: list_Epistemic_fm_a] : ( append9179727413925872949c_fm_a @ Zs @ Ys )
        @ Xs2 ) ) ).

% tl_append
thf(fact_468_rev_Osimps_I2_J,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( rev_se1616163181097742432c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) )
      = ( append5257919162946131733c_fm_a @ ( rev_se1616163181097742432c_fm_a @ Xs2 ) @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ) ).

% rev.simps(2)
thf(fact_469_rev_Osimps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ) ).

% rev.simps(2)
thf(fact_470_rev_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ Xs2 ) @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) ).

% rev.simps(2)
thf(fact_471_remdups__adj__append__two,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a,Y: set_Epistemic_fm_a] :
      ( ( remdup2256950222776403766c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ ( cons_s4394448069393209776c_fm_a @ Y @ nil_se102576565402781184c_fm_a ) ) ) )
      = ( append5257919162946131733c_fm_a @ ( remdup2256950222776403766c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ) @ ( if_lis3811715425919989702c_fm_a @ ( X2 = Y ) @ nil_se102576565402781184c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% remdups_adj_append_two
thf(fact_472_remdups__adj__append__two,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( remdup8355899821003448156c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ ( cons_l8134865115577406678c_fm_a @ Y @ nil_li2451196919128234278c_fm_a ) ) ) )
      = ( append1384085151619559355c_fm_a @ ( remdup8355899821003448156c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ) @ ( if_lis342421823373228652c_fm_a @ ( X2 = Y ) @ nil_li2451196919128234278c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% remdups_adj_append_two
thf(fact_473_remdups__adj__append__two,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a,Y: epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) ) )
      = ( append9179727413925872949c_fm_a @ ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) @ ( if_lis2878681784746929638c_fm_a @ ( X2 = Y ) @ nil_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) ) ) ).

% remdups_adj_append_two
thf(fact_474_filter_Osimps_I2_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( P4 @ X2 )
       => ( ( filter441479637125139101c_fm_a @ P4 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
          = ( cons_l8134865115577406678c_fm_a @ X2 @ ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) ) ) )
      & ( ~ ( P4 @ X2 )
       => ( ( filter441479637125139101c_fm_a @ P4 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
          = ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% filter.simps(2)
thf(fact_475_filter_Osimps_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( P4 @ X2 )
       => ( ( filter7636273809395300631c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( cons_Epistemic_fm_a @ X2 @ ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) ) ) )
      & ( ~ ( P4 @ X2 )
       => ( ( filter7636273809395300631c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% filter.simps(2)
thf(fact_476_filter_Osimps_I1_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o] :
      ( ( filter441479637125139101c_fm_a @ P4 @ nil_li2451196919128234278c_fm_a )
      = nil_li2451196919128234278c_fm_a ) ).

% filter.simps(1)
thf(fact_477_filter_Osimps_I1_J,axiom,
    ! [P4: set_Epistemic_fm_a > $o] :
      ( ( filter2620125754611450615c_fm_a @ P4 @ nil_se102576565402781184c_fm_a )
      = nil_se102576565402781184c_fm_a ) ).

% filter.simps(1)
thf(fact_478_filter_Osimps_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ( filter7636273809395300631c_fm_a @ P4 @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% filter.simps(1)
thf(fact_479_rev_Osimps_I1_J,axiom,
    ( ( rev_li1443896382544221062c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% rev.simps(1)
thf(fact_480_rev_Osimps_I1_J,axiom,
    ( ( rev_se1616163181097742432c_fm_a @ nil_se102576565402781184c_fm_a )
    = nil_se102576565402781184c_fm_a ) ).

% rev.simps(1)
thf(fact_481_rev_Osimps_I1_J,axiom,
    ( ( rev_Epistemic_fm_a @ nil_Epistemic_fm_a )
    = nil_Epistemic_fm_a ) ).

% rev.simps(1)
thf(fact_482_rev__concat,axiom,
    ! [Xs2: list_l3671048651222332332c_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
      = ( concat6109960377493484129c_fm_a @ ( map_li8347733892191492164c_fm_a @ rev_li1443896382544221062c_fm_a @ ( rev_li4363396572682915852c_fm_a @ Xs2 ) ) ) ) ).

% rev_concat
thf(fact_483_rev__concat,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
      = ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ rev_Epistemic_fm_a @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ) ).

% rev_concat
thf(fact_484_rev__map,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
      = ( map_Ep1988204514693272906c_fm_a @ F @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_485_rev__map,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_li1443896382544221062c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
      = ( map_li3080774272885743684c_fm_a @ F @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_486_rev__map,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rev_li4363396572682915852c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
      = ( map_Ep4939040189629079504c_fm_a @ F @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_487_rev__map,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_li4363396572682915852c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) )
      = ( map_li3858915945532548554c_fm_a @ F @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_488_rev__map,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) )
      = ( map_li5516866612190465598c_fm_a @ F @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_489_rev__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rev_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ F @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% rev_map
thf(fact_490_Cons__eq__appendI,axiom,
    ! [X2: list_Epistemic_fm_a,Xs1: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs1 )
        = Ys )
     => ( ( Xs2
          = ( append1384085151619559355c_fm_a @ Xs1 @ Zs3 ) )
       => ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
          = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) ) ) ) ).

% Cons_eq_appendI
thf(fact_491_Cons__eq__appendI,axiom,
    ! [X2: epistemic_fm_a,Xs1: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs1 )
        = Ys )
     => ( ( Xs2
          = ( append9179727413925872949c_fm_a @ Xs1 @ Zs3 ) )
       => ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
          = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) ) ) ) ).

% Cons_eq_appendI
thf(fact_492_append__Cons,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) @ Ys )
      = ( cons_l8134865115577406678c_fm_a @ X2 @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) ) ) ).

% append_Cons
thf(fact_493_append__Cons,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys )
      = ( cons_Epistemic_fm_a @ X2 @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) ) ) ).

% append_Cons
thf(fact_494_eq__Nil__appendI,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 = Ys )
     => ( Xs2
        = ( append1384085151619559355c_fm_a @ nil_li2451196919128234278c_fm_a @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_495_eq__Nil__appendI,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( Xs2 = Ys )
     => ( Xs2
        = ( append5257919162946131733c_fm_a @ nil_se102576565402781184c_fm_a @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_496_eq__Nil__appendI,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( Xs2
        = ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_497_append_Oleft__neutral,axiom,
    ! [A2: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ nil_li2451196919128234278c_fm_a @ A2 )
      = A2 ) ).

% append.left_neutral
thf(fact_498_append_Oleft__neutral,axiom,
    ! [A2: list_s580375451141968640c_fm_a] :
      ( ( append5257919162946131733c_fm_a @ nil_se102576565402781184c_fm_a @ A2 )
      = A2 ) ).

% append.left_neutral
thf(fact_499_append_Oleft__neutral,axiom,
    ! [A2: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ A2 )
      = A2 ) ).

% append.left_neutral
thf(fact_500_append__Nil,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a] :
      ( ( append1384085151619559355c_fm_a @ nil_li2451196919128234278c_fm_a @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_501_append__Nil,axiom,
    ! [Ys: list_s580375451141968640c_fm_a] :
      ( ( append5257919162946131733c_fm_a @ nil_se102576565402781184c_fm_a @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_502_append__Nil,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( append9179727413925872949c_fm_a @ nil_Epistemic_fm_a @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_503_map__tailrec__rev,axiom,
    ( map_ta3940434083879480187c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_Epistemic_fm_a,As3: list_Epistemic_fm_a] : ( append1384085151619559355c_fm_a @ ( rev_li1443896382544221062c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_504_map__tailrec__rev,axiom,
    ( map_ta5197791105168353781c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_Epistemic_fm_a,As3: list_l6083326122719238310c_fm_a] : ( append1384085151619559355c_fm_a @ ( rev_li1443896382544221062c_fm_a @ ( map_li3080774272885743684c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_505_map__tailrec__rev,axiom,
    ( map_ta7056057021911689601c_fm_a
    = ( ^ [F2: epistemic_fm_a > list_l6083326122719238310c_fm_a,As3: list_Epistemic_fm_a] : ( append9013695642829458881c_fm_a @ ( rev_li4363396572682915852c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_506_map__tailrec__rev,axiom,
    ( map_ta2731075953164296955c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,As3: list_l6083326122719238310c_fm_a] : ( append9013695642829458881c_fm_a @ ( rev_li4363396572682915852c_fm_a @ ( map_li3858915945532548554c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_507_map__tailrec__rev,axiom,
    ( map_ta7469096181376672879c_fm_a
    = ( ^ [F2: list_Epistemic_fm_a > epistemic_fm_a,As3: list_l6083326122719238310c_fm_a] : ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_508_map__tailrec__rev,axiom,
    ( map_ta6565535454553546997c_fm_a
    = ( ^ [F2: epistemic_fm_a > epistemic_fm_a,As3: list_Epistemic_fm_a] : ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F2 @ As3 ) ) ) ) ) ).

% map_tailrec_rev
thf(fact_509_append__eq__map__conv,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Ys @ Zs3 )
        = ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep1988204514693272906c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep1988204514693272906c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_510_append__eq__map__conv,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Ys @ Zs3 )
        = ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li3080774272885743684c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li3080774272885743684c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_511_append__eq__map__conv,axiom,
    ! [Ys: list_l3671048651222332332c_fm_a,Zs3: list_l3671048651222332332c_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( append9013695642829458881c_fm_a @ Ys @ Zs3 )
        = ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep4939040189629079504c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep4939040189629079504c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_512_append__eq__map__conv,axiom,
    ! [Ys: list_l3671048651222332332c_fm_a,Zs3: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( append9013695642829458881c_fm_a @ Ys @ Zs3 )
        = ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li3858915945532548554c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li3858915945532548554c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_513_append__eq__map__conv,axiom,
    ! [Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Ys @ Zs3 )
        = ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li5516866612190465598c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li5516866612190465598c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_514_append__eq__map__conv,axiom,
    ! [Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Ys @ Zs3 )
        = ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep7084560364594560580c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep7084560364594560580c_fm_a @ F @ Vs ) ) ) ) ) ).

% append_eq_map_conv
thf(fact_515_map__eq__append__conv,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep1988204514693272906c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep1988204514693272906c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_516_map__eq__append__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li3080774272885743684c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li3080774272885743684c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_517_map__eq__append__conv,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_l3671048651222332332c_fm_a,Zs3: list_l3671048651222332332c_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = ( append9013695642829458881c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep4939040189629079504c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep4939040189629079504c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_518_map__eq__append__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l3671048651222332332c_fm_a,Zs3: list_l3671048651222332332c_fm_a] :
      ( ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
        = ( append9013695642829458881c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li3858915945532548554c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li3858915945532548554c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_519_map__eq__append__conv,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_li5516866612190465598c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_li5516866612190465598c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_520_map__eq__append__conv,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Us2 @ Vs ) )
            & ( Ys
              = ( map_Ep7084560364594560580c_fm_a @ F @ Us2 ) )
            & ( Zs3
              = ( map_Ep7084560364594560580c_fm_a @ F @ Vs ) ) ) ) ) ).

% map_eq_append_conv
thf(fact_521_list_Osel_I3_J,axiom,
    ! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( tl_lis3363300823944467983c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
      = X22 ) ).

% list.sel(3)
thf(fact_522_list_Osel_I3_J,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( tl_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = X22 ) ).

% list.sel(3)
thf(fact_523_list_Osel_I2_J,axiom,
    ( ( tl_lis3363300823944467983c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% list.sel(2)
thf(fact_524_list_Osel_I2_J,axiom,
    ( ( tl_set2007602089164433257c_fm_a @ nil_se102576565402781184c_fm_a )
    = nil_se102576565402781184c_fm_a ) ).

% list.sel(2)
thf(fact_525_list_Osel_I2_J,axiom,
    ( ( tl_Epistemic_fm_a @ nil_Epistemic_fm_a )
    = nil_Epistemic_fm_a ) ).

% list.sel(2)
thf(fact_526_remdups__adj_Osimps_I3_J,axiom,
    ! [X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( X2 = Y )
       => ( ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ ( cons_l8134865115577406678c_fm_a @ Y @ Xs2 ) ) )
          = ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) ) )
      & ( ( X2 != Y )
       => ( ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ ( cons_l8134865115577406678c_fm_a @ Y @ Xs2 ) ) )
          = ( cons_l8134865115577406678c_fm_a @ X2 @ ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y @ Xs2 ) ) ) ) ) ) ).

% remdups_adj.simps(3)
thf(fact_527_remdups__adj_Osimps_I3_J,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( X2 = Y )
       => ( ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) )
          = ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) )
      & ( ( X2 != Y )
       => ( ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) )
          = ( cons_Epistemic_fm_a @ X2 @ ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) ) ) ) ) ).

% remdups_adj.simps(3)
thf(fact_528_remdups__adj_Osimps_I1_J,axiom,
    ( ( remdup8355899821003448156c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% remdups_adj.simps(1)
thf(fact_529_remdups__adj_Osimps_I1_J,axiom,
    ( ( remdup2256950222776403766c_fm_a @ nil_se102576565402781184c_fm_a )
    = nil_se102576565402781184c_fm_a ) ).

% remdups_adj.simps(1)
thf(fact_530_remdups__adj_Osimps_I1_J,axiom,
    ( ( remdup1727679340039403862c_fm_a @ nil_Epistemic_fm_a )
    = nil_Epistemic_fm_a ) ).

% remdups_adj.simps(1)
thf(fact_531_map__tl,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( map_Ep1988204514693272906c_fm_a @ F @ ( tl_Epistemic_fm_a @ Xs2 ) )
      = ( tl_lis3363300823944467983c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_532_map__tl,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_li3080774272885743684c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) )
      = ( tl_lis3363300823944467983c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_533_map__tl,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( map_Ep4939040189629079504c_fm_a @ F @ ( tl_Epistemic_fm_a @ Xs2 ) )
      = ( tl_lis547664705162099221c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_534_map__tl,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_li3858915945532548554c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) )
      = ( tl_lis547664705162099221c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_535_map__tl,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( map_li5516866612190465598c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) )
      = ( tl_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_536_map__tl,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( tl_Epistemic_fm_a @ Xs2 ) )
      = ( tl_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) ) ) ).

% map_tl
thf(fact_537_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_538_ord_Olexordp__eq__pref,axiom,
    ! [Less: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,U: list_l6083326122719238310c_fm_a,V: list_l6083326122719238310c_fm_a] : ( lexord3118506718869075820c_fm_a @ Less @ U @ ( append1384085151619559355c_fm_a @ U @ V ) ) ).

% ord.lexordp_eq_pref
thf(fact_539_ord_Olexordp__eq__pref,axiom,
    ! [Less: epistemic_fm_a > epistemic_fm_a > $o,U: list_Epistemic_fm_a,V: list_Epistemic_fm_a] : ( lexord491902619044731238c_fm_a @ Less @ U @ ( append9179727413925872949c_fm_a @ U @ V ) ) ).

% ord.lexordp_eq_pref
thf(fact_540_list_Opred__inject_I1_J,axiom,
    ! [P4: list_Epistemic_fm_a > $o] : ( list_a5890043570083025364c_fm_a @ P4 @ nil_li2451196919128234278c_fm_a ) ).

% list.pred_inject(1)
thf(fact_541_list_Opred__inject_I1_J,axiom,
    ! [P4: set_Epistemic_fm_a > $o] : ( list_a5130230249644717486c_fm_a @ P4 @ nil_se102576565402781184c_fm_a ) ).

% list.pred_inject(1)
thf(fact_542_list_Opred__inject_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] : ( list_a5841931967666341838c_fm_a @ P4 @ nil_Epistemic_fm_a ) ).

% list.pred_inject(1)
thf(fact_543_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_544_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_545_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_546_eval_Osimps_I3_J,axiom,
    ! [G3: list_char > $o,H3: epistemic_fm_a > $o,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_eval_a @ G3 @ H3 @ ( epistemic_Dis_a @ P @ Q ) )
      = ( ( epistemic_eval_a @ G3 @ H3 @ P )
        | ( epistemic_eval_a @ G3 @ H3 @ Q ) ) ) ).

% eval.simps(3)
thf(fact_547_concat__eq__appendD,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( concat6109960377493484129c_fm_a @ Xss2 )
        = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) )
     => ( ( Xss2 != nil_li5178944226519631276c_fm_a )
       => ? [Xss1: list_l3671048651222332332c_fm_a,Xs3: list_l6083326122719238310c_fm_a,Xs4: list_l6083326122719238310c_fm_a,Xss22: list_l3671048651222332332c_fm_a] :
            ( ( Xss2
              = ( append9013695642829458881c_fm_a @ Xss1 @ ( cons_l2479501935080859996c_fm_a @ ( append1384085151619559355c_fm_a @ Xs3 @ Xs4 ) @ Xss22 ) ) )
            & ( Ys
              = ( append1384085151619559355c_fm_a @ ( concat6109960377493484129c_fm_a @ Xss1 ) @ Xs3 ) )
            & ( Zs3
              = ( append1384085151619559355c_fm_a @ Xs4 @ ( concat6109960377493484129c_fm_a @ Xss22 ) ) ) ) ) ) ).

% concat_eq_appendD
thf(fact_548_concat__eq__appendD,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( concat2780896542826320603c_fm_a @ Xss2 )
        = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) )
     => ( ( Xss2 != nil_li2451196919128234278c_fm_a )
       => ? [Xss1: list_l6083326122719238310c_fm_a,Xs3: list_Epistemic_fm_a,Xs4: list_Epistemic_fm_a,Xss22: list_l6083326122719238310c_fm_a] :
            ( ( Xss2
              = ( append1384085151619559355c_fm_a @ Xss1 @ ( cons_l8134865115577406678c_fm_a @ ( append9179727413925872949c_fm_a @ Xs3 @ Xs4 ) @ Xss22 ) ) )
            & ( Ys
              = ( append9179727413925872949c_fm_a @ ( concat2780896542826320603c_fm_a @ Xss1 ) @ Xs3 ) )
            & ( Zs3
              = ( append9179727413925872949c_fm_a @ Xs4 @ ( concat2780896542826320603c_fm_a @ Xss22 ) ) ) ) ) ) ).

% concat_eq_appendD
thf(fact_549_list_Omap__cong__pred,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5890043570083025364c_fm_a
          @ ^ [Z: list_Epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_li3080774272885743684c_fm_a @ F @ X2 )
          = ( map_li3080774272885743684c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_550_list_Omap__cong__pred,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5890043570083025364c_fm_a
          @ ^ [Z: list_Epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_li3858915945532548554c_fm_a @ F @ X2 )
          = ( map_li3858915945532548554c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_551_list_Omap__cong__pred,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5890043570083025364c_fm_a
          @ ^ [Z: list_Epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_li5516866612190465598c_fm_a @ F @ X2 )
          = ( map_li5516866612190465598c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_552_list_Omap__cong__pred,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5841931967666341838c_fm_a
          @ ^ [Z: epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_Ep1988204514693272906c_fm_a @ F @ X2 )
          = ( map_Ep1988204514693272906c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_553_list_Omap__cong__pred,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5841931967666341838c_fm_a
          @ ^ [Z: epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_Ep4939040189629079504c_fm_a @ F @ X2 )
          = ( map_Ep4939040189629079504c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_554_list_Omap__cong__pred,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ( list_a5841931967666341838c_fm_a
          @ ^ [Z: epistemic_fm_a] :
              ( ( F @ Z )
              = ( G3 @ Z ) )
          @ Ya )
       => ( ( map_Ep7084560364594560580c_fm_a @ F @ X2 )
          = ( map_Ep7084560364594560580c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong_pred
thf(fact_555_rev__induct,axiom,
    ! [P4: list_s580375451141968640c_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
      ( ( P4 @ nil_se102576565402781184c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
            ( ( P4 @ Xs3 )
           => ( P4 @ ( append5257919162946131733c_fm_a @ Xs3 @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) ) )
       => ( P4 @ Xs2 ) ) ) ).

% rev_induct
thf(fact_556_rev__induct,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( P4 @ nil_li2451196919128234278c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
            ( ( P4 @ Xs3 )
           => ( P4 @ ( append1384085151619559355c_fm_a @ Xs3 @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) ) )
       => ( P4 @ Xs2 ) ) ) ).

% rev_induct
thf(fact_557_rev__induct,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( P4 @ nil_Epistemic_fm_a )
     => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
            ( ( P4 @ Xs3 )
           => ( P4 @ ( append9179727413925872949c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) )
       => ( P4 @ Xs2 ) ) ) ).

% rev_induct
thf(fact_558_rev__exhaust,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ~ ! [Ys2: list_s580375451141968640c_fm_a,Y2: set_Epistemic_fm_a] :
            ( Xs2
           != ( append5257919162946131733c_fm_a @ Ys2 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% rev_exhaust
thf(fact_559_rev__exhaust,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ~ ! [Ys2: list_l6083326122719238310c_fm_a,Y2: list_Epistemic_fm_a] :
            ( Xs2
           != ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% rev_exhaust
thf(fact_560_rev__exhaust,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ~ ! [Ys2: list_Epistemic_fm_a,Y2: epistemic_fm_a] :
            ( Xs2
           != ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ Y2 @ nil_Epistemic_fm_a ) ) ) ) ).

% rev_exhaust
thf(fact_561_Cons__eq__append__conv,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a,Zs3: list_s580375451141968640c_fm_a] :
      ( ( ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 )
        = ( append5257919162946131733c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Ys = nil_se102576565402781184c_fm_a )
          & ( ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 )
            = Zs3 ) )
        | ? [Ys4: list_s580375451141968640c_fm_a] :
            ( ( ( cons_s4394448069393209776c_fm_a @ X2 @ Ys4 )
              = Ys )
            & ( Xs2
              = ( append5257919162946131733c_fm_a @ Ys4 @ Zs3 ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_562_Cons__eq__append__conv,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Ys = nil_li2451196919128234278c_fm_a )
          & ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
            = Zs3 ) )
        | ? [Ys4: list_l6083326122719238310c_fm_a] :
            ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Ys4 )
              = Ys )
            & ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys4 @ Zs3 ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_563_Cons__eq__append__conv,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Ys = nil_Epistemic_fm_a )
          & ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
            = Zs3 ) )
        | ? [Ys4: list_Epistemic_fm_a] :
            ( ( ( cons_Epistemic_fm_a @ X2 @ Ys4 )
              = Ys )
            & ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys4 @ Zs3 ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_564_append__eq__Cons__conv,axiom,
    ! [Ys: list_s580375451141968640c_fm_a,Zs3: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( append5257919162946131733c_fm_a @ Ys @ Zs3 )
        = ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) )
      = ( ( ( Ys = nil_se102576565402781184c_fm_a )
          & ( Zs3
            = ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) ) )
        | ? [Ys4: list_s580375451141968640c_fm_a] :
            ( ( Ys
              = ( cons_s4394448069393209776c_fm_a @ X2 @ Ys4 ) )
            & ( ( append5257919162946131733c_fm_a @ Ys4 @ Zs3 )
              = Xs2 ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_565_append__eq__Cons__conv,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( append1384085151619559355c_fm_a @ Ys @ Zs3 )
        = ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( ( ( Ys = nil_li2451196919128234278c_fm_a )
          & ( Zs3
            = ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) )
        | ? [Ys4: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( cons_l8134865115577406678c_fm_a @ X2 @ Ys4 ) )
            & ( ( append1384085151619559355c_fm_a @ Ys4 @ Zs3 )
              = Xs2 ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_566_append__eq__Cons__conv,axiom,
    ! [Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Ys @ Zs3 )
        = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ( ( Ys = nil_Epistemic_fm_a )
          & ( Zs3
            = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) )
        | ? [Ys4: list_Epistemic_fm_a] :
            ( ( Ys
              = ( cons_Epistemic_fm_a @ X2 @ Ys4 ) )
            & ( ( append9179727413925872949c_fm_a @ Ys4 @ Zs3 )
              = Xs2 ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_567_rev__nonempty__induct,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,P4: list_s580375451141968640c_fm_a > $o] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ! [X3: set_Epistemic_fm_a] : ( P4 @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
       => ( ! [X3: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
              ( ( Xs3 != nil_se102576565402781184c_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( append5257919162946131733c_fm_a @ Xs3 @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% rev_nonempty_induct
thf(fact_568_rev__nonempty__induct,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ! [X3: list_Epistemic_fm_a] : ( P4 @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
       => ( ! [X3: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
              ( ( Xs3 != nil_li2451196919128234278c_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( append1384085151619559355c_fm_a @ Xs3 @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% rev_nonempty_induct
thf(fact_569_rev__nonempty__induct,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ! [X3: epistemic_fm_a] : ( P4 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
       => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( Xs3 != nil_Epistemic_fm_a )
             => ( ( P4 @ Xs3 )
               => ( P4 @ ( append9179727413925872949c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) ) )
         => ( P4 @ Xs2 ) ) ) ) ).

% rev_nonempty_induct
thf(fact_570_concat__eq__append__conv,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a,Ys: list_l6083326122719238310c_fm_a,Zs3: list_l6083326122719238310c_fm_a] :
      ( ( ( concat6109960377493484129c_fm_a @ Xss2 )
        = ( append1384085151619559355c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Xss2 = nil_li5178944226519631276c_fm_a )
         => ( ( Ys = nil_li2451196919128234278c_fm_a )
            & ( Zs3 = nil_li2451196919128234278c_fm_a ) ) )
        & ( ( Xss2 != nil_li5178944226519631276c_fm_a )
         => ? [Xss12: list_l3671048651222332332c_fm_a,Xs: list_l6083326122719238310c_fm_a,Xs5: list_l6083326122719238310c_fm_a,Xss23: list_l3671048651222332332c_fm_a] :
              ( ( Xss2
                = ( append9013695642829458881c_fm_a @ Xss12 @ ( cons_l2479501935080859996c_fm_a @ ( append1384085151619559355c_fm_a @ Xs @ Xs5 ) @ Xss23 ) ) )
              & ( Ys
                = ( append1384085151619559355c_fm_a @ ( concat6109960377493484129c_fm_a @ Xss12 ) @ Xs ) )
              & ( Zs3
                = ( append1384085151619559355c_fm_a @ Xs5 @ ( concat6109960377493484129c_fm_a @ Xss23 ) ) ) ) ) ) ) ).

% concat_eq_append_conv
thf(fact_571_concat__eq__append__conv,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a,Ys: list_s580375451141968640c_fm_a,Zs3: list_s580375451141968640c_fm_a] :
      ( ( ( concat2941956077894552763c_fm_a @ Xss2 )
        = ( append5257919162946131733c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Xss2 = nil_li5433889876484989702c_fm_a )
         => ( ( Ys = nil_se102576565402781184c_fm_a )
            & ( Zs3 = nil_se102576565402781184c_fm_a ) ) )
        & ( ( Xss2 != nil_li5433889876484989702c_fm_a )
         => ? [Xss12: list_l985973790606564998c_fm_a,Xs: list_s580375451141968640c_fm_a,Xs5: list_s580375451141968640c_fm_a,Xss23: list_l985973790606564998c_fm_a] :
              ( ( Xss2
                = ( append6809593887757133211c_fm_a @ Xss12 @ ( cons_l1626872963913326262c_fm_a @ ( append5257919162946131733c_fm_a @ Xs @ Xs5 ) @ Xss23 ) ) )
              & ( Ys
                = ( append5257919162946131733c_fm_a @ ( concat2941956077894552763c_fm_a @ Xss12 ) @ Xs ) )
              & ( Zs3
                = ( append5257919162946131733c_fm_a @ Xs5 @ ( concat2941956077894552763c_fm_a @ Xss23 ) ) ) ) ) ) ) ).

% concat_eq_append_conv
thf(fact_572_concat__eq__append__conv,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a,Ys: list_Epistemic_fm_a,Zs3: list_Epistemic_fm_a] :
      ( ( ( concat2780896542826320603c_fm_a @ Xss2 )
        = ( append9179727413925872949c_fm_a @ Ys @ Zs3 ) )
      = ( ( ( Xss2 = nil_li2451196919128234278c_fm_a )
         => ( ( Ys = nil_Epistemic_fm_a )
            & ( Zs3 = nil_Epistemic_fm_a ) ) )
        & ( ( Xss2 != nil_li2451196919128234278c_fm_a )
         => ? [Xss12: list_l6083326122719238310c_fm_a,Xs: list_Epistemic_fm_a,Xs5: list_Epistemic_fm_a,Xss23: list_l6083326122719238310c_fm_a] :
              ( ( Xss2
                = ( append1384085151619559355c_fm_a @ Xss12 @ ( cons_l8134865115577406678c_fm_a @ ( append9179727413925872949c_fm_a @ Xs @ Xs5 ) @ Xss23 ) ) )
              & ( Ys
                = ( append9179727413925872949c_fm_a @ ( concat2780896542826320603c_fm_a @ Xss12 ) @ Xs ) )
              & ( Zs3
                = ( append9179727413925872949c_fm_a @ Xs5 @ ( concat2780896542826320603c_fm_a @ Xss23 ) ) ) ) ) ) ) ).

% concat_eq_append_conv
thf(fact_573_Nil__tl,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( tl_set2007602089164433257c_fm_a @ Xs2 ) )
      = ( ( Xs2 = nil_se102576565402781184c_fm_a )
        | ? [X: set_Epistemic_fm_a] :
            ( Xs2
            = ( cons_s4394448069393209776c_fm_a @ X @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% Nil_tl
thf(fact_574_Nil__tl,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( tl_lis3363300823944467983c_fm_a @ Xs2 ) )
      = ( ( Xs2 = nil_li2451196919128234278c_fm_a )
        | ? [X: list_Epistemic_fm_a] :
            ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ X @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% Nil_tl
thf(fact_575_Nil__tl,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( tl_Epistemic_fm_a @ Xs2 ) )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        | ? [X: epistemic_fm_a] :
            ( Xs2
            = ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a ) ) ) ) ).

% Nil_tl
thf(fact_576_tl__Nil,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( tl_set2007602089164433257c_fm_a @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( ( Xs2 = nil_se102576565402781184c_fm_a )
        | ? [X: set_Epistemic_fm_a] :
            ( Xs2
            = ( cons_s4394448069393209776c_fm_a @ X @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% tl_Nil
thf(fact_577_tl__Nil,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( tl_lis3363300823944467983c_fm_a @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( ( Xs2 = nil_li2451196919128234278c_fm_a )
        | ? [X: list_Epistemic_fm_a] :
            ( Xs2
            = ( cons_l8134865115577406678c_fm_a @ X @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% tl_Nil
thf(fact_578_tl__Nil,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( tl_Epistemic_fm_a @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        | ? [X: epistemic_fm_a] :
            ( Xs2
            = ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a ) ) ) ) ).

% tl_Nil
thf(fact_579_filter__concat,axiom,
    ! [P: list_Epistemic_fm_a > $o,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( filter441479637125139101c_fm_a @ P @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
      = ( concat6109960377493484129c_fm_a @ ( map_li8347733892191492164c_fm_a @ ( filter441479637125139101c_fm_a @ P ) @ Xs2 ) ) ) ).

% filter_concat
thf(fact_580_filter__concat,axiom,
    ! [P: epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( filter7636273809395300631c_fm_a @ P @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
      = ( concat2780896542826320603c_fm_a @ ( map_li3080774272885743684c_fm_a @ ( filter7636273809395300631c_fm_a @ P ) @ Xs2 ) ) ) ).

% filter_concat
thf(fact_581_remdups__adj_Osimps_I2_J,axiom,
    ! [X2: set_Epistemic_fm_a] :
      ( ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) )
      = ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ).

% remdups_adj.simps(2)
thf(fact_582_remdups__adj_Osimps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a] :
      ( ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) )
      = ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ).

% remdups_adj.simps(2)
thf(fact_583_remdups__adj_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
      = ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ).

% remdups_adj.simps(2)
thf(fact_584_remdups__adj_Oelims,axiom,
    ! [X2: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
      ( ( ( remdup2256950222776403766c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_se102576565402781184c_fm_a )
         => ( Y != nil_se102576565402781184c_fm_a ) )
       => ( ! [X3: set_Epistemic_fm_a] :
              ( ( X2
                = ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
             => ( Y
               != ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) )
         => ~ ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
                ( ( X2
                  = ( cons_s4394448069393209776c_fm_a @ X3 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) )
               => ~ ( ( ( X3 = Y2 )
                     => ( Y
                        = ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) ) ) )
                    & ( ( X3 != Y2 )
                     => ( Y
                        = ( cons_s4394448069393209776c_fm_a @ X3 @ ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ) ).

% remdups_adj.elims
thf(fact_585_remdups__adj_Oelims,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( remdup8355899821003448156c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_li2451196919128234278c_fm_a )
         => ( Y != nil_li2451196919128234278c_fm_a ) )
       => ( ! [X3: list_Epistemic_fm_a] :
              ( ( X2
                = ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
             => ( Y
               != ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) )
         => ~ ! [X3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
                ( ( X2
                  = ( cons_l8134865115577406678c_fm_a @ X3 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) )
               => ~ ( ( ( X3 = Y2 )
                     => ( Y
                        = ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) ) ) )
                    & ( ( X3 != Y2 )
                     => ( Y
                        = ( cons_l8134865115577406678c_fm_a @ X3 @ ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ) ).

% remdups_adj.elims
thf(fact_586_remdups__adj_Oelims,axiom,
    ! [X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( remdup1727679340039403862c_fm_a @ X2 )
        = Y )
     => ( ( ( X2 = nil_Epistemic_fm_a )
         => ( Y != nil_Epistemic_fm_a ) )
       => ( ! [X3: epistemic_fm_a] :
              ( ( X2
                = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
             => ( Y
               != ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
         => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( X2
                  = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
               => ~ ( ( ( X3 = Y2 )
                     => ( Y
                        = ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) ) ) )
                    & ( ( X3 != Y2 )
                     => ( Y
                        = ( cons_Epistemic_fm_a @ X3 @ ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ) ).

% remdups_adj.elims
thf(fact_587_list_Omap__sel_I2_J,axiom,
    ! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_se102576565402781184c_fm_a )
     => ( ( tl_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ A2 ) )
        = ( map_se8248101584983471204c_fm_a @ F @ ( tl_set2007602089164433257c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_588_list_Omap__sel_I2_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( tl_lis3363300823944467983c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ A2 ) )
        = ( map_Ep1988204514693272906c_fm_a @ F @ ( tl_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_589_list_Omap__sel_I2_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( tl_lis3363300823944467983c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ A2 ) )
        = ( map_li3080774272885743684c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_590_list_Omap__sel_I2_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( tl_lis547664705162099221c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ A2 ) )
        = ( map_Ep4939040189629079504c_fm_a @ F @ ( tl_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_591_list_Omap__sel_I2_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( tl_lis547664705162099221c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ A2 ) )
        = ( map_li3858915945532548554c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_592_list_Omap__sel_I2_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( tl_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ A2 ) )
        = ( map_li5516866612190465598c_fm_a @ F @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_593_list_Omap__sel_I2_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( tl_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ A2 ) )
        = ( map_Ep7084560364594560580c_fm_a @ F @ ( tl_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(2)
thf(fact_594_concat_Osimps_I2_J,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xs2: list_l3671048651222332332c_fm_a] :
      ( ( concat6109960377493484129c_fm_a @ ( cons_l2479501935080859996c_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ X2 @ ( concat6109960377493484129c_fm_a @ Xs2 ) ) ) ).

% concat.simps(2)
thf(fact_595_concat_Osimps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( concat2780896542826320603c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append9179727413925872949c_fm_a @ X2 @ ( concat2780896542826320603c_fm_a @ Xs2 ) ) ) ).

% concat.simps(2)
thf(fact_596_maps__simps_I1_J,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( maps_E7773696912818698439c_fm_a @ F @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ ( F @ X2 ) @ ( maps_E7773696912818698439c_fm_a @ F @ Xs2 ) ) ) ).

% maps_simps(1)
thf(fact_597_maps__simps_I1_J,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( maps_E6072454603808916545c_fm_a @ F @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( append9179727413925872949c_fm_a @ ( F @ X2 ) @ ( maps_E6072454603808916545c_fm_a @ F @ Xs2 ) ) ) ).

% maps_simps(1)
thf(fact_598_maps__simps_I1_J,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( maps_l3685687229838205249c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ ( F @ X2 ) @ ( maps_l3685687229838205249c_fm_a @ F @ Xs2 ) ) ) ).

% maps_simps(1)
thf(fact_599_maps__simps_I1_J,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( maps_l2078986973461115323c_fm_a @ F @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append9179727413925872949c_fm_a @ ( F @ X2 ) @ ( maps_l2078986973461115323c_fm_a @ F @ Xs2 ) ) ) ).

% maps_simps(1)
thf(fact_600_tl__def,axiom,
    ( tl_lis3363300823944467983c_fm_a
    = ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
      @ ^ [X213: list_Epistemic_fm_a,X223: list_l6083326122719238310c_fm_a] : X223 ) ) ).

% tl_def
thf(fact_601_tl__def,axiom,
    ( tl_set2007602089164433257c_fm_a
    = ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
      @ ^ [X213: set_Epistemic_fm_a,X223: list_s580375451141968640c_fm_a] : X223 ) ) ).

% tl_def
thf(fact_602_tl__def,axiom,
    ( tl_Epistemic_fm_a
    = ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
      @ ^ [X213: epistemic_fm_a,X223: list_Epistemic_fm_a] : X223 ) ) ).

% tl_def
thf(fact_603_ShiftD,axiom,
    ! [Kl3: list_l6083326122719238310c_fm_a,Kl4: set_li1092409891198325638c_fm_a,K2: list_Epistemic_fm_a] :
      ( ( member7465314387053329231c_fm_a @ Kl3 @ ( bNF_Gr2321306230395443647c_fm_a @ Kl4 @ K2 ) )
     => ( member7465314387053329231c_fm_a @ ( cons_l8134865115577406678c_fm_a @ K2 @ Kl3 ) @ Kl4 ) ) ).

% ShiftD
thf(fact_604_ShiftD,axiom,
    ! [Kl3: list_Epistemic_fm_a,Kl4: set_li769143395467472256c_fm_a,K2: epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Kl3 @ ( bNF_Gr8437504134799245625c_fm_a @ Kl4 @ K2 ) )
     => ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ K2 @ Kl3 ) @ Kl4 ) ) ).

% ShiftD
thf(fact_605_remdups__adj_Opelims,axiom,
    ! [X2: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
      ( ( ( remdup2256950222776403766c_fm_a @ X2 )
        = Y )
     => ( ( accp_l5045591749613577993c_fm_a @ remdup208960868507390979c_fm_a @ X2 )
       => ( ( ( X2 = nil_se102576565402781184c_fm_a )
           => ( ( Y = nil_se102576565402781184c_fm_a )
             => ~ ( accp_l5045591749613577993c_fm_a @ remdup208960868507390979c_fm_a @ nil_se102576565402781184c_fm_a ) ) )
         => ( ! [X3: set_Epistemic_fm_a] :
                ( ( X2
                  = ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
               => ( ( Y
                    = ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) )
                 => ~ ( accp_l5045591749613577993c_fm_a @ remdup208960868507390979c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ nil_se102576565402781184c_fm_a ) ) ) )
           => ~ ! [X3: set_Epistemic_fm_a,Y2: set_Epistemic_fm_a,Xs3: list_s580375451141968640c_fm_a] :
                  ( ( X2
                    = ( cons_s4394448069393209776c_fm_a @ X3 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) )
                 => ( ( ( ( X3 = Y2 )
                       => ( Y
                          = ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ Xs3 ) ) ) )
                      & ( ( X3 != Y2 )
                       => ( Y
                          = ( cons_s4394448069393209776c_fm_a @ X3 @ ( remdup2256950222776403766c_fm_a @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) ) ) ) )
                   => ~ ( accp_l5045591749613577993c_fm_a @ remdup208960868507390979c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X3 @ ( cons_s4394448069393209776c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).

% remdups_adj.pelims
thf(fact_606_remdups__adj_Opelims,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( ( remdup8355899821003448156c_fm_a @ X2 )
        = Y )
     => ( ( accp_l7472382826029824047c_fm_a @ remdup6698152994906117545c_fm_a @ X2 )
       => ( ( ( X2 = nil_li2451196919128234278c_fm_a )
           => ( ( Y = nil_li2451196919128234278c_fm_a )
             => ~ ( accp_l7472382826029824047c_fm_a @ remdup6698152994906117545c_fm_a @ nil_li2451196919128234278c_fm_a ) ) )
         => ( ! [X3: list_Epistemic_fm_a] :
                ( ( X2
                  = ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
               => ( ( Y
                    = ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) )
                 => ~ ( accp_l7472382826029824047c_fm_a @ remdup6698152994906117545c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ nil_li2451196919128234278c_fm_a ) ) ) )
           => ~ ! [X3: list_Epistemic_fm_a,Y2: list_Epistemic_fm_a,Xs3: list_l6083326122719238310c_fm_a] :
                  ( ( X2
                    = ( cons_l8134865115577406678c_fm_a @ X3 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) )
                 => ( ( ( ( X3 = Y2 )
                       => ( Y
                          = ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ Xs3 ) ) ) )
                      & ( ( X3 != Y2 )
                       => ( Y
                          = ( cons_l8134865115577406678c_fm_a @ X3 @ ( remdup8355899821003448156c_fm_a @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) ) ) ) )
                   => ~ ( accp_l7472382826029824047c_fm_a @ remdup6698152994906117545c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X3 @ ( cons_l8134865115577406678c_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).

% remdups_adj.pelims
thf(fact_607_remdups__adj_Opelims,axiom,
    ! [X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( remdup1727679340039403862c_fm_a @ X2 )
        = Y )
     => ( ( accp_l2570680006282209577c_fm_a @ remdup2768244663267211811c_fm_a @ X2 )
       => ( ( ( X2 = nil_Epistemic_fm_a )
           => ( ( Y = nil_Epistemic_fm_a )
             => ~ ( accp_l2570680006282209577c_fm_a @ remdup2768244663267211811c_fm_a @ nil_Epistemic_fm_a ) ) )
         => ( ! [X3: epistemic_fm_a] :
                ( ( X2
                  = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
               => ( ( Y
                    = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
                 => ~ ( accp_l2570680006282209577c_fm_a @ remdup2768244663267211811c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) )
           => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                  ( ( X2
                    = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
                 => ( ( ( ( X3 = Y2 )
                       => ( Y
                          = ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) ) ) )
                      & ( ( X3 != Y2 )
                       => ( Y
                          = ( cons_Epistemic_fm_a @ X3 @ ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) )
                   => ~ ( accp_l2570680006282209577c_fm_a @ remdup2768244663267211811c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).

% remdups_adj.pelims
thf(fact_608_KB4__5,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% KB4_5
thf(fact_609_transpose__aux__filter__head,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( concat2941956077894552763c_fm_a
        @ ( map_li1341364954853471300c_fm_a
          @ ( case_l6572946392233364704c_fm_a @ nil_se102576565402781184c_fm_a
            @ ^ [H: set_Epistemic_fm_a,T2: list_s580375451141968640c_fm_a] : ( cons_s4394448069393209776c_fm_a @ H @ nil_se102576565402781184c_fm_a ) )
          @ Xss2 ) )
      = ( map_li3594797534415244862c_fm_a @ hd_set2739578467680395621c_fm_a
        @ ( filter1974008165531859069c_fm_a
          @ ^ [Ys3: list_s580375451141968640c_fm_a] : ( Ys3 != nil_se102576565402781184c_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_head
thf(fact_610_transpose__aux__filter__head,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( concat6109960377493484129c_fm_a
        @ ( map_li8347733892191492164c_fm_a
          @ ( case_l116314299590685792c_fm_a @ nil_li2451196919128234278c_fm_a
            @ ^ [H: list_Epistemic_fm_a,T2: list_l6083326122719238310c_fm_a] : ( cons_l8134865115577406678c_fm_a @ H @ nil_li2451196919128234278c_fm_a ) )
          @ Xss2 ) )
      = ( map_li8743910666895923134c_fm_a @ hd_lis6228752984540680715c_fm_a
        @ ( filter389827114350055331c_fm_a
          @ ^ [Ys3: list_l6083326122719238310c_fm_a] : ( Ys3 != nil_li2451196919128234278c_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_head
thf(fact_611_transpose__aux__filter__head,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( concat2780896542826320603c_fm_a
        @ ( map_li3080774272885743684c_fm_a
          @ ( case_l8442927312758267104c_fm_a @ nil_Epistemic_fm_a
            @ ^ [H: epistemic_fm_a,T2: list_Epistemic_fm_a] : ( cons_Epistemic_fm_a @ H @ nil_Epistemic_fm_a ) )
          @ Xss2 ) )
      = ( map_li5516866612190465598c_fm_a @ hd_Epistemic_fm_a
        @ ( filter441479637125139101c_fm_a
          @ ^ [Ys3: list_Epistemic_fm_a] : ( Ys3 != nil_Epistemic_fm_a )
          @ Xss2 ) ) ) ).

% transpose_aux_filter_head
thf(fact_612_S5_H__B,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ) ) ).

% S5'_B
thf(fact_613_accp__subset__induct,axiom,
    ! [D: list_l6083326122719238310c_fm_a > $o,R2: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,X2: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( ord_le2363486873338524983fm_a_o @ D @ ( accp_l7472382826029824047c_fm_a @ R2 ) )
     => ( ! [X3: list_l6083326122719238310c_fm_a,Z2: list_l6083326122719238310c_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: list_l6083326122719238310c_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: list_l6083326122719238310c_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_614_accp__subset__induct,axiom,
    ! [D: list_Epistemic_fm_a > $o,R2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( ord_le5289359451089373629fm_a_o @ D @ ( accp_l2570680006282209577c_fm_a @ R2 ) )
     => ( ! [X3: list_Epistemic_fm_a,Z2: list_Epistemic_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: list_Epistemic_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: list_Epistemic_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_615_accp__subset__induct,axiom,
    ! [D: produc7493720319326827993c_fm_a > $o,R2: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,X2: produc7493720319326827993c_fm_a,P4: produc7493720319326827993c_fm_a > $o] :
      ( ( ord_le7091422540096163780fm_a_o @ D @ ( accp_P8153917284782618338c_fm_a @ R2 ) )
     => ( ! [X3: produc7493720319326827993c_fm_a,Z2: produc7493720319326827993c_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: produc7493720319326827993c_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: produc7493720319326827993c_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_616_accp__subset__induct,axiom,
    ! [D: produc3921445516396586231c_fm_a > $o,R2: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,X2: produc3921445516396586231c_fm_a,P4: produc3921445516396586231c_fm_a > $o] :
      ( ( ord_le60185291540232248fm_a_o @ D @ ( accp_P3999429264564614062c_fm_a @ R2 ) )
     => ( ! [X3: produc3921445516396586231c_fm_a,Z2: produc3921445516396586231c_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: produc3921445516396586231c_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: produc3921445516396586231c_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_617_accp__subset__induct,axiom,
    ! [D: produc5756089960658898087c_fm_a > $o,R2: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,X2: produc5756089960658898087c_fm_a,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( ord_le3724781943004833654fm_a_o @ D @ ( accp_P1207204058359408560c_fm_a @ R2 ) )
     => ( ! [X3: produc5756089960658898087c_fm_a,Z2: produc5756089960658898087c_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: produc5756089960658898087c_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: produc5756089960658898087c_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_618_accp__subset__induct,axiom,
    ! [D: epistemic_fm_a > $o,R2: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( ord_le4043730696559282883fm_a_o @ D @ ( accp_Epistemic_fm_a @ R2 ) )
     => ( ! [X3: epistemic_fm_a,Z2: epistemic_fm_a] :
            ( ( D @ X3 )
           => ( ( R2 @ Z2 @ X3 )
             => ( D @ Z2 ) ) )
       => ( ( D @ X2 )
         => ( ! [X3: epistemic_fm_a] :
                ( ( D @ X3 )
               => ( ! [Z3: epistemic_fm_a] :
                      ( ( R2 @ Z3 @ X3 )
                     => ( P4 @ Z3 ) )
                 => ( P4 @ X3 ) ) )
           => ( P4 @ X2 ) ) ) ) ) ).

% accp_subset_induct
thf(fact_619_Succ__def,axiom,
    ( bNF_Gr1807846264492387989c_fm_a
    = ( ^ [Kl: set_li4204741992506657632c_fm_a,Kl2: list_s580375451141968640c_fm_a] :
          ( collec2519470961442302949c_fm_a
          @ ^ [K: set_Epistemic_fm_a] : ( member2328277852289759785c_fm_a @ ( append5257919162946131733c_fm_a @ Kl2 @ ( cons_s4394448069393209776c_fm_a @ K @ nil_se102576565402781184c_fm_a ) ) @ Kl ) ) ) ) ).

% Succ_def
thf(fact_620_Succ__def,axiom,
    ( bNF_Gr7181009441526892347c_fm_a
    = ( ^ [Kl: set_li1092409891198325638c_fm_a,Kl2: list_l6083326122719238310c_fm_a] :
          ( collec5191077796991884427c_fm_a
          @ ^ [K: list_Epistemic_fm_a] : ( member7465314387053329231c_fm_a @ ( append1384085151619559355c_fm_a @ Kl2 @ ( cons_l8134865115577406678c_fm_a @ K @ nil_li2451196919128234278c_fm_a ) ) @ Kl ) ) ) ) ).

% Succ_def
thf(fact_621_Succ__def,axiom,
    ( bNF_Gr1093487135560555701c_fm_a
    = ( ^ [Kl: set_li769143395467472256c_fm_a,Kl2: list_Epistemic_fm_a] :
          ( collec4904205152690461189c_fm_a
          @ ^ [K: epistemic_fm_a] : ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl2 @ ( cons_Epistemic_fm_a @ K @ nil_Epistemic_fm_a ) ) @ Kl ) ) ) ) ).

% Succ_def
thf(fact_622_K4__L,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ epistemic_FF_a ) ) @ epistemic_FF_a ) @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% K4_L
thf(fact_623_S5_H__4,axiom,
    ! [A: epistemic_fm_a > $o,I: a,P: epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
       => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ) ) ).

% S5'_4
thf(fact_624_hd__remdups__adj,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( hd_lis6228752984540680715c_fm_a @ ( remdup8355899821003448156c_fm_a @ Xs2 ) )
      = ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ).

% hd_remdups_adj
thf(fact_625_hd__remdups__adj,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( hd_Epistemic_fm_a @ ( remdup1727679340039403862c_fm_a @ Xs2 ) )
      = ( hd_Epistemic_fm_a @ Xs2 ) ) ).

% hd_remdups_adj
thf(fact_626_hd__append2,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
        = ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ).

% hd_append2
thf(fact_627_hd__append2,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( hd_set2739578467680395621c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
        = ( hd_set2739578467680395621c_fm_a @ Xs2 ) ) ) ).

% hd_append2
thf(fact_628_hd__append2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( hd_Epistemic_fm_a @ Xs2 ) ) ) ).

% hd_append2
thf(fact_629_hd__Cons__tl,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ Xs2 ) @ ( tl_set2007602089164433257c_fm_a @ Xs2 ) )
        = Xs2 ) ) ).

% hd_Cons_tl
thf(fact_630_hd__Cons__tl,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) )
        = Xs2 ) ) ).

% hd_Cons_tl
thf(fact_631_hd__Cons__tl,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ Xs2 ) @ ( tl_Epistemic_fm_a @ Xs2 ) )
        = Xs2 ) ) ).

% hd_Cons_tl
thf(fact_632_list_Ocollapse,axiom,
    ! [List: list_s580375451141968640c_fm_a] :
      ( ( List != nil_se102576565402781184c_fm_a )
     => ( ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ List ) @ ( tl_set2007602089164433257c_fm_a @ List ) )
        = List ) ) ).

% list.collapse
thf(fact_633_list_Ocollapse,axiom,
    ! [List: list_l6083326122719238310c_fm_a] :
      ( ( List != nil_li2451196919128234278c_fm_a )
     => ( ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ List ) @ ( tl_lis3363300823944467983c_fm_a @ List ) )
        = List ) ) ).

% list.collapse
thf(fact_634_list_Ocollapse,axiom,
    ! [List: list_Epistemic_fm_a] :
      ( ( List != nil_Epistemic_fm_a )
     => ( ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) )
        = List ) ) ).

% list.collapse
thf(fact_635_list_Osel_I1_J,axiom,
    ! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] :
      ( ( hd_lis6228752984540680715c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) )
      = X21 ) ).

% list.sel(1)
thf(fact_636_list_Osel_I1_J,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( hd_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = X21 ) ).

% list.sel(1)
thf(fact_637_imply__append,axiom,
    ! [Ps: list_Epistemic_fm_a,Ps2: list_Epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( epistemic_imply_a @ ( append9179727413925872949c_fm_a @ Ps @ Ps2 ) @ Q )
      = ( epistemic_imply_a @ Ps @ ( epistemic_imply_a @ Ps2 @ Q ) ) ) ).

% imply_append
thf(fact_638_accp__subset,axiom,
    ! [R1: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,R22: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o] :
      ( ( ord_le7821966774285193230fm_a_o @ R1 @ R22 )
     => ( ord_le2363486873338524983fm_a_o @ ( accp_l7472382826029824047c_fm_a @ R22 ) @ ( accp_l7472382826029824047c_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_639_accp__subset,axiom,
    ! [R1: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,R22: list_Epistemic_fm_a > list_Epistemic_fm_a > $o] :
      ( ( ord_le358832340130632078fm_a_o @ R1 @ R22 )
     => ( ord_le5289359451089373629fm_a_o @ ( accp_l2570680006282209577c_fm_a @ R22 ) @ ( accp_l2570680006282209577c_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_640_accp__subset,axiom,
    ! [R1: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,R22: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o] :
      ( ( ord_le8486165426724920142fm_a_o @ R1 @ R22 )
     => ( ord_le7091422540096163780fm_a_o @ ( accp_P8153917284782618338c_fm_a @ R22 ) @ ( accp_P8153917284782618338c_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_641_accp__subset,axiom,
    ! [R1: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,R22: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o] :
      ( ( ord_le6327050188937335480fm_a_o @ R1 @ R22 )
     => ( ord_le60185291540232248fm_a_o @ ( accp_P3999429264564614062c_fm_a @ R22 ) @ ( accp_P3999429264564614062c_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_642_accp__subset,axiom,
    ! [R1: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,R22: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o] :
      ( ( ord_le2311501905961223630fm_a_o @ R1 @ R22 )
     => ( ord_le3724781943004833654fm_a_o @ ( accp_P1207204058359408560c_fm_a @ R22 ) @ ( accp_P1207204058359408560c_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_643_accp__subset,axiom,
    ! [R1: epistemic_fm_a > epistemic_fm_a > $o,R22: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( ord_le3934200179093585166fm_a_o @ R1 @ R22 )
     => ( ord_le4043730696559282883fm_a_o @ ( accp_Epistemic_fm_a @ R22 ) @ ( accp_Epistemic_fm_a @ R1 ) ) ) ).

% accp_subset
thf(fact_644_hd__concat,axiom,
    ! [Xs2: list_l3671048651222332332c_fm_a] :
      ( ( Xs2 != nil_li5178944226519631276c_fm_a )
     => ( ( ( hd_lis1359242352192849937c_fm_a @ Xs2 )
         != nil_li2451196919128234278c_fm_a )
       => ( ( hd_lis6228752984540680715c_fm_a @ ( concat6109960377493484129c_fm_a @ Xs2 ) )
          = ( hd_lis6228752984540680715c_fm_a @ ( hd_lis1359242352192849937c_fm_a @ Xs2 ) ) ) ) ) ).

% hd_concat
thf(fact_645_hd__concat,axiom,
    ! [Xs2: list_l985973790606564998c_fm_a] :
      ( ( Xs2 != nil_li5433889876484989702c_fm_a )
     => ( ( ( hd_lis8341250705491003371c_fm_a @ Xs2 )
         != nil_se102576565402781184c_fm_a )
       => ( ( hd_set2739578467680395621c_fm_a @ ( concat2941956077894552763c_fm_a @ Xs2 ) )
          = ( hd_set2739578467680395621c_fm_a @ ( hd_lis8341250705491003371c_fm_a @ Xs2 ) ) ) ) ) ).

% hd_concat
thf(fact_646_hd__concat,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( ( hd_lis6228752984540680715c_fm_a @ Xs2 )
         != nil_Epistemic_fm_a )
       => ( ( hd_Epistemic_fm_a @ ( concat2780896542826320603c_fm_a @ Xs2 ) )
          = ( hd_Epistemic_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ) ) ).

% hd_concat
thf(fact_647_list_Omap__sel_I1_J,axiom,
    ! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_se102576565402781184c_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_set2739578467680395621c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_648_list_Omap__sel_I1_J,axiom,
    ! [A2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( A2 != nil_se102576565402781184c_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_se6909769656262425450c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_set2739578467680395621c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_649_list_Omap__sel_I1_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_650_list_Omap__sel_I1_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_651_list_Omap__sel_I1_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( hd_lis1359242352192849937c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_652_list_Omap__sel_I1_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_lis1359242352192849937c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_653_list_Omap__sel_I1_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_654_list_Omap__sel_I1_J,axiom,
    ! [A2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ A2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ A2 ) ) ) ) ).

% list.map_sel(1)
thf(fact_655_hd__map,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_se8248101584983471204c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_set2739578467680395621c_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_656_hd__map,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_se6909769656262425450c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_set2739578467680395621c_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_657_hd__map,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_658_hd__map,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_lis6228752984540680715c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_659_hd__map,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( hd_lis1359242352192849937c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_660_hd__map,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_lis1359242352192849937c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_661_hd__map,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_662_hd__map,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( hd_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
        = ( F @ ( hd_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% hd_map
thf(fact_663_longest__common__prefix,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
    ? [Ps3: list_l6083326122719238310c_fm_a,Xs4: list_l6083326122719238310c_fm_a,Ys5: list_l6083326122719238310c_fm_a] :
      ( ( Xs2
        = ( append1384085151619559355c_fm_a @ Ps3 @ Xs4 ) )
      & ( Ys
        = ( append1384085151619559355c_fm_a @ Ps3 @ Ys5 ) )
      & ( ( Xs4 = nil_li2451196919128234278c_fm_a )
        | ( Ys5 = nil_li2451196919128234278c_fm_a )
        | ( ( hd_lis6228752984540680715c_fm_a @ Xs4 )
         != ( hd_lis6228752984540680715c_fm_a @ Ys5 ) ) ) ) ).

% longest_common_prefix
thf(fact_664_longest__common__prefix,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
    ? [Ps3: list_s580375451141968640c_fm_a,Xs4: list_s580375451141968640c_fm_a,Ys5: list_s580375451141968640c_fm_a] :
      ( ( Xs2
        = ( append5257919162946131733c_fm_a @ Ps3 @ Xs4 ) )
      & ( Ys
        = ( append5257919162946131733c_fm_a @ Ps3 @ Ys5 ) )
      & ( ( Xs4 = nil_se102576565402781184c_fm_a )
        | ( Ys5 = nil_se102576565402781184c_fm_a )
        | ( ( hd_set2739578467680395621c_fm_a @ Xs4 )
         != ( hd_set2739578467680395621c_fm_a @ Ys5 ) ) ) ) ).

% longest_common_prefix
thf(fact_665_longest__common__prefix,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
    ? [Ps3: list_Epistemic_fm_a,Xs4: list_Epistemic_fm_a,Ys5: list_Epistemic_fm_a] :
      ( ( Xs2
        = ( append9179727413925872949c_fm_a @ Ps3 @ Xs4 ) )
      & ( Ys
        = ( append9179727413925872949c_fm_a @ Ps3 @ Ys5 ) )
      & ( ( Xs4 = nil_Epistemic_fm_a )
        | ( Ys5 = nil_Epistemic_fm_a )
        | ( ( hd_Epistemic_fm_a @ Xs4 )
         != ( hd_Epistemic_fm_a @ Ys5 ) ) ) ) ).

% longest_common_prefix
thf(fact_666_hd__append,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( Xs2 = nil_li2451196919128234278c_fm_a )
       => ( ( hd_lis6228752984540680715c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
          = ( hd_lis6228752984540680715c_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_li2451196919128234278c_fm_a )
       => ( ( hd_lis6228752984540680715c_fm_a @ ( append1384085151619559355c_fm_a @ Xs2 @ Ys ) )
          = ( hd_lis6228752984540680715c_fm_a @ Xs2 ) ) ) ) ).

% hd_append
thf(fact_667_hd__append,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a] :
      ( ( ( Xs2 = nil_se102576565402781184c_fm_a )
       => ( ( hd_set2739578467680395621c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
          = ( hd_set2739578467680395621c_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_se102576565402781184c_fm_a )
       => ( ( hd_set2739578467680395621c_fm_a @ ( append5257919162946131733c_fm_a @ Xs2 @ Ys ) )
          = ( hd_set2739578467680395621c_fm_a @ Xs2 ) ) ) ) ).

% hd_append
thf(fact_668_hd__append,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
       => ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( hd_Epistemic_fm_a @ Ys ) ) )
      & ( ( Xs2 != nil_Epistemic_fm_a )
       => ( ( hd_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( hd_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% hd_append
thf(fact_669_list_Oexpand,axiom,
    ! [List: list_l6083326122719238310c_fm_a,List2: list_l6083326122719238310c_fm_a] :
      ( ( ( List = nil_li2451196919128234278c_fm_a )
        = ( List2 = nil_li2451196919128234278c_fm_a ) )
     => ( ( ( List != nil_li2451196919128234278c_fm_a )
         => ( ( List2 != nil_li2451196919128234278c_fm_a )
           => ( ( ( hd_lis6228752984540680715c_fm_a @ List )
                = ( hd_lis6228752984540680715c_fm_a @ List2 ) )
              & ( ( tl_lis3363300823944467983c_fm_a @ List )
                = ( tl_lis3363300823944467983c_fm_a @ List2 ) ) ) ) )
       => ( List = List2 ) ) ) ).

% list.expand
thf(fact_670_list_Oexpand,axiom,
    ! [List: list_s580375451141968640c_fm_a,List2: list_s580375451141968640c_fm_a] :
      ( ( ( List = nil_se102576565402781184c_fm_a )
        = ( List2 = nil_se102576565402781184c_fm_a ) )
     => ( ( ( List != nil_se102576565402781184c_fm_a )
         => ( ( List2 != nil_se102576565402781184c_fm_a )
           => ( ( ( hd_set2739578467680395621c_fm_a @ List )
                = ( hd_set2739578467680395621c_fm_a @ List2 ) )
              & ( ( tl_set2007602089164433257c_fm_a @ List )
                = ( tl_set2007602089164433257c_fm_a @ List2 ) ) ) ) )
       => ( List = List2 ) ) ) ).

% list.expand
thf(fact_671_list_Oexpand,axiom,
    ! [List: list_Epistemic_fm_a,List2: list_Epistemic_fm_a] :
      ( ( ( List = nil_Epistemic_fm_a )
        = ( List2 = nil_Epistemic_fm_a ) )
     => ( ( ( List != nil_Epistemic_fm_a )
         => ( ( List2 != nil_Epistemic_fm_a )
           => ( ( ( hd_Epistemic_fm_a @ List )
                = ( hd_Epistemic_fm_a @ List2 ) )
              & ( ( tl_Epistemic_fm_a @ List )
                = ( tl_Epistemic_fm_a @ List2 ) ) ) ) )
       => ( List = List2 ) ) ) ).

% list.expand
thf(fact_672_S5__S5_H,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_AxB_a @ P2 )
            | ( epistemic_Ax4_a @ P2 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_Ax5_a @ P2 ) )
        @ P ) ) ).

% S5_S5'
thf(fact_673_S5_H__S5,axiom,
    ! [P: epistemic_fm_a] :
      ( ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_Ax5_a @ P2 ) )
        @ P )
     => ( epistemic_AK_a
        @ ^ [P2: epistemic_fm_a] :
            ( ( epistemic_AxT_a @ P2 )
            | ( epistemic_AxB_a @ P2 )
            | ( epistemic_Ax4_a @ P2 ) )
        @ P ) ) ).

% S5'_S5
thf(fact_674_AxT_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_AxT_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ P ) ) ).

% AxT.intros
thf(fact_675_AxT_Osimps,axiom,
    ( epistemic_AxT_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P2 ) @ P2 ) ) ) ) ).

% AxT.simps
thf(fact_676_AxT_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_AxT_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P3 ) @ P3 ) ) ) ).

% AxT.cases
thf(fact_677_Ax4_Ointros,axiom,
    ! [I: a,P: epistemic_fm_a] : ( epistemic_Ax4_a @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ P ) @ ( epistemic_K_a @ I @ ( epistemic_K_a @ I @ P ) ) ) ) ).

% Ax4.intros
thf(fact_678_Ax4_Osimps,axiom,
    ( epistemic_Ax4_a
    = ( ^ [A4: epistemic_fm_a] :
        ? [I2: a,P2: epistemic_fm_a] :
          ( A4
          = ( epistemic_Imp_a @ ( epistemic_K_a @ I2 @ P2 ) @ ( epistemic_K_a @ I2 @ ( epistemic_K_a @ I2 @ P2 ) ) ) ) ) ) ).

% Ax4.simps
thf(fact_679_Ax4_Ocases,axiom,
    ! [A2: epistemic_fm_a] :
      ( ( epistemic_Ax4_a @ A2 )
     => ~ ! [I3: a,P3: epistemic_fm_a] :
            ( A2
           != ( epistemic_Imp_a @ ( epistemic_K_a @ I3 @ P3 ) @ ( epistemic_K_a @ I3 @ ( epistemic_K_a @ I3 @ P3 ) ) ) ) ) ).

% Ax4.cases
thf(fact_680_list_Oexhaust__sel,axiom,
    ! [List: list_s580375451141968640c_fm_a] :
      ( ( List != nil_se102576565402781184c_fm_a )
     => ( List
        = ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ List ) @ ( tl_set2007602089164433257c_fm_a @ List ) ) ) ) ).

% list.exhaust_sel
thf(fact_681_list_Oexhaust__sel,axiom,
    ! [List: list_l6083326122719238310c_fm_a] :
      ( ( List != nil_li2451196919128234278c_fm_a )
     => ( List
        = ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ List ) @ ( tl_lis3363300823944467983c_fm_a @ List ) ) ) ) ).

% list.exhaust_sel
thf(fact_682_list_Oexhaust__sel,axiom,
    ! [List: list_Epistemic_fm_a] :
      ( ( List != nil_Epistemic_fm_a )
     => ( List
        = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ).

% list.exhaust_sel
thf(fact_683_list_Ocase__eq__if,axiom,
    ( case_l8442927312758267104c_fm_a
    = ( ^ [F12: list_Epistemic_fm_a,F23: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List3: list_Epistemic_fm_a] : ( if_lis2878681784746929638c_fm_a @ ( List3 = nil_Epistemic_fm_a ) @ F12 @ ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ).

% list.case_eq_if
thf(fact_684_list_Ocase__eq__if,axiom,
    ( case_l5707353781634818138c_fm_a
    = ( ^ [F12: list_l6083326122719238310c_fm_a,F23: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List3: list_Epistemic_fm_a] : ( if_lis342421823373228652c_fm_a @ ( List3 = nil_Epistemic_fm_a ) @ F12 @ ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ).

% list.case_eq_if
thf(fact_685_list_Ocase__eq__if,axiom,
    ( case_l2021589626981272552c_fm_a
    = ( ^ [F12: $o,F23: epistemic_fm_a > list_Epistemic_fm_a > $o,List3: list_Epistemic_fm_a] :
          ( ( ( List3 = nil_Epistemic_fm_a )
           => F12 )
          & ( ( List3 != nil_Epistemic_fm_a )
           => ( F23 @ ( hd_Epistemic_fm_a @ List3 ) @ ( tl_Epistemic_fm_a @ List3 ) ) ) ) ) ) ).

% list.case_eq_if
thf(fact_686_accp_Ocases,axiom,
    ! [R: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,A2: list_l6083326122719238310c_fm_a] :
      ( ( accp_l7472382826029824047c_fm_a @ R @ A2 )
     => ! [Y4: list_l6083326122719238310c_fm_a] :
          ( ( R @ Y4 @ A2 )
         => ( accp_l7472382826029824047c_fm_a @ R @ Y4 ) ) ) ).

% accp.cases
thf(fact_687_accp_Ocases,axiom,
    ! [R: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A2: list_Epistemic_fm_a] :
      ( ( accp_l2570680006282209577c_fm_a @ R @ A2 )
     => ! [Y4: list_Epistemic_fm_a] :
          ( ( R @ Y4 @ A2 )
         => ( accp_l2570680006282209577c_fm_a @ R @ Y4 ) ) ) ).

% accp.cases
thf(fact_688_accp_Ocases,axiom,
    ! [R: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,A2: produc7493720319326827993c_fm_a] :
      ( ( accp_P8153917284782618338c_fm_a @ R @ A2 )
     => ! [Y4: produc7493720319326827993c_fm_a] :
          ( ( R @ Y4 @ A2 )
         => ( accp_P8153917284782618338c_fm_a @ R @ Y4 ) ) ) ).

% accp.cases
thf(fact_689_accp_Ocases,axiom,
    ! [R: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,A2: produc3921445516396586231c_fm_a] :
      ( ( accp_P3999429264564614062c_fm_a @ R @ A2 )
     => ! [Y4: produc3921445516396586231c_fm_a] :
          ( ( R @ Y4 @ A2 )
         => ( accp_P3999429264564614062c_fm_a @ R @ Y4 ) ) ) ).

% accp.cases
thf(fact_690_accp_Ocases,axiom,
    ! [R: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,A2: produc5756089960658898087c_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ R @ A2 )
     => ! [Y4: produc5756089960658898087c_fm_a] :
          ( ( R @ Y4 @ A2 )
         => ( accp_P1207204058359408560c_fm_a @ R @ Y4 ) ) ) ).

% accp.cases
thf(fact_691_accp_Osimps,axiom,
    ( accp_l7472382826029824047c_fm_a
    = ( ^ [R3: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,A4: list_l6083326122719238310c_fm_a] :
        ? [X: list_l6083326122719238310c_fm_a] :
          ( ( A4 = X )
          & ! [Y3: list_l6083326122719238310c_fm_a] :
              ( ( R3 @ Y3 @ X )
             => ( accp_l7472382826029824047c_fm_a @ R3 @ Y3 ) ) ) ) ) ).

% accp.simps
thf(fact_692_accp_Osimps,axiom,
    ( accp_l2570680006282209577c_fm_a
    = ( ^ [R3: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A4: list_Epistemic_fm_a] :
        ? [X: list_Epistemic_fm_a] :
          ( ( A4 = X )
          & ! [Y3: list_Epistemic_fm_a] :
              ( ( R3 @ Y3 @ X )
             => ( accp_l2570680006282209577c_fm_a @ R3 @ Y3 ) ) ) ) ) ).

% accp.simps
thf(fact_693_accp_Osimps,axiom,
    ( accp_P8153917284782618338c_fm_a
    = ( ^ [R3: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,A4: produc7493720319326827993c_fm_a] :
        ? [X: produc7493720319326827993c_fm_a] :
          ( ( A4 = X )
          & ! [Y3: produc7493720319326827993c_fm_a] :
              ( ( R3 @ Y3 @ X )
             => ( accp_P8153917284782618338c_fm_a @ R3 @ Y3 ) ) ) ) ) ).

% accp.simps
thf(fact_694_accp_Osimps,axiom,
    ( accp_P3999429264564614062c_fm_a
    = ( ^ [R3: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,A4: produc3921445516396586231c_fm_a] :
        ? [X: produc3921445516396586231c_fm_a] :
          ( ( A4 = X )
          & ! [Y3: produc3921445516396586231c_fm_a] :
              ( ( R3 @ Y3 @ X )
             => ( accp_P3999429264564614062c_fm_a @ R3 @ Y3 ) ) ) ) ) ).

% accp.simps
thf(fact_695_accp_Osimps,axiom,
    ( accp_P1207204058359408560c_fm_a
    = ( ^ [R3: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,A4: produc5756089960658898087c_fm_a] :
        ? [X: produc5756089960658898087c_fm_a] :
          ( ( A4 = X )
          & ! [Y3: produc5756089960658898087c_fm_a] :
              ( ( R3 @ Y3 @ X )
             => ( accp_P1207204058359408560c_fm_a @ R3 @ Y3 ) ) ) ) ) ).

% accp.simps
thf(fact_696_accpI,axiom,
    ! [R: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,X2: list_l6083326122719238310c_fm_a] :
      ( ! [Y2: list_l6083326122719238310c_fm_a] :
          ( ( R @ Y2 @ X2 )
         => ( accp_l7472382826029824047c_fm_a @ R @ Y2 ) )
     => ( accp_l7472382826029824047c_fm_a @ R @ X2 ) ) ).

% accpI
thf(fact_697_accpI,axiom,
    ! [R: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a] :
      ( ! [Y2: list_Epistemic_fm_a] :
          ( ( R @ Y2 @ X2 )
         => ( accp_l2570680006282209577c_fm_a @ R @ Y2 ) )
     => ( accp_l2570680006282209577c_fm_a @ R @ X2 ) ) ).

% accpI
thf(fact_698_accpI,axiom,
    ! [R: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,X2: produc7493720319326827993c_fm_a] :
      ( ! [Y2: produc7493720319326827993c_fm_a] :
          ( ( R @ Y2 @ X2 )
         => ( accp_P8153917284782618338c_fm_a @ R @ Y2 ) )
     => ( accp_P8153917284782618338c_fm_a @ R @ X2 ) ) ).

% accpI
thf(fact_699_accpI,axiom,
    ! [R: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,X2: produc3921445516396586231c_fm_a] :
      ( ! [Y2: produc3921445516396586231c_fm_a] :
          ( ( R @ Y2 @ X2 )
         => ( accp_P3999429264564614062c_fm_a @ R @ Y2 ) )
     => ( accp_P3999429264564614062c_fm_a @ R @ X2 ) ) ).

% accpI
thf(fact_700_accpI,axiom,
    ! [R: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,X2: produc5756089960658898087c_fm_a] :
      ( ! [Y2: produc5756089960658898087c_fm_a] :
          ( ( R @ Y2 @ X2 )
         => ( accp_P1207204058359408560c_fm_a @ R @ Y2 ) )
     => ( accp_P1207204058359408560c_fm_a @ R @ X2 ) ) ).

% accpI
thf(fact_701_accp__induct,axiom,
    ! [R: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,A2: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( accp_l7472382826029824047c_fm_a @ R @ A2 )
     => ( ! [X3: list_l6083326122719238310c_fm_a] :
            ( ( accp_l7472382826029824047c_fm_a @ R @ X3 )
           => ( ! [Y4: list_l6083326122719238310c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct
thf(fact_702_accp__induct,axiom,
    ! [R: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( accp_l2570680006282209577c_fm_a @ R @ A2 )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( accp_l2570680006282209577c_fm_a @ R @ X3 )
           => ( ! [Y4: list_Epistemic_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct
thf(fact_703_accp__induct,axiom,
    ! [R: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,A2: produc7493720319326827993c_fm_a,P4: produc7493720319326827993c_fm_a > $o] :
      ( ( accp_P8153917284782618338c_fm_a @ R @ A2 )
     => ( ! [X3: produc7493720319326827993c_fm_a] :
            ( ( accp_P8153917284782618338c_fm_a @ R @ X3 )
           => ( ! [Y4: produc7493720319326827993c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct
thf(fact_704_accp__induct,axiom,
    ! [R: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,A2: produc3921445516396586231c_fm_a,P4: produc3921445516396586231c_fm_a > $o] :
      ( ( accp_P3999429264564614062c_fm_a @ R @ A2 )
     => ( ! [X3: produc3921445516396586231c_fm_a] :
            ( ( accp_P3999429264564614062c_fm_a @ R @ X3 )
           => ( ! [Y4: produc3921445516396586231c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct
thf(fact_705_accp__induct,axiom,
    ! [R: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,A2: produc5756089960658898087c_fm_a,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( accp_P1207204058359408560c_fm_a @ R @ A2 )
     => ( ! [X3: produc5756089960658898087c_fm_a] :
            ( ( accp_P1207204058359408560c_fm_a @ R @ X3 )
           => ( ! [Y4: produc5756089960658898087c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct
thf(fact_706_accp__downward,axiom,
    ! [R: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,B: list_l6083326122719238310c_fm_a,A2: list_l6083326122719238310c_fm_a] :
      ( ( accp_l7472382826029824047c_fm_a @ R @ B )
     => ( ( R @ A2 @ B )
       => ( accp_l7472382826029824047c_fm_a @ R @ A2 ) ) ) ).

% accp_downward
thf(fact_707_accp__downward,axiom,
    ! [R: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,B: list_Epistemic_fm_a,A2: list_Epistemic_fm_a] :
      ( ( accp_l2570680006282209577c_fm_a @ R @ B )
     => ( ( R @ A2 @ B )
       => ( accp_l2570680006282209577c_fm_a @ R @ A2 ) ) ) ).

% accp_downward
thf(fact_708_accp__downward,axiom,
    ! [R: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,B: produc7493720319326827993c_fm_a,A2: produc7493720319326827993c_fm_a] :
      ( ( accp_P8153917284782618338c_fm_a @ R @ B )
     => ( ( R @ A2 @ B )
       => ( accp_P8153917284782618338c_fm_a @ R @ A2 ) ) ) ).

% accp_downward
thf(fact_709_accp__downward,axiom,
    ! [R: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,B: produc3921445516396586231c_fm_a,A2: produc3921445516396586231c_fm_a] :
      ( ( accp_P3999429264564614062c_fm_a @ R @ B )
     => ( ( R @ A2 @ B )
       => ( accp_P3999429264564614062c_fm_a @ R @ A2 ) ) ) ).

% accp_downward
thf(fact_710_accp__downward,axiom,
    ! [R: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,B: produc5756089960658898087c_fm_a,A2: produc5756089960658898087c_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ R @ B )
     => ( ( R @ A2 @ B )
       => ( accp_P1207204058359408560c_fm_a @ R @ A2 ) ) ) ).

% accp_downward
thf(fact_711_not__accp__down,axiom,
    ! [R2: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,X2: list_l6083326122719238310c_fm_a] :
      ( ~ ( accp_l7472382826029824047c_fm_a @ R2 @ X2 )
     => ~ ! [Z2: list_l6083326122719238310c_fm_a] :
            ( ( R2 @ Z2 @ X2 )
           => ( accp_l7472382826029824047c_fm_a @ R2 @ Z2 ) ) ) ).

% not_accp_down
thf(fact_712_not__accp__down,axiom,
    ! [R2: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,X2: list_Epistemic_fm_a] :
      ( ~ ( accp_l2570680006282209577c_fm_a @ R2 @ X2 )
     => ~ ! [Z2: list_Epistemic_fm_a] :
            ( ( R2 @ Z2 @ X2 )
           => ( accp_l2570680006282209577c_fm_a @ R2 @ Z2 ) ) ) ).

% not_accp_down
thf(fact_713_not__accp__down,axiom,
    ! [R2: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,X2: produc7493720319326827993c_fm_a] :
      ( ~ ( accp_P8153917284782618338c_fm_a @ R2 @ X2 )
     => ~ ! [Z2: produc7493720319326827993c_fm_a] :
            ( ( R2 @ Z2 @ X2 )
           => ( accp_P8153917284782618338c_fm_a @ R2 @ Z2 ) ) ) ).

% not_accp_down
thf(fact_714_not__accp__down,axiom,
    ! [R2: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,X2: produc3921445516396586231c_fm_a] :
      ( ~ ( accp_P3999429264564614062c_fm_a @ R2 @ X2 )
     => ~ ! [Z2: produc3921445516396586231c_fm_a] :
            ( ( R2 @ Z2 @ X2 )
           => ( accp_P3999429264564614062c_fm_a @ R2 @ Z2 ) ) ) ).

% not_accp_down
thf(fact_715_not__accp__down,axiom,
    ! [R2: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,X2: produc5756089960658898087c_fm_a] :
      ( ~ ( accp_P1207204058359408560c_fm_a @ R2 @ X2 )
     => ~ ! [Z2: produc5756089960658898087c_fm_a] :
            ( ( R2 @ Z2 @ X2 )
           => ( accp_P1207204058359408560c_fm_a @ R2 @ Z2 ) ) ) ).

% not_accp_down
thf(fact_716_accp__induct__rule,axiom,
    ! [R: list_l6083326122719238310c_fm_a > list_l6083326122719238310c_fm_a > $o,A2: list_l6083326122719238310c_fm_a,P4: list_l6083326122719238310c_fm_a > $o] :
      ( ( accp_l7472382826029824047c_fm_a @ R @ A2 )
     => ( ! [X3: list_l6083326122719238310c_fm_a] :
            ( ( accp_l7472382826029824047c_fm_a @ R @ X3 )
           => ( ! [Y4: list_l6083326122719238310c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct_rule
thf(fact_717_accp__induct__rule,axiom,
    ! [R: list_Epistemic_fm_a > list_Epistemic_fm_a > $o,A2: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( accp_l2570680006282209577c_fm_a @ R @ A2 )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( accp_l2570680006282209577c_fm_a @ R @ X3 )
           => ( ! [Y4: list_Epistemic_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct_rule
thf(fact_718_accp__induct__rule,axiom,
    ! [R: produc7493720319326827993c_fm_a > produc7493720319326827993c_fm_a > $o,A2: produc7493720319326827993c_fm_a,P4: produc7493720319326827993c_fm_a > $o] :
      ( ( accp_P8153917284782618338c_fm_a @ R @ A2 )
     => ( ! [X3: produc7493720319326827993c_fm_a] :
            ( ( accp_P8153917284782618338c_fm_a @ R @ X3 )
           => ( ! [Y4: produc7493720319326827993c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct_rule
thf(fact_719_accp__induct__rule,axiom,
    ! [R: produc3921445516396586231c_fm_a > produc3921445516396586231c_fm_a > $o,A2: produc3921445516396586231c_fm_a,P4: produc3921445516396586231c_fm_a > $o] :
      ( ( accp_P3999429264564614062c_fm_a @ R @ A2 )
     => ( ! [X3: produc3921445516396586231c_fm_a] :
            ( ( accp_P3999429264564614062c_fm_a @ R @ X3 )
           => ( ! [Y4: produc3921445516396586231c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct_rule
thf(fact_720_accp__induct__rule,axiom,
    ! [R: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a > $o,A2: produc5756089960658898087c_fm_a,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( accp_P1207204058359408560c_fm_a @ R @ A2 )
     => ( ! [X3: produc5756089960658898087c_fm_a] :
            ( ( accp_P1207204058359408560c_fm_a @ R @ X3 )
           => ( ! [Y4: produc5756089960658898087c_fm_a] :
                  ( ( R @ Y4 @ X3 )
                 => ( P4 @ Y4 ) )
             => ( P4 @ X3 ) ) )
       => ( P4 @ A2 ) ) ) ).

% accp_induct_rule
thf(fact_721_list_Osplit__sel__asm,axiom,
    ! [P4: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
      = ( ~ ( ( ( List = nil_Epistemic_fm_a )
              & ~ ( P4 @ F1 ) )
            | ( ( List
                = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
              & ~ ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).

% list.split_sel_asm
thf(fact_722_list_Osplit__sel__asm,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
      = ( ~ ( ( ( List = nil_Epistemic_fm_a )
              & ~ ( P4 @ F1 ) )
            | ( ( List
                = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
              & ~ ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).

% list.split_sel_asm
thf(fact_723_list_Osplit__sel__asm,axiom,
    ! [P4: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
      = ( ~ ( ( ( List = nil_Epistemic_fm_a )
              & ~ ( P4 @ F1 ) )
            | ( ( List
                = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
              & ~ ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ) ).

% list.split_sel_asm
thf(fact_724_list_Osplit__sel,axiom,
    ! [P4: list_Epistemic_fm_a > $o,F1: list_Epistemic_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_Epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l8442927312758267104c_fm_a @ F1 @ F22 @ List ) )
      = ( ( ( List = nil_Epistemic_fm_a )
         => ( P4 @ F1 ) )
        & ( ( List
            = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
         => ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).

% list.split_sel
thf(fact_725_list_Osplit__sel,axiom,
    ! [P4: list_l6083326122719238310c_fm_a > $o,F1: list_l6083326122719238310c_fm_a,F22: epistemic_fm_a > list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l5707353781634818138c_fm_a @ F1 @ F22 @ List ) )
      = ( ( ( List = nil_Epistemic_fm_a )
         => ( P4 @ F1 ) )
        & ( ( List
            = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
         => ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).

% list.split_sel
thf(fact_726_list_Osplit__sel,axiom,
    ! [P4: $o > $o,F1: $o,F22: epistemic_fm_a > list_Epistemic_fm_a > $o,List: list_Epistemic_fm_a] :
      ( ( P4 @ ( case_l2021589626981272552c_fm_a @ F1 @ F22 @ List ) )
      = ( ( ( List = nil_Epistemic_fm_a )
         => ( P4 @ F1 ) )
        & ( ( List
            = ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) )
         => ( P4 @ ( F22 @ ( hd_Epistemic_fm_a @ List ) @ ( tl_Epistemic_fm_a @ List ) ) ) ) ) ) ).

% list.split_sel
thf(fact_727_Succ__Shift,axiom,
    ! [Kl4: set_li1092409891198325638c_fm_a,K2: list_Epistemic_fm_a,Kl3: list_l6083326122719238310c_fm_a] :
      ( ( bNF_Gr7181009441526892347c_fm_a @ ( bNF_Gr2321306230395443647c_fm_a @ Kl4 @ K2 ) @ Kl3 )
      = ( bNF_Gr7181009441526892347c_fm_a @ Kl4 @ ( cons_l8134865115577406678c_fm_a @ K2 @ Kl3 ) ) ) ).

% Succ_Shift
thf(fact_728_Succ__Shift,axiom,
    ! [Kl4: set_li769143395467472256c_fm_a,K2: epistemic_fm_a,Kl3: list_Epistemic_fm_a] :
      ( ( bNF_Gr1093487135560555701c_fm_a @ ( bNF_Gr8437504134799245625c_fm_a @ Kl4 @ K2 ) @ Kl3 )
      = ( bNF_Gr1093487135560555701c_fm_a @ Kl4 @ ( cons_Epistemic_fm_a @ K2 @ Kl3 ) ) ) ).

% Succ_Shift
thf(fact_729_empty__Shift,axiom,
    ! [Kl4: set_li5400946639045803789c_fm_a,K2: produc2203834439629243303c_fm_a] :
      ( ( member914871927696214614c_fm_a @ nil_Pr2379126408512758701c_fm_a @ Kl4 )
     => ( ( member5029746173879296720c_fm_a @ K2 @ ( bNF_Gr1067639066622367170c_fm_a @ Kl4 @ nil_Pr2379126408512758701c_fm_a ) )
       => ( member914871927696214614c_fm_a @ nil_Pr2379126408512758701c_fm_a @ ( bNF_Gr2566093624500959302c_fm_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_730_empty__Shift,axiom,
    ! [Kl4: set_li5579717781341779981c_fm_a,K2: produc5756089960658898087c_fm_a] :
      ( ( member2056814488595083094c_fm_a @ nil_Pr1848654487927912109c_fm_a @ Kl4 )
     => ( ( member3265983909902097104c_fm_a @ K2 @ ( bNF_Gr4364940288494914498c_fm_a @ Kl4 @ nil_Pr1848654487927912109c_fm_a ) )
       => ( member2056814488595083094c_fm_a @ nil_Pr1848654487927912109c_fm_a @ ( bNF_Gr6190719756362435142c_fm_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_731_empty__Shift,axiom,
    ! [Kl4: set_list_a,K2: a] :
      ( ( member_list_a @ nil_a @ Kl4 )
     => ( ( member_a @ K2 @ ( bNF_Greatest_Succ_a @ Kl4 @ nil_a ) )
       => ( member_list_a @ nil_a @ ( bNF_Greatest_Shift_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_732_empty__Shift,axiom,
    ! [Kl4: set_li1092409891198325638c_fm_a,K2: list_Epistemic_fm_a] :
      ( ( member7465314387053329231c_fm_a @ nil_li2451196919128234278c_fm_a @ Kl4 )
     => ( ( member5906877432388582473c_fm_a @ K2 @ ( bNF_Gr7181009441526892347c_fm_a @ Kl4 @ nil_li2451196919128234278c_fm_a ) )
       => ( member7465314387053329231c_fm_a @ nil_li2451196919128234278c_fm_a @ ( bNF_Gr2321306230395443647c_fm_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_733_empty__Shift,axiom,
    ! [Kl4: set_li4204741992506657632c_fm_a,K2: set_Epistemic_fm_a] :
      ( ( member2328277852289759785c_fm_a @ nil_se102576565402781184c_fm_a @ Kl4 )
     => ( ( member536094252920883875c_fm_a @ K2 @ ( bNF_Gr1807846264492387989c_fm_a @ Kl4 @ nil_se102576565402781184c_fm_a ) )
       => ( member2328277852289759785c_fm_a @ nil_se102576565402781184c_fm_a @ ( bNF_Gr7707547485936239385c_fm_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_734_empty__Shift,axiom,
    ! [Kl4: set_li769143395467472256c_fm_a,K2: epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ Kl4 )
     => ( ( member6642669571620171971c_fm_a @ K2 @ ( bNF_Gr1093487135560555701c_fm_a @ Kl4 @ nil_Epistemic_fm_a ) )
       => ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( bNF_Gr8437504134799245625c_fm_a @ Kl4 @ K2 ) ) ) ) ).

% empty_Shift
thf(fact_735_T__L,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ ( epistemic_Imp_a @ ( epistemic_K_a @ I @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) ) @ epistemic_FF_a ) ) ) ) ).

% T_L
thf(fact_736_SuccI,axiom,
    ! [Kl3: list_P3099032918374241197c_fm_a,K2: produc2203834439629243303c_fm_a,Kl4: set_li5400946639045803789c_fm_a] :
      ( ( member914871927696214614c_fm_a @ ( append8587712973440712258c_fm_a @ Kl3 @ ( cons_P6232728021713608541c_fm_a @ K2 @ nil_Pr2379126408512758701c_fm_a ) ) @ Kl4 )
     => ( member5029746173879296720c_fm_a @ K2 @ ( bNF_Gr1067639066622367170c_fm_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_737_SuccI,axiom,
    ! [Kl3: list_P7917480606449584557c_fm_a,K2: produc5756089960658898087c_fm_a,Kl4: set_li5579717781341779981c_fm_a] :
      ( ( member2056814488595083094c_fm_a @ ( append9053776140663174210c_fm_a @ Kl3 @ ( cons_P7190808671141380701c_fm_a @ K2 @ nil_Pr1848654487927912109c_fm_a ) ) @ Kl4 )
     => ( member3265983909902097104c_fm_a @ K2 @ ( bNF_Gr4364940288494914498c_fm_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_738_SuccI,axiom,
    ! [Kl3: list_a,K2: a,Kl4: set_list_a] :
      ( ( member_list_a @ ( append_a @ Kl3 @ ( cons_a @ K2 @ nil_a ) ) @ Kl4 )
     => ( member_a @ K2 @ ( bNF_Greatest_Succ_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_739_SuccI,axiom,
    ! [Kl3: list_s580375451141968640c_fm_a,K2: set_Epistemic_fm_a,Kl4: set_li4204741992506657632c_fm_a] :
      ( ( member2328277852289759785c_fm_a @ ( append5257919162946131733c_fm_a @ Kl3 @ ( cons_s4394448069393209776c_fm_a @ K2 @ nil_se102576565402781184c_fm_a ) ) @ Kl4 )
     => ( member536094252920883875c_fm_a @ K2 @ ( bNF_Gr1807846264492387989c_fm_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_740_SuccI,axiom,
    ! [Kl3: list_l6083326122719238310c_fm_a,K2: list_Epistemic_fm_a,Kl4: set_li1092409891198325638c_fm_a] :
      ( ( member7465314387053329231c_fm_a @ ( append1384085151619559355c_fm_a @ Kl3 @ ( cons_l8134865115577406678c_fm_a @ K2 @ nil_li2451196919128234278c_fm_a ) ) @ Kl4 )
     => ( member5906877432388582473c_fm_a @ K2 @ ( bNF_Gr7181009441526892347c_fm_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_741_SuccI,axiom,
    ! [Kl3: list_Epistemic_fm_a,K2: epistemic_fm_a,Kl4: set_li769143395467472256c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl3 @ ( cons_Epistemic_fm_a @ K2 @ nil_Epistemic_fm_a ) ) @ Kl4 )
     => ( member6642669571620171971c_fm_a @ K2 @ ( bNF_Gr1093487135560555701c_fm_a @ Kl4 @ Kl3 ) ) ) ).

% SuccI
thf(fact_742_SuccD,axiom,
    ! [K2: produc2203834439629243303c_fm_a,Kl4: set_li5400946639045803789c_fm_a,Kl3: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ K2 @ ( bNF_Gr1067639066622367170c_fm_a @ Kl4 @ Kl3 ) )
     => ( member914871927696214614c_fm_a @ ( append8587712973440712258c_fm_a @ Kl3 @ ( cons_P6232728021713608541c_fm_a @ K2 @ nil_Pr2379126408512758701c_fm_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_743_SuccD,axiom,
    ! [K2: produc5756089960658898087c_fm_a,Kl4: set_li5579717781341779981c_fm_a,Kl3: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ K2 @ ( bNF_Gr4364940288494914498c_fm_a @ Kl4 @ Kl3 ) )
     => ( member2056814488595083094c_fm_a @ ( append9053776140663174210c_fm_a @ Kl3 @ ( cons_P7190808671141380701c_fm_a @ K2 @ nil_Pr1848654487927912109c_fm_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_744_SuccD,axiom,
    ! [K2: a,Kl4: set_list_a,Kl3: list_a] :
      ( ( member_a @ K2 @ ( bNF_Greatest_Succ_a @ Kl4 @ Kl3 ) )
     => ( member_list_a @ ( append_a @ Kl3 @ ( cons_a @ K2 @ nil_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_745_SuccD,axiom,
    ! [K2: set_Epistemic_fm_a,Kl4: set_li4204741992506657632c_fm_a,Kl3: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ K2 @ ( bNF_Gr1807846264492387989c_fm_a @ Kl4 @ Kl3 ) )
     => ( member2328277852289759785c_fm_a @ ( append5257919162946131733c_fm_a @ Kl3 @ ( cons_s4394448069393209776c_fm_a @ K2 @ nil_se102576565402781184c_fm_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_746_SuccD,axiom,
    ! [K2: list_Epistemic_fm_a,Kl4: set_li1092409891198325638c_fm_a,Kl3: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ K2 @ ( bNF_Gr7181009441526892347c_fm_a @ Kl4 @ Kl3 ) )
     => ( member7465314387053329231c_fm_a @ ( append1384085151619559355c_fm_a @ Kl3 @ ( cons_l8134865115577406678c_fm_a @ K2 @ nil_li2451196919128234278c_fm_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_747_SuccD,axiom,
    ! [K2: epistemic_fm_a,Kl4: set_li769143395467472256c_fm_a,Kl3: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ K2 @ ( bNF_Gr1093487135560555701c_fm_a @ Kl4 @ Kl3 ) )
     => ( member5906877432388582473c_fm_a @ ( append9179727413925872949c_fm_a @ Kl3 @ ( cons_Epistemic_fm_a @ K2 @ nil_Epistemic_fm_a ) ) @ Kl4 ) ) ).

% SuccD
thf(fact_748_S5__S5_H__assms,axiom,
    ! [G5: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_AxB_a @ P2 )
                  | ( epistemic_Ax4_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) )
      = ( ? [Qs: list_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ G5 )
            & ( epistemic_AK_a
              @ ^ [P2: epistemic_fm_a] :
                  ( ( epistemic_AxT_a @ P2 )
                  | ( epistemic_Ax5_a @ P2 ) )
              @ ( epistemic_imply_a @ Qs @ P ) ) ) ) ) ).

% S5_S5'_assms
thf(fact_749_rotate1__hd__tl,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( ( rotate2699689030021285965c_fm_a @ Xs2 )
        = ( append5257919162946131733c_fm_a @ ( tl_set2007602089164433257c_fm_a @ Xs2 ) @ ( cons_s4394448069393209776c_fm_a @ ( hd_set2739578467680395621c_fm_a @ Xs2 ) @ nil_se102576565402781184c_fm_a ) ) ) ) ).

% rotate1_hd_tl
thf(fact_750_rotate1__hd__tl,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( ( rotate2311183321535120627c_fm_a @ Xs2 )
        = ( append1384085151619559355c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ Xs2 ) @ ( cons_l8134865115577406678c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) @ nil_li2451196919128234278c_fm_a ) ) ) ) ).

% rotate1_hd_tl
thf(fact_751_rotate1__hd__tl,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( rotate3540958558250653293c_fm_a @ Xs2 )
        = ( append9179727413925872949c_fm_a @ ( tl_Epistemic_fm_a @ Xs2 ) @ ( cons_Epistemic_fm_a @ ( hd_Epistemic_fm_a @ Xs2 ) @ nil_Epistemic_fm_a ) ) ) ) ).

% rotate1_hd_tl
thf(fact_752_fm_Oexhaust,axiom,
    ! [Y: epistemic_fm_a] :
      ( ( Y != epistemic_FF_a )
     => ( ! [X24: list_char] :
            ( Y
           != ( epistemic_Pro_a @ X24 ) )
       => ( ! [X312: epistemic_fm_a,X322: epistemic_fm_a] :
              ( Y
             != ( epistemic_Dis_a @ X312 @ X322 ) )
         => ( ! [X412: epistemic_fm_a,X422: epistemic_fm_a] :
                ( Y
               != ( epistemic_Con_a @ X412 @ X422 ) )
           => ( ! [X512: epistemic_fm_a,X522: epistemic_fm_a] :
                  ( Y
                 != ( epistemic_Imp_a @ X512 @ X522 ) )
             => ~ ! [X612: a,X622: epistemic_fm_a] :
                    ( Y
                   != ( epistemic_K_a @ X612 @ X622 ) ) ) ) ) ) ) ).

% fm.exhaust
thf(fact_753_pred__subset__eq,axiom,
    ! [R2: set_Pr8948481099588399239c_fm_a,S: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le4942933042592423798fm_a_o
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ R2 )
        @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ S ) )
      = ( ord_le8222437384497874983c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_754_pred__subset__eq,axiom,
    ! [R2: set_Pr3219225162411408519c_fm_a,S: set_Pr3219225162411408519c_fm_a] :
      ( ( ord_le3724781943004833654fm_a_o
        @ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ R2 )
        @ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ S ) )
      = ( ord_le8873477448617899047c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_755_pred__subset__eq,axiom,
    ! [R2: set_se5208064806568342746c_fm_a,S: set_se5208064806568342746c_fm_a] :
      ( ( ord_le1568123225352354019fm_a_o
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ R2 )
        @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ S ) )
      = ( ord_le7112219575281605754c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_756_pred__subset__eq,axiom,
    ! [R2: set_a,S: set_a] :
      ( ( ord_less_eq_a_o
        @ ^ [X: a] : ( member_a @ X @ R2 )
        @ ^ [X: a] : ( member_a @ X @ S ) )
      = ( ord_less_eq_set_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_757_pred__subset__eq,axiom,
    ! [R2: set_li769143395467472256c_fm_a,S: set_li769143395467472256c_fm_a] :
      ( ( ord_le5289359451089373629fm_a_o
        @ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ R2 )
        @ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ S ) )
      = ( ord_le2931979837777675552c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_758_pred__subset__eq,axiom,
    ! [R2: set_Epistemic_fm_a,S: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ R2 )
        @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ S ) )
      = ( ord_le3275665582123262618c_fm_a @ R2 @ S ) ) ).

% pred_subset_eq
thf(fact_759_fm_Oinject_I1_J,axiom,
    ! [X25: list_char,Y23: list_char] :
      ( ( ( epistemic_Pro_a @ X25 )
        = ( epistemic_Pro_a @ Y23 ) )
      = ( X25 = Y23 ) ) ).

% fm.inject(1)
thf(fact_760_map__eq__conv,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = ( map_Ep1988204514693272906c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_761_map__eq__conv,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = ( map_Ep4939040189629079504c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_762_map__eq__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = ( map_li3080774272885743684c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_763_map__eq__conv,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
        = ( map_li3858915945532548554c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_764_map__eq__conv,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = ( map_li5516866612190465598c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_765_map__eq__conv,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( map_Ep7084560364594560580c_fm_a @ G3 @ Xs2 ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( ( F @ X )
              = ( G3 @ X ) ) ) ) ) ).

% map_eq_conv
thf(fact_766_filter__True,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ( P4 @ X3 ) )
     => ( ( filter7636273809395300631c_fm_a @ P4 @ Xs2 )
        = Xs2 ) ) ).

% filter_True
thf(fact_767_filter__True,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ( P4 @ X3 ) )
     => ( ( filter441479637125139101c_fm_a @ P4 @ Xs2 )
        = Xs2 ) ) ).

% filter_True
thf(fact_768_set__rev,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( rev_Epistemic_fm_a @ Xs2 ) )
      = ( set_Epistemic_fm_a2 @ Xs2 ) ) ).

% set_rev
thf(fact_769_set__rev,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( set_li8442223810127165109c_fm_a @ ( rev_li1443896382544221062c_fm_a @ Xs2 ) )
      = ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ).

% set_rev
thf(fact_770_remdups__adj__set,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( set_li8442223810127165109c_fm_a @ ( remdup8355899821003448156c_fm_a @ Xs2 ) )
      = ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ).

% remdups_adj_set
thf(fact_771_remdups__adj__set,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( remdup1727679340039403862c_fm_a @ Xs2 ) )
      = ( set_Epistemic_fm_a2 @ Xs2 ) ) ).

% remdups_adj_set
thf(fact_772_rotate1__is__Nil__conv,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( rotate2311183321535120627c_fm_a @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( Xs2 = nil_li2451196919128234278c_fm_a ) ) ).

% rotate1_is_Nil_conv
thf(fact_773_rotate1__is__Nil__conv,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( rotate2699689030021285965c_fm_a @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( Xs2 = nil_se102576565402781184c_fm_a ) ) ).

% rotate1_is_Nil_conv
thf(fact_774_rotate1__is__Nil__conv,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( rotate3540958558250653293c_fm_a @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% rotate1_is_Nil_conv
thf(fact_775_set__rotate1,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( rotate3540958558250653293c_fm_a @ Xs2 ) )
      = ( set_Epistemic_fm_a2 @ Xs2 ) ) ).

% set_rotate1
thf(fact_776_set__rotate1,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( set_li8442223810127165109c_fm_a @ ( rotate2311183321535120627c_fm_a @ Xs2 ) )
      = ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ).

% set_rotate1
thf(fact_777_in__set__insert,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ( ( insert423680279517344963c_fm_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_778_in__set__insert,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ( ( insert7000960152310464963c_fm_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_779_in__set__insert,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ( ( insert1868103382419917334c_fm_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_780_in__set__insert,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ( ( insert_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_781_in__set__insert,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ( ( insert177310161492556854c_fm_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_782_in__set__insert,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ( ( insert335162795743670844c_fm_a @ X2 @ Xs2 )
        = Xs2 ) ) ).

% in_set_insert
thf(fact_783_set__filter,axiom,
    ! [P4: produc2203834439629243303c_fm_a > $o,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( set_Pr6083076219314900284c_fm_a @ ( filter326375931097202980c_fm_a @ P4 @ Xs2 ) )
      = ( collec7391038856303340306c_fm_a
        @ ^ [X: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_784_set__filter,axiom,
    ! [P4: produc5756089960658898087c_fm_a > $o,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( set_Pr5015285182815091004c_fm_a @ ( filter8648851334721324324c_fm_a @ P4 @ Xs2 ) )
      = ( collec6124610372686893330c_fm_a
        @ ^ [X: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_785_set__filter,axiom,
    ! [P4: a > $o,Xs2: list_a] :
      ( ( set_a2 @ ( filter_a @ P4 @ Xs2 ) )
      = ( collect_a
        @ ^ [X: a] :
            ( ( member_a @ X @ ( set_a2 @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_786_set__filter,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
      ( ( set_se8855941934996405007c_fm_a @ ( filter2620125754611450615c_fm_a @ P4 @ Xs2 ) )
      = ( collec2519470961442302949c_fm_a
        @ ^ [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_787_set__filter,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) )
      = ( collec4904205152690461189c_fm_a
        @ ^ [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_788_set__filter,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( set_li8442223810127165109c_fm_a @ ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) )
      = ( collec5191077796991884427c_fm_a
        @ ^ [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) ) ) ).

% set_filter
thf(fact_789_filter__False,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ! [X3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
         => ~ ( P4 @ X3 ) )
     => ( ( filter2620125754611450615c_fm_a @ P4 @ Xs2 )
        = nil_se102576565402781184c_fm_a ) ) ).

% filter_False
thf(fact_790_filter__False,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ~ ( P4 @ X3 ) )
     => ( ( filter441479637125139101c_fm_a @ P4 @ Xs2 )
        = nil_li2451196919128234278c_fm_a ) ) ).

% filter_False
thf(fact_791_filter__False,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ~ ( P4 @ X3 ) )
     => ( ( filter7636273809395300631c_fm_a @ P4 @ Xs2 )
        = nil_Epistemic_fm_a ) ) ).

% filter_False
thf(fact_792_not__in__set__insert,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ( ( insert423680279517344963c_fm_a @ X2 @ Xs2 )
        = ( cons_P6232728021713608541c_fm_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_793_not__in__set__insert,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ( ( insert7000960152310464963c_fm_a @ X2 @ Xs2 )
        = ( cons_P7190808671141380701c_fm_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_794_not__in__set__insert,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ( ( insert1868103382419917334c_fm_a @ X2 @ Xs2 )
        = ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_795_not__in__set__insert,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ~ ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ( ( insert_a @ X2 @ Xs2 )
        = ( cons_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_796_not__in__set__insert,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ( ( insert335162795743670844c_fm_a @ X2 @ Xs2 )
        = ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_797_not__in__set__insert,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ( ( insert177310161492556854c_fm_a @ X2 @ Xs2 )
        = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) ).

% not_in_set_insert
thf(fact_798_subset__Collect__iff,axiom,
    ! [B2: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( ord_le8222437384497874983c_fm_a @ B2 @ A )
     => ( ( ord_le8222437384497874983c_fm_a @ B2
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: produc2203834439629243303c_fm_a] :
              ( ( member5029746173879296720c_fm_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_799_subset__Collect__iff,axiom,
    ! [B2: set_Pr3219225162411408519c_fm_a,A: set_Pr3219225162411408519c_fm_a,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( ord_le8873477448617899047c_fm_a @ B2 @ A )
     => ( ( ord_le8873477448617899047c_fm_a @ B2
          @ ( collec6124610372686893330c_fm_a
            @ ^ [X: produc5756089960658898087c_fm_a] :
                ( ( member3265983909902097104c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: produc5756089960658898087c_fm_a] :
              ( ( member3265983909902097104c_fm_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_800_subset__Collect__iff,axiom,
    ! [B2: set_a,A: set_a,P4: a > $o] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ( ord_less_eq_set_a @ B2
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: a] :
              ( ( member_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_801_subset__Collect__iff,axiom,
    ! [B2: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,P4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ B2 @ A )
     => ( ( ord_le7112219575281605754c_fm_a @ B2
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: set_Epistemic_fm_a] :
              ( ( member536094252920883875c_fm_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_802_subset__Collect__iff,axiom,
    ! [B2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ B2 @ A )
     => ( ( ord_le3275665582123262618c_fm_a @ B2
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_803_subset__Collect__iff,axiom,
    ! [B2: set_li769143395467472256c_fm_a,A: set_li769143395467472256c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( ord_le2931979837777675552c_fm_a @ B2 @ A )
     => ( ( ord_le2931979837777675552c_fm_a @ B2
          @ ( collec5191077796991884427c_fm_a
            @ ^ [X: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) )
        = ( ! [X: list_Epistemic_fm_a] :
              ( ( member5906877432388582473c_fm_a @ X @ B2 )
             => ( P4 @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_804_subset__CollectI,axiom,
    ! [B2: set_Pr8948481099588399239c_fm_a,A: set_Pr8948481099588399239c_fm_a,Q4: produc2203834439629243303c_fm_a > $o,P4: produc2203834439629243303c_fm_a > $o] :
      ( ( ord_le8222437384497874983c_fm_a @ B2 @ A )
     => ( ! [X3: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_le8222437384497874983c_fm_a
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collec7391038856303340306c_fm_a
            @ ^ [X: produc2203834439629243303c_fm_a] :
                ( ( member5029746173879296720c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_805_subset__CollectI,axiom,
    ! [B2: set_Pr3219225162411408519c_fm_a,A: set_Pr3219225162411408519c_fm_a,Q4: produc5756089960658898087c_fm_a > $o,P4: produc5756089960658898087c_fm_a > $o] :
      ( ( ord_le8873477448617899047c_fm_a @ B2 @ A )
     => ( ! [X3: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_le8873477448617899047c_fm_a
          @ ( collec6124610372686893330c_fm_a
            @ ^ [X: produc5756089960658898087c_fm_a] :
                ( ( member3265983909902097104c_fm_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collec6124610372686893330c_fm_a
            @ ^ [X: produc5756089960658898087c_fm_a] :
                ( ( member3265983909902097104c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_806_subset__CollectI,axiom,
    ! [B2: set_a,A: set_a,Q4: a > $o,P4: a > $o] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ! [X3: a] :
            ( ( member_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_less_eq_set_a
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collect_a
            @ ^ [X: a] :
                ( ( member_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_807_subset__CollectI,axiom,
    ! [B2: set_se5208064806568342746c_fm_a,A: set_se5208064806568342746c_fm_a,Q4: set_Epistemic_fm_a > $o,P4: set_Epistemic_fm_a > $o] :
      ( ( ord_le7112219575281605754c_fm_a @ B2 @ A )
     => ( ! [X3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_le7112219575281605754c_fm_a
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collec2519470961442302949c_fm_a
            @ ^ [X: set_Epistemic_fm_a] :
                ( ( member536094252920883875c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_808_subset__CollectI,axiom,
    ! [B2: set_Epistemic_fm_a,A: set_Epistemic_fm_a,Q4: epistemic_fm_a > $o,P4: epistemic_fm_a > $o] :
      ( ( ord_le3275665582123262618c_fm_a @ B2 @ A )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_le3275665582123262618c_fm_a
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collec4904205152690461189c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_809_subset__CollectI,axiom,
    ! [B2: set_li769143395467472256c_fm_a,A: set_li769143395467472256c_fm_a,Q4: list_Epistemic_fm_a > $o,P4: list_Epistemic_fm_a > $o] :
      ( ( ord_le2931979837777675552c_fm_a @ B2 @ A )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X3 @ B2 )
           => ( ( Q4 @ X3 )
             => ( P4 @ X3 ) ) )
       => ( ord_le2931979837777675552c_fm_a
          @ ( collec5191077796991884427c_fm_a
            @ ^ [X: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ X @ B2 )
                & ( Q4 @ X ) ) )
          @ ( collec5191077796991884427c_fm_a
            @ ^ [X: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ X @ A )
                & ( P4 @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_810_subset__code_I1_J,axiom,
    ! [Xs2: list_P3099032918374241197c_fm_a,B2: set_Pr8948481099588399239c_fm_a] :
      ( ( ord_le8222437384497874983c_fm_a @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) @ B2 )
      = ( ! [X: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
           => ( member5029746173879296720c_fm_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_811_subset__code_I1_J,axiom,
    ! [Xs2: list_P7917480606449584557c_fm_a,B2: set_Pr3219225162411408519c_fm_a] :
      ( ( ord_le8873477448617899047c_fm_a @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) @ B2 )
      = ( ! [X: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
           => ( member3265983909902097104c_fm_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_812_subset__code_I1_J,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,B2: set_se5208064806568342746c_fm_a] :
      ( ( ord_le7112219575281605754c_fm_a @ ( set_se8855941934996405007c_fm_a @ Xs2 ) @ B2 )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
           => ( member536094252920883875c_fm_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_813_subset__code_I1_J,axiom,
    ! [Xs2: list_a,B2: set_a] :
      ( ( ord_less_eq_set_a @ ( set_a2 @ Xs2 ) @ B2 )
      = ( ! [X: a] :
            ( ( member_a @ X @ ( set_a2 @ Xs2 ) )
           => ( member_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_814_subset__code_I1_J,axiom,
    ! [Xs2: list_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) @ B2 )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( member6642669571620171971c_fm_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_815_subset__code_I1_J,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,B2: set_li769143395467472256c_fm_a] :
      ( ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ Xs2 ) @ B2 )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( member5906877432388582473c_fm_a @ X @ B2 ) ) ) ) ).

% subset_code(1)
thf(fact_816_set__ConsD,axiom,
    ! [Y: produc2203834439629243303c_fm_a,X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_817_set__ConsD,axiom,
    ! [Y: produc5756089960658898087c_fm_a,X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_818_set__ConsD,axiom,
    ! [Y: set_Epistemic_fm_a,X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_819_set__ConsD,axiom,
    ! [Y: a,X2: a,Xs2: list_a] :
      ( ( member_a @ Y @ ( set_a2 @ ( cons_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member_a @ Y @ ( set_a2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_820_set__ConsD,axiom,
    ! [Y: list_Epistemic_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_821_set__ConsD,axiom,
    ! [Y: epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) )
     => ( ( Y = X2 )
        | ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ Xs2 ) ) ) ) ).

% set_ConsD
thf(fact_822_list_Oset__cases,axiom,
    ! [E: produc2203834439629243303c_fm_a,A2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ E @ ( set_Pr6083076219314900284c_fm_a @ A2 ) )
     => ( ! [Z22: list_P3099032918374241197c_fm_a] :
            ( A2
           != ( cons_P6232728021713608541c_fm_a @ E @ Z22 ) )
       => ~ ! [Z1: produc2203834439629243303c_fm_a,Z22: list_P3099032918374241197c_fm_a] :
              ( ( A2
                = ( cons_P6232728021713608541c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member5029746173879296720c_fm_a @ E @ ( set_Pr6083076219314900284c_fm_a @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_823_list_Oset__cases,axiom,
    ! [E: produc5756089960658898087c_fm_a,A2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ E @ ( set_Pr5015285182815091004c_fm_a @ A2 ) )
     => ( ! [Z22: list_P7917480606449584557c_fm_a] :
            ( A2
           != ( cons_P7190808671141380701c_fm_a @ E @ Z22 ) )
       => ~ ! [Z1: produc5756089960658898087c_fm_a,Z22: list_P7917480606449584557c_fm_a] :
              ( ( A2
                = ( cons_P7190808671141380701c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member3265983909902097104c_fm_a @ E @ ( set_Pr5015285182815091004c_fm_a @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_824_list_Oset__cases,axiom,
    ! [E: set_Epistemic_fm_a,A2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ E @ ( set_se8855941934996405007c_fm_a @ A2 ) )
     => ( ! [Z22: list_s580375451141968640c_fm_a] :
            ( A2
           != ( cons_s4394448069393209776c_fm_a @ E @ Z22 ) )
       => ~ ! [Z1: set_Epistemic_fm_a,Z22: list_s580375451141968640c_fm_a] :
              ( ( A2
                = ( cons_s4394448069393209776c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member536094252920883875c_fm_a @ E @ ( set_se8855941934996405007c_fm_a @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_825_list_Oset__cases,axiom,
    ! [E: a,A2: list_a] :
      ( ( member_a @ E @ ( set_a2 @ A2 ) )
     => ( ! [Z22: list_a] :
            ( A2
           != ( cons_a @ E @ Z22 ) )
       => ~ ! [Z1: a,Z22: list_a] :
              ( ( A2
                = ( cons_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( set_a2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_826_list_Oset__cases,axiom,
    ! [E: list_Epistemic_fm_a,A2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ E @ ( set_li8442223810127165109c_fm_a @ A2 ) )
     => ( ! [Z22: list_l6083326122719238310c_fm_a] :
            ( A2
           != ( cons_l8134865115577406678c_fm_a @ E @ Z22 ) )
       => ~ ! [Z1: list_Epistemic_fm_a,Z22: list_l6083326122719238310c_fm_a] :
              ( ( A2
                = ( cons_l8134865115577406678c_fm_a @ Z1 @ Z22 ) )
             => ~ ( member5906877432388582473c_fm_a @ E @ ( set_li8442223810127165109c_fm_a @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_827_list_Oset__cases,axiom,
    ! [E: epistemic_fm_a,A2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ E @ ( set_Epistemic_fm_a2 @ A2 ) )
     => ( ! [Z22: list_Epistemic_fm_a] :
            ( A2
           != ( cons_Epistemic_fm_a @ E @ Z22 ) )
       => ~ ! [Z1: epistemic_fm_a,Z22: list_Epistemic_fm_a] :
              ( ( A2
                = ( cons_Epistemic_fm_a @ Z1 @ Z22 ) )
             => ~ ( member6642669571620171971c_fm_a @ E @ ( set_Epistemic_fm_a2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_828_list_Oset__intros_I1_J,axiom,
    ! [X21: produc2203834439629243303c_fm_a,X22: list_P3099032918374241197c_fm_a] : ( member5029746173879296720c_fm_a @ X21 @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_829_list_Oset__intros_I1_J,axiom,
    ! [X21: produc5756089960658898087c_fm_a,X22: list_P7917480606449584557c_fm_a] : ( member3265983909902097104c_fm_a @ X21 @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_830_list_Oset__intros_I1_J,axiom,
    ! [X21: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a] : ( member536094252920883875c_fm_a @ X21 @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_831_list_Oset__intros_I1_J,axiom,
    ! [X21: a,X22: list_a] : ( member_a @ X21 @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_832_list_Oset__intros_I1_J,axiom,
    ! [X21: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a] : ( member5906877432388582473c_fm_a @ X21 @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_833_list_Oset__intros_I1_J,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X21 @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_834_list_Oset__intros_I2_J,axiom,
    ! [Y: produc2203834439629243303c_fm_a,X22: list_P3099032918374241197c_fm_a,X21: produc2203834439629243303c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ X22 ) )
     => ( member5029746173879296720c_fm_a @ Y @ ( set_Pr6083076219314900284c_fm_a @ ( cons_P6232728021713608541c_fm_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_835_list_Oset__intros_I2_J,axiom,
    ! [Y: produc5756089960658898087c_fm_a,X22: list_P7917480606449584557c_fm_a,X21: produc5756089960658898087c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ X22 ) )
     => ( member3265983909902097104c_fm_a @ Y @ ( set_Pr5015285182815091004c_fm_a @ ( cons_P7190808671141380701c_fm_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_836_list_Oset__intros_I2_J,axiom,
    ! [Y: set_Epistemic_fm_a,X22: list_s580375451141968640c_fm_a,X21: set_Epistemic_fm_a] :
      ( ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ X22 ) )
     => ( member536094252920883875c_fm_a @ Y @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_837_list_Oset__intros_I2_J,axiom,
    ! [Y: a,X22: list_a,X21: a] :
      ( ( member_a @ Y @ ( set_a2 @ X22 ) )
     => ( member_a @ Y @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_838_list_Oset__intros_I2_J,axiom,
    ! [Y: list_Epistemic_fm_a,X22: list_l6083326122719238310c_fm_a,X21: list_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ X22 ) )
     => ( member5906877432388582473c_fm_a @ Y @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_839_list_Oset__intros_I2_J,axiom,
    ! [Y: epistemic_fm_a,X22: list_Epistemic_fm_a,X21: epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ X22 ) )
     => ( member6642669571620171971c_fm_a @ Y @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_840_set__subset__Cons,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ Xs2 ) @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) ) ) ).

% set_subset_Cons
thf(fact_841_set__subset__Cons,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) ).

% set_subset_Cons
thf(fact_842_list_Omap__cong,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_Ep1988204514693272906c_fm_a @ F @ X2 )
          = ( map_Ep1988204514693272906c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_843_list_Omap__cong,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_Ep4939040189629079504c_fm_a @ F @ X2 )
          = ( map_Ep4939040189629079504c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_844_list_Omap__cong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_li3080774272885743684c_fm_a @ F @ X2 )
          = ( map_li3080774272885743684c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_845_list_Omap__cong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_li3858915945532548554c_fm_a @ F @ X2 )
          = ( map_li3858915945532548554c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_846_list_Omap__cong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_li5516866612190465598c_fm_a @ F @ X2 )
          = ( map_li5516866612190465598c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_847_list_Omap__cong,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( X2 = Ya )
     => ( ! [Z2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ Ya ) )
           => ( ( F @ Z2 )
              = ( G3 @ Z2 ) ) )
       => ( ( map_Ep7084560364594560580c_fm_a @ F @ X2 )
          = ( map_Ep7084560364594560580c_fm_a @ G3 @ Ya ) ) ) ) ).

% list.map_cong
thf(fact_848_list_Omap__cong0,axiom,
    ! [X2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [Z2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_Ep1988204514693272906c_fm_a @ F @ X2 )
        = ( map_Ep1988204514693272906c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_849_list_Omap__cong0,axiom,
    ! [X2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [Z2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_Ep4939040189629079504c_fm_a @ F @ X2 )
        = ( map_Ep4939040189629079504c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_850_list_Omap__cong0,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_li3080774272885743684c_fm_a @ F @ X2 )
        = ( map_li3080774272885743684c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_851_list_Omap__cong0,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_li3858915945532548554c_fm_a @ F @ X2 )
        = ( map_li3858915945532548554c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_852_list_Omap__cong0,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_li5516866612190465598c_fm_a @ F @ X2 )
        = ( map_li5516866612190465598c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_853_list_Omap__cong0,axiom,
    ! [X2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ! [Z2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( F @ Z2 )
            = ( G3 @ Z2 ) ) )
     => ( ( map_Ep7084560364594560580c_fm_a @ F @ X2 )
        = ( map_Ep7084560364594560580c_fm_a @ G3 @ X2 ) ) ) ).

% list.map_cong0
thf(fact_854_list_Oinj__map__strong,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,Fa: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [Z2: epistemic_fm_a,Za: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( member6642669571620171971c_fm_a @ Za @ ( set_Epistemic_fm_a2 @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_Ep1988204514693272906c_fm_a @ F @ X2 )
          = ( map_Ep1988204514693272906c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_855_list_Oinj__map__strong,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Fa: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [Z2: epistemic_fm_a,Za: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( member6642669571620171971c_fm_a @ Za @ ( set_Epistemic_fm_a2 @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_Ep4939040189629079504c_fm_a @ F @ X2 )
          = ( map_Ep4939040189629079504c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_856_list_Oinj__map__strong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,Fa: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_li3080774272885743684c_fm_a @ F @ X2 )
          = ( map_li3080774272885743684c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_857_list_Oinj__map__strong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Fa: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_li3858915945532548554c_fm_a @ F @ X2 )
          = ( map_li3858915945532548554c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_858_list_Oinj__map__strong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Xa: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,Fa: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a,Za: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
         => ( ( member5906877432388582473c_fm_a @ Za @ ( set_li8442223810127165109c_fm_a @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_li5516866612190465598c_fm_a @ F @ X2 )
          = ( map_li5516866612190465598c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_859_list_Oinj__map__strong,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,Fa: epistemic_fm_a > epistemic_fm_a] :
      ( ! [Z2: epistemic_fm_a,Za: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
         => ( ( member6642669571620171971c_fm_a @ Za @ ( set_Epistemic_fm_a2 @ Xa ) )
           => ( ( ( F @ Z2 )
                = ( Fa @ Za ) )
             => ( Z2 = Za ) ) ) )
     => ( ( ( map_Ep7084560364594560580c_fm_a @ F @ X2 )
          = ( map_Ep7084560364594560580c_fm_a @ Fa @ Xa ) )
       => ( X2 = Xa ) ) ) ).

% list.inj_map_strong
thf(fact_860_list_Omap__ident__strong,axiom,
    ! [T: list_P3099032918374241197c_fm_a,F: produc2203834439629243303c_fm_a > produc2203834439629243303c_fm_a] :
      ( ! [Z2: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ Z2 @ ( set_Pr6083076219314900284c_fm_a @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_Pr2297397278705060868c_fm_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_861_list_Omap__ident__strong,axiom,
    ! [T: list_P7917480606449584557c_fm_a,F: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a] :
      ( ! [Z2: produc5756089960658898087c_fm_a] :
          ( ( member3265983909902097104c_fm_a @ Z2 @ ( set_Pr5015285182815091004c_fm_a @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_Pr5661761254319454724c_fm_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_862_list_Omap__ident__strong,axiom,
    ! [T: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [Z2: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ Z2 @ ( set_se8855941934996405007c_fm_a @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_se7333198834109155908c_fm_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_863_list_Omap__ident__strong,axiom,
    ! [T: list_a,F: a > a] :
      ( ! [Z2: a] :
          ( ( member_a @ Z2 @ ( set_a2 @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_a_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_864_list_Omap__ident__strong,axiom,
    ! [T: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [Z2: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_li3080774272885743684c_fm_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_865_list_Omap__ident__strong,axiom,
    ! [T: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ! [Z2: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ T ) )
         => ( ( F @ Z2 )
            = Z2 ) )
     => ( ( map_Ep7084560364594560580c_fm_a @ F @ T )
        = T ) ) ).

% list.map_ident_strong
thf(fact_866_map__ext,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
        = ( map_Ep1988204514693272906c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_867_map__ext,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
        = ( map_Ep4939040189629079504c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_868_map__ext,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = ( map_li3080774272885743684c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_869_map__ext,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
        = ( map_li3858915945532548554c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_870_map__ext,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
        = ( map_li5516866612190465598c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_871_map__ext,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ( ( F @ X3 )
            = ( G3 @ X3 ) ) )
     => ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( map_Ep7084560364594560580c_fm_a @ G3 @ Xs2 ) ) ) ).

% map_ext
thf(fact_872_map__idI,axiom,
    ! [Xs2: list_P3099032918374241197c_fm_a,F: produc2203834439629243303c_fm_a > produc2203834439629243303c_fm_a] :
      ( ! [X3: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_Pr2297397278705060868c_fm_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_873_map__idI,axiom,
    ! [Xs2: list_P7917480606449584557c_fm_a,F: produc5756089960658898087c_fm_a > produc5756089960658898087c_fm_a] :
      ( ! [X3: produc5756089960658898087c_fm_a] :
          ( ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_Pr5661761254319454724c_fm_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_874_map__idI,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,F: set_Epistemic_fm_a > set_Epistemic_fm_a] :
      ( ! [X3: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_se7333198834109155908c_fm_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_875_map__idI,axiom,
    ! [Xs2: list_a,F: a > a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ ( set_a2 @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_a_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_876_map__idI,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ! [X3: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_877_map__idI,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ! [X3: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
         => ( ( F @ X3 )
            = X3 ) )
     => ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = Xs2 ) ) ).

% map_idI
thf(fact_878_map__cong,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 )
          = ( map_Ep1988204514693272906c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_879_map__cong,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 )
          = ( map_Ep4939040189629079504c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_880_map__cong,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a,G3: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_li3080774272885743684c_fm_a @ F @ Xs2 )
          = ( map_li3080774272885743684c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_881_map__cong,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,G3: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_li3858915945532548554c_fm_a @ F @ Xs2 )
          = ( map_li3858915945532548554c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_882_map__cong,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a,G3: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_li5516866612190465598c_fm_a @ F @ Xs2 )
          = ( map_li5516866612190465598c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_883_map__cong,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
          = ( map_Ep7084560364594560580c_fm_a @ G3 @ Ys ) ) ) ) ).

% map_cong
thf(fact_884_ex__map__conv,axiom,
    ! [Ys: list_l3671048651222332332c_fm_a,F: epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( ? [Xs: list_Epistemic_fm_a] :
            ( Ys
            = ( map_Ep4939040189629079504c_fm_a @ F @ Xs ) ) )
      = ( ! [X: list_l6083326122719238310c_fm_a] :
            ( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Ys ) )
           => ? [Y3: epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_885_ex__map__conv,axiom,
    ! [Ys: list_l3671048651222332332c_fm_a,F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a] :
      ( ( ? [Xs: list_l6083326122719238310c_fm_a] :
            ( Ys
            = ( map_li3858915945532548554c_fm_a @ F @ Xs ) ) )
      = ( ! [X: list_l6083326122719238310c_fm_a] :
            ( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Ys ) )
           => ? [Y3: list_Epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_886_ex__map__conv,axiom,
    ! [Ys: list_Epistemic_fm_a,F: list_Epistemic_fm_a > epistemic_fm_a] :
      ( ( ? [Xs: list_l6083326122719238310c_fm_a] :
            ( Ys
            = ( map_li5516866612190465598c_fm_a @ F @ Xs ) ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ? [Y3: list_Epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_887_ex__map__conv,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( ? [Xs: list_Epistemic_fm_a] :
            ( Ys
            = ( map_Ep1988204514693272906c_fm_a @ F @ Xs ) ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ? [Y3: epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_888_ex__map__conv,axiom,
    ! [Ys: list_l6083326122719238310c_fm_a,F: list_Epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( ? [Xs: list_l6083326122719238310c_fm_a] :
            ( Ys
            = ( map_li3080774272885743684c_fm_a @ F @ Xs ) ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ? [Y3: list_Epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_889_ex__map__conv,axiom,
    ! [Ys: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( ? [Xs: list_Epistemic_fm_a] :
            ( Ys
            = ( map_Ep7084560364594560580c_fm_a @ F @ Xs ) ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ? [Y3: epistemic_fm_a] :
                ( X
                = ( F @ Y3 ) ) ) ) ) ).

% ex_map_conv
thf(fact_890_filter__cong,axiom,
    ! [Xs2: list_P3099032918374241197c_fm_a,Ys: list_P3099032918374241197c_fm_a,P4: produc2203834439629243303c_fm_a > $o,Q4: produc2203834439629243303c_fm_a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ X3 @ ( set_Pr6083076219314900284c_fm_a @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter326375931097202980c_fm_a @ P4 @ Xs2 )
          = ( filter326375931097202980c_fm_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_891_filter__cong,axiom,
    ! [Xs2: list_P7917480606449584557c_fm_a,Ys: list_P7917480606449584557c_fm_a,P4: produc5756089960658898087c_fm_a > $o,Q4: produc5756089960658898087c_fm_a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ X3 @ ( set_Pr5015285182815091004c_fm_a @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter8648851334721324324c_fm_a @ P4 @ Xs2 )
          = ( filter8648851334721324324c_fm_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_892_filter__cong,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a,P4: set_Epistemic_fm_a > $o,Q4: set_Epistemic_fm_a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X3 @ ( set_se8855941934996405007c_fm_a @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter2620125754611450615c_fm_a @ P4 @ Xs2 )
          = ( filter2620125754611450615c_fm_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_893_filter__cong,axiom,
    ! [Xs2: list_a,Ys: list_a,P4: a > $o,Q4: a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: a] :
            ( ( member_a @ X3 @ ( set_a2 @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter_a @ P4 @ Xs2 )
          = ( filter_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_894_filter__cong,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,P4: epistemic_fm_a > $o,Q4: epistemic_fm_a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter7636273809395300631c_fm_a @ P4 @ Xs2 )
          = ( filter7636273809395300631c_fm_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_895_filter__cong,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o,Q4: list_Epistemic_fm_a > $o] :
      ( ( Xs2 = Ys )
     => ( ! [X3: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X3 @ ( set_li8442223810127165109c_fm_a @ Ys ) )
           => ( ( P4 @ X3 )
              = ( Q4 @ X3 ) ) )
       => ( ( filter441479637125139101c_fm_a @ P4 @ Xs2 )
          = ( filter441479637125139101c_fm_a @ Q4 @ Ys ) ) ) ) ).

% filter_cong
thf(fact_896_filter__id__conv,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( ( filter7636273809395300631c_fm_a @ P4 @ Xs2 )
        = Xs2 )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( P4 @ X ) ) ) ) ).

% filter_id_conv
thf(fact_897_filter__id__conv,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( filter441479637125139101c_fm_a @ P4 @ Xs2 )
        = Xs2 )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( P4 @ X ) ) ) ) ).

% filter_id_conv
thf(fact_898_filter__is__subset,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] : ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) ) @ ( set_Epistemic_fm_a2 @ Xs2 ) ) ).

% filter_is_subset
thf(fact_899_filter__is__subset,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( set_li8442223810127165109c_fm_a @ ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) ) @ ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ).

% filter_is_subset
thf(fact_900_list_Opred__mono__strong,axiom,
    ! [P4: produc2203834439629243303c_fm_a > $o,X2: list_P3099032918374241197c_fm_a,Pa: produc2203834439629243303c_fm_a > $o] :
      ( ( list_a7787577967835477083c_fm_a @ P4 @ X2 )
     => ( ! [Z2: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ Z2 @ ( set_Pr6083076219314900284c_fm_a @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_a7787577967835477083c_fm_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_901_list_Opred__mono__strong,axiom,
    ! [P4: produc5756089960658898087c_fm_a > $o,X2: list_P7917480606449584557c_fm_a,Pa: produc5756089960658898087c_fm_a > $o] :
      ( ( list_a4957036963921897819c_fm_a @ P4 @ X2 )
     => ( ! [Z2: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ Z2 @ ( set_Pr5015285182815091004c_fm_a @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_a4957036963921897819c_fm_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_902_list_Opred__mono__strong,axiom,
    ! [P4: set_Epistemic_fm_a > $o,X2: list_s580375451141968640c_fm_a,Pa: set_Epistemic_fm_a > $o] :
      ( ( list_a5130230249644717486c_fm_a @ P4 @ X2 )
     => ( ! [Z2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z2 @ ( set_se8855941934996405007c_fm_a @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_a5130230249644717486c_fm_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_903_list_Opred__mono__strong,axiom,
    ! [P4: a > $o,X2: list_a,Pa: a > $o] :
      ( ( list_all_a @ P4 @ X2 )
     => ( ! [Z2: a] :
            ( ( member_a @ Z2 @ ( set_a2 @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_all_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_904_list_Opred__mono__strong,axiom,
    ! [P4: list_Epistemic_fm_a > $o,X2: list_l6083326122719238310c_fm_a,Pa: list_Epistemic_fm_a > $o] :
      ( ( list_a5890043570083025364c_fm_a @ P4 @ X2 )
     => ( ! [Z2: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_a5890043570083025364c_fm_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_905_list_Opred__mono__strong,axiom,
    ! [P4: epistemic_fm_a > $o,X2: list_Epistemic_fm_a,Pa: epistemic_fm_a > $o] :
      ( ( list_a5841931967666341838c_fm_a @ P4 @ X2 )
     => ( ! [Z2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ X2 ) )
           => ( ( P4 @ Z2 )
             => ( Pa @ Z2 ) ) )
       => ( list_a5841931967666341838c_fm_a @ Pa @ X2 ) ) ) ).

% list.pred_mono_strong
thf(fact_906_list__all__cong,axiom,
    ! [X2: list_P3099032918374241197c_fm_a,Ya: list_P3099032918374241197c_fm_a,P4: produc2203834439629243303c_fm_a > $o,Pa: produc2203834439629243303c_fm_a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: produc2203834439629243303c_fm_a] :
            ( ( member5029746173879296720c_fm_a @ Z2 @ ( set_Pr6083076219314900284c_fm_a @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_a7787577967835477083c_fm_a @ P4 @ X2 )
          = ( list_a7787577967835477083c_fm_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_907_list__all__cong,axiom,
    ! [X2: list_P7917480606449584557c_fm_a,Ya: list_P7917480606449584557c_fm_a,P4: produc5756089960658898087c_fm_a > $o,Pa: produc5756089960658898087c_fm_a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: produc5756089960658898087c_fm_a] :
            ( ( member3265983909902097104c_fm_a @ Z2 @ ( set_Pr5015285182815091004c_fm_a @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_a4957036963921897819c_fm_a @ P4 @ X2 )
          = ( list_a4957036963921897819c_fm_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_908_list__all__cong,axiom,
    ! [X2: list_s580375451141968640c_fm_a,Ya: list_s580375451141968640c_fm_a,P4: set_Epistemic_fm_a > $o,Pa: set_Epistemic_fm_a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ Z2 @ ( set_se8855941934996405007c_fm_a @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_a5130230249644717486c_fm_a @ P4 @ X2 )
          = ( list_a5130230249644717486c_fm_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_909_list__all__cong,axiom,
    ! [X2: list_a,Ya: list_a,P4: a > $o,Pa: a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: a] :
            ( ( member_a @ Z2 @ ( set_a2 @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_all_a @ P4 @ X2 )
          = ( list_all_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_910_list__all__cong,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Ya: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o,Pa: list_Epistemic_fm_a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ Z2 @ ( set_li8442223810127165109c_fm_a @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_a5890043570083025364c_fm_a @ P4 @ X2 )
          = ( list_a5890043570083025364c_fm_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_911_list__all__cong,axiom,
    ! [X2: list_Epistemic_fm_a,Ya: list_Epistemic_fm_a,P4: epistemic_fm_a > $o,Pa: epistemic_fm_a > $o] :
      ( ( X2 = Ya )
     => ( ! [Z2: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Z2 @ ( set_Epistemic_fm_a2 @ Ya ) )
           => ( ( P4 @ Z2 )
              = ( Pa @ Z2 ) ) )
       => ( ( list_a5841931967666341838c_fm_a @ P4 @ X2 )
          = ( list_a5841931967666341838c_fm_a @ Pa @ Ya ) ) ) ) ).

% list_all_cong
thf(fact_912_fm_Odistinct_I15_J,axiom,
    ! [X25: list_char,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X25 )
     != ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.distinct(15)
thf(fact_913_fm_Odistinct_I17_J,axiom,
    ! [X25: list_char,X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X25 )
     != ( epistemic_K_a @ X61 @ X62 ) ) ).

% fm.distinct(17)
thf(fact_914_fm_Odistinct_I1_J,axiom,
    ! [X25: list_char] :
      ( epistemic_FF_a
     != ( epistemic_Pro_a @ X25 ) ) ).

% fm.distinct(1)
thf(fact_915_fm_Odistinct_I13_J,axiom,
    ! [X25: list_char,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X25 )
     != ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.distinct(13)
thf(fact_916_fm_Odistinct_I11_J,axiom,
    ! [X25: list_char,X31: epistemic_fm_a,X32: epistemic_fm_a] :
      ( ( epistemic_Pro_a @ X25 )
     != ( epistemic_Dis_a @ X31 @ X32 ) ) ).

% fm.distinct(11)
thf(fact_917_eval_Osimps_I2_J,axiom,
    ! [G3: list_char > $o,Uw: epistemic_fm_a > $o,X2: list_char] :
      ( ( epistemic_eval_a @ G3 @ Uw @ ( epistemic_Pro_a @ X2 ) )
      = ( G3 @ X2 ) ) ).

% eval.simps(2)
thf(fact_918_rotate1_Osimps_I1_J,axiom,
    ( ( rotate2311183321535120627c_fm_a @ nil_li2451196919128234278c_fm_a )
    = nil_li2451196919128234278c_fm_a ) ).

% rotate1.simps(1)
thf(fact_919_rotate1_Osimps_I1_J,axiom,
    ( ( rotate2699689030021285965c_fm_a @ nil_se102576565402781184c_fm_a )
    = nil_se102576565402781184c_fm_a ) ).

% rotate1.simps(1)
thf(fact_920_rotate1_Osimps_I1_J,axiom,
    ( ( rotate3540958558250653293c_fm_a @ nil_Epistemic_fm_a )
    = nil_Epistemic_fm_a ) ).

% rotate1.simps(1)
thf(fact_921_list__bind__cong,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,F: epistemic_fm_a > list_Epistemic_fm_a,G3: epistemic_fm_a > list_Epistemic_fm_a] :
      ( ( Xs2 = Ys )
     => ( ! [X3: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X3 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( ( F @ X3 )
              = ( G3 @ X3 ) ) )
       => ( ( bind_E8451893407412458119c_fm_a @ Xs2 @ F )
          = ( bind_E8451893407412458119c_fm_a @ Ys @ G3 ) ) ) ) ).

% list_bind_cong
thf(fact_922_rotate1__map,axiom,
    ! [F: epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rotate2311183321535120627c_fm_a @ ( map_Ep1988204514693272906c_fm_a @ F @ Xs2 ) )
      = ( map_Ep1988204514693272906c_fm_a @ F @ ( rotate3540958558250653293c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_923_rotate1__map,axiom,
    ! [F: list_Epistemic_fm_a > list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rotate2311183321535120627c_fm_a @ ( map_li3080774272885743684c_fm_a @ F @ Xs2 ) )
      = ( map_li3080774272885743684c_fm_a @ F @ ( rotate2311183321535120627c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_924_rotate1__map,axiom,
    ! [F: epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rotate9059992183176259321c_fm_a @ ( map_Ep4939040189629079504c_fm_a @ F @ Xs2 ) )
      = ( map_Ep4939040189629079504c_fm_a @ F @ ( rotate3540958558250653293c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_925_rotate1__map,axiom,
    ! [F: list_Epistemic_fm_a > list_l6083326122719238310c_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rotate9059992183176259321c_fm_a @ ( map_li3858915945532548554c_fm_a @ F @ Xs2 ) )
      = ( map_li3858915945532548554c_fm_a @ F @ ( rotate2311183321535120627c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_926_rotate1__map,axiom,
    ! [F: list_Epistemic_fm_a > epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rotate3540958558250653293c_fm_a @ ( map_li5516866612190465598c_fm_a @ F @ Xs2 ) )
      = ( map_li5516866612190465598c_fm_a @ F @ ( rotate2311183321535120627c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_927_rotate1__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rotate3540958558250653293c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ F @ ( rotate3540958558250653293c_fm_a @ Xs2 ) ) ) ).

% rotate1_map
thf(fact_928_list__ex1__iff,axiom,
    ( list_e6284074732749938928c_fm_a
    = ( ^ [P6: produc2203834439629243303c_fm_a > $o,Xs: list_P3099032918374241197c_fm_a] :
        ? [X: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: produc2203834439629243303c_fm_a] :
              ( ( ( member5029746173879296720c_fm_a @ Y3 @ ( set_Pr6083076219314900284c_fm_a @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_929_list__ex1__iff,axiom,
    ( list_e8094467569734695152c_fm_a
    = ( ^ [P6: produc5756089960658898087c_fm_a > $o,Xs: list_P7917480606449584557c_fm_a] :
        ? [X: produc5756089960658898087c_fm_a] :
          ( ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: produc5756089960658898087c_fm_a] :
              ( ( ( member3265983909902097104c_fm_a @ Y3 @ ( set_Pr5015285182815091004c_fm_a @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_930_list__ex1__iff,axiom,
    ( list_e3415556844334454979c_fm_a
    = ( ^ [P6: set_Epistemic_fm_a > $o,Xs: list_s580375451141968640c_fm_a] :
        ? [X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: set_Epistemic_fm_a] :
              ( ( ( member536094252920883875c_fm_a @ Y3 @ ( set_se8855941934996405007c_fm_a @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_931_list__ex1__iff,axiom,
    ( list_ex1_a
    = ( ^ [P6: a > $o,Xs: list_a] :
        ? [X: a] :
          ( ( member_a @ X @ ( set_a2 @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: a] :
              ( ( ( member_a @ Y3 @ ( set_a2 @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_932_list__ex1__iff,axiom,
    ( list_e1371837923195959913c_fm_a
    = ( ^ [P6: list_Epistemic_fm_a > $o,Xs: list_l6083326122719238310c_fm_a] :
        ? [X: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: list_Epistemic_fm_a] :
              ( ( ( member5906877432388582473c_fm_a @ Y3 @ ( set_li8442223810127165109c_fm_a @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_933_list__ex1__iff,axiom,
    ( list_e2031426293596896995c_fm_a
    = ( ^ [P6: epistemic_fm_a > $o,Xs: list_Epistemic_fm_a] :
        ? [X: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) )
          & ( P6 @ X )
          & ! [Y3: epistemic_fm_a] :
              ( ( ( member6642669571620171971c_fm_a @ Y3 @ ( set_Epistemic_fm_a2 @ Xs ) )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% list_ex1_iff
thf(fact_934_split__list__first__prop__iff,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( ? [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) )
      = ( ? [Ys3: list_l6083326122719238310c_fm_a,X: list_Epistemic_fm_a] :
            ( ? [Zs: list_l6083326122719238310c_fm_a] :
                ( Xs2
                = ( append1384085151619559355c_fm_a @ Ys3 @ ( cons_l8134865115577406678c_fm_a @ X @ Zs ) ) )
            & ( P4 @ X )
            & ! [Y3: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ Y3 @ ( set_li8442223810127165109c_fm_a @ Ys3 ) )
               => ~ ( P4 @ Y3 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_935_split__list__first__prop__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( ? [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
            & ( P4 @ X ) ) )
      = ( ? [Ys3: list_Epistemic_fm_a,X: epistemic_fm_a] :
            ( ? [Zs: list_Epistemic_fm_a] :
                ( Xs2
                = ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ X @ Zs ) ) )
            & ( P4 @ X )
            & ! [Y3: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ Y3 @ ( set_Epistemic_fm_a2 @ Ys3 ) )
               => ~ ( P4 @ Y3 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_936_split__list__last__prop__iff,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ( ? [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
            & ( P4 @ X ) ) )
      = ( ? [Ys3: list_l6083326122719238310c_fm_a,X: list_Epistemic_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys3 @ ( cons_l8134865115577406678c_fm_a @ X @ Zs ) ) )
            & ( P4 @ X )
            & ! [Y3: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ Y3 @ ( set_li8442223810127165109c_fm_a @ Zs ) )
               => ~ ( P4 @ Y3 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_937_split__list__last__prop__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ( ? [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
            & ( P4 @ X ) ) )
      = ( ? [Ys3: list_Epistemic_fm_a,X: epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ X @ Zs ) ) )
            & ( P4 @ X )
            & ! [Y3: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ Y3 @ ( set_Epistemic_fm_a2 @ Zs ) )
               => ~ ( P4 @ Y3 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_938_in__set__conv__decomp__first,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P3099032918374241197c_fm_a,Zs: list_P3099032918374241197c_fm_a] :
            ( ( Xs2
              = ( append8587712973440712258c_fm_a @ Ys3 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_939_in__set__conv__decomp__first,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P7917480606449584557c_fm_a,Zs: list_P7917480606449584557c_fm_a] :
            ( ( Xs2
              = ( append9053776140663174210c_fm_a @ Ys3 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_940_in__set__conv__decomp__first,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_s580375451141968640c_fm_a,Zs: list_s580375451141968640c_fm_a] :
            ( ( Xs2
              = ( append5257919162946131733c_fm_a @ Ys3 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_941_in__set__conv__decomp__first,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
      = ( ? [Ys3: list_a,Zs: list_a] :
            ( ( Xs2
              = ( append_a @ Ys3 @ ( cons_a @ X2 @ Zs ) ) )
            & ~ ( member_a @ X2 @ ( set_a2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_942_in__set__conv__decomp__first,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_l6083326122719238310c_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys3 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_943_in__set__conv__decomp__first,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
      = ( ? [Ys3: list_Epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ X2 @ Zs ) ) )
            & ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_944_in__set__conv__decomp__last,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P3099032918374241197c_fm_a,Zs: list_P3099032918374241197c_fm_a] :
            ( ( Xs2
              = ( append8587712973440712258c_fm_a @ Ys3 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_945_in__set__conv__decomp__last,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P7917480606449584557c_fm_a,Zs: list_P7917480606449584557c_fm_a] :
            ( ( Xs2
              = ( append9053776140663174210c_fm_a @ Ys3 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_946_in__set__conv__decomp__last,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_s580375451141968640c_fm_a,Zs: list_s580375451141968640c_fm_a] :
            ( ( Xs2
              = ( append5257919162946131733c_fm_a @ Ys3 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_947_in__set__conv__decomp__last,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
      = ( ? [Ys3: list_a,Zs: list_a] :
            ( ( Xs2
              = ( append_a @ Ys3 @ ( cons_a @ X2 @ Zs ) ) )
            & ~ ( member_a @ X2 @ ( set_a2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_948_in__set__conv__decomp__last,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_l6083326122719238310c_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys3 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs ) ) )
            & ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_949_in__set__conv__decomp__last,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
      = ( ? [Ys3: list_Epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ X2 @ Zs ) ) )
            & ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_950_split__list__first__propE,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] :
            ( ? [Zs2: list_l6083326122719238310c_fm_a] :
                ( Xs2
                = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
           => ( ( P4 @ X3 )
             => ~ ! [Xa2: list_Epistemic_fm_a] :
                    ( ( member5906877432388582473c_fm_a @ Xa2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
                   => ~ ( P4 @ Xa2 ) ) ) ) ) ).

% split_list_first_propE
thf(fact_951_split__list__first__propE,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a] :
            ( ? [Zs2: list_Epistemic_fm_a] :
                ( Xs2
                = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
           => ( ( P4 @ X3 )
             => ~ ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ys2 ) )
                   => ~ ( P4 @ Xa2 ) ) ) ) ) ).

% split_list_first_propE
thf(fact_952_split__list__last__propE,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
            ( ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
           => ( ( P4 @ X3 )
             => ~ ! [Xa2: list_Epistemic_fm_a] :
                    ( ( member5906877432388582473c_fm_a @ Xa2 @ ( set_li8442223810127165109c_fm_a @ Zs2 ) )
                   => ~ ( P4 @ Xa2 ) ) ) ) ) ).

% split_list_last_propE
thf(fact_953_split__list__last__propE,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
           => ( ( P4 @ X3 )
             => ~ ! [Xa2: epistemic_fm_a] :
                    ( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Zs2 ) )
                   => ~ ( P4 @ Xa2 ) ) ) ) ) ).

% split_list_last_propE
thf(fact_954_split__list__first__prop,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] :
          ( ? [Zs2: list_l6083326122719238310c_fm_a] :
              ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 )
          & ! [Xa2: list_Epistemic_fm_a] :
              ( ( member5906877432388582473c_fm_a @ Xa2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) )
             => ~ ( P4 @ Xa2 ) ) ) ) ).

% split_list_first_prop
thf(fact_955_split__list__first__prop,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a] :
          ( ? [Zs2: list_Epistemic_fm_a] :
              ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 )
          & ! [Xa2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Ys2 ) )
             => ~ ( P4 @ Xa2 ) ) ) ) ).

% split_list_first_prop
thf(fact_956_split__list__last__prop,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 )
          & ! [Xa2: list_Epistemic_fm_a] :
              ( ( member5906877432388582473c_fm_a @ Xa2 @ ( set_li8442223810127165109c_fm_a @ Zs2 ) )
             => ~ ( P4 @ Xa2 ) ) ) ) ).

% split_list_last_prop
thf(fact_957_split__list__last__prop,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 )
          & ! [Xa2: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ Xa2 @ ( set_Epistemic_fm_a2 @ Zs2 ) )
             => ~ ( P4 @ Xa2 ) ) ) ) ).

% split_list_last_prop
thf(fact_958_in__set__conv__decomp,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P3099032918374241197c_fm_a,Zs: list_P3099032918374241197c_fm_a] :
            ( Xs2
            = ( append8587712973440712258c_fm_a @ Ys3 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_959_in__set__conv__decomp,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_P7917480606449584557c_fm_a,Zs: list_P7917480606449584557c_fm_a] :
            ( Xs2
            = ( append9053776140663174210c_fm_a @ Ys3 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_960_in__set__conv__decomp,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_s580375451141968640c_fm_a,Zs: list_s580375451141968640c_fm_a] :
            ( Xs2
            = ( append5257919162946131733c_fm_a @ Ys3 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_961_in__set__conv__decomp,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
      = ( ? [Ys3: list_a,Zs: list_a] :
            ( Xs2
            = ( append_a @ Ys3 @ ( cons_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_962_in__set__conv__decomp,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
      = ( ? [Ys3: list_l6083326122719238310c_fm_a,Zs: list_l6083326122719238310c_fm_a] :
            ( Xs2
            = ( append1384085151619559355c_fm_a @ Ys3 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_963_in__set__conv__decomp,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
      = ( ? [Ys3: list_Epistemic_fm_a,Zs: list_Epistemic_fm_a] :
            ( Xs2
            = ( append9179727413925872949c_fm_a @ Ys3 @ ( cons_Epistemic_fm_a @ X2 @ Zs ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_964_append__Cons__eq__iff,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a,Ys: list_P3099032918374241197c_fm_a,Xs6: list_P3099032918374241197c_fm_a,Ys6: list_P3099032918374241197c_fm_a] :
      ( ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ( ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Ys ) )
       => ( ( ( append8587712973440712258c_fm_a @ Xs2 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Ys ) )
            = ( append8587712973440712258c_fm_a @ Xs6 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_965_append__Cons__eq__iff,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a,Ys: list_P7917480606449584557c_fm_a,Xs6: list_P7917480606449584557c_fm_a,Ys6: list_P7917480606449584557c_fm_a] :
      ( ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ( ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Ys ) )
       => ( ( ( append9053776140663174210c_fm_a @ Xs2 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Ys ) )
            = ( append9053776140663174210c_fm_a @ Xs6 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_966_append__Cons__eq__iff,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a,Ys: list_s580375451141968640c_fm_a,Xs6: list_s580375451141968640c_fm_a,Ys6: list_s580375451141968640c_fm_a] :
      ( ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ( ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Ys ) )
       => ( ( ( append5257919162946131733c_fm_a @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Ys ) )
            = ( append5257919162946131733c_fm_a @ Xs6 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_967_append__Cons__eq__iff,axiom,
    ! [X2: a,Xs2: list_a,Ys: list_a,Xs6: list_a,Ys6: list_a] :
      ( ~ ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ( ~ ( member_a @ X2 @ ( set_a2 @ Ys ) )
       => ( ( ( append_a @ Xs2 @ ( cons_a @ X2 @ Ys ) )
            = ( append_a @ Xs6 @ ( cons_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_968_append__Cons__eq__iff,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,Ys: list_l6083326122719238310c_fm_a,Xs6: list_l6083326122719238310c_fm_a,Ys6: list_l6083326122719238310c_fm_a] :
      ( ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ( ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys ) )
       => ( ( ( append1384085151619559355c_fm_a @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Ys ) )
            = ( append1384085151619559355c_fm_a @ Xs6 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_969_append__Cons__eq__iff,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Xs6: list_Epistemic_fm_a,Ys6: list_Epistemic_fm_a] :
      ( ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ( ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys ) )
       => ( ( ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ Ys ) )
            = ( append9179727413925872949c_fm_a @ Xs6 @ ( cons_Epistemic_fm_a @ X2 @ Ys6 ) ) )
          = ( ( Xs2 = Xs6 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_970_split__list__propE,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] :
            ( ? [Zs2: list_l6083326122719238310c_fm_a] :
                ( Xs2
                = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
           => ~ ( P4 @ X3 ) ) ) ).

% split_list_propE
thf(fact_971_split__list__propE,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ~ ! [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a] :
            ( ? [Zs2: list_Epistemic_fm_a] :
                ( Xs2
                = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
           => ~ ( P4 @ X3 ) ) ) ).

% split_list_propE
thf(fact_972_split__list__first,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P3099032918374241197c_fm_a,Zs2: list_P3099032918374241197c_fm_a] :
          ( ( Xs2
            = ( append8587712973440712258c_fm_a @ Ys2 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_973_split__list__first,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P7917480606449584557c_fm_a,Zs2: list_P7917480606449584557c_fm_a] :
          ( ( Xs2
            = ( append9053776140663174210c_fm_a @ Ys2 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_974_split__list__first,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ? [Ys2: list_s580375451141968640c_fm_a,Zs2: list_s580375451141968640c_fm_a] :
          ( ( Xs2
            = ( append5257919162946131733c_fm_a @ Ys2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_975_split__list__first,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ? [Ys2: list_a,Zs2: list_a] :
          ( ( Xs2
            = ( append_a @ Ys2 @ ( cons_a @ X2 @ Zs2 ) ) )
          & ~ ( member_a @ X2 @ ( set_a2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_976_split__list__first,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_977_split__list__first,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ? [Ys2: list_Epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_978_split__list__prop,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o] :
      ( ? [X4: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,X3: list_Epistemic_fm_a] :
          ( ? [Zs2: list_l6083326122719238310c_fm_a] :
              ( Xs2
              = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 ) ) ) ).

% split_list_prop
thf(fact_979_split__list__prop,axiom,
    ! [Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o] :
      ( ? [X4: epistemic_fm_a] :
          ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
          & ( P4 @ X4 ) )
     => ? [Ys2: list_Epistemic_fm_a,X3: epistemic_fm_a] :
          ( ? [Zs2: list_Epistemic_fm_a] :
              ( Xs2
              = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X3 @ Zs2 ) ) )
          & ( P4 @ X3 ) ) ) ).

% split_list_prop
thf(fact_980_split__list__last,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P3099032918374241197c_fm_a,Zs2: list_P3099032918374241197c_fm_a] :
          ( ( Xs2
            = ( append8587712973440712258c_fm_a @ Ys2 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_981_split__list__last,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P7917480606449584557c_fm_a,Zs2: list_P7917480606449584557c_fm_a] :
          ( ( Xs2
            = ( append9053776140663174210c_fm_a @ Ys2 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_982_split__list__last,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ? [Ys2: list_s580375451141968640c_fm_a,Zs2: list_s580375451141968640c_fm_a] :
          ( ( Xs2
            = ( append5257919162946131733c_fm_a @ Ys2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_983_split__list__last,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ? [Ys2: list_a,Zs2: list_a] :
          ( ( Xs2
            = ( append_a @ Ys2 @ ( cons_a @ X2 @ Zs2 ) ) )
          & ~ ( member_a @ X2 @ ( set_a2 @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_984_split__list__last,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( ( Xs2
            = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_985_split__list__last,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ? [Ys2: list_Epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( ( Xs2
            = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X2 @ Zs2 ) ) )
          & ~ ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_986_split__list,axiom,
    ! [X2: produc2203834439629243303c_fm_a,Xs2: list_P3099032918374241197c_fm_a] :
      ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P3099032918374241197c_fm_a,Zs2: list_P3099032918374241197c_fm_a] :
          ( Xs2
          = ( append8587712973440712258c_fm_a @ Ys2 @ ( cons_P6232728021713608541c_fm_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_987_split__list,axiom,
    ! [X2: produc5756089960658898087c_fm_a,Xs2: list_P7917480606449584557c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) )
     => ? [Ys2: list_P7917480606449584557c_fm_a,Zs2: list_P7917480606449584557c_fm_a] :
          ( Xs2
          = ( append9053776140663174210c_fm_a @ Ys2 @ ( cons_P7190808671141380701c_fm_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_988_split__list,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
     => ? [Ys2: list_s580375451141968640c_fm_a,Zs2: list_s580375451141968640c_fm_a] :
          ( Xs2
          = ( append5257919162946131733c_fm_a @ Ys2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_989_split__list,axiom,
    ! [X2: a,Xs2: list_a] :
      ( ( member_a @ X2 @ ( set_a2 @ Xs2 ) )
     => ? [Ys2: list_a,Zs2: list_a] :
          ( Xs2
          = ( append_a @ Ys2 @ ( cons_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_990_split__list,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
     => ? [Ys2: list_l6083326122719238310c_fm_a,Zs2: list_l6083326122719238310c_fm_a] :
          ( Xs2
          = ( append1384085151619559355c_fm_a @ Ys2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_991_split__list,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ? [Ys2: list_Epistemic_fm_a,Zs2: list_Epistemic_fm_a] :
          ( Xs2
          = ( append9179727413925872949c_fm_a @ Ys2 @ ( cons_Epistemic_fm_a @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_992_empty__filter__conv,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( filter2620125754611450615c_fm_a @ P4 @ Xs2 ) )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% empty_filter_conv
thf(fact_993_empty__filter__conv,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( filter441479637125139101c_fm_a @ P4 @ Xs2 ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% empty_filter_conv
thf(fact_994_empty__filter__conv,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( filter7636273809395300631c_fm_a @ P4 @ Xs2 ) )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% empty_filter_conv
thf(fact_995_filter__empty__conv,axiom,
    ! [P4: set_Epistemic_fm_a > $o,Xs2: list_s580375451141968640c_fm_a] :
      ( ( ( filter2620125754611450615c_fm_a @ P4 @ Xs2 )
        = nil_se102576565402781184c_fm_a )
      = ( ! [X: set_Epistemic_fm_a] :
            ( ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% filter_empty_conv
thf(fact_996_filter__empty__conv,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( filter441479637125139101c_fm_a @ P4 @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% filter_empty_conv
thf(fact_997_filter__empty__conv,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( ( filter7636273809395300631c_fm_a @ P4 @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ~ ( P4 @ X ) ) ) ) ).

% filter_empty_conv
thf(fact_998_list_Oset__sel_I1_J,axiom,
    ! [A2: list_P3099032918374241197c_fm_a] :
      ( ( A2 != nil_Pr2379126408512758701c_fm_a )
     => ( member5029746173879296720c_fm_a @ ( hd_Pro2014797444510195858c_fm_a @ A2 ) @ ( set_Pr6083076219314900284c_fm_a @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_999_list_Oset__sel_I1_J,axiom,
    ! [A2: list_P7917480606449584557c_fm_a] :
      ( ( A2 != nil_Pr1848654487927912109c_fm_a )
     => ( member3265983909902097104c_fm_a @ ( hd_Pro993334397642901138c_fm_a @ A2 ) @ ( set_Pr5015285182815091004c_fm_a @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_1000_list_Oset__sel_I1_J,axiom,
    ! [A2: list_a] :
      ( ( A2 != nil_a )
     => ( member_a @ ( hd_a @ A2 ) @ ( set_a2 @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_1001_list_Oset__sel_I1_J,axiom,
    ! [A2: list_s580375451141968640c_fm_a] :
      ( ( A2 != nil_se102576565402781184c_fm_a )
     => ( member536094252920883875c_fm_a @ ( hd_set2739578467680395621c_fm_a @ A2 ) @ ( set_se8855941934996405007c_fm_a @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_1002_list_Oset__sel_I1_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( member5906877432388582473c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ A2 ) @ ( set_li8442223810127165109c_fm_a @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_1003_list_Oset__sel_I1_J,axiom,
    ! [A2: list_Epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( member6642669571620171971c_fm_a @ ( hd_Epistemic_fm_a @ A2 ) @ ( set_Epistemic_fm_a2 @ A2 ) ) ) ).

% list.set_sel(1)
thf(fact_1004_hd__in__set,axiom,
    ! [Xs2: list_P3099032918374241197c_fm_a] :
      ( ( Xs2 != nil_Pr2379126408512758701c_fm_a )
     => ( member5029746173879296720c_fm_a @ ( hd_Pro2014797444510195858c_fm_a @ Xs2 ) @ ( set_Pr6083076219314900284c_fm_a @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1005_hd__in__set,axiom,
    ! [Xs2: list_P7917480606449584557c_fm_a] :
      ( ( Xs2 != nil_Pr1848654487927912109c_fm_a )
     => ( member3265983909902097104c_fm_a @ ( hd_Pro993334397642901138c_fm_a @ Xs2 ) @ ( set_Pr5015285182815091004c_fm_a @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1006_hd__in__set,axiom,
    ! [Xs2: list_a] :
      ( ( Xs2 != nil_a )
     => ( member_a @ ( hd_a @ Xs2 ) @ ( set_a2 @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1007_hd__in__set,axiom,
    ! [Xs2: list_s580375451141968640c_fm_a] :
      ( ( Xs2 != nil_se102576565402781184c_fm_a )
     => ( member536094252920883875c_fm_a @ ( hd_set2739578467680395621c_fm_a @ Xs2 ) @ ( set_se8855941934996405007c_fm_a @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1008_hd__in__set,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( Xs2 != nil_li2451196919128234278c_fm_a )
     => ( member5906877432388582473c_fm_a @ ( hd_lis6228752984540680715c_fm_a @ Xs2 ) @ ( set_li8442223810127165109c_fm_a @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1009_hd__in__set,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( member6642669571620171971c_fm_a @ ( hd_Epistemic_fm_a @ Xs2 ) @ ( set_Epistemic_fm_a2 @ Xs2 ) ) ) ).

% hd_in_set
thf(fact_1010_list_Oset__sel_I2_J,axiom,
    ! [A2: list_P3099032918374241197c_fm_a,X2: produc2203834439629243303c_fm_a] :
      ( ( A2 != nil_Pr2379126408512758701c_fm_a )
     => ( ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ ( tl_Pro4131336186639185046c_fm_a @ A2 ) ) )
       => ( member5029746173879296720c_fm_a @ X2 @ ( set_Pr6083076219314900284c_fm_a @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1011_list_Oset__sel_I2_J,axiom,
    ! [A2: list_P7917480606449584557c_fm_a,X2: produc5756089960658898087c_fm_a] :
      ( ( A2 != nil_Pr1848654487927912109c_fm_a )
     => ( ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ ( tl_Pro8821402481993660054c_fm_a @ A2 ) ) )
       => ( member3265983909902097104c_fm_a @ X2 @ ( set_Pr5015285182815091004c_fm_a @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1012_list_Oset__sel_I2_J,axiom,
    ! [A2: list_a,X2: a] :
      ( ( A2 != nil_a )
     => ( ( member_a @ X2 @ ( set_a2 @ ( tl_a @ A2 ) ) )
       => ( member_a @ X2 @ ( set_a2 @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1013_list_Oset__sel_I2_J,axiom,
    ! [A2: list_s580375451141968640c_fm_a,X2: set_Epistemic_fm_a] :
      ( ( A2 != nil_se102576565402781184c_fm_a )
     => ( ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ ( tl_set2007602089164433257c_fm_a @ A2 ) ) )
       => ( member536094252920883875c_fm_a @ X2 @ ( set_se8855941934996405007c_fm_a @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1014_list_Oset__sel_I2_J,axiom,
    ! [A2: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a] :
      ( ( A2 != nil_li2451196919128234278c_fm_a )
     => ( ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ ( tl_lis3363300823944467983c_fm_a @ A2 ) ) )
       => ( member5906877432388582473c_fm_a @ X2 @ ( set_li8442223810127165109c_fm_a @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1015_list_Oset__sel_I2_J,axiom,
    ! [A2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( A2 != nil_Epistemic_fm_a )
     => ( ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ ( tl_Epistemic_fm_a @ A2 ) ) )
       => ( member6642669571620171971c_fm_a @ X2 @ ( set_Epistemic_fm_a2 @ A2 ) ) ) ) ).

% list.set_sel(2)
thf(fact_1016_K__imply__weaken,axiom,
    ! [A: epistemic_fm_a > $o,Ps: list_Epistemic_fm_a,Q: epistemic_fm_a,Ps2: list_Epistemic_fm_a] :
      ( ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps @ Q ) )
     => ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Ps2 ) )
       => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ Ps2 @ Q ) ) ) ) ).

% K_imply_weaken
thf(fact_1017_List_Oinsert__def,axiom,
    ( insert423680279517344963c_fm_a
    = ( ^ [X: produc2203834439629243303c_fm_a,Xs: list_P3099032918374241197c_fm_a] : ( if_lis4277834422595218803c_fm_a @ ( member5029746173879296720c_fm_a @ X @ ( set_Pr6083076219314900284c_fm_a @ Xs ) ) @ Xs @ ( cons_P6232728021713608541c_fm_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1018_List_Oinsert__def,axiom,
    ( insert7000960152310464963c_fm_a
    = ( ^ [X: produc5756089960658898087c_fm_a,Xs: list_P7917480606449584557c_fm_a] : ( if_lis974313005191179635c_fm_a @ ( member3265983909902097104c_fm_a @ X @ ( set_Pr5015285182815091004c_fm_a @ Xs ) ) @ Xs @ ( cons_P7190808671141380701c_fm_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1019_List_Oinsert__def,axiom,
    ( insert1868103382419917334c_fm_a
    = ( ^ [X: set_Epistemic_fm_a,Xs: list_s580375451141968640c_fm_a] : ( if_lis3811715425919989702c_fm_a @ ( member536094252920883875c_fm_a @ X @ ( set_se8855941934996405007c_fm_a @ Xs ) ) @ Xs @ ( cons_s4394448069393209776c_fm_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1020_List_Oinsert__def,axiom,
    ( insert_a
    = ( ^ [X: a,Xs: list_a] : ( if_list_a @ ( member_a @ X @ ( set_a2 @ Xs ) ) @ Xs @ ( cons_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1021_List_Oinsert__def,axiom,
    ( insert335162795743670844c_fm_a
    = ( ^ [X: list_Epistemic_fm_a,Xs: list_l6083326122719238310c_fm_a] : ( if_lis342421823373228652c_fm_a @ ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs ) ) @ Xs @ ( cons_l8134865115577406678c_fm_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1022_List_Oinsert__def,axiom,
    ( insert177310161492556854c_fm_a
    = ( ^ [X: epistemic_fm_a,Xs: list_Epistemic_fm_a] : ( if_lis2878681784746929638c_fm_a @ ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs ) ) @ Xs @ ( cons_Epistemic_fm_a @ X @ Xs ) ) ) ) ).

% List.insert_def
thf(fact_1023_Cons__eq__filterD,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( filter441479637125139101c_fm_a @ P4 @ Ys ) )
     => ? [Us3: list_l6083326122719238310c_fm_a,Vs2: list_l6083326122719238310c_fm_a] :
          ( ( Ys
            = ( append1384085151619559355c_fm_a @ Us3 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Vs2 ) ) )
          & ! [X4: list_Epistemic_fm_a] :
              ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Us3 ) )
             => ~ ( P4 @ X4 ) )
          & ( P4 @ X2 )
          & ( Xs2
            = ( filter441479637125139101c_fm_a @ P4 @ Vs2 ) ) ) ) ).

% Cons_eq_filterD
thf(fact_1024_Cons__eq__filterD,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( filter7636273809395300631c_fm_a @ P4 @ Ys ) )
     => ? [Us3: list_Epistemic_fm_a,Vs2: list_Epistemic_fm_a] :
          ( ( Ys
            = ( append9179727413925872949c_fm_a @ Us3 @ ( cons_Epistemic_fm_a @ X2 @ Vs2 ) ) )
          & ! [X4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Us3 ) )
             => ~ ( P4 @ X4 ) )
          & ( P4 @ X2 )
          & ( Xs2
            = ( filter7636273809395300631c_fm_a @ P4 @ Vs2 ) ) ) ) ).

% Cons_eq_filterD
thf(fact_1025_filter__eq__ConsD,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( filter441479637125139101c_fm_a @ P4 @ Ys )
        = ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
     => ? [Us3: list_l6083326122719238310c_fm_a,Vs2: list_l6083326122719238310c_fm_a] :
          ( ( Ys
            = ( append1384085151619559355c_fm_a @ Us3 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Vs2 ) ) )
          & ! [X4: list_Epistemic_fm_a] :
              ( ( member5906877432388582473c_fm_a @ X4 @ ( set_li8442223810127165109c_fm_a @ Us3 ) )
             => ~ ( P4 @ X4 ) )
          & ( P4 @ X2 )
          & ( Xs2
            = ( filter441479637125139101c_fm_a @ P4 @ Vs2 ) ) ) ) ).

% filter_eq_ConsD
thf(fact_1026_filter__eq__ConsD,axiom,
    ! [P4: epistemic_fm_a > $o,Ys: list_Epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( filter7636273809395300631c_fm_a @ P4 @ Ys )
        = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
     => ? [Us3: list_Epistemic_fm_a,Vs2: list_Epistemic_fm_a] :
          ( ( Ys
            = ( append9179727413925872949c_fm_a @ Us3 @ ( cons_Epistemic_fm_a @ X2 @ Vs2 ) ) )
          & ! [X4: epistemic_fm_a] :
              ( ( member6642669571620171971c_fm_a @ X4 @ ( set_Epistemic_fm_a2 @ Us3 ) )
             => ~ ( P4 @ X4 ) )
          & ( P4 @ X2 )
          & ( Xs2
            = ( filter7636273809395300631c_fm_a @ P4 @ Vs2 ) ) ) ) ).

% filter_eq_ConsD
thf(fact_1027_Cons__eq__filter__iff,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a,P4: list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a] :
      ( ( ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 )
        = ( filter441479637125139101c_fm_a @ P4 @ Ys ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( append1384085151619559355c_fm_a @ Us2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Vs ) ) )
            & ! [X: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Us2 ) )
               => ~ ( P4 @ X ) )
            & ( P4 @ X2 )
            & ( Xs2
              = ( filter441479637125139101c_fm_a @ P4 @ Vs ) ) ) ) ) ).

% Cons_eq_filter_iff
thf(fact_1028_Cons__eq__filter__iff,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,P4: epistemic_fm_a > $o,Ys: list_Epistemic_fm_a] :
      ( ( ( cons_Epistemic_fm_a @ X2 @ Xs2 )
        = ( filter7636273809395300631c_fm_a @ P4 @ Ys ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Ys
              = ( append9179727413925872949c_fm_a @ Us2 @ ( cons_Epistemic_fm_a @ X2 @ Vs ) ) )
            & ! [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Us2 ) )
               => ~ ( P4 @ X ) )
            & ( P4 @ X2 )
            & ( Xs2
              = ( filter7636273809395300631c_fm_a @ P4 @ Vs ) ) ) ) ) ).

% Cons_eq_filter_iff
thf(fact_1029_filter__eq__Cons__iff,axiom,
    ! [P4: list_Epistemic_fm_a > $o,Ys: list_l6083326122719238310c_fm_a,X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( filter441479637125139101c_fm_a @ P4 @ Ys )
        = ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( ? [Us2: list_l6083326122719238310c_fm_a,Vs: list_l6083326122719238310c_fm_a] :
            ( ( Ys
              = ( append1384085151619559355c_fm_a @ Us2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ Vs ) ) )
            & ! [X: list_Epistemic_fm_a] :
                ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Us2 ) )
               => ~ ( P4 @ X ) )
            & ( P4 @ X2 )
            & ( Xs2
              = ( filter441479637125139101c_fm_a @ P4 @ Vs ) ) ) ) ) ).

% filter_eq_Cons_iff
thf(fact_1030_filter__eq__Cons__iff,axiom,
    ! [P4: epistemic_fm_a > $o,Ys: list_Epistemic_fm_a,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( filter7636273809395300631c_fm_a @ P4 @ Ys )
        = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ? [Us2: list_Epistemic_fm_a,Vs: list_Epistemic_fm_a] :
            ( ( Ys
              = ( append9179727413925872949c_fm_a @ Us2 @ ( cons_Epistemic_fm_a @ X2 @ Vs ) ) )
            & ! [X: epistemic_fm_a] :
                ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Us2 ) )
               => ~ ( P4 @ X ) )
            & ( P4 @ X2 )
            & ( Xs2
              = ( filter7636273809395300631c_fm_a @ P4 @ Vs ) ) ) ) ) ).

% filter_eq_Cons_iff
thf(fact_1031_hd__def,axiom,
    ( hd_Epistemic_fm_a
    = ( case_l5911136813010175462c_fm_a @ undefi6158949259153642370c_fm_a
      @ ^ [X213: epistemic_fm_a,X223: list_Epistemic_fm_a] : X213 ) ) ).

% hd_def
thf(fact_1032_hd__def,axiom,
    ( hd_lis6228752984540680715c_fm_a
    = ( case_l5930680263517320678c_fm_a @ undefi2327196743408399240c_fm_a
      @ ^ [X213: list_Epistemic_fm_a,X223: list_l6083326122719238310c_fm_a] : X213 ) ) ).

% hd_def
thf(fact_1033_tautology__imply__superset,axiom,
    ! [Ps: list_Epistemic_fm_a,Qs2: list_Epistemic_fm_a,R: epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Ps ) @ ( set_Epistemic_fm_a2 @ Qs2 ) )
     => ! [G2: list_char > $o,H2: epistemic_fm_a > $o] : ( epistemic_eval_a @ G2 @ H2 @ ( epistemic_Imp_a @ ( epistemic_imply_a @ Ps @ R ) @ ( epistemic_imply_a @ Qs2 @ R ) ) ) ) ).

% tautology_imply_superset
thf(fact_1034_rotate1_Osimps_I2_J,axiom,
    ! [X2: set_Epistemic_fm_a,Xs2: list_s580375451141968640c_fm_a] :
      ( ( rotate2699689030021285965c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ Xs2 ) )
      = ( append5257919162946131733c_fm_a @ Xs2 @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) ) ).

% rotate1.simps(2)
thf(fact_1035_rotate1_Osimps_I2_J,axiom,
    ! [X2: list_Epistemic_fm_a,Xs2: list_l6083326122719238310c_fm_a] :
      ( ( rotate2311183321535120627c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ Xs2 ) )
      = ( append1384085151619559355c_fm_a @ Xs2 @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) ) ).

% rotate1.simps(2)
thf(fact_1036_rotate1_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( rotate3540958558250653293c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) ).

% rotate1.simps(2)
thf(fact_1037_can__select__set__list__ex1,axiom,
    ! [P4: list_Epistemic_fm_a > $o,A: list_l6083326122719238310c_fm_a] :
      ( ( can_se7491264451046533021c_fm_a @ P4 @ ( set_li8442223810127165109c_fm_a @ A ) )
      = ( list_e1371837923195959913c_fm_a @ P4 @ A ) ) ).

% can_select_set_list_ex1
thf(fact_1038_can__select__set__list__ex1,axiom,
    ! [P4: epistemic_fm_a > $o,A: list_Epistemic_fm_a] :
      ( ( can_se5173380710277125655c_fm_a @ P4 @ ( set_Epistemic_fm_a2 @ A ) )
      = ( list_e2031426293596896995c_fm_a @ P4 @ A ) ) ).

% can_select_set_list_ex1
thf(fact_1039_less__eq__set__def,axiom,
    ( ord_le8222437384497874983c_fm_a
    = ( ^ [A3: set_Pr8948481099588399239c_fm_a,B3: set_Pr8948481099588399239c_fm_a] :
          ( ord_le4942933042592423798fm_a_o
          @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ A3 )
          @ ^ [X: produc2203834439629243303c_fm_a] : ( member5029746173879296720c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1040_less__eq__set__def,axiom,
    ( ord_le8873477448617899047c_fm_a
    = ( ^ [A3: set_Pr3219225162411408519c_fm_a,B3: set_Pr3219225162411408519c_fm_a] :
          ( ord_le3724781943004833654fm_a_o
          @ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ A3 )
          @ ^ [X: produc5756089960658898087c_fm_a] : ( member3265983909902097104c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1041_less__eq__set__def,axiom,
    ( ord_le7112219575281605754c_fm_a
    = ( ^ [A3: set_se5208064806568342746c_fm_a,B3: set_se5208064806568342746c_fm_a] :
          ( ord_le1568123225352354019fm_a_o
          @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ A3 )
          @ ^ [X: set_Epistemic_fm_a] : ( member536094252920883875c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1042_less__eq__set__def,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( ord_less_eq_a_o
          @ ^ [X: a] : ( member_a @ X @ A3 )
          @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1043_less__eq__set__def,axiom,
    ( ord_le3275665582123262618c_fm_a
    = ( ^ [A3: set_Epistemic_fm_a,B3: set_Epistemic_fm_a] :
          ( ord_le4043730696559282883fm_a_o
          @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ A3 )
          @ ^ [X: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1044_less__eq__set__def,axiom,
    ( ord_le2931979837777675552c_fm_a
    = ( ^ [A3: set_li769143395467472256c_fm_a,B3: set_li769143395467472256c_fm_a] :
          ( ord_le5289359451089373629fm_a_o
          @ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ A3 )
          @ ^ [X: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1045_the__elem__set,axiom,
    ! [X2: set_Epistemic_fm_a] :
      ( ( the_el1285646365920873327c_fm_a @ ( set_se8855941934996405007c_fm_a @ ( cons_s4394448069393209776c_fm_a @ X2 @ nil_se102576565402781184c_fm_a ) ) )
      = X2 ) ).

% the_elem_set
thf(fact_1046_the__elem__set,axiom,
    ! [X2: list_Epistemic_fm_a] :
      ( ( the_el8584007648813340437c_fm_a @ ( set_li8442223810127165109c_fm_a @ ( cons_l8134865115577406678c_fm_a @ X2 @ nil_li2451196919128234278c_fm_a ) ) )
      = X2 ) ).

% the_elem_set
thf(fact_1047_the__elem__set,axiom,
    ! [X2: epistemic_fm_a] :
      ( ( the_el2173195877760541071c_fm_a @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) )
      = X2 ) ).

% the_elem_set
thf(fact_1048_fm_Orel__cases,axiom,
    ! [R2: a > a > $o,A2: epistemic_fm_a,B: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ A2 @ B )
     => ( ( ( A2 = epistemic_FF_a )
         => ( B != epistemic_FF_a ) )
       => ( ! [X3: list_char] :
              ( ( A2
                = ( epistemic_Pro_a @ X3 ) )
             => ! [Y2: list_char] :
                  ( ( B
                    = ( epistemic_Pro_a @ Y2 ) )
                 => ( X3 != Y2 ) ) )
         => ( ! [X12: epistemic_fm_a,X2a: epistemic_fm_a] :
                ( ( A2
                  = ( epistemic_Dis_a @ X12 @ X2a ) )
               => ! [Y1: epistemic_fm_a,Y2a: epistemic_fm_a] :
                    ( ( B
                      = ( epistemic_Dis_a @ Y1 @ Y2a ) )
                   => ( ( epistemic_rel_fm_a_a @ R2 @ X12 @ Y1 )
                     => ~ ( epistemic_rel_fm_a_a @ R2 @ X2a @ Y2a ) ) ) )
           => ( ! [X1a: epistemic_fm_a,X2b: epistemic_fm_a] :
                  ( ( A2
                    = ( epistemic_Con_a @ X1a @ X2b ) )
                 => ! [Y1a: epistemic_fm_a,Y2b: epistemic_fm_a] :
                      ( ( B
                        = ( epistemic_Con_a @ Y1a @ Y2b ) )
                     => ( ( epistemic_rel_fm_a_a @ R2 @ X1a @ Y1a )
                       => ~ ( epistemic_rel_fm_a_a @ R2 @ X2b @ Y2b ) ) ) )
             => ( ! [X1b: epistemic_fm_a,X2c: epistemic_fm_a] :
                    ( ( A2
                      = ( epistemic_Imp_a @ X1b @ X2c ) )
                   => ! [Y1b: epistemic_fm_a,Y2c: epistemic_fm_a] :
                        ( ( B
                          = ( epistemic_Imp_a @ Y1b @ Y2c ) )
                       => ( ( epistemic_rel_fm_a_a @ R2 @ X1b @ Y1b )
                         => ~ ( epistemic_rel_fm_a_a @ R2 @ X2c @ Y2c ) ) ) )
               => ~ ! [X1c: a,X2d: epistemic_fm_a] :
                      ( ( A2
                        = ( epistemic_K_a @ X1c @ X2d ) )
                     => ! [Y1c: a,Y2d: epistemic_fm_a] :
                          ( ( B
                            = ( epistemic_K_a @ Y1c @ Y2d ) )
                         => ( ( R2 @ X1c @ Y1c )
                           => ~ ( epistemic_rel_fm_a_a @ R2 @ X2d @ Y2d ) ) ) ) ) ) ) ) ) ) ).

% fm.rel_cases
thf(fact_1049_fm_Orel__induct,axiom,
    ! [R2: a > a > $o,X2: epistemic_fm_a,Y: epistemic_fm_a,Q4: epistemic_fm_a > epistemic_fm_a > $o] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X2 @ Y )
     => ( ( Q4 @ epistemic_FF_a @ epistemic_FF_a )
       => ( ! [A24: list_char,B22: list_char] :
              ( ( A24 = B22 )
             => ( Q4 @ ( epistemic_Pro_a @ A24 ) @ ( epistemic_Pro_a @ B22 ) ) )
         => ( ! [A31: epistemic_fm_a,A32: epistemic_fm_a,B31: epistemic_fm_a,B32: epistemic_fm_a] :
                ( ( Q4 @ A31 @ B31 )
               => ( ( Q4 @ A32 @ B32 )
                 => ( Q4 @ ( epistemic_Dis_a @ A31 @ A32 ) @ ( epistemic_Dis_a @ B31 @ B32 ) ) ) )
           => ( ! [A41: epistemic_fm_a,A42: epistemic_fm_a,B41: epistemic_fm_a,B42: epistemic_fm_a] :
                  ( ( Q4 @ A41 @ B41 )
                 => ( ( Q4 @ A42 @ B42 )
                   => ( Q4 @ ( epistemic_Con_a @ A41 @ A42 ) @ ( epistemic_Con_a @ B41 @ B42 ) ) ) )
             => ( ! [A51: epistemic_fm_a,A52: epistemic_fm_a,B51: epistemic_fm_a,B52: epistemic_fm_a] :
                    ( ( Q4 @ A51 @ B51 )
                   => ( ( Q4 @ A52 @ B52 )
                     => ( Q4 @ ( epistemic_Imp_a @ A51 @ A52 ) @ ( epistemic_Imp_a @ B51 @ B52 ) ) ) )
               => ( ! [A61: a,A62: epistemic_fm_a,B61: a,B62: epistemic_fm_a] :
                      ( ( R2 @ A61 @ B61 )
                     => ( ( Q4 @ A62 @ B62 )
                       => ( Q4 @ ( epistemic_K_a @ A61 @ A62 ) @ ( epistemic_K_a @ B61 @ B62 ) ) ) )
                 => ( Q4 @ X2 @ Y ) ) ) ) ) ) ) ) ).

% fm.rel_induct
thf(fact_1050_Nil__eq__concat__conv,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( nil_li2451196919128234278c_fm_a
        = ( concat6109960377493484129c_fm_a @ Xss2 ) )
      = ( ! [X: list_l6083326122719238310c_fm_a] :
            ( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Xss2 ) )
           => ( X = nil_li2451196919128234278c_fm_a ) ) ) ) ).

% Nil_eq_concat_conv
thf(fact_1051_Nil__eq__concat__conv,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( nil_se102576565402781184c_fm_a
        = ( concat2941956077894552763c_fm_a @ Xss2 ) )
      = ( ! [X: list_s580375451141968640c_fm_a] :
            ( ( member2328277852289759785c_fm_a @ X @ ( set_li3422124509070804117c_fm_a @ Xss2 ) )
           => ( X = nil_se102576565402781184c_fm_a ) ) ) ) ).

% Nil_eq_concat_conv
thf(fact_1052_Nil__eq__concat__conv,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( nil_Epistemic_fm_a
        = ( concat2780896542826320603c_fm_a @ Xss2 ) )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xss2 ) )
           => ( X = nil_Epistemic_fm_a ) ) ) ) ).

% Nil_eq_concat_conv
thf(fact_1053_concat__eq__Nil__conv,axiom,
    ! [Xss2: list_l3671048651222332332c_fm_a] :
      ( ( ( concat6109960377493484129c_fm_a @ Xss2 )
        = nil_li2451196919128234278c_fm_a )
      = ( ! [X: list_l6083326122719238310c_fm_a] :
            ( ( member7465314387053329231c_fm_a @ X @ ( set_li647609056391172027c_fm_a @ Xss2 ) )
           => ( X = nil_li2451196919128234278c_fm_a ) ) ) ) ).

% concat_eq_Nil_conv
thf(fact_1054_concat__eq__Nil__conv,axiom,
    ! [Xss2: list_l985973790606564998c_fm_a] :
      ( ( ( concat2941956077894552763c_fm_a @ Xss2 )
        = nil_se102576565402781184c_fm_a )
      = ( ! [X: list_s580375451141968640c_fm_a] :
            ( ( member2328277852289759785c_fm_a @ X @ ( set_li3422124509070804117c_fm_a @ Xss2 ) )
           => ( X = nil_se102576565402781184c_fm_a ) ) ) ) ).

% concat_eq_Nil_conv
thf(fact_1055_concat__eq__Nil__conv,axiom,
    ! [Xss2: list_l6083326122719238310c_fm_a] :
      ( ( ( concat2780896542826320603c_fm_a @ Xss2 )
        = nil_Epistemic_fm_a )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xss2 ) )
           => ( X = nil_Epistemic_fm_a ) ) ) ) ).

% concat_eq_Nil_conv
thf(fact_1056_fm_Orel__refl,axiom,
    ! [Ra: a > a > $o,X2: epistemic_fm_a] :
      ( ! [X3: a] : ( Ra @ X3 @ X3 )
     => ( epistemic_rel_fm_a_a @ Ra @ X2 @ X2 ) ) ).

% fm.rel_refl
thf(fact_1057_fm_Orel__eq,axiom,
    ( ( epistemic_rel_fm_a_a
      @ ^ [Y5: a,Z4: a] : ( Y5 = Z4 ) )
    = ( ^ [Y5: epistemic_fm_a,Z4: epistemic_fm_a] : ( Y5 = Z4 ) ) ) ).

% fm.rel_eq
thf(fact_1058_fm_Orel__intros_I5_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,Y51: epistemic_fm_a,X52: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ) ) ).

% fm.rel_intros(5)
thf(fact_1059_fm_Orel__inject_I5_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X51 @ Y51 )
        & ( epistemic_rel_fm_a_a @ R2 @ X52 @ Y52 ) ) ) ).

% fm.rel_inject(5)
thf(fact_1060_fm_Orel__intros_I6_J,axiom,
    ! [R2: a > a > $o,X61: a,Y61: a,X62: epistemic_fm_a,Y62: epistemic_fm_a] :
      ( ( R2 @ X61 @ Y61 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ) ) ).

% fm.rel_intros(6)
thf(fact_1061_fm_Orel__inject_I6_J,axiom,
    ! [R2: a > a > $o,X61: a,X62: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ X61 @ X62 ) @ ( epistemic_K_a @ Y61 @ Y62 ) )
      = ( ( R2 @ X61 @ Y61 )
        & ( epistemic_rel_fm_a_a @ R2 @ X62 @ Y62 ) ) ) ).

% fm.rel_inject(6)
thf(fact_1062_fm_Octr__transfer_I1_J,axiom,
    ! [R2: a > a > $o] : ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ epistemic_FF_a ) ).

% fm.ctr_transfer(1)
thf(fact_1063_fm_Orel__mono,axiom,
    ! [R2: a > a > $o,Ra: a > a > $o] :
      ( ( ord_less_eq_a_a_o @ R2 @ Ra )
     => ( ord_le3934200179093585166fm_a_o @ ( epistemic_rel_fm_a_a @ R2 ) @ ( epistemic_rel_fm_a_a @ Ra ) ) ) ).

% fm.rel_mono
thf(fact_1064_fm_Orel__intros_I4_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,Y41: epistemic_fm_a,X42: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X41 @ Y41 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X42 @ Y42 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) ) ) ) ).

% fm.rel_intros(4)
thf(fact_1065_fm_Orel__inject_I4_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y41: epistemic_fm_a,Y42: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Con_a @ Y41 @ Y42 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X41 @ Y41 )
        & ( epistemic_rel_fm_a_a @ R2 @ X42 @ Y42 ) ) ) ).

% fm.rel_inject(4)
thf(fact_1066_fm_Orel__intros_I2_J,axiom,
    ! [X25: list_char,Y23: list_char,R2: a > a > $o] :
      ( ( X25 = Y23 )
     => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X25 ) @ ( epistemic_Pro_a @ Y23 ) ) ) ).

% fm.rel_intros(2)
thf(fact_1067_fm_Orel__inject_I2_J,axiom,
    ! [R2: a > a > $o,X25: list_char,Y23: list_char] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X25 ) @ ( epistemic_Pro_a @ Y23 ) )
      = ( X25 = Y23 ) ) ).

% fm.rel_inject(2)
thf(fact_1068_fm_Orel__intros_I3_J,axiom,
    ! [R2: a > a > $o,X31: epistemic_fm_a,Y31: epistemic_fm_a,X32: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ X31 @ Y31 )
     => ( ( epistemic_rel_fm_a_a @ R2 @ X32 @ Y32 )
       => ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X31 @ X32 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) ) ) ) ).

% fm.rel_intros(3)
thf(fact_1069_fm_Orel__inject_I3_J,axiom,
    ! [R2: a > a > $o,X31: epistemic_fm_a,X32: epistemic_fm_a,Y31: epistemic_fm_a,Y32: epistemic_fm_a] :
      ( ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X31 @ X32 ) @ ( epistemic_Dis_a @ Y31 @ Y32 ) )
      = ( ( epistemic_rel_fm_a_a @ R2 @ X31 @ Y31 )
        & ( epistemic_rel_fm_a_a @ R2 @ X32 @ Y32 ) ) ) ).

% fm.rel_inject(3)
thf(fact_1070_can__select__def,axiom,
    ( can_se4087753133389225508c_fm_a
    = ( ^ [P6: produc2203834439629243303c_fm_a > $o,A3: set_Pr8948481099588399239c_fm_a] :
        ? [X: produc2203834439629243303c_fm_a] :
          ( ( member5029746173879296720c_fm_a @ X @ A3 )
          & ( P6 @ X )
          & ! [Y3: produc2203834439629243303c_fm_a] :
              ( ( ( member5029746173879296720c_fm_a @ Y3 @ A3 )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% can_select_def
thf(fact_1071_can__select__def,axiom,
    ( can_se5687140424174772772c_fm_a
    = ( ^ [P6: produc5756089960658898087c_fm_a > $o,A3: set_Pr3219225162411408519c_fm_a] :
        ? [X: produc5756089960658898087c_fm_a] :
          ( ( member3265983909902097104c_fm_a @ X @ A3 )
          & ( P6 @ X )
          & ! [Y3: produc5756089960658898087c_fm_a] :
              ( ( ( member3265983909902097104c_fm_a @ Y3 @ A3 )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% can_select_def
thf(fact_1072_can__select__def,axiom,
    ( can_se7491264451046533021c_fm_a
    = ( ^ [P6: list_Epistemic_fm_a > $o,A3: set_li769143395467472256c_fm_a] :
        ? [X: list_Epistemic_fm_a] :
          ( ( member5906877432388582473c_fm_a @ X @ A3 )
          & ( P6 @ X )
          & ! [Y3: list_Epistemic_fm_a] :
              ( ( ( member5906877432388582473c_fm_a @ Y3 @ A3 )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% can_select_def
thf(fact_1073_can__select__def,axiom,
    ( can_se8336582597686632439c_fm_a
    = ( ^ [P6: set_Epistemic_fm_a > $o,A3: set_se5208064806568342746c_fm_a] :
        ? [X: set_Epistemic_fm_a] :
          ( ( member536094252920883875c_fm_a @ X @ A3 )
          & ( P6 @ X )
          & ! [Y3: set_Epistemic_fm_a] :
              ( ( ( member536094252920883875c_fm_a @ Y3 @ A3 )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% can_select_def
thf(fact_1074_can__select__def,axiom,
    ( can_select_a
    = ( ^ [P6: a > $o,A3: set_a] :
        ? [X: a] :
          ( ( member_a @ X @ A3 )
          & ( P6 @ X )
          & ! [Y3: a] :
              ( ( ( member_a @ Y3 @ A3 )
                & ( P6 @ Y3 ) )
             => ( Y3 = X ) ) ) ) ) ).

% can_select_def
thf(fact_1075_subseqs__refl,axiom,
    ! [Xs2: list_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ Xs2 @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs2 ) ) ) ).

% subseqs_refl
thf(fact_1076_fm_Orel__distinct_I29_J,axiom,
    ! [R2: a > a > $o,X51: epistemic_fm_a,X52: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ X51 @ X52 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(29)
thf(fact_1077_fm_Orel__distinct_I30_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X51: epistemic_fm_a,X52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Imp_a @ X51 @ X52 ) ) ).

% fm.rel_distinct(30)
thf(fact_1078_fm_Orel__distinct_I8_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(8)
thf(fact_1079_fm_Orel__distinct_I7_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(7)
thf(fact_1080_fm_Orel__distinct_I10_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ epistemic_FF_a ) ).

% fm.rel_distinct(10)
thf(fact_1081_fm_Orel__distinct_I9_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ epistemic_FF_a @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(9)
thf(fact_1082_fm_Orel__distinct_I25_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(25)
thf(fact_1083_fm_Orel__distinct_I26_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(26)
thf(fact_1084_fm_Orel__distinct_I27_J,axiom,
    ! [R2: a > a > $o,X41: epistemic_fm_a,X42: epistemic_fm_a,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Con_a @ X41 @ X42 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(27)
thf(fact_1085_fm_Orel__distinct_I28_J,axiom,
    ! [R2: a > a > $o,Y61: a,Y62: epistemic_fm_a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_K_a @ Y61 @ Y62 ) @ ( epistemic_Con_a @ X41 @ X42 ) ) ).

% fm.rel_distinct(28)
thf(fact_1086_fm_Orel__distinct_I15_J,axiom,
    ! [R2: a > a > $o,X25: list_char,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X25 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(15)
thf(fact_1087_fm_Orel__distinct_I16_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X25: list_char] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Pro_a @ X25 ) ) ).

% fm.rel_distinct(16)
thf(fact_1088_fm_Orel__distinct_I21_J,axiom,
    ! [R2: a > a > $o,X31: epistemic_fm_a,X32: epistemic_fm_a,Y51: epistemic_fm_a,Y52: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Dis_a @ X31 @ X32 ) @ ( epistemic_Imp_a @ Y51 @ Y52 ) ) ).

% fm.rel_distinct(21)
thf(fact_1089_fm_Orel__distinct_I22_J,axiom,
    ! [R2: a > a > $o,Y51: epistemic_fm_a,Y52: epistemic_fm_a,X31: epistemic_fm_a,X32: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Imp_a @ Y51 @ Y52 ) @ ( epistemic_Dis_a @ X31 @ X32 ) ) ).

% fm.rel_distinct(22)
thf(fact_1090_fm_Orel__distinct_I17_J,axiom,
    ! [R2: a > a > $o,X25: list_char,Y61: a,Y62: epistemic_fm_a] :
      ~ ( epistemic_rel_fm_a_a @ R2 @ ( epistemic_Pro_a @ X25 ) @ ( epistemic_K_a @ Y61 @ Y62 ) ) ).

% fm.rel_distinct(17)
thf(fact_1091_Cons__in__subseqsD,axiom,
    ! [Y: epistemic_fm_a,Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Y @ Ys ) @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs2 ) ) )
     => ( member5906877432388582473c_fm_a @ Ys @ ( set_li8442223810127165109c_fm_a @ ( subseq859285839621985007c_fm_a @ Xs2 ) ) ) ) ).

% Cons_in_subseqsD
thf(fact_1092_transpose__empty,axiom,
    ! [Xs2: list_l6083326122719238310c_fm_a] :
      ( ( ( transp2882070860200649898c_fm_a @ Xs2 )
        = nil_li2451196919128234278c_fm_a )
      = ( ! [X: list_Epistemic_fm_a] :
            ( ( member5906877432388582473c_fm_a @ X @ ( set_li8442223810127165109c_fm_a @ Xs2 ) )
           => ( X = nil_Epistemic_fm_a ) ) ) ) ).

% transpose_empty
thf(fact_1093_subset__code_I3_J,axiom,
    ~ ( ord_le3275665582123262618c_fm_a @ ( coset_Epistemic_fm_a @ nil_Epistemic_fm_a ) @ ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) ) ).

% subset_code(3)
thf(fact_1094_tl__remdups__adj,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( Ys != nil_Epistemic_fm_a )
     => ( ( tl_Epistemic_fm_a @ ( remdup1727679340039403862c_fm_a @ Ys ) )
        = ( remdup1727679340039403862c_fm_a
          @ ( dropWh6715642967443873729c_fm_a
            @ ^ [X: epistemic_fm_a] :
                ( X
                = ( hd_Epistemic_fm_a @ Ys ) )
            @ ( tl_Epistemic_fm_a @ Ys ) ) ) ) ) ).

% tl_remdups_adj
thf(fact_1095_consistent__def,axiom,
    ( episte2285483198712856226tent_a
    = ( ^ [A3: epistemic_fm_a > $o,S2: set_Epistemic_fm_a] :
          ~ ? [Qs: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ Qs ) @ S2 )
              & ( epistemic_AK_a @ A3 @ ( epistemic_imply_a @ Qs @ epistemic_FF_a ) ) ) ) ) ).

% consistent_def
thf(fact_1096_remdups__adj__append_H,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
        | ( Ys = nil_Epistemic_fm_a )
        | ( ( last_Epistemic_fm_a @ Xs2 )
         != ( hd_Epistemic_fm_a @ Ys ) ) )
     => ( ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( append9179727413925872949c_fm_a @ ( remdup1727679340039403862c_fm_a @ Xs2 ) @ ( remdup1727679340039403862c_fm_a @ Ys ) ) ) ) ).

% remdups_adj_append'
thf(fact_1097_fm_Oset__cases,axiom,
    ! [E: a,A2: epistemic_fm_a] :
      ( ( member_a @ E @ ( epistemic_set_fm_a @ A2 ) )
     => ( ! [Z1: epistemic_fm_a] :
            ( ? [Z22: epistemic_fm_a] :
                ( A2
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
           => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
       => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
              ( ( A2
                = ( epistemic_Dis_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
         => ( ! [Z1: epistemic_fm_a] :
                ( ? [Z22: epistemic_fm_a] :
                    ( A2
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
               => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
           => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                  ( ( A2
                    = ( epistemic_Con_a @ Z1 @ Z22 ) )
                 => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
             => ( ! [Z1: epistemic_fm_a] :
                    ( ? [Z22: epistemic_fm_a] :
                        ( A2
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                   => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z1 ) ) )
               => ( ! [Z1: epistemic_fm_a,Z22: epistemic_fm_a] :
                      ( ( A2
                        = ( epistemic_Imp_a @ Z1 @ Z22 ) )
                     => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) )
                 => ( ! [Z22: epistemic_fm_a] :
                        ( A2
                       != ( epistemic_K_a @ E @ Z22 ) )
                   => ~ ! [Z1: a,Z22: epistemic_fm_a] :
                          ( ( A2
                            = ( epistemic_K_a @ Z1 @ Z22 ) )
                         => ~ ( member_a @ E @ ( epistemic_set_fm_a @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fm.set_cases
thf(fact_1098_dropWhile__eq__Nil__conv,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 )
        = nil_Epistemic_fm_a )
      = ( ! [X: epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ X @ ( set_Epistemic_fm_a2 @ Xs2 ) )
           => ( P4 @ X ) ) ) ) ).

% dropWhile_eq_Nil_conv
thf(fact_1099_last__appendL,axiom,
    ! [Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( Ys = nil_Epistemic_fm_a )
     => ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( last_Epistemic_fm_a @ Xs2 ) ) ) ).

% last_appendL
thf(fact_1100_last__appendR,axiom,
    ! [Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( Ys != nil_Epistemic_fm_a )
     => ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( last_Epistemic_fm_a @ Ys ) ) ) ).

% last_appendR
thf(fact_1101_last__snoc,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) )
      = X2 ) ).

% last_snoc
thf(fact_1102_dropWhile_Osimps_I2_J,axiom,
    ! [P4: epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( P4 @ X2 )
       => ( ( dropWh6715642967443873729c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 ) ) )
      & ( ~ ( P4 @ X2 )
       => ( ( dropWh6715642967443873729c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) ) ) ).

% dropWhile.simps(2)
thf(fact_1103_dropWhile_Osimps_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ( dropWh6715642967443873729c_fm_a @ P4 @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% dropWhile.simps(1)
thf(fact_1104_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_1105_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_1106_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_1107_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_1108_fm_Oset__intros_I4_J,axiom,
    ! [Yd: a,X42: epistemic_fm_a,X41: epistemic_fm_a] :
      ( ( member_a @ Yd @ ( epistemic_set_fm_a @ X42 ) )
     => ( member_a @ Yd @ ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(4)
thf(fact_1109_fm_Oset__intros_I3_J,axiom,
    ! [Yc: a,X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( member_a @ Yc @ ( epistemic_set_fm_a @ X41 ) )
     => ( member_a @ Yc @ ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) ) ) ) ).

% fm.set_intros(3)
thf(fact_1110_remdups__adj__append_H_H,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
        = ( append9179727413925872949c_fm_a @ ( remdup1727679340039403862c_fm_a @ Xs2 )
          @ ( remdup1727679340039403862c_fm_a
            @ ( dropWh6715642967443873729c_fm_a
              @ ^ [Y3: epistemic_fm_a] :
                  ( Y3
                  = ( last_Epistemic_fm_a @ Xs2 ) )
              @ Ys ) ) ) ) ) ).

% remdups_adj_append''
thf(fact_1111_dropWhile__append3,axiom,
    ! [P4: epistemic_fm_a > $o,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ~ ( P4 @ Y )
     => ( ( dropWh6715642967443873729c_fm_a @ P4 @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) )
        = ( append9179727413925872949c_fm_a @ ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) ) ).

% dropWhile_append3
thf(fact_1112_hd__dropWhile,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 )
       != nil_Epistemic_fm_a )
     => ~ ( P4 @ ( hd_Epistemic_fm_a @ ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% hd_dropWhile
thf(fact_1113_dropWhile__eq__self__iff,axiom,
    ! [P4: epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a] :
      ( ( ( dropWh6715642967443873729c_fm_a @ P4 @ Xs2 )
        = Xs2 )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        | ~ ( P4 @ ( hd_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% dropWhile_eq_self_iff
thf(fact_1114_last_Osimps,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
       => ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = X2 ) )
      & ( ( Xs2 != nil_Epistemic_fm_a )
       => ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( last_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% last.simps
thf(fact_1115_last__ConsL,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( Xs2 = nil_Epistemic_fm_a )
     => ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
        = X2 ) ) ).

% last_ConsL
thf(fact_1116_last__ConsR,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( last_Epistemic_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
        = ( last_Epistemic_fm_a @ Xs2 ) ) ) ).

% last_ConsR
thf(fact_1117_last__in__set,axiom,
    ! [As2: list_Epistemic_fm_a] :
      ( ( As2 != nil_Epistemic_fm_a )
     => ( member6642669571620171971c_fm_a @ ( last_Epistemic_fm_a @ As2 ) @ ( set_Epistemic_fm_a2 @ As2 ) ) ) ).

% last_in_set
thf(fact_1118_last__map,axiom,
    ! [Xs2: list_Epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( last_Epistemic_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
        = ( F @ ( last_Epistemic_fm_a @ Xs2 ) ) ) ) ).

% last_map
thf(fact_1119_last__append,axiom,
    ! [Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( Ys = nil_Epistemic_fm_a )
       => ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( last_Epistemic_fm_a @ Xs2 ) ) )
      & ( ( Ys != nil_Epistemic_fm_a )
       => ( ( last_Epistemic_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( last_Epistemic_fm_a @ Ys ) ) ) ) ).

% last_append
thf(fact_1120_longest__common__suffix,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
    ? [Ss: list_Epistemic_fm_a,Xs4: list_Epistemic_fm_a,Ys5: list_Epistemic_fm_a] :
      ( ( Xs2
        = ( append9179727413925872949c_fm_a @ Xs4 @ Ss ) )
      & ( Ys
        = ( append9179727413925872949c_fm_a @ Ys5 @ Ss ) )
      & ( ( Xs4 = nil_Epistemic_fm_a )
        | ( Ys5 = nil_Epistemic_fm_a )
        | ( ( last_Epistemic_fm_a @ Xs4 )
         != ( last_Epistemic_fm_a @ Ys5 ) ) ) ) ).

% longest_common_suffix
thf(fact_1121_hd__Nil__eq__last,axiom,
    ( ( hd_Epistemic_fm_a @ nil_Epistemic_fm_a )
    = ( last_Epistemic_fm_a @ nil_Epistemic_fm_a ) ) ).

% hd_Nil_eq_last
thf(fact_1122_last__tl,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
        | ( ( tl_Epistemic_fm_a @ Xs2 )
         != nil_Epistemic_fm_a ) )
     => ( ( last_Epistemic_fm_a @ ( tl_Epistemic_fm_a @ Xs2 ) )
        = ( last_Epistemic_fm_a @ Xs2 ) ) ) ).

% last_tl
thf(fact_1123_remdups__adj__Cons_H,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( cons_Epistemic_fm_a @ X2
        @ ( remdup1727679340039403862c_fm_a
          @ ( dropWh6715642967443873729c_fm_a
            @ ^ [Y3: epistemic_fm_a] : ( Y3 = X2 )
            @ Xs2 ) ) ) ) ).

% remdups_adj_Cons'
thf(fact_1124_remdups__adj__append__dropWhile,axiom,
    ! [Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) )
      = ( append9179727413925872949c_fm_a @ ( remdup1727679340039403862c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) )
        @ ( remdup1727679340039403862c_fm_a
          @ ( dropWh6715642967443873729c_fm_a
            @ ^ [X: epistemic_fm_a] : ( X = Y )
            @ Ys ) ) ) ) ).

% remdups_adj_append_dropWhile
thf(fact_1125_AxB__symmetric_H,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,W: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxB_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V2 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
         => ( ( episte2285483198712856226tent_a @ A @ W )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W )
             => ( ( member536094252920883875c_fm_a @ W
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V2 ) ) ) ) )
               => ( member536094252920883875c_fm_a @ V2
                  @ ( collec2519470961442302949c_fm_a
                    @ ( ord_le3275665582123262618c_fm_a
                      @ ( collec4904205152690461189c_fm_a
                        @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ W ) ) ) ) ) ) ) ) ) ) ) ).

% AxB_symmetric'
thf(fact_1126_Ax5__Euclidean,axiom,
    ! [A: epistemic_fm_a > $o,U2: set_Epistemic_fm_a,V2: set_Epistemic_fm_a,W: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax5_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ U2 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ U2 )
         => ( ( episte2285483198712856226tent_a @ A @ V2 )
           => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
             => ( ( episte2285483198712856226tent_a @ A @ W )
               => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ W )
                 => ( ( member536094252920883875c_fm_a @ V2
                      @ ( collec2519470961442302949c_fm_a
                        @ ( ord_le3275665582123262618c_fm_a
                          @ ( collec4904205152690461189c_fm_a
                            @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ U2 ) ) ) ) )
                   => ( ( member536094252920883875c_fm_a @ W
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ U2 ) ) ) ) )
                     => ( member536094252920883875c_fm_a @ W
                        @ ( collec2519470961442302949c_fm_a
                          @ ( ord_le3275665582123262618c_fm_a
                            @ ( collec4904205152690461189c_fm_a
                              @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% Ax5_Euclidean
thf(fact_1127_Ax4__transitive,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,W: set_Epistemic_fm_a,I: a,U2: set_Epistemic_fm_a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_Ax4_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V2 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
         => ( ( member536094252920883875c_fm_a @ W
              @ ( collec2519470961442302949c_fm_a
                @ ( ord_le3275665582123262618c_fm_a
                  @ ( collec4904205152690461189c_fm_a
                    @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V2 ) ) ) ) )
           => ( ( member536094252920883875c_fm_a @ U2
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ W ) ) ) ) )
             => ( member536094252920883875c_fm_a @ U2
                @ ( collec2519470961442302949c_fm_a
                  @ ( ord_le3275665582123262618c_fm_a
                    @ ( collec4904205152690461189c_fm_a
                      @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V2 ) ) ) ) ) ) ) ) ) ) ).

% Ax4_transitive
thf(fact_1128_AxT__reflexive,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,I: a] :
      ( ( ord_le4043730696559282883fm_a_o @ epistemic_AxT_a @ A )
     => ( ( episte2285483198712856226tent_a @ A @ V2 )
       => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
         => ( member536094252920883875c_fm_a @ V2
            @ ( collec2519470961442302949c_fm_a
              @ ( ord_le3275665582123262618c_fm_a
                @ ( collec4904205152690461189c_fm_a
                  @ ^ [P2: epistemic_fm_a] : ( member6642669571620171971c_fm_a @ ( epistemic_K_a @ I @ P2 ) @ V2 ) ) ) ) ) ) ) ) ).

% AxT_reflexive
thf(fact_1129_append__butlast__last__id,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( Xs2 != nil_Epistemic_fm_a )
     => ( ( append9179727413925872949c_fm_a @ ( butlas2200625790165101420c_fm_a @ Xs2 ) @ ( cons_Epistemic_fm_a @ ( last_Epistemic_fm_a @ Xs2 ) @ nil_Epistemic_fm_a ) )
        = Xs2 ) ) ).

% append_butlast_last_id
thf(fact_1130_butlast__snoc,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) )
      = Xs2 ) ).

% butlast_snoc
thf(fact_1131_butlast_Osimps_I1_J,axiom,
    ( ( butlas2200625790165101420c_fm_a @ nil_Epistemic_fm_a )
    = nil_Epistemic_fm_a ) ).

% butlast.simps(1)
thf(fact_1132_map__butlast,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( butlas2200625790165101420c_fm_a @ Xs2 ) )
      = ( butlas2200625790165101420c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) ) ) ).

% map_butlast
thf(fact_1133_butlast_Osimps_I2_J,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a] :
      ( ( ( Xs2 = nil_Epistemic_fm_a )
       => ( ( butlas2200625790165101420c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = nil_Epistemic_fm_a ) )
      & ( ( Xs2 != nil_Epistemic_fm_a )
       => ( ( butlas2200625790165101420c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
          = ( cons_Epistemic_fm_a @ X2 @ ( butlas2200625790165101420c_fm_a @ Xs2 ) ) ) ) ) ).

% butlast.simps(2)
thf(fact_1134_butlast__append,axiom,
    ! [Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( Ys = nil_Epistemic_fm_a )
       => ( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( butlas2200625790165101420c_fm_a @ Xs2 ) ) )
      & ( ( Ys != nil_Epistemic_fm_a )
       => ( ( butlas2200625790165101420c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
          = ( append9179727413925872949c_fm_a @ Xs2 @ ( butlas2200625790165101420c_fm_a @ Ys ) ) ) ) ) ).

% butlast_append
thf(fact_1135_consequent__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
       => ( ( member6642669571620171971c_fm_a @ P @ V2 )
         => ( ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ Q ) @ V2 )
           => ( member6642669571620171971c_fm_a @ Q @ V2 ) ) ) ) ) ).

% consequent_in_maximal
thf(fact_1136_deriv__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
       => ( ( epistemic_AK_a @ A @ P )
         => ( member6642669571620171971c_fm_a @ P @ V2 ) ) ) ) ).

% deriv_in_maximal
thf(fact_1137_exactly__one__in__maximal,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ( maxima3264069584562520521c_fm_a @ ( episte2285483198712856226tent_a @ A ) @ V2 )
       => ( ( member6642669571620171971c_fm_a @ P @ V2 )
          = ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ V2 ) ) ) ) ) ).

% exactly_one_in_maximal
thf(fact_1138_snoc__eq__iff__butlast,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) )
        = Ys )
      = ( ( Ys != nil_Epistemic_fm_a )
        & ( ( butlas2200625790165101420c_fm_a @ Ys )
          = Xs2 )
        & ( ( last_Epistemic_fm_a @ Ys )
          = X2 ) ) ) ).

% snoc_eq_iff_butlast
thf(fact_1139_distinct__adj__append__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( distin8123941861610682872c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( ( distin8123941861610682872c_fm_a @ Xs2 )
        & ( distin8123941861610682872c_fm_a @ Ys )
        & ( ( Xs2 = nil_Epistemic_fm_a )
          | ( Ys = nil_Epistemic_fm_a )
          | ( ( last_Epistemic_fm_a @ Xs2 )
           != ( hd_Epistemic_fm_a @ Ys ) ) ) ) ) ).

% distinct_adj_append_iff
thf(fact_1140_successively__append__iff,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ P4 @ ( append9179727413925872949c_fm_a @ Xs2 @ Ys ) )
      = ( ( succes6989878846294031341c_fm_a @ P4 @ Xs2 )
        & ( succes6989878846294031341c_fm_a @ P4 @ Ys )
        & ( ( Xs2 = nil_Epistemic_fm_a )
          | ( Ys = nil_Epistemic_fm_a )
          | ( P4 @ ( last_Epistemic_fm_a @ Xs2 ) @ ( hd_Epistemic_fm_a @ Ys ) ) ) ) ) ).

% successively_append_iff
thf(fact_1141_distinct__adj__Cons__Cons,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) )
      = ( ( X2 != Y )
        & ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) ) ) ).

% distinct_adj_Cons_Cons
thf(fact_1142_successively_Osimps_I1_J,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o] : ( succes6989878846294031341c_fm_a @ P4 @ nil_Epistemic_fm_a ) ).

% successively.simps(1)
thf(fact_1143_successively_Oelims_I3_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
      ( ~ ( succes6989878846294031341c_fm_a @ X2 @ Xa )
     => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
            ( ( Xa
              = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
           => ( ( X2 @ X3 @ Y2 )
              & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ).

% successively.elims(3)
thf(fact_1144_successively_Osimps_I3_J,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) )
      = ( ( P4 @ X2 @ Y )
        & ( succes6989878846294031341c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) ) ) ).

% successively.simps(3)
thf(fact_1145_distinct__adj__ConsD,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
     => ( distin8123941861610682872c_fm_a @ Xs2 ) ) ).

% distinct_adj_ConsD
thf(fact_1146_distinct__adj__Nil,axiom,
    distin8123941861610682872c_fm_a @ nil_Epistemic_fm_a ).

% distinct_adj_Nil
thf(fact_1147_distinct__adj__mapD,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( distin8123941861610682872c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
     => ( distin8123941861610682872c_fm_a @ Xs2 ) ) ).

% distinct_adj_mapD
thf(fact_1148_successively__map,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ P4 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( succes6989878846294031341c_fm_a
        @ ^ [X: epistemic_fm_a,Y3: epistemic_fm_a] : ( P4 @ ( F @ X ) @ ( F @ Y3 ) )
        @ Xs2 ) ) ).

% successively_map
thf(fact_1149_successively_Oelims_I2_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ X2 @ Xa )
     => ( ( Xa != nil_Epistemic_fm_a )
       => ( ! [X3: epistemic_fm_a] :
              ( Xa
             != ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
         => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( Xa
                  = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
               => ~ ( ( X2 @ X3 @ Y2 )
                    & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ).

% successively.elims(2)
thf(fact_1150_successively_Oelims_I1_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a,Y: $o] :
      ( ( ( succes6989878846294031341c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Epistemic_fm_a )
         => ~ Y )
       => ( ( ? [X3: epistemic_fm_a] :
                ( Xa
                = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
           => ~ Y )
         => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( Xa
                  = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
               => ( Y
                  = ( ~ ( ( X2 @ X3 @ Y2 )
                        & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).

% successively.elims(1)
thf(fact_1151_successively_Osimps_I2_J,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a] : ( succes6989878846294031341c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ).

% successively.simps(2)
thf(fact_1152_distinct__adj__singleton,axiom,
    ! [X2: epistemic_fm_a] : ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ).

% distinct_adj_singleton
thf(fact_1153_successively__Cons,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        | ( ( P4 @ X2 @ ( hd_Epistemic_fm_a @ Xs2 ) )
          & ( succes6989878846294031341c_fm_a @ P4 @ Xs2 ) ) ) ) ).

% successively_Cons
thf(fact_1154_distinct__adj__Cons,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( distin8123941861610682872c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        | ( ( X2
           != ( hd_Epistemic_fm_a @ Xs2 ) )
          & ( distin8123941861610682872c_fm_a @ Xs2 ) ) ) ) ).

% distinct_adj_Cons
thf(fact_1155_Cons__in__shuffles__iff,axiom,
    ! [Z5: epistemic_fm_a,Zs3: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Z5 @ Zs3 ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) )
      = ( ( ( Xs2 != nil_Epistemic_fm_a )
          & ( ( hd_Epistemic_fm_a @ Xs2 )
            = Z5 )
          & ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ ( tl_Epistemic_fm_a @ Xs2 ) @ Ys ) ) )
        | ( ( Ys != nil_Epistemic_fm_a )
          & ( ( hd_Epistemic_fm_a @ Ys )
            = Z5 )
          & ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs2 @ ( tl_Epistemic_fm_a @ Ys ) ) ) ) ) ) ).

% Cons_in_shuffles_iff
thf(fact_1156_Nil__in__shuffles,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        & ( Ys = nil_Epistemic_fm_a ) ) ) ).

% Nil_in_shuffles
thf(fact_1157_list_Oset__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,V: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( map_Ep7084560364594560580c_fm_a @ F @ V ) )
      = ( image_4449434806354059013c_fm_a @ F @ ( set_Epistemic_fm_a2 @ V ) ) ) ).

% list.set_map
thf(fact_1158_Cons__in__shuffles__rightI,axiom,
    ! [Zs3: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Z5: epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) )
     => ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Z5 @ Zs3 ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Z5 @ Ys ) ) ) ) ).

% Cons_in_shuffles_rightI
thf(fact_1159_Cons__in__shuffles__leftI,axiom,
    ! [Zs3: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,Z5: epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) )
     => ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ Z5 @ Zs3 ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ Z5 @ Xs2 ) @ Ys ) ) ) ).

% Cons_in_shuffles_leftI
thf(fact_1160_Nil__in__shufflesI,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( Xs2 = nil_Epistemic_fm_a )
     => ( ( Ys = nil_Epistemic_fm_a )
       => ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) ) ) ) ).

% Nil_in_shufflesI
thf(fact_1161_image__set,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( image_4449434806354059013c_fm_a @ F @ ( set_Epistemic_fm_a2 @ Xs2 ) )
      = ( set_Epistemic_fm_a2 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) ) ) ).

% image_set
thf(fact_1162_shufflesE,axiom,
    ! [Zs3: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ Zs3 @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) )
     => ( ( ( Zs3 = Xs2 )
         => ( Ys != nil_Epistemic_fm_a ) )
       => ( ( ( Zs3 = Ys )
           => ( Xs2 != nil_Epistemic_fm_a ) )
         => ( ! [X3: epistemic_fm_a,Xs4: list_Epistemic_fm_a] :
                ( ( Xs2
                  = ( cons_Epistemic_fm_a @ X3 @ Xs4 ) )
               => ! [Z2: epistemic_fm_a,Zs4: list_Epistemic_fm_a] :
                    ( ( Zs3
                      = ( cons_Epistemic_fm_a @ Z2 @ Zs4 ) )
                   => ( ( X3 = Z2 )
                     => ~ ( member5906877432388582473c_fm_a @ Zs4 @ ( shuffl511019022169630517c_fm_a @ Xs4 @ Ys ) ) ) ) )
           => ~ ! [Y2: epistemic_fm_a,Ys5: list_Epistemic_fm_a] :
                  ( ( Ys
                    = ( cons_Epistemic_fm_a @ Y2 @ Ys5 ) )
                 => ! [Z2: epistemic_fm_a,Zs4: list_Epistemic_fm_a] :
                      ( ( Zs3
                        = ( cons_Epistemic_fm_a @ Z2 @ Zs4 ) )
                     => ( ( Y2 = Z2 )
                       => ~ ( member5906877432388582473c_fm_a @ Zs4 @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys5 ) ) ) ) ) ) ) ) ) ).

% shufflesE
thf(fact_1163_Cons__shuffles__subset1,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys ) ) ).

% Cons_shuffles_subset1
thf(fact_1164_Cons__shuffles__subset2,axiom,
    ! [Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] : ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ Ys ) ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) ).

% Cons_shuffles_subset2
thf(fact_1165_rev__conv__fold,axiom,
    ( rev_Epistemic_fm_a
    = ( ^ [Xs: list_Epistemic_fm_a] : ( fold_E7642651028368403345c_fm_a @ cons_Epistemic_fm_a @ Xs @ nil_Epistemic_fm_a ) ) ) ).

% rev_conv_fold
thf(fact_1166_fold__Cons__rev,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( fold_E7642651028368403345c_fm_a @ cons_Epistemic_fm_a @ Xs2 )
      = ( append9179727413925872949c_fm_a @ ( rev_Epistemic_fm_a @ Xs2 ) ) ) ).

% fold_Cons_rev
thf(fact_1167_map__lists__mono,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ord_le3275665582123262618c_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) @ B2 )
     => ( ord_le2931979837777675552c_fm_a @ ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) ) @ ( lists_Epistemic_fm_a @ B2 ) ) ) ).

% map_lists_mono
thf(fact_1168_Cons__in__lists__iff,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( lists_Epistemic_fm_a @ A ) )
      = ( ( member6642669571620171971c_fm_a @ X2 @ A )
        & ( member5906877432388582473c_fm_a @ Xs2 @ ( lists_Epistemic_fm_a @ A ) ) ) ) ).

% Cons_in_lists_iff
thf(fact_1169_Nil__in__lists,axiom,
    ! [A: set_Epistemic_fm_a] : ( member5906877432388582473c_fm_a @ nil_Epistemic_fm_a @ ( lists_Epistemic_fm_a @ A ) ) ).

% Nil_in_lists
thf(fact_1170_lists_OCons,axiom,
    ! [A2: epistemic_fm_a,A: set_Epistemic_fm_a,L: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ A )
     => ( ( member5906877432388582473c_fm_a @ L @ ( lists_Epistemic_fm_a @ A ) )
       => ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ A2 @ L ) @ ( lists_Epistemic_fm_a @ A ) ) ) ) ).

% lists.Cons
thf(fact_1171_listsE,axiom,
    ! [X2: epistemic_fm_a,L: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ L ) @ ( lists_Epistemic_fm_a @ A ) )
     => ~ ( ( member6642669571620171971c_fm_a @ X2 @ A )
         => ~ ( member5906877432388582473c_fm_a @ L @ ( lists_Epistemic_fm_a @ A ) ) ) ) ).

% listsE
thf(fact_1172_lists_Ocases,axiom,
    ! [A2: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ A2 @ ( lists_Epistemic_fm_a @ A ) )
     => ( ( A2 != nil_Epistemic_fm_a )
       => ~ ! [A5: epistemic_fm_a,L2: list_Epistemic_fm_a] :
              ( ( A2
                = ( cons_Epistemic_fm_a @ A5 @ L2 ) )
             => ( ( member6642669571620171971c_fm_a @ A5 @ A )
               => ~ ( member5906877432388582473c_fm_a @ L2 @ ( lists_Epistemic_fm_a @ A ) ) ) ) ) ) ).

% lists.cases
thf(fact_1173_lists_Osimps,axiom,
    ! [A2: list_Epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( member5906877432388582473c_fm_a @ A2 @ ( lists_Epistemic_fm_a @ A ) )
      = ( ( A2 = nil_Epistemic_fm_a )
        | ? [A4: epistemic_fm_a,L3: list_Epistemic_fm_a] :
            ( ( A2
              = ( cons_Epistemic_fm_a @ A4 @ L3 ) )
            & ( member6642669571620171971c_fm_a @ A4 @ A )
            & ( member5906877432388582473c_fm_a @ L3 @ ( lists_Epistemic_fm_a @ A ) ) ) ) ) ).

% lists.simps
thf(fact_1174_map__lists__surjective,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a,B2: set_Epistemic_fm_a] :
      ( ( ( image_4449434806354059013c_fm_a @ F @ A )
        = B2 )
     => ( ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) )
        = ( lists_Epistemic_fm_a @ B2 ) ) ) ).

% map_lists_surjective
thf(fact_1175_lists__image,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( lists_Epistemic_fm_a @ ( image_4449434806354059013c_fm_a @ F @ A ) )
      = ( image_7387318756023638021c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) ) ) ).

% lists_image
thf(fact_1176_concat__conv__foldr,axiom,
    ( concat2780896542826320603c_fm_a
    = ( ^ [Xss3: list_l6083326122719238310c_fm_a] : ( foldr_4993282926644240039c_fm_a @ append9179727413925872949c_fm_a @ Xss3 @ nil_Epistemic_fm_a ) ) ) ).

% concat_conv_foldr
thf(fact_1177_sorted__wrt_Ocases,axiom,
    ! [X2: produc7493720319326827993c_fm_a] :
      ( ! [P7: epistemic_fm_a > epistemic_fm_a > $o] :
          ( X2
         != ( produc2047528423811058377c_fm_a @ P7 @ nil_Epistemic_fm_a ) )
     => ~ ! [P7: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
            ( X2
           != ( produc2047528423811058377c_fm_a @ P7 @ ( cons_Epistemic_fm_a @ X3 @ Ys2 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_1178_successively_Ocases,axiom,
    ! [X2: produc7493720319326827993c_fm_a] :
      ( ! [P7: epistemic_fm_a > epistemic_fm_a > $o] :
          ( X2
         != ( produc2047528423811058377c_fm_a @ P7 @ nil_Epistemic_fm_a ) )
     => ( ! [P7: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a] :
            ( X2
           != ( produc2047528423811058377c_fm_a @ P7 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) )
       => ~ ! [P7: epistemic_fm_a > epistemic_fm_a > $o,X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( X2
             != ( produc2047528423811058377c_fm_a @ P7 @ ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_1179_successively_Opelims_I1_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a,Y: $o] :
      ( ( ( succes6989878846294031341c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ Xa ) )
       => ( ( ( Xa = nil_Epistemic_fm_a )
           => ( Y
             => ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) )
         => ( ! [X3: epistemic_fm_a] :
                ( ( Xa
                  = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
               => ( Y
                 => ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) ) )
           => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                  ( ( Xa
                    = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
                 => ( ( Y
                      = ( ( X2 @ X3 @ Y2 )
                        & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) )
                   => ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ) ).

% successively.pelims(1)
thf(fact_1180_successively_Opelims_I2_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
      ( ( succes6989878846294031341c_fm_a @ X2 @ Xa )
     => ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ Xa ) )
       => ( ( ( Xa = nil_Epistemic_fm_a )
           => ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ nil_Epistemic_fm_a ) ) )
         => ( ! [X3: epistemic_fm_a] :
                ( ( Xa
                  = ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) )
               => ~ ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ X3 @ nil_Epistemic_fm_a ) ) ) )
           => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                  ( ( Xa
                    = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
                 => ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) )
                   => ~ ( ( X2 @ X3 @ Y2 )
                        & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ) ) ).

% successively.pelims(2)
thf(fact_1181_shuffles_Ocases,axiom,
    ! [X2: produc5756089960658898087c_fm_a] :
      ( ! [Ys2: list_Epistemic_fm_a] :
          ( X2
         != ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
     => ( ! [Xs3: list_Epistemic_fm_a] :
            ( X2
           != ( produc6057521592714631063c_fm_a @ Xs3 @ nil_Epistemic_fm_a ) )
       => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
              ( X2
             != ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) ) ) ) ).

% shuffles.cases
thf(fact_1182_splice_Ocases,axiom,
    ! [X2: produc5756089960658898087c_fm_a] :
      ( ! [Ys2: list_Epistemic_fm_a] :
          ( X2
         != ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
     => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
            ( X2
           != ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 ) ) ) ).

% splice.cases
thf(fact_1183_successively_Opelims_I3_J,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a > $o,Xa: list_Epistemic_fm_a] :
      ( ~ ( succes6989878846294031341c_fm_a @ X2 @ Xa )
     => ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ Xa ) )
       => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( Xa
                = ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) )
             => ( ( accp_P8153917284782618338c_fm_a @ succes1799848765894333516c_fm_a @ ( produc2047528423811058377c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ X3 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) )
               => ( ( X2 @ X3 @ Y2 )
                  & ( succes6989878846294031341c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y2 @ Xs3 ) ) ) ) ) ) ) ).

% successively.pelims(3)
thf(fact_1184_map__tailrec__rev_Opelims,axiom,
    ! [X2: epistemic_fm_a > epistemic_fm_a,Xa: list_Epistemic_fm_a,Xb: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( map_ta6565535454553546997c_fm_a @ X2 @ Xa @ Xb )
        = Y )
     => ( ( accp_P3999429264564614062c_fm_a @ map_ta8878590677389437508c_fm_a @ ( produc7072357272616189097c_fm_a @ X2 @ ( produc6057521592714631063c_fm_a @ Xa @ Xb ) ) )
       => ( ( ( Xa = nil_Epistemic_fm_a )
           => ( ( Y = Xb )
             => ~ ( accp_P3999429264564614062c_fm_a @ map_ta8878590677389437508c_fm_a @ ( produc7072357272616189097c_fm_a @ X2 @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xb ) ) ) ) )
         => ~ ! [A5: epistemic_fm_a,As: list_Epistemic_fm_a] :
                ( ( Xa
                  = ( cons_Epistemic_fm_a @ A5 @ As ) )
               => ( ( Y
                    = ( map_ta6565535454553546997c_fm_a @ X2 @ As @ ( cons_Epistemic_fm_a @ ( X2 @ A5 ) @ Xb ) ) )
                 => ~ ( accp_P3999429264564614062c_fm_a @ map_ta8878590677389437508c_fm_a @ ( produc7072357272616189097c_fm_a @ X2 @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ A5 @ As ) @ Xb ) ) ) ) ) ) ) ) ).

% map_tailrec_rev.pelims
thf(fact_1185_splice_Opinduct,axiom,
    ! [A0: list_Epistemic_fm_a,A12: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > list_Epistemic_fm_a > $o] :
      ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ A0 @ A12 ) )
     => ( ! [Ys2: list_Epistemic_fm_a] :
            ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
           => ( P4 @ nil_Epistemic_fm_a @ Ys2 ) )
       => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
              ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 ) )
             => ( ( P4 @ Ys2 @ Xs3 )
               => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 ) ) )
         => ( P4 @ A0 @ A12 ) ) ) ) ).

% splice.pinduct
thf(fact_1186_snoc__listrel1__snoc__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,X2: epistemic_fm_a,Ys: list_Epistemic_fm_a,Y: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( append9179727413925872949c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) @ ( append9179727413925872949c_fm_a @ Ys @ ( cons_Epistemic_fm_a @ Y @ nil_Epistemic_fm_a ) ) ) @ ( listre1262483926937514105c_fm_a @ R ) )
      = ( ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) )
          & ( X2 = Y ) )
        | ( ( Xs2 = Ys )
          & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y ) @ R ) ) ) ) ).

% snoc_listrel1_snoc_iff
thf(fact_1187_shuffles_Opinduct,axiom,
    ! [A0: list_Epistemic_fm_a,A12: list_Epistemic_fm_a,P4: list_Epistemic_fm_a > list_Epistemic_fm_a > $o] :
      ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ A0 @ A12 ) )
     => ( ! [Ys2: list_Epistemic_fm_a] :
            ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys2 ) )
           => ( P4 @ nil_Epistemic_fm_a @ Ys2 ) )
       => ( ! [Xs3: list_Epistemic_fm_a] :
              ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs3 @ nil_Epistemic_fm_a ) )
             => ( P4 @ Xs3 @ nil_Epistemic_fm_a ) )
         => ( ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a,Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) )
               => ( ( P4 @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                 => ( ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 )
                   => ( P4 @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) ) ) )
           => ( P4 @ A0 @ A12 ) ) ) ) ) ).

% shuffles.pinduct
thf(fact_1188_Cons__listrel1__Cons,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) @ ( listre1262483926937514105c_fm_a @ R ) )
      = ( ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y ) @ R )
          & ( Xs2 = Ys ) )
        | ( ( X2 = Y )
          & ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ) ) ).

% Cons_listrel1_Cons
thf(fact_1189_listrel1I2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,X2: epistemic_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) )
     => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ X2 @ Ys ) ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ).

% listrel1I2
thf(fact_1190_not__listrel1__Nil,axiom,
    ! [Xs2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ nil_Epistemic_fm_a ) @ ( listre1262483926937514105c_fm_a @ R ) ) ).

% not_listrel1_Nil
thf(fact_1191_not__Nil__listrel1,axiom,
    ! [Xs2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xs2 ) @ ( listre1262483926937514105c_fm_a @ R ) ) ).

% not_Nil_listrel1
thf(fact_1192_Cons__listrel1E2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) @ ( listre1262483926937514105c_fm_a @ R ) )
     => ( ! [X3: epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ X3 @ Ys ) )
           => ~ ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X3 @ Y ) @ R ) )
       => ~ ! [Zs2: list_Epistemic_fm_a] :
              ( ( Xs2
                = ( cons_Epistemic_fm_a @ Y @ Zs2 ) )
             => ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Zs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ) ) ).

% Cons_listrel1E2
thf(fact_1193_Cons__listrel1E1,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) )
     => ( ! [Y2: epistemic_fm_a] :
            ( ( Ys
              = ( cons_Epistemic_fm_a @ Y2 @ Xs2 ) )
           => ~ ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y2 ) @ R ) )
       => ~ ! [Zs2: list_Epistemic_fm_a] :
              ( ( Ys
                = ( cons_Epistemic_fm_a @ X2 @ Zs2 ) )
             => ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Zs2 ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ) ) ).

% Cons_listrel1E1
thf(fact_1194_listrel1I1,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y ) @ R )
     => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ).

% listrel1I1
thf(fact_1195_listrel1E,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) )
     => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a] :
            ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X3 @ Y2 ) @ R )
           => ! [Us3: list_Epistemic_fm_a,Vs2: list_Epistemic_fm_a] :
                ( ( Xs2
                  = ( append9179727413925872949c_fm_a @ Us3 @ ( cons_Epistemic_fm_a @ X3 @ Vs2 ) ) )
               => ( Ys
                 != ( append9179727413925872949c_fm_a @ Us3 @ ( cons_Epistemic_fm_a @ Y2 @ Vs2 ) ) ) ) ) ) ).

% listrel1E
thf(fact_1196_listrel1I,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,Xs2: list_Epistemic_fm_a,Us: list_Epistemic_fm_a,Vs3: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y ) @ R )
     => ( ( Xs2
          = ( append9179727413925872949c_fm_a @ Us @ ( cons_Epistemic_fm_a @ X2 @ Vs3 ) ) )
       => ( ( Ys
            = ( append9179727413925872949c_fm_a @ Us @ ( cons_Epistemic_fm_a @ Y @ Vs3 ) ) )
         => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1262483926937514105c_fm_a @ R ) ) ) ) ) ).

% listrel1I
thf(fact_1197_splice_Opelims,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( splice5109564810699471347c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ Xa ) )
       => ( ( ( X2 = nil_Epistemic_fm_a )
           => ( ( Y = Xa )
             => ~ ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xa ) ) ) )
         => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( X2
                  = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
               => ( ( Y
                    = ( cons_Epistemic_fm_a @ X3 @ ( splice5109564810699471347c_fm_a @ Xa @ Xs3 ) ) )
                 => ~ ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Xa ) ) ) ) ) ) ) ).

% splice.pelims
thf(fact_1198_splice_Opsimps_I1_J,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys ) )
     => ( ( splice5109564810699471347c_fm_a @ nil_Epistemic_fm_a @ Ys )
        = Ys ) ) ).

% splice.psimps(1)
thf(fact_1199_splice_Opsimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ splice3620800875729116614c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys ) )
     => ( ( splice5109564810699471347c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys )
        = ( cons_Epistemic_fm_a @ X2 @ ( splice5109564810699471347c_fm_a @ Ys @ Xs2 ) ) ) ) ).

% splice.psimps(2)
thf(fact_1200_split__Nil__iff,axiom,
    ! [Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( splice5109564810699471347c_fm_a @ Xs2 @ Ys )
        = nil_Epistemic_fm_a )
      = ( ( Xs2 = nil_Epistemic_fm_a )
        & ( Ys = nil_Epistemic_fm_a ) ) ) ).

% split_Nil_iff
thf(fact_1201_splice__Nil2,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( splice5109564810699471347c_fm_a @ Xs2 @ nil_Epistemic_fm_a )
      = Xs2 ) ).

% splice_Nil2
thf(fact_1202_splice_Osimps_I1_J,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( splice5109564810699471347c_fm_a @ nil_Epistemic_fm_a @ Ys )
      = Ys ) ).

% splice.simps(1)
thf(fact_1203_splice_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( splice5109564810699471347c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys )
      = ( cons_Epistemic_fm_a @ X2 @ ( splice5109564810699471347c_fm_a @ Ys @ Xs2 ) ) ) ).

% splice.simps(2)
thf(fact_1204_splice_Oelims,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( ( splice5109564810699471347c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( ( X2 = nil_Epistemic_fm_a )
         => ( Y != Xa ) )
       => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( X2
                = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
             => ( Y
               != ( cons_Epistemic_fm_a @ X3 @ ( splice5109564810699471347c_fm_a @ Xa @ Xs3 ) ) ) ) ) ) ).

% splice.elims
thf(fact_1205_shuffles_Opsimps_I3_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) )
     => ( ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) )
        = ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys ) ) ) ) ) ).

% shuffles.psimps(3)
thf(fact_1206_lexord__append__left__rightI,axiom,
    ! [A2: epistemic_fm_a,B: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,U: list_Epistemic_fm_a,X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B ) @ R )
     => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( append9179727413925872949c_fm_a @ U @ ( cons_Epistemic_fm_a @ A2 @ X2 ) ) @ ( append9179727413925872949c_fm_a @ U @ ( cons_Epistemic_fm_a @ B @ Y ) ) ) @ ( lexord7736047576645873805c_fm_a @ R ) ) ) ).

% lexord_append_left_rightI
thf(fact_1207_lexord__cons__cons,axiom,
    ! [A2: epistemic_fm_a,X2: list_Epistemic_fm_a,B: epistemic_fm_a,Y: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ A2 @ X2 ) @ ( cons_Epistemic_fm_a @ B @ Y ) ) @ ( lexord7736047576645873805c_fm_a @ R ) )
      = ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ A2 @ B ) @ R )
        | ( ( A2 = B )
          & ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ Y ) @ ( lexord7736047576645873805c_fm_a @ R ) ) ) ) ) ).

% lexord_cons_cons
thf(fact_1208_lexord__Nil__left,axiom,
    ! [Y: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Y ) @ ( lexord7736047576645873805c_fm_a @ R ) )
      = ( ? [A4: epistemic_fm_a,X: list_Epistemic_fm_a] :
            ( Y
            = ( cons_Epistemic_fm_a @ A4 @ X ) ) ) ) ).

% lexord_Nil_left
thf(fact_1209_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_1210_fm_Osimps_I93_J,axiom,
    ! [X41: epistemic_fm_a,X42: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_Con_a @ X41 @ X42 ) )
      = ( sup_sup_set_a @ ( epistemic_set_fm_a @ X41 ) @ ( epistemic_set_fm_a @ X42 ) ) ) ).

% fm.simps(93)
thf(fact_1211_lexord__Nil__right,axiom,
    ! [X2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ nil_Epistemic_fm_a ) @ ( lexord7736047576645873805c_fm_a @ R ) ) ).

% lexord_Nil_right
thf(fact_1212_shuffles_Osimps_I3_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) )
      = ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X2 ) @ ( shuffl511019022169630517c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ Ys ) ) ) ) ).

% shuffles.simps(3)
thf(fact_1213_lexord__append__rightI,axiom,
    ! [Y: list_Epistemic_fm_a,X2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ? [B4: epistemic_fm_a,Z3: list_Epistemic_fm_a] :
          ( Y
          = ( cons_Epistemic_fm_a @ B4 @ Z3 ) )
     => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ ( append9179727413925872949c_fm_a @ X2 @ Y ) ) @ ( lexord7736047576645873805c_fm_a @ R ) ) ) ).

% lexord_append_rightI
thf(fact_1214_shuffles_Opelims,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: set_li769143395467472256c_fm_a] :
      ( ( ( shuffl511019022169630517c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ Xa ) )
       => ( ( ( X2 = nil_Epistemic_fm_a )
           => ( ( Y
                = ( insert6567282714061225712c_fm_a @ Xa @ bot_bo8284763806281179116c_fm_a ) )
             => ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xa ) ) ) )
         => ( ( ( Xa = nil_Epistemic_fm_a )
             => ( ( Y
                  = ( insert6567282714061225712c_fm_a @ X2 @ bot_bo8284763806281179116c_fm_a ) )
               => ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ) )
           => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                  ( ( X2
                    = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
                 => ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                      ( ( Xa
                        = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                     => ( ( Y
                          = ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X3 ) @ ( shuffl511019022169630517c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y2 ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 ) ) ) )
                       => ~ ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) ) ) ) ) ) ) ) ) ).

% shuffles.pelims
thf(fact_1215_set__empty,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( ( set_Epistemic_fm_a2 @ Xs2 )
        = bot_bo3626323581529592678c_fm_a )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% set_empty
thf(fact_1216_set__empty2,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( bot_bo3626323581529592678c_fm_a
        = ( set_Epistemic_fm_a2 @ Xs2 ) )
      = ( Xs2 = nil_Epistemic_fm_a ) ) ).

% set_empty2
thf(fact_1217_list_Osimps_I15_J,axiom,
    ! [X21: epistemic_fm_a,X22: list_Epistemic_fm_a] :
      ( ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X21 @ X22 ) )
      = ( insert7817948963269374698c_fm_a @ X21 @ ( set_Epistemic_fm_a2 @ X22 ) ) ) ).

% list.simps(15)
thf(fact_1218_fm_Osimps_I95_J,axiom,
    ! [X61: a,X62: epistemic_fm_a] :
      ( ( epistemic_set_fm_a @ ( epistemic_K_a @ X61 @ X62 ) )
      = ( insert_a2 @ X61 @ ( epistemic_set_fm_a @ X62 ) ) ) ).

% fm.simps(95)
thf(fact_1219_lists__empty,axiom,
    ( ( lists_Epistemic_fm_a @ bot_bo3626323581529592678c_fm_a )
    = ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) ) ).

% lists_empty
thf(fact_1220_shuffles_Osimps_I1_J,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( shuffl511019022169630517c_fm_a @ nil_Epistemic_fm_a @ Ys )
      = ( insert6567282714061225712c_fm_a @ Ys @ bot_bo8284763806281179116c_fm_a ) ) ).

% shuffles.simps(1)
thf(fact_1221_shuffles_Osimps_I2_J,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( shuffl511019022169630517c_fm_a @ Xs2 @ nil_Epistemic_fm_a )
      = ( insert6567282714061225712c_fm_a @ Xs2 @ bot_bo8284763806281179116c_fm_a ) ) ).

% shuffles.simps(2)
thf(fact_1222_Pow__set_I2_J,axiom,
    ! [X2: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) ) )
      = ( sup_su4305657963326700718c_fm_a @ ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) ) @ ( image_8582343580727714565c_fm_a @ ( insert7817948963269374698c_fm_a @ X2 ) @ ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) ) ) ) ) ).

% Pow_set(2)
thf(fact_1223_empty__set,axiom,
    ( bot_bo3626323581529592678c_fm_a
    = ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) ) ).

% empty_set
thf(fact_1224_shuffles_Opsimps_I1_J,axiom,
    ! [Ys: list_Epistemic_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Ys ) )
     => ( ( shuffl511019022169630517c_fm_a @ nil_Epistemic_fm_a @ Ys )
        = ( insert6567282714061225712c_fm_a @ Ys @ bot_bo8284763806281179116c_fm_a ) ) ) ).

% shuffles.psimps(1)
thf(fact_1225_shuffles_Opsimps_I2_J,axiom,
    ! [Xs2: list_Epistemic_fm_a] :
      ( ( accp_P1207204058359408560c_fm_a @ shuffl1320156749143720708c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ nil_Epistemic_fm_a ) )
     => ( ( shuffl511019022169630517c_fm_a @ Xs2 @ nil_Epistemic_fm_a )
        = ( insert6567282714061225712c_fm_a @ Xs2 @ bot_bo8284763806281179116c_fm_a ) ) ) ).

% shuffles.psimps(2)
thf(fact_1226_shuffles_Oelims,axiom,
    ! [X2: list_Epistemic_fm_a,Xa: list_Epistemic_fm_a,Y: set_li769143395467472256c_fm_a] :
      ( ( ( shuffl511019022169630517c_fm_a @ X2 @ Xa )
        = Y )
     => ( ( ( X2 = nil_Epistemic_fm_a )
         => ( Y
           != ( insert6567282714061225712c_fm_a @ Xa @ bot_bo8284763806281179116c_fm_a ) ) )
       => ( ( ( Xa = nil_Epistemic_fm_a )
           => ( Y
             != ( insert6567282714061225712c_fm_a @ X2 @ bot_bo8284763806281179116c_fm_a ) ) )
         => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
                ( ( X2
                  = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
               => ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
                    ( ( Xa
                      = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                   => ( Y
                     != ( sup_su1755902861286427476c_fm_a @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ X3 ) @ ( shuffl511019022169630517c_fm_a @ Xs3 @ ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) ) ) @ ( image_7387318756023638021c_fm_a @ ( cons_Epistemic_fm_a @ Y2 ) @ ( shuffl511019022169630517c_fm_a @ ( cons_Epistemic_fm_a @ X3 @ Xs3 ) @ Ys2 ) ) ) ) ) ) ) ) ) ).

% shuffles.elims
thf(fact_1227_partition_Osimps_I1_J,axiom,
    ! [P4: epistemic_fm_a > $o] :
      ( ( partit1738664135152837401c_fm_a @ P4 @ nil_Epistemic_fm_a )
      = ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) ) ).

% partition.simps(1)
thf(fact_1228_set__Cons__sing__Nil,axiom,
    ! [A: set_Epistemic_fm_a] :
      ( ( set_Co4868574198862222544c_fm_a @ A @ ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) )
      = ( image_4430763730358542731c_fm_a
        @ ^ [X: epistemic_fm_a] : ( cons_Epistemic_fm_a @ X @ nil_Epistemic_fm_a )
        @ A ) ) ).

% set_Cons_sing_Nil
thf(fact_1229_listset_Osimps_I1_J,axiom,
    ( ( listse5025355581707466111c_fm_a @ nil_se102576565402781184c_fm_a )
    = ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) ) ).

% listset.simps(1)
thf(fact_1230_consistent__consequent_H,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ( member6642669571620171971c_fm_a @ P @ V2 )
       => ( ! [G4: list_char > $o,H4: epistemic_fm_a > $o] : ( epistemic_eval_a @ G4 @ H4 @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V2 ) ) ) ) ) ).

% consistent_consequent'
thf(fact_1231_consistent__consequent,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a,Q: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ( member6642669571620171971c_fm_a @ P @ V2 )
       => ( ( epistemic_AK_a @ A @ ( epistemic_Imp_a @ P @ Q ) )
         => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ Q @ bot_bo3626323581529592678c_fm_a ) @ V2 ) ) ) ) ) ).

% consistent_consequent
thf(fact_1232_inconsistent__imply,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,G5: list_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ ( set_Epistemic_fm_a2 @ G5 ) ) )
     => ( epistemic_AK_a @ A @ ( epistemic_imply_a @ G5 @ P ) ) ) ).

% inconsistent_imply
thf(fact_1233_inconsistent__subset,axiom,
    ! [A: epistemic_fm_a > $o,V2: set_Epistemic_fm_a,P: epistemic_fm_a] :
      ( ( episte2285483198712856226tent_a @ A @ V2 )
     => ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ P @ bot_bo3626323581529592678c_fm_a ) @ V2 ) )
       => ~ ! [V3: list_Epistemic_fm_a] :
              ( ( ord_le3275665582123262618c_fm_a @ ( set_Epistemic_fm_a2 @ V3 ) @ V2 )
             => ~ ( epistemic_AK_a @ A @ ( epistemic_imply_a @ ( cons_Epistemic_fm_a @ P @ V3 ) @ epistemic_FF_a ) ) ) ) ) ).

% inconsistent_subset
thf(fact_1234_Pow__set_I1_J,axiom,
    ( ( pow_Epistemic_fm_a @ ( set_Epistemic_fm_a2 @ nil_Epistemic_fm_a ) )
    = ( insert7129737658439086282c_fm_a @ bot_bo3626323581529592678c_fm_a @ bot_bo1868452413526482246c_fm_a ) ) ).

% Pow_set(1)
thf(fact_1235_List_Omap_Ocomp,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( comp_l5131143140338395773c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( map_Ep7084560364594560580c_fm_a @ G3 ) )
      = ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G3 ) ) ) ).

% List.map.comp
thf(fact_1236_map__comp__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a] :
      ( ( comp_l5131143140338395773c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( map_Ep7084560364594560580c_fm_a @ G3 ) )
      = ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G3 ) ) ) ).

% map_comp_map
thf(fact_1237_list_Omap__comp,axiom,
    ! [G3: epistemic_fm_a > epistemic_fm_a,F: epistemic_fm_a > epistemic_fm_a,V: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ G3 @ ( map_Ep7084560364594560580c_fm_a @ F @ V ) )
      = ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ G3 @ F ) @ V ) ) ).

% list.map_comp
thf(fact_1238_List_Omap_Ocompositionality,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a,List: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( map_Ep7084560364594560580c_fm_a @ G3 @ List ) )
      = ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G3 ) @ List ) ) ).

% List.map.compositionality
thf(fact_1239_map__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,G3: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( map_Ep7084560364594560580c_fm_a @ F @ ( map_Ep7084560364594560580c_fm_a @ G3 @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ ( comp_E612253880081530103c_fm_a @ F @ G3 ) @ Xs2 ) ) ).

% map_map
thf(fact_1240_exists__finite__inconsistent,axiom,
    ! [A: epistemic_fm_a > $o,P: epistemic_fm_a,V2: set_Epistemic_fm_a] :
      ( ~ ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V2 ) )
     => ~ ! [W2: set_Epistemic_fm_a] :
            ( ( ord_le3275665582123262618c_fm_a @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W2 ) @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ V2 ) )
           => ( ~ ( member6642669571620171971c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ W2 )
             => ( ( finite3304564945125563331c_fm_a @ W2 )
               => ( episte2285483198712856226tent_a @ A @ ( sup_su1367922730591523534c_fm_a @ ( insert7817948963269374698c_fm_a @ ( epistemic_Imp_a @ P @ epistemic_FF_a ) @ bot_bo3626323581529592678c_fm_a ) @ W2 ) ) ) ) ) ) ).

% exists_finite_inconsistent
thf(fact_1241_list_Opred__map,axiom,
    ! [Q4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,X2: list_Epistemic_fm_a] :
      ( ( list_a5841931967666341838c_fm_a @ Q4 @ ( map_Ep7084560364594560580c_fm_a @ F @ X2 ) )
      = ( list_a5841931967666341838c_fm_a @ ( comp_E2819036835534555897c_fm_a @ Q4 @ F ) @ X2 ) ) ).

% list.pred_map
thf(fact_1242_dropWhile__map,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( dropWh6715642967443873729c_fm_a @ P4 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ F @ ( dropWh6715642967443873729c_fm_a @ ( comp_E2819036835534555897c_fm_a @ P4 @ F ) @ Xs2 ) ) ) ).

% dropWhile_map
thf(fact_1243_filter__map,axiom,
    ! [P4: epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( filter7636273809395300631c_fm_a @ P4 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( map_Ep7084560364594560580c_fm_a @ F @ ( filter7636273809395300631c_fm_a @ ( comp_E2819036835534555897c_fm_a @ P4 @ F ) @ Xs2 ) ) ) ).

% filter_map
thf(fact_1244_listrel_ONil,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] : ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) @ ( listre1023041962361757425c_fm_a @ R ) ) ).

% listrel.Nil
thf(fact_1245_listrel__Nil1,axiom,
    ! [Xs2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ nil_Epistemic_fm_a @ Xs2 ) @ ( listre1023041962361757425c_fm_a @ R ) )
     => ( Xs2 = nil_Epistemic_fm_a ) ) ).

% listrel_Nil1
thf(fact_1246_listrel__Nil2,axiom,
    ! [Xs2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ nil_Epistemic_fm_a ) @ ( listre1023041962361757425c_fm_a @ R ) )
     => ( Xs2 = nil_Epistemic_fm_a ) ) ).

% listrel_Nil2
thf(fact_1247_listrel__Cons2,axiom,
    ! [Xs2: list_Epistemic_fm_a,Y: epistemic_fm_a,Ys: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) @ ( listre1023041962361757425c_fm_a @ R ) )
     => ~ ! [X3: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
           => ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X3 @ Y ) @ R )
             => ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs3 @ Ys ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ).

% listrel_Cons2
thf(fact_1248_listrel__Cons1,axiom,
    ! [Y: epistemic_fm_a,Ys: list_Epistemic_fm_a,Xs2: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ Y @ Ys ) @ Xs2 ) @ ( listre1023041962361757425c_fm_a @ R ) )
     => ~ ! [Y2: epistemic_fm_a,Ys2: list_Epistemic_fm_a] :
            ( ( Xs2
              = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
           => ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ Y @ Y2 ) @ R )
             => ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Ys @ Ys2 ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ).

% listrel_Cons1
thf(fact_1249_listrel_OCons,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X2 @ Y ) @ R )
     => ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs2 @ Ys ) @ ( listre1023041962361757425c_fm_a @ R ) )
       => ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ).

% listrel.Cons
thf(fact_1250_listrel_Ocases,axiom,
    ! [A12: list_Epistemic_fm_a,A23: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ A12 @ A23 ) @ ( listre1023041962361757425c_fm_a @ R ) )
     => ( ( ( A12 = nil_Epistemic_fm_a )
         => ( A23 != nil_Epistemic_fm_a ) )
       => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( A12
                = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
             => ! [Ys2: list_Epistemic_fm_a] :
                  ( ( A23
                    = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                 => ( ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X3 @ Y2 ) @ R )
                   => ~ ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs3 @ Ys2 ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ) ) ).

% listrel.cases
thf(fact_1251_listrel_Osimps,axiom,
    ! [A12: list_Epistemic_fm_a,A23: list_Epistemic_fm_a,R: set_Pr8948481099588399239c_fm_a] :
      ( ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ A12 @ A23 ) @ ( listre1023041962361757425c_fm_a @ R ) )
      = ( ( ( A12 = nil_Epistemic_fm_a )
          & ( A23 = nil_Epistemic_fm_a ) )
        | ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
            ( ( A12
              = ( cons_Epistemic_fm_a @ X @ Xs ) )
            & ( A23
              = ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) )
            & ( member5029746173879296720c_fm_a @ ( produc8582950737844404375c_fm_a @ X @ Y3 ) @ R )
            & ( member3265983909902097104c_fm_a @ ( produc6057521592714631063c_fm_a @ Xs @ Ys3 ) @ ( listre1023041962361757425c_fm_a @ R ) ) ) ) ) ).

% listrel.simps
thf(fact_1252_listrelp_ONil,axiom,
    ! [R: epistemic_fm_a > epistemic_fm_a > $o] : ( listre7830505053103709503c_fm_a @ R @ nil_Epistemic_fm_a @ nil_Epistemic_fm_a ) ).

% listrelp.Nil
thf(fact_1253_listrelp_OCons,axiom,
    ! [R: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( R @ X2 @ Y )
     => ( ( listre7830505053103709503c_fm_a @ R @ Xs2 @ Ys )
       => ( listre7830505053103709503c_fm_a @ R @ ( cons_Epistemic_fm_a @ X2 @ Xs2 ) @ ( cons_Epistemic_fm_a @ Y @ Ys ) ) ) ) ).

% listrelp.Cons
thf(fact_1254_listrelp_Ocases,axiom,
    ! [R: epistemic_fm_a > epistemic_fm_a > $o,A12: list_Epistemic_fm_a,A23: list_Epistemic_fm_a] :
      ( ( listre7830505053103709503c_fm_a @ R @ A12 @ A23 )
     => ( ( ( A12 = nil_Epistemic_fm_a )
         => ( A23 != nil_Epistemic_fm_a ) )
       => ~ ! [X3: epistemic_fm_a,Y2: epistemic_fm_a,Xs3: list_Epistemic_fm_a] :
              ( ( A12
                = ( cons_Epistemic_fm_a @ X3 @ Xs3 ) )
             => ! [Ys2: list_Epistemic_fm_a] :
                  ( ( A23
                    = ( cons_Epistemic_fm_a @ Y2 @ Ys2 ) )
                 => ( ( R @ X3 @ Y2 )
                   => ~ ( listre7830505053103709503c_fm_a @ R @ Xs3 @ Ys2 ) ) ) ) ) ) ).

% listrelp.cases
thf(fact_1255_listrelp_Osimps,axiom,
    ( listre7830505053103709503c_fm_a
    = ( ^ [R3: epistemic_fm_a > epistemic_fm_a > $o,A1: list_Epistemic_fm_a,A22: list_Epistemic_fm_a] :
          ( ( ( A1 = nil_Epistemic_fm_a )
            & ( A22 = nil_Epistemic_fm_a ) )
          | ? [X: epistemic_fm_a,Y3: epistemic_fm_a,Xs: list_Epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
              ( ( A1
                = ( cons_Epistemic_fm_a @ X @ Xs ) )
              & ( A22
                = ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) )
              & ( R3 @ X @ Y3 )
              & ( listre7830505053103709503c_fm_a @ R3 @ Xs @ Ys3 ) ) ) ) ) ).

% listrelp.simps
thf(fact_1256_listrel__Nil,axiom,
    ! [R: set_Pr8948481099588399239c_fm_a] :
      ( ( image_8549928002725978067c_fm_a @ ( listre1023041962361757425c_fm_a @ R ) @ ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) )
      = ( insert6567282714061225712c_fm_a @ nil_Epistemic_fm_a @ bot_bo8284763806281179116c_fm_a ) ) ).

% listrel_Nil
thf(fact_1257_removeAll_Osimps_I1_J,axiom,
    ! [X2: epistemic_fm_a] :
      ( ( remove817376121289147686c_fm_a @ X2 @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% removeAll.simps(1)
thf(fact_1258_removeAll_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( X2 = Y )
       => ( ( remove817376121289147686c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) )
          = ( remove817376121289147686c_fm_a @ X2 @ Xs2 ) ) )
      & ( ( X2 != Y )
       => ( ( remove817376121289147686c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) )
          = ( cons_Epistemic_fm_a @ Y @ ( remove817376121289147686c_fm_a @ X2 @ Xs2 ) ) ) ) ) ).

% removeAll.simps(2)
thf(fact_1259_remove1_Osimps_I2_J,axiom,
    ! [X2: epistemic_fm_a,Y: epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( ( X2 = Y )
       => ( ( remove8001893531712236214c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) )
          = Xs2 ) )
      & ( ( X2 != Y )
       => ( ( remove8001893531712236214c_fm_a @ X2 @ ( cons_Epistemic_fm_a @ Y @ Xs2 ) )
          = ( cons_Epistemic_fm_a @ Y @ ( remove8001893531712236214c_fm_a @ X2 @ Xs2 ) ) ) ) ) ).

% remove1.simps(2)
thf(fact_1260_remove1_Osimps_I1_J,axiom,
    ! [X2: epistemic_fm_a] :
      ( ( remove8001893531712236214c_fm_a @ X2 @ nil_Epistemic_fm_a )
      = nil_Epistemic_fm_a ) ).

% remove1.simps(1)
thf(fact_1261_remove1__split,axiom,
    ! [A2: epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( member6642669571620171971c_fm_a @ A2 @ ( set_Epistemic_fm_a2 @ Xs2 ) )
     => ( ( ( remove8001893531712236214c_fm_a @ A2 @ Xs2 )
          = Ys )
        = ( ? [Ls: list_Epistemic_fm_a,Rs: list_Epistemic_fm_a] :
              ( ( Xs2
                = ( append9179727413925872949c_fm_a @ Ls @ ( cons_Epistemic_fm_a @ A2 @ Rs ) ) )
              & ~ ( member6642669571620171971c_fm_a @ A2 @ ( set_Epistemic_fm_a2 @ Ls ) )
              & ( Ys
                = ( append9179727413925872949c_fm_a @ Ls @ Rs ) ) ) ) ) ) ).

% remove1_split
thf(fact_1262_sorted__wrt_Osimps_I1_J,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o] : ( sorted73444913887879815c_fm_a @ P4 @ nil_Epistemic_fm_a ) ).

% sorted_wrt.simps(1)
thf(fact_1263_sorted__wrt__map,axiom,
    ! [R2: epistemic_fm_a > epistemic_fm_a > $o,F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( sorted73444913887879815c_fm_a @ R2 @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( sorted73444913887879815c_fm_a
        @ ^ [X: epistemic_fm_a,Y3: epistemic_fm_a] : ( R2 @ ( F @ X ) @ ( F @ Y3 ) )
        @ Xs2 ) ) ).

% sorted_wrt_map
thf(fact_1264_sorted__wrt1,axiom,
    ! [P4: epistemic_fm_a > epistemic_fm_a > $o,X2: epistemic_fm_a] : ( sorted73444913887879815c_fm_a @ P4 @ ( cons_Epistemic_fm_a @ X2 @ nil_Epistemic_fm_a ) ) ).

% sorted_wrt1
thf(fact_1265_not__distinct__decomp,axiom,
    ! [Ws: list_Epistemic_fm_a] :
      ( ~ ( distin5379319156202237459c_fm_a @ Ws )
     => ? [Xs3: list_Epistemic_fm_a,Ys2: list_Epistemic_fm_a,Zs2: list_Epistemic_fm_a,Y2: epistemic_fm_a] :
          ( Ws
          = ( append9179727413925872949c_fm_a @ Xs3 @ ( append9179727413925872949c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ nil_Epistemic_fm_a ) @ ( append9179727413925872949c_fm_a @ Ys2 @ ( append9179727413925872949c_fm_a @ ( cons_Epistemic_fm_a @ Y2 @ nil_Epistemic_fm_a ) @ Zs2 ) ) ) ) ) ) ).

% not_distinct_decomp
thf(fact_1266_not__distinct__conv__prefix,axiom,
    ! [As2: list_Epistemic_fm_a] :
      ( ( ~ ( distin5379319156202237459c_fm_a @ As2 ) )
      = ( ? [Xs: list_Epistemic_fm_a,Y3: epistemic_fm_a,Ys3: list_Epistemic_fm_a] :
            ( ( member6642669571620171971c_fm_a @ Y3 @ ( set_Epistemic_fm_a2 @ Xs ) )
            & ( distin5379319156202237459c_fm_a @ Xs )
            & ( As2
              = ( append9179727413925872949c_fm_a @ Xs @ ( cons_Epistemic_fm_a @ Y3 @ Ys3 ) ) ) ) ) ) ).

% not_distinct_conv_prefix
thf(fact_1267_map__inj__on,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
        = ( map_Ep7084560364594560580c_fm_a @ F @ Ys ) )
     => ( ( inj_on1950397435265702513c_fm_a @ F @ ( sup_su1367922730591523534c_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) @ ( set_Epistemic_fm_a2 @ Ys ) ) )
       => ( Xs2 = Ys ) ) ) ).

% map_inj_on
thf(fact_1268_inj__on__map__eq__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a,Ys: list_Epistemic_fm_a] :
      ( ( inj_on1950397435265702513c_fm_a @ F @ ( sup_su1367922730591523534c_fm_a @ ( set_Epistemic_fm_a2 @ Xs2 ) @ ( set_Epistemic_fm_a2 @ Ys ) ) )
     => ( ( ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 )
          = ( map_Ep7084560364594560580c_fm_a @ F @ Ys ) )
        = ( Xs2 = Ys ) ) ) ).

% inj_on_map_eq_map
thf(fact_1269_inj__on__mapI,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_li769143395467472256c_fm_a] :
      ( ( inj_on1950397435265702513c_fm_a @ F @ ( comple7868773486375872231c_fm_a @ ( image_971165786557580383c_fm_a @ set_Epistemic_fm_a2 @ A ) ) )
     => ( inj_on6772092451049867121c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ A ) ) ).

% inj_on_mapI
thf(fact_1270_distinct_Osimps_I1_J,axiom,
    distin5379319156202237459c_fm_a @ nil_Epistemic_fm_a ).

% distinct.simps(1)
thf(fact_1271_inj__on__map__lists,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,A: set_Epistemic_fm_a] :
      ( ( inj_on1950397435265702513c_fm_a @ F @ A )
     => ( inj_on6772092451049867121c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F ) @ ( lists_Epistemic_fm_a @ A ) ) ) ).

% inj_on_map_lists
thf(fact_1272_distinct__map,axiom,
    ! [F: epistemic_fm_a > epistemic_fm_a,Xs2: list_Epistemic_fm_a] :
      ( ( distin5379319156202237459c_fm_a @ ( map_Ep7084560364594560580c_fm_a @ F @ Xs2 ) )
      = ( ( distin5379319156202237459c_fm_a @ Xs2 )
        & ( inj_on1950397435265702513c_fm_a @ F @ ( set_Epistemic_fm_a2 @ Xs2 ) ) ) ) ).

% distinct_map

% Helper facts (13)
thf(help_If_2_1_If_001t__List__Olist_Itf__a_J_T,axiom,
    ! [X2: list_a,Y: list_a] :
      ( ( if_list_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_Itf__a_J_T,axiom,
    ! [X2: list_a,Y: list_a] :
      ( ( if_list_a @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
    ! [X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( if_lis2878681784746929638c_fm_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_T,axiom,
    ! [X2: list_Epistemic_fm_a,Y: list_Epistemic_fm_a] :
      ( ( if_lis2878681784746929638c_fm_a @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
      ( ( if_lis3811715425919989702c_fm_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Set__Oset_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_s580375451141968640c_fm_a,Y: list_s580375451141968640c_fm_a] :
      ( ( if_lis3811715425919989702c_fm_a @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( if_lis342421823373228652c_fm_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_l6083326122719238310c_fm_a,Y: list_l6083326122719238310c_fm_a] :
      ( ( if_lis342421823373228652c_fm_a @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_P3099032918374241197c_fm_a,Y: list_P3099032918374241197c_fm_a] :
      ( ( if_lis4277834422595218803c_fm_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Epistemic____Logic__Ofm_Itf__a_J_Mt__Epistemic____Logic__Ofm_Itf__a_J_J_J_T,axiom,
    ! [X2: list_P3099032918374241197c_fm_a,Y: list_P3099032918374241197c_fm_a] :
      ( ( if_lis4277834422595218803c_fm_a @ $true @ X2 @ Y )
      = X2 ) ).

thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
    ! [P4: $o] :
      ( ( P4 = $true )
      | ( P4 = $false ) ) ).

thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
    ! [X2: list_P7917480606449584557c_fm_a,Y: list_P7917480606449584557c_fm_a] :
      ( ( if_lis974313005191179635c_fm_a @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_Mt__List__Olist_It__Epistemic____Logic__Ofm_Itf__a_J_J_J_J_T,axiom,
    ! [X2: list_P7917480606449584557c_fm_a,Y: list_P7917480606449584557c_fm_a] :
      ( ( if_lis974313005191179635c_fm_a @ $true @ X2 @ Y )
      = X2 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    epistemic_AK_a @ a2 @ ( epistemic_Imp_a @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( epistemic_K_a @ i @ ( stalnaker_conjunct_a @ ga ) ) ) @ ( epistemic_Con_a @ ( epistemic_K_a @ i @ a3 ) @ ( stalnaker_conjunct_a @ ( map_Ep7084560364594560580c_fm_a @ ( epistemic_K_a @ i ) @ ga ) ) ) ) ).

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