%------------------------------------------------------------------------------
% File     : ITP186^1 : TPTP v9.0.0. Released v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer Strong_Late_Sim_SC problem prob_570__3414234_1
% Version  : Especial.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : Strong_Late_Sim_SC/prob_570__3414234_1 [Des21]

% Status   : Theorem
% Rating   : 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% Syntax   : Number of formulae    :  500 ( 188 unt; 147 typ;   0 def)
%            Number of atoms       : 1166 ( 353 equ;   0 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives : 5562 ( 179   ~;  22   |;  43   &;4369   @)
%                                         (   0 <=>; 949  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (  10 avg)
%            Number of types       :   17 (  16 usr)
%            Number of type conns  : 1188 (1188   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  134 ( 131 usr;  15 con; 0-12 aty)
%            Number of variables   : 2021 (  59   ^;1940   !;  22   ?;2021   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Sledgehammer 2021-02-23 15:31:37.047
%------------------------------------------------------------------------------
% Could-be-implicit typings (16)
thf(ty_n_t__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J,type,
    noptio751120898ion_pi: $tType ).

thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J,type,
    noptio2087446135ion_pi: $tType ).

thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J_J,type,
    noptio570777408ubject: $tType ).

thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J_J,type,
    noptio435234344reeRes: $tType ).

thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_J,type,
    noptio1926134715n_name: $tType ).

thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
    noptio354675977ion_pi: $tType ).

thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
    noption_Late_subject: $tType ).

thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
    noption_Late_freeRes: $tType ).

thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
    noption_name: $tType ).

thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
    noption_pi: $tType ).

thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
    set_name: $tType ).

thf(ty_n_t__Late____Semantics__Oresidual,type,
    late_residual: $tType ).

thf(ty_n_t__Late____Semantics__Osubject,type,
    late_subject: $tType ).

thf(ty_n_t__Late____Semantics__OfreeRes,type,
    late_freeRes: $tType ).

thf(ty_n_t__Agent__Oname,type,
    name: $tType ).

thf(ty_n_t__Agent__Opi,type,
    pi: $tType ).

% Explicit typings (131)
thf(sy_c_Agent_Opi_OBang,type,
    bang: pi > pi ).

thf(sy_c_Agent_Opi_OInput,type,
    input: name > name > pi > pi ).

thf(sy_c_Agent_Opi_OMatch,type,
    match: name > name > pi > pi ).

thf(sy_c_Agent_Opi_OMismatch,type,
    mismatch: name > name > pi > pi ).

thf(sy_c_Agent_Opi_OOutput,type,
    output: name > name > pi > pi ).

thf(sy_c_Agent_Opi_OPar,type,
    par: pi > pi > pi ).

thf(sy_c_Agent_Opi_OPiNil,type,
    piNil: pi ).

thf(sy_c_Agent_Opi_ORes,type,
    res: name > pi > pi ).

thf(sy_c_Agent_Opi_OSum,type,
    sum: pi > pi > pi ).

thf(sy_c_Agent_Opi_OTau,type,
    tau: pi > pi ).

thf(sy_c_Agent_Opi_Opi__rec_001t__Agent__Opi,type,
    pi_rec_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi ).

thf(sy_c_Agent_Opi_Opi__rec__set_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
    pi_rec802206470ion_pi: ( name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > ( name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > ( name > noption_pi ) > name > noption_pi ) > pi > ( name > noption_pi ) > $o ).

thf(sy_c_Agent_Opi_Opi__rec__set_001t__Agent__Oname,type,
    pi_rec_set_name: name > ( name > name > pi > name > name ) > ( pi > name > name ) > ( name > name > pi > name > name ) > ( name > name > pi > name > name ) > ( name > name > pi > name > name ) > ( pi > pi > name > name > name ) > ( pi > pi > name > name > name ) > ( name > pi > name > name ) > ( pi > name > name ) > pi > name > $o ).

thf(sy_c_Agent_Opi_Opi__rec__set_001t__Agent__Opi,type,
    pi_rec_set_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi > $o ).

thf(sy_c_Agent_Opi_Opi__rec__set_001t__Late____Semantics__OfreeRes,type,
    pi_rec1156860983reeRes: late_freeRes > ( name > name > pi > late_freeRes > late_freeRes ) > ( pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > ( name > pi > late_freeRes > late_freeRes ) > ( pi > late_freeRes > late_freeRes ) > pi > late_freeRes > $o ).

thf(sy_c_Agent_Opi_Opi__rec__set_001t__Late____Semantics__Osubject,type,
    pi_rec232630607ubject: late_subject > ( name > name > pi > late_subject > late_subject ) > ( pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( pi > pi > late_subject > late_subject > late_subject ) > ( pi > pi > late_subject > late_subject > late_subject ) > ( name > pi > late_subject > late_subject ) > ( pi > late_subject > late_subject ) > pi > late_subject > $o ).

thf(sy_c_Agent_Osubs,type,
    subs: pi > name > name > pi ).

thf(sy_c_Agent_Osubst__name,type,
    subst_name: name > name > name > name ).

thf(sy_c_Finite__Set_Ofinite_001t__Agent__Oname,type,
    finite_finite_name: set_name > $o ).

thf(sy_c_If_001t__Agent__Oname,type,
    if_name: $o > name > name > name ).

thf(sy_c_Late__Semantics_ObangPred,type,
    late_bangPred: pi > pi > $o ).

thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
    late_OutputR: name > name > late_freeRes ).

thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
    late_TauR: late_freeRes ).

thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
    late_BoundR: late_subject > name > pi > late_residual ).

thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
    late_FreeR: late_freeRes > pi > late_residual ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Agent__Oname,type,
    late_r1174711868c_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Agent__Opi,type,
    late_residual_rec_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Late____Semantics__OfreeRes,type,
    late_r124702629reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Late____Semantics__Osubject,type,
    late_r1347955901ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
    late_r750878080ion_pi: ( late_subject > name > pi > name > noption_pi ) > ( late_freeRes > pi > name > noption_pi ) > late_residual > ( name > noption_pi ) > $o ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Agent__Oname,type,
    late_r1742481968t_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name > $o ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Agent__Opi,type,
    late_r1261898622set_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi > $o ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Late____Semantics__OfreeRes,type,
    late_r1613948593reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes > $o ).

thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Late____Semantics__Osubject,type,
    late_r689718217ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject > $o ).

thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
    late_BoundOutputS: name > late_subject ).

thf(sy_c_Late__Semantics_Osubject_OInputS,type,
    late_InputS: name > late_subject ).

thf(sy_c_Late__Semantics_Otransitions,type,
    late_transitions: pi > late_residual > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Agent__Oname_J,type,
    sup_sup_set_name: set_name > set_name > set_name ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
    abs_fu446471607ion_pi: name > ( name > noptio354675977ion_pi ) > name > noptio2087446135ion_pi ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
    abs_fu1394407909n_name: name > ( name > noption_name ) > name > noptio1926134715n_name ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
    abs_fu1614711987ion_pi: name > ( name > noption_pi ) > name > noptio354675977ion_pi ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
    abs_fu1763130856reeRes: name > ( name > noption_Late_freeRes ) > name > noptio435234344reeRes ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
    abs_fu1705804544ubject: name > ( name > noption_Late_subject ) > name > noptio570777408ubject ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
    abs_fu1682643010ion_pi: name > ( late_freeRes > pi > name > noption_pi ) > name > noptio751120898ion_pi ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
    abs_fun_name_name: name > name > name > noption_name ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
    abs_fun_name_pi: name > pi > name > noption_pi ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
    abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).

thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
    abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_J,type,
    fresh_1575363742ion_pi: name > ( name > noptio2087446135ion_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_J_J,type,
    fresh_1742414570n_name: name > ( name > noptio1926134715n_name ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
    fresh_92802872ion_pi: name > ( name > noptio354675977ion_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J_J_J,type,
    fresh_1215331279reeRes: name > ( name > noptio435234344reeRes ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J_J_J,type,
    fresh_600418535ubject: name > ( name > noptio570777408ubject ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_J,type,
    fresh_481208489ion_pi: name > ( name > noptio751120898ion_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
    fresh_1093033124n_name: name > ( name > noption_name ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
    fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
    fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
    fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
    fresh_7927363ion_pi: name > ( late_freeRes > pi > name > noption_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Agent__Oname_J_J,type,
    fresh_1030632537i_name: name > ( late_freeRes > pi > name ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
    fresh_1011532071_pi_pi: name > ( late_freeRes > pi > pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J,type,
    fresh_256112244reeRes: name > ( late_freeRes > pi > late_freeRes ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J,type,
    fresh_198785932ubject: name > ( late_freeRes > pi > late_subject ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J,type,
    fresh_747777846ion_pi: name > ( late_subject > name > pi > name > noption_pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Oname_J_J_J,type,
    fresh_621211324i_name: name > ( late_subject > name > pi > name ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
    fresh_1438126218_pi_pi: name > ( late_subject > name > pi > pi ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_J,type,
    fresh_660367079reeRes: name > ( late_subject > name > pi > late_freeRes ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_J,type,
    fresh_795910143ubject: name > ( late_subject > name > pi > late_subject ) > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
    fresh_name_name: name > name > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
    fresh_name_pi: name > pi > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
    fresh_81631222sidual: name > late_residual > $o ).

thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
    fresh_717452603ubject: name > late_subject > $o ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_J_001t__Agent__Oname,type,
    supp_n1987783534i_name: ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Agent__Oname_J_J_J_J_001t__Agent__Oname,type,
    supp_n612431512e_name: ( name > name > pi > name > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J_001t__Agent__Oname,type,
    supp_n1977765016i_name: ( name > name > pi > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J_J_J_001t__Agent__Oname,type,
    supp_n337505932s_name: ( name > name > pi > late_freeRes > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J_J_J_001t__Agent__Oname,type,
    supp_n200783964t_name: ( name > name > pi > late_subject > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_001t__Agent__Oname,type,
    supp_n52582513i_name: ( name > pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Agent__Oname_J_J_J_001t__Agent__Oname,type,
    supp_n116460699e_name: ( name > pi > name > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J_001t__Agent__Oname,type,
    supp_n96533147i_name: ( name > pi > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J_J_001t__Agent__Oname,type,
    supp_n1410452111s_name: ( name > pi > late_freeRes > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J_J_001t__Agent__Oname,type,
    supp_n122125407t_name: ( name > pi > late_subject > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_001t__Agent__Oname,type,
    supp_n1003758744i_name: ( name > noptio354675977ion_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_001t__Agent__Oname,type,
    supp_n352473082e_name: ( name > noption_name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
    supp_n468628396i_name: ( name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J_001t__Agent__Oname,type,
    supp_n252280103s_name: ( name > noption_Late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J_001t__Agent__Oname,type,
    supp_n1630792207t_name: ( name > noption_Late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_001t__Agent__Oname,type,
    supp_p1320058820i_name: ( pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__Agent__Oname,type,
    supp_p1239856366e_name: ( pi > name > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_J_001t__Agent__Oname,type,
    supp_p1592910632i_name: ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_It__Agent__Oname_M_062_It__Agent__Oname_Mt__Agent__Oname_J_J_J_J_001t__Agent__Oname,type,
    supp_p1618090470e_name: ( pi > pi > name > name > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J_001t__Agent__Oname,type,
    supp_p812767768i_name: ( pi > pi > pi > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_It__Late____Semantics__OfreeRes_M_062_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J_J_J_001t__Agent__Oname,type,
    supp_p1358344533s_name: ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_M_062_It__Late____Semantics__Osubject_M_062_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J_J_J_001t__Agent__Oname,type,
    supp_p1221108749t_name: ( pi > pi > late_subject > late_subject > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_001t__Agent__Oname,type,
    supp_pi_pi_pi_name: ( pi > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J_001t__Agent__Oname,type,
    supp_p71246050s_name: ( pi > late_freeRes > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Agent__Opi_M_062_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J_001t__Agent__Oname,type,
    supp_p742701746t_name: ( pi > late_subject > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_001t__Agent__Oname,type,
    supp_L635439693i_name: ( late_freeRes > pi > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Agent__Oname_J_J_001t__Agent__Oname,type,
    supp_L926407557e_name: ( late_freeRes > pi > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_001t__Agent__Oname,type,
    supp_L2052723895i_name: ( late_freeRes > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_001t__Agent__Oname,type,
    supp_L381160156s_name: ( late_freeRes > pi > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_001t__Agent__Oname,type,
    supp_L1759672260t_name: ( late_freeRes > pi > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_001t__Agent__Oname,type,
    supp_L3230824i_name: ( late_subject > name > pi > name > noption_pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Oname_J_J_J_001t__Agent__Oname,type,
    supp_L538372628e_name: ( late_subject > name > pi > name ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J_001t__Agent__Oname,type,
    supp_L729745222i_name: ( late_subject > name > pi > pi ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_J_001t__Agent__Oname,type,
    supp_L1178477943s_name: ( late_subject > name > pi > late_freeRes ) > set_name ).

thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_J_001t__Agent__Oname,type,
    supp_L1144036959t_name: ( late_subject > name > pi > late_subject ) > set_name ).

thf(sy_c_Nominal_Osupp_001t__Agent__Oname_001t__Agent__Oname,type,
    supp_name_name: name > set_name ).

thf(sy_c_Nominal_Osupp_001t__Agent__Opi_001t__Agent__Oname,type,
    supp_pi_name: pi > set_name ).

thf(sy_c_Nominal_Osupp_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
    supp_L1228270395s_name: late_freeRes > set_name ).

thf(sy_c_Nominal_Osupp_001t__Late____Semantics__Oresidual_001t__Agent__Oname,type,
    supp_L1174042202l_name: late_residual > set_name ).

thf(sy_c_Nominal_Osupp_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
    supp_L1174290467t_name: late_subject > set_name ).

thf(sy_c_Nominal_Osupports_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
    suppor1289515356ion_pi: set_name > ( name > noption_pi ) > $o ).

thf(sy_c_Nominal_Osupports_001t__Agent__Oname_001t__Agent__Oname,type,
    supports_name_name: set_name > name > $o ).

thf(sy_c_Nominal_Osupports_001t__Agent__Oname_001t__Agent__Opi,type,
    supports_name_pi: set_name > pi > $o ).

thf(sy_c_Nominal_Osupports_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
    suppor1556658829reeRes: set_name > late_freeRes > $o ).

thf(sy_c_Nominal_Osupports_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
    suppor632428453ubject: set_name > late_subject > $o ).

thf(sy_c_Set_OCollect_001t__Agent__Oname,type,
    collect_name: ( name > $o ) > set_name ).

thf(sy_c_member_001t__Agent__Oname,type,
    member_name: name > set_name > $o ).

thf(sy_v_P,type,
    p: pi ).

thf(sy_v_PQR____,type,
    pqr: pi ).

thf(sy_v_P_H____,type,
    p2: pi ).

thf(sy_v_Q,type,
    q: pi ).

thf(sy_v_QR____,type,
    qr: pi ).

thf(sy_v_Q_H____,type,
    q2: pi ).

thf(sy_v_R,type,
    r: pi ).

thf(sy_v__092_060alpha_062____,type,
    alpha: late_freeRes ).

thf(sy_v_a____,type,
    a: name ).

thf(sy_v_b____,type,
    b: name ).

thf(sy_v_x____,type,
    x: name ).

% Relevant facts (349)
thf(fact_0_cComm2_Ohyps_I9_J,axiom,
    alpha = late_TauR ).

% cComm2.hyps(9)
thf(fact_1_cComm2_Ohyps_I5_J,axiom,
    x != a ).

% cComm2.hyps(5)
thf(fact_2_cComm2_Ohyps_I6_J,axiom,
    x != b ).

% cComm2.hyps(6)
thf(fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062,axiom,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ) ).

% \<open>P \<parallel> Q \<longmapsto> \<tau> \<prec> P' \<parallel> Q'[x::=b]\<close>
thf(fact_4_Free_Ohyps,axiom,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).

% Free.hyps
thf(fact_5_cComm2_Ohyps_I8_J,axiom,
    fresh_name_pi @ x @ q ).

% cComm2.hyps(8)
thf(fact_6_cComm2_Ohyps_I3_J,axiom,
    fresh_name_pi @ x @ p ).

% cComm2.hyps(3)
thf(fact_7_cComm2_Ohyps_I7_J,axiom,
    fresh_name_pi @ x @ p2 ).

% cComm2.hyps(7)
thf(fact_8_cComm2_Ohyps_I4_J,axiom,
    fresh_name_pi @ x @ ( par @ q @ r ) ).

% cComm2.hyps(4)
thf(fact_9_cComm2_Ohyps_I1_J,axiom,
    late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ) ).

% cComm2.hyps(1)
thf(fact_10_simps_I8_J,axiom,
    ! [P: pi,Q: pi,C: name,D: name] :
      ( ( subs @ ( par @ P @ Q ) @ C @ D )
      = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).

% simps(8)
thf(fact_11_Par1F,axiom,
    ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
      ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
     => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).

% Par1F
thf(fact_12_Par2F,axiom,
    ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
      ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
     => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).

% Par2F
thf(fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
    fresh_name_pi @ x @ r ).

% \<open>x \<sharp> R\<close>
thf(fact_14_subst__identity,axiom,
    ! [P: pi,A: name] :
      ( ( subs @ P @ A @ A )
      = P ) ).

% subst_identity
thf(fact_15_cPar1_Ohyps,axiom,
    late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).

% cPar1.hyps
thf(fact_16_cComm2_Ohyps_I2_J,axiom,
    late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).

% cComm2.hyps(2)
thf(fact_17_residual_Oinject_I2_J,axiom,
    ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
      ( ( ( late_FreeR @ X2 @ X1 )
        = ( late_FreeR @ Y2 @ Y1 ) )
      = ( ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% residual.inject(2)
thf(fact_18_pi_Oinject_I7_J,axiom,
    ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
      ( ( ( par @ X2 @ X1 )
        = ( par @ Y2 @ Y1 ) )
      = ( ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% pi.inject(7)
thf(fact_19_tauCases,axiom,
    ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
     => ( ( ( Alpha = late_TauR )
         => ( ( P = P2 )
           => ( Prop @ late_TauR @ P ) ) )
       => ( Prop @ Alpha @ P2 ) ) ) ).

% tauCases
thf(fact_20_tauCases_H,axiom,
    ! [P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( tau @ P ) @ Rs )
     => ~ ! [P3: pi] :
            ( ( ( tau @ P )
              = ( tau @ P3 ) )
           => ( Rs
             != ( late_FreeR @ late_TauR @ P3 ) ) ) ) ).

% tauCases'
thf(fact_21_Late__Semantics_OfreeRes_Oinject,axiom,
    ! [X2: name,X1: name,Y2: name,Y1: name] :
      ( ( ( late_OutputR @ X2 @ X1 )
        = ( late_OutputR @ Y2 @ Y1 ) )
      = ( ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% Late_Semantics.freeRes.inject
thf(fact_22_pi_Ofresh_I8_J,axiom,
    ! [A: name,X2: pi,X1: pi] :
      ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
      = ( ( fresh_name_pi @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% pi.fresh(8)
thf(fact_23_substTrans,axiom,
    ! [B: name,P: pi,A: name,C: name] :
      ( ( fresh_name_pi @ B @ P )
     => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
        = ( subs @ P @ A @ C ) ) ) ).

% substTrans
thf(fact_24_pi_Ofresh_I3_J,axiom,
    ! [A: name,X1: pi] :
      ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
      = ( fresh_name_pi @ A @ X1 ) ) ).

% pi.fresh(3)
thf(fact_25_simps_I2_J,axiom,
    ! [P: pi,C: name,D: name] :
      ( ( subs @ ( tau @ P ) @ C @ D )
      = ( tau @ ( subs @ P @ C @ D ) ) ) ).

% simps(2)
thf(fact_26_pi_Oinject_I2_J,axiom,
    ! [X1: pi,Y1: pi] :
      ( ( ( tau @ X1 )
        = ( tau @ Y1 ) )
      = ( X1 = Y1 ) ) ).

% pi.inject(2)
thf(fact_27_freshBoundDerivative_I2_J,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_name_pi @ Y @ P )
       => ( ( Y != X )
         => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).

% freshBoundDerivative(2)
thf(fact_28_name__exists__fresh,axiom,
    ! [X: late_subject] :
      ~ ! [C2: name] :
          ~ ( fresh_717452603ubject @ C2 @ X ) ).

% name_exists_fresh
thf(fact_29_name__exists__fresh,axiom,
    ! [X: late_freeRes] :
      ~ ! [C2: name] :
          ~ ( fresh_1641682979reeRes @ C2 @ X ) ).

% name_exists_fresh
thf(fact_30_name__exists__fresh,axiom,
    ! [X: name] :
      ~ ! [C2: name] :
          ~ ( fresh_name_name @ C2 @ X ) ).

% name_exists_fresh
thf(fact_31_name__exists__fresh,axiom,
    ! [X: pi] :
      ~ ! [C2: name] :
          ~ ( fresh_name_pi @ C2 @ X ) ).

% name_exists_fresh
thf(fact_32_tauBoundTrans,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi] :
      ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).

% tauBoundTrans
thf(fact_33_residual_Ostrong__induct,axiom,
    ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: late_subject] :
          ( ( fresh_717452603ubject @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_induct
thf(fact_34_residual_Ostrong__induct,axiom,
    ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: late_freeRes] :
          ( ( fresh_1641682979reeRes @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_induct
thf(fact_35_residual_Ostrong__induct,axiom,
    ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: name] :
          ( ( fresh_name_name @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_induct
thf(fact_36_residual_Ostrong__induct,axiom,
    ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: pi] :
          ( ( fresh_name_pi @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_induct
thf(fact_37_residual_Ostrong__inducts,axiom,
    ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: late_subject] :
          ( ( fresh_717452603ubject @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_inducts
thf(fact_38_residual_Ostrong__inducts,axiom,
    ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: late_freeRes] :
          ( ( fresh_1641682979reeRes @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_inducts
thf(fact_39_residual_Ostrong__inducts,axiom,
    ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: name] :
          ( ( fresh_name_name @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_inducts
thf(fact_40_residual_Ostrong__inducts,axiom,
    ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi,Z2: pi] :
          ( ( fresh_name_pi @ Name @ Z2 )
         => ( ( fresh_717452603ubject @ Name @ Subject )
           => ( P @ Z2 @ ( late_BoundR @ Subject @ Name @ Pi ) ) ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Z @ Residual ) ) ) ).

% residual.strong_inducts
thf(fact_41_residual_Oinducts,axiom,
    ! [P: late_residual > $o,Residual: late_residual] :
      ( ! [Subject: late_subject,Name: name,Pi: pi] : ( P @ ( late_BoundR @ Subject @ Name @ Pi ) )
     => ( ! [FreeRes: late_freeRes,Pi: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi ) )
       => ( P @ Residual ) ) ) ).

% residual.inducts
thf(fact_42_residual_Odistinct_I1_J,axiom,
    ! [Subject2: late_subject,Name2: name,Pi2: pi,FreeRes2: late_freeRes,Pi3: pi] :
      ( ( late_BoundR @ Subject2 @ Name2 @ Pi2 )
     != ( late_FreeR @ FreeRes2 @ Pi3 ) ) ).

% residual.distinct(1)
thf(fact_43_fresh__fact2,axiom,
    ! [A: name,B: name,P: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).

% fresh_fact2
thf(fact_44_fresh__fact1,axiom,
    ! [A: name,P: pi,C: name,B: name] :
      ( ( fresh_name_pi @ A @ P )
     => ( ( A != C )
       => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).

% fresh_fact1
thf(fact_45_forget,axiom,
    ! [A: name,P: pi,B: name] :
      ( ( fresh_name_pi @ A @ P )
     => ( ( subs @ P @ A @ B )
        = P ) ) ).

% forget
thf(fact_46_parCasesB,axiom,
    ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
      ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
     => ( ( fresh_name_pi @ X @ P )
       => ( ( fresh_name_pi @ X @ Q )
         => ( ! [P4: pi] :
                ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
               => ( Prop @ ( par @ P4 @ Q ) ) )
           => ( ! [Q3: pi] :
                  ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
                 => ( Prop @ ( par @ P @ Q3 ) ) )
             => ( Prop @ PQ ) ) ) ) ) ) ).

% parCasesB
thf(fact_47_Late__Semantics_OPar2B,axiom,
    ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
      ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
     => ( ( fresh_name_pi @ X @ P )
       => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).

% Late_Semantics.Par2B
thf(fact_48_Late__Semantics_OPar1B,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_name_pi @ X @ Q )
       => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).

% Late_Semantics.Par1B
thf(fact_49_pi_Odistinct_I43_J,axiom,
    ! [Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( tau @ Pi2 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(43)
thf(fact_50_freeRes_Oinducts,axiom,
    ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
      ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
     => ( ( P @ late_TauR )
       => ( P @ FreeRes3 ) ) ) ).

% freeRes.inducts
thf(fact_51_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
    ! [Name12: name,Name23: name] :
      ( ( late_OutputR @ Name12 @ Name23 )
     != late_TauR ) ).

% Late_Semantics.freeRes.distinct(1)
thf(fact_52_mem__Collect__eq,axiom,
    ! [A: name,P: name > $o] :
      ( ( member_name @ A @ ( collect_name @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_53_Collect__mem__eq,axiom,
    ! [A2: set_name] :
      ( ( collect_name
        @ ^ [X3: name] : ( member_name @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_54_Collect__cong,axiom,
    ! [P: name > $o,Q: name > $o] :
      ( ! [X4: name] :
          ( ( P @ X4 )
          = ( Q @ X4 ) )
     => ( ( collect_name @ P )
        = ( collect_name @ Q ) ) ) ).

% Collect_cong
thf(fact_55_tauOutputTrans,axiom,
    ! [P: pi,A: name,B: name,P2: pi] :
      ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).

% tauOutputTrans
thf(fact_56_transitions_OComm2,axiom,
    ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
       => ( ( fresh_name_pi @ X @ P )
         => ( ( fresh_name_pi @ X @ Q )
           => ( ( X != A )
             => ( ( X != B )
               => ( ( fresh_name_pi @ X @ P2 )
                 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).

% transitions.Comm2
thf(fact_57_transitions_OComm1,axiom,
    ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
       => ( ( fresh_name_pi @ X @ P )
         => ( ( fresh_name_pi @ X @ Q )
           => ( ( X != A )
             => ( ( X != B )
               => ( ( fresh_name_pi @ X @ Q2 )
                 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).

% transitions.Comm1
thf(fact_58_freshFreeDerivative_I2_J,axiom,
    ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
     => ( ( fresh_name_pi @ Y @ P )
       => ( fresh_name_pi @ Y @ P2 ) ) ) ).

% freshFreeDerivative(2)
thf(fact_59_Late__Semantics_OComm2,axiom,
    ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).

% Late_Semantics.Comm2
thf(fact_60_Late__Semantics_OComm1,axiom,
    ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).

% Late_Semantics.Comm1
thf(fact_61_Tau,axiom,
    ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).

% Tau
thf(fact_62_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
    ! [X1: name,Y1: name] :
      ( ( ( late_InputS @ X1 )
        = ( late_InputS @ Y1 ) )
      = ( X1 = Y1 ) ) ).

% Late_Semantics1.subject.inject(1)
thf(fact_63_Late__Semantics1_OfreeRes_Oinject,axiom,
    ! [X11: name,X12: name,Y11: name,Y12: name] :
      ( ( ( late_OutputR @ X11 @ X12 )
        = ( late_OutputR @ Y11 @ Y12 ) )
      = ( ( X11 = Y11 )
        & ( X12 = Y12 ) ) ) ).

% Late_Semantics1.freeRes.inject
thf(fact_64_freeRes_Oexhaust,axiom,
    ! [Y: late_freeRes] :
      ( ! [X112: name,X122: name] :
          ( Y
         != ( late_OutputR @ X112 @ X122 ) )
     => ( Y = late_TauR ) ) ).

% freeRes.exhaust
thf(fact_65_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
    ! [X11: name,X12: name] :
      ( ( late_OutputR @ X11 @ X12 )
     != late_TauR ) ).

% Late_Semantics1.freeRes.distinct(1)
thf(fact_66_transitions_OClose2,axiom,
    ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
       => ( ( fresh_name_pi @ X @ P )
         => ( ( fresh_name_pi @ X @ Q )
           => ( ( fresh_name_pi @ Y @ P )
             => ( ( fresh_name_pi @ Y @ Q )
               => ( ( X != A )
                 => ( ( fresh_name_pi @ X @ P2 )
                   => ( ( Y != A )
                     => ( ( fresh_name_pi @ Y @ Q2 )
                       => ( ( X != Y )
                         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% transitions.Close2
thf(fact_67_transitions_OClose1,axiom,
    ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
       => ( ( fresh_name_pi @ X @ P )
         => ( ( fresh_name_pi @ X @ Q )
           => ( ( fresh_name_pi @ Y @ P )
             => ( ( fresh_name_pi @ Y @ Q )
               => ( ( X != A )
                 => ( ( fresh_name_pi @ X @ Q2 )
                   => ( ( Y != A )
                     => ( ( fresh_name_pi @ Y @ P2 )
                       => ( ( X != Y )
                         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% transitions.Close1
thf(fact_68_Late__Semantics_OClose2,axiom,
    ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
       => ( ( fresh_name_pi @ Y @ Q )
         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).

% Late_Semantics.Close2
thf(fact_69_freeRes_Ofresh_I1_J,axiom,
    ! [A: name,X2: name,X1: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
      = ( ( fresh_name_name @ A @ X2 )
        & ( fresh_name_name @ A @ X1 ) ) ) ).

% freeRes.fresh(1)
thf(fact_70_Late__Semantics_Osubject_Oinject_I2_J,axiom,
    ! [X1: name,Y1: name] :
      ( ( ( late_BoundOutputS @ X1 )
        = ( late_BoundOutputS @ Y1 ) )
      = ( X1 = Y1 ) ) ).

% Late_Semantics.subject.inject(2)
thf(fact_71_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
    ! [X2: name,Y2: name] :
      ( ( ( late_BoundOutputS @ X2 )
        = ( late_BoundOutputS @ Y2 ) )
      = ( X2 = Y2 ) ) ).

% Late_Semantics1.subject.inject(2)
thf(fact_72_freeRes_Ofresh_I2_J,axiom,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).

% freeRes.fresh(2)
thf(fact_73_residual_Ofresh_I2_J,axiom,
    ! [A: name,X2: late_freeRes,X1: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
      = ( ( fresh_1641682979reeRes @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% residual.fresh(2)
thf(fact_74_simps_I9_J,axiom,
    ! [X: name,C: name,D: name,P: pi] :
      ( ( X != C )
     => ( ( X != D )
       => ( ( subs @ ( res @ X @ P ) @ C @ D )
          = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).

% simps(9)
thf(fact_75_subject_Ofresh_I1_J,axiom,
    ! [A: name,X1: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
      = ( fresh_name_name @ A @ X1 ) ) ).

% subject.fresh(1)
thf(fact_76_subject_Ofresh_I2_J,axiom,
    ! [A: name,X1: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
      = ( fresh_name_name @ A @ X1 ) ) ).

% subject.fresh(2)
thf(fact_77_subject_Oexhaust,axiom,
    ! [Y: late_subject] :
      ( ! [X13: name] :
          ( Y
         != ( late_InputS @ X13 ) )
     => ~ ! [X22: name] :
            ( Y
           != ( late_BoundOutputS @ X22 ) ) ) ).

% subject.exhaust
thf(fact_78_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
    ! [X1: name,X2: name] :
      ( ( late_InputS @ X1 )
     != ( late_BoundOutputS @ X2 ) ) ).

% Late_Semantics1.subject.distinct(1)
thf(fact_79_Late__Semantics_OResB,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_717452603ubject @ Y @ A )
       => ( ( Y != X )
         => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).

% Late_Semantics.ResB
thf(fact_80_resCasesF,axiom,
    ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
      ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
     => ( ! [P4: pi] :
            ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
           => ( ( fresh_1641682979reeRes @ X @ Alpha )
             => ( F @ ( res @ X @ P4 ) ) ) )
       => ( F @ XP ) ) ) ).

% resCasesF
thf(fact_81_resCasesF_H,axiom,
    ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
      ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
     => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
            ( ( ( res @ X @ P )
              = ( res @ Y3 @ P3 ) )
           => ( ( ( late_FreeR @ Alpha @ P2 )
                = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
             => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
               => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).

% resCasesF'
thf(fact_82_ResF,axiom,
    ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
     => ( ( fresh_1641682979reeRes @ Y @ Alpha )
       => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).

% ResF
thf(fact_83_pi_Odistinct_I85_J,axiom,
    ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
      ( ( par @ Pi12 @ Pi23 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(85)
thf(fact_84_freshRes,axiom,
    ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).

% freshRes
thf(fact_85_pi_Odistinct_I45_J,axiom,
    ! [Pi2: pi,Name3: name,Pi3: pi] :
      ( ( tau @ Pi2 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(45)
thf(fact_86_resCases_H,axiom,
    ! [X: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( res @ X @ P ) @ Rs )
     => ( ! [P3: pi,A3: name,B2: name] :
            ( ( ( res @ X @ P )
              = ( res @ B2 @ P3 ) )
           => ! [P4: pi] :
                ( ( Rs
                  = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
               => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
                 => ( A3 = B2 ) ) ) )
       => ( ! [P3: pi,A3: late_subject,X4: name,P4: pi,Y3: name] :
              ( ( ( res @ X @ P )
                = ( res @ Y3 @ P3 ) )
             => ( ( Rs
                  = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P4 ) ) )
               => ( ( late_transitions @ P3 @ ( late_BoundR @ A3 @ X4 @ P4 ) )
                 => ( ( fresh_717452603ubject @ Y3 @ A3 )
                   => ( ( Y3 != X4 )
                     => ( ( fresh_name_pi @ X4 @ P3 )
                       => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
         => ~ ! [P3: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
                ( ( ( res @ X @ P )
                  = ( res @ Y3 @ P3 ) )
               => ( ( Rs
                    = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
                 => ( ( late_transitions @ P3 @ ( late_FreeR @ Alpha2 @ P4 ) )
                   => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).

% resCases'
thf(fact_87_transitions_OResB,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_717452603ubject @ Y @ A )
       => ( ( Y != X )
         => ( ( fresh_name_pi @ X @ P )
           => ( ( fresh_717452603ubject @ X @ A )
             => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).

% transitions.ResB
thf(fact_88_subject_Oinducts,axiom,
    ! [P: late_subject > $o,Subject2: late_subject] :
      ( ! [Name: name] : ( P @ ( late_InputS @ Name ) )
     => ( ! [Name: name] : ( P @ ( late_BoundOutputS @ Name ) )
       => ( P @ Subject2 ) ) ) ).

% subject.inducts
thf(fact_89_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
    ! [Name2: name,Name3: name] :
      ( ( late_InputS @ Name2 )
     != ( late_BoundOutputS @ Name3 ) ) ).

% Late_Semantics.subject.distinct(1)
thf(fact_90_resCasesB_H,axiom,
    ! [X5: name,P: pi,A: late_subject,Y4: name,P2: pi] :
      ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
     => ( ! [P3: pi,A3: name,B2: name] :
            ( ( ( res @ X5 @ P )
              = ( res @ B2 @ P3 ) )
           => ! [P4: pi] :
                ( ( ( late_BoundR @ A @ Y4 @ P2 )
                  = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
               => ( ( late_transitions @ P3 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
                 => ( A3 = B2 ) ) ) )
       => ~ ! [P3: pi,A3: late_subject,X4: name,P4: pi,Y3: name] :
              ( ( ( res @ X5 @ P )
                = ( res @ Y3 @ P3 ) )
             => ( ( ( late_BoundR @ A @ Y4 @ P2 )
                  = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P4 ) ) )
               => ( ( late_transitions @ P3 @ ( late_BoundR @ A3 @ X4 @ P4 ) )
                 => ( ( fresh_717452603ubject @ Y3 @ A3 )
                   => ( ( Y3 != X4 )
                     => ( ( fresh_name_pi @ X4 @ P3 )
                       => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).

% resCasesB'
thf(fact_91_freshResidual,axiom,
    ! [P: pi,Rs: late_residual,X: name] :
      ( ( late_transitions @ P @ Rs )
     => ( ( fresh_name_pi @ X @ P )
       => ( fresh_81631222sidual @ X @ Rs ) ) ) ).

% freshResidual
thf(fact_92_substRes3,axiom,
    ! [B: name,P: pi,A: name] :
      ( ( fresh_name_pi @ B @ P )
     => ( ( subs @ ( res @ A @ P ) @ A @ B )
        = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).

% substRes3
thf(fact_93_substRes2,axiom,
    ! [B: name,P: pi,A: name] :
      ( ( fresh_name_pi @ B @ P )
     => ( ( res @ A @ P )
        = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).

% substRes2
thf(fact_94_Open,axiom,
    ! [P: pi,A: name,B: name,P2: pi] :
      ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
     => ( ( A != B )
       => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).

% Open
thf(fact_95_freshFreeDerivative_I1_J,axiom,
    ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
     => ( ( fresh_name_pi @ Y @ P )
       => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).

% freshFreeDerivative(1)
thf(fact_96_freshBoundDerivative_I1_J,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_name_pi @ Y @ P )
       => ( fresh_717452603ubject @ Y @ A ) ) ) ).

% freshBoundDerivative(1)
thf(fact_97_resTauBoundTrans,axiom,
    ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).

% resTauBoundTrans
thf(fact_98_parCasesB_H,axiom,
    ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
      ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
     => ( ! [P3: pi,A3: late_subject,X4: name,P4: pi,Q4: pi] :
            ( ( ( par @ P @ Q )
              = ( par @ P3 @ Q4 ) )
           => ( ( ( late_BoundR @ B @ Y @ P2 )
                = ( late_BoundR @ A3 @ X4 @ ( par @ P4 @ Q4 ) ) )
             => ( ( late_transitions @ P3 @ ( late_BoundR @ A3 @ X4 @ P4 ) )
               => ( ( fresh_name_pi @ X4 @ P3 )
                 => ( ( fresh_name_pi @ X4 @ Q4 )
                   => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) )
       => ~ ! [Q4: pi,A3: late_subject,X4: name,Q3: pi,P3: pi] :
              ( ( ( par @ P @ Q )
                = ( par @ P3 @ Q4 ) )
             => ( ( ( late_BoundR @ B @ Y @ P2 )
                  = ( late_BoundR @ A3 @ X4 @ ( par @ P3 @ Q3 ) ) )
               => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X4 @ Q3 ) )
                 => ( ( fresh_name_pi @ X4 @ P3 )
                   => ( ( fresh_name_pi @ X4 @ Q4 )
                     => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ).

% parCasesB'
thf(fact_99_transitions_OPar1B,axiom,
    ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
     => ( ( fresh_name_pi @ X @ P )
       => ( ( fresh_name_pi @ X @ Q )
         => ( ( fresh_717452603ubject @ X @ A )
           => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).

% transitions.Par1B
thf(fact_100_transitions_OPar2B,axiom,
    ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
      ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
     => ( ( fresh_name_pi @ X @ P )
       => ( ( fresh_name_pi @ X @ Q )
         => ( ( fresh_717452603ubject @ X @ A )
           => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).

% transitions.Par2B
thf(fact_101_resTauOutputTrans,axiom,
    ! [X: name,P: pi,A: name,B: name,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).

% resTauOutputTrans
thf(fact_102_Late__Semantics_OClose1,axiom,
    ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
      ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
     => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
       => ( ( fresh_name_pi @ Y @ P )
         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).

% Late_Semantics.Close1
thf(fact_103_resOutputTauTrans,axiom,
    ! [X: name,A: name,B: name,P: pi,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).

% resOutputTauTrans
thf(fact_104_resOutputInputTrans,axiom,
    ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).

% resOutputInputTrans
thf(fact_105_resOutputOutputTrans,axiom,
    ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).

% resOutputOutputTrans
thf(fact_106_resInputBoundOutputTrans,axiom,
    ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).

% resInputBoundOutputTrans
thf(fact_107_outputTauTrans,axiom,
    ! [A: name,B: name,P: pi,P2: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).

% outputTauTrans
thf(fact_108_outputCases,axiom,
    ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
     => ( ( ( Alpha
            = ( late_OutputR @ A @ B ) )
         => ( ( P = P2 )
           => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
       => ( Prop @ Alpha @ P2 ) ) ) ).

% outputCases
thf(fact_109_outputCases_H,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
     => ~ ! [A3: name,B2: name,P3: pi] :
            ( ( ( A = A3 )
              & ( B = B2 )
              & ( P = P3 ) )
           => ( Rs
             != ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P3 ) ) ) ) ).

% outputCases'
thf(fact_110_name__fresh,axiom,
    ( fresh_name_name
    = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).

% name_fresh
thf(fact_111_pi_Ofresh_I2_J,axiom,
    ! [A: name,X32: name,X2: name,X1: pi] :
      ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
      = ( ( fresh_name_name @ A @ X32 )
        & ( fresh_name_name @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% pi.fresh(2)
thf(fact_112_pi_Odistinct_I21_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( input @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(21)
thf(fact_113_pi_Oinject_I1_J,axiom,
    ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
      ( ( ( output @ X32 @ X2 @ X1 )
        = ( output @ Y32 @ Y2 @ Y1 ) )
      = ( ( X32 = Y32 )
        & ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% pi.inject(1)
thf(fact_114_pi_Odistinct_I55_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(55)
thf(fact_115_pi_Odistinct_I57_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(57)
thf(fact_116_pi_Odistinct_I29_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(29)
thf(fact_117_pi_Odistinct_I31_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(31)
thf(fact_118_pi_Odistinct_I35_J,axiom,
    ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( tau @ Pi2 )
     != ( input @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(35)
thf(fact_119_pi_Odistinct_I19_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( tau @ Pi3 ) ) ).

% pi.distinct(19)
thf(fact_120_resTrans_I2_J,axiom,
    ! [X: name,Y: name,P: pi,Rs: late_residual] :
      ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).

% resTrans(2)
thf(fact_121_inputFreeTrans,axiom,
    ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
      ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).

% inputFreeTrans
thf(fact_122_resTrans_I1_J,axiom,
    ! [X: name,B: name,P: pi,Rs: late_residual] :
      ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).

% resTrans(1)
thf(fact_123_outputBoundTrans,axiom,
    ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).

% outputBoundTrans
thf(fact_124_outputFreshTrans,axiom,
    ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
      ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
     => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
          | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).

% outputFreshTrans
thf(fact_125_resInputFreeTrans,axiom,
    ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
      ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).

% resInputFreeTrans
thf(fact_126_Late__Semantics_OInput,axiom,
    ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).

% Late_Semantics.Input
thf(fact_127_transitions_OInput,axiom,
    ! [X: name,A: name,P: pi] :
      ( ( X != A )
     => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).

% transitions.Input
thf(fact_128_inputBoundOutputTrans,axiom,
    ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
      ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).

% inputBoundOutputTrans
thf(fact_129_inputIneqTrans,axiom,
    ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
      ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
     => ~ ( fresh_717452603ubject @ A @ B ) ) ).

% inputIneqTrans
thf(fact_130_Output,axiom,
    ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).

% Output
thf(fact_131_outputIneqTrans,axiom,
    ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
      ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
     => ~ ( ( A != C )
          | ( B != D ) ) ) ).

% outputIneqTrans
thf(fact_132_residual_Ofresh_I1_J,axiom,
    ! [A: name,X32: late_subject,X1: name,X2: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
      = ( ( fresh_717452603ubject @ A @ X32 )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).

% residual.fresh(1)
thf(fact_133_simps_I3_J,axiom,
    ! [A: name,B: name,P: pi,C: name,D: name] :
      ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
      = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).

% simps(3)
thf(fact_134_substInput,axiom,
    ! [X: name,B: name,C: name,A: name,P: pi] :
      ( ( X != B )
     => ( ( X != C )
       => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
          = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).

% substInput
thf(fact_135_simps_I4_J,axiom,
    ! [X: name,A: name,C: name,D: name,P: pi] :
      ( ( X != A )
     => ( ( X != C )
       => ( ( X != D )
         => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
            = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).

% simps(4)
thf(fact_136_inputCases_H,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
     => ~ ! [X4: name,A3: name,P3: pi] :
            ( ( ( A = A3 )
              & ( ( abs_fun_name_pi @ B @ P )
                = ( abs_fun_name_pi @ X4 @ P3 ) ) )
           => ( ( Rs
                = ( late_BoundR @ ( late_InputS @ A3 ) @ X4 @ P3 ) )
             => ( X4 = A3 ) ) ) ) ).

% inputCases'
thf(fact_137_pi_Ofresh_I9_J,axiom,
    ! [A: name,X1: name,X2: pi] :
      ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
      = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).

% pi.fresh(9)
thf(fact_138_pi_Ofresh_I4_J,axiom,
    ! [A: name,X32: name,X1: name,X2: pi] :
      ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
      = ( ( fresh_name_name @ A @ X32 )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).

% pi.fresh(4)
thf(fact_139_pi_Oinject_I8_J,axiom,
    ! [X1: name,X2: pi,Y1: name,Y2: pi] :
      ( ( ( res @ X1 @ X2 )
        = ( res @ Y1 @ Y2 ) )
      = ( ( abs_fun_name_pi @ X1 @ X2 )
        = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).

% pi.inject(8)
thf(fact_140_residual_Oinject_I1_J,axiom,
    ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
      ( ( ( late_BoundR @ X32 @ X1 @ X2 )
        = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
      = ( ( X32 = Y32 )
        & ( ( abs_fun_name_pi @ X1 @ X2 )
          = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).

% residual.inject(1)
thf(fact_141_subst__name__def,axiom,
    ( subst_name
    = ( ^ [A4: name,B3: name,C3: name] : ( if_name @ ( A4 = B3 ) @ C3 @ A4 ) ) ) ).

% subst_name_def
thf(fact_142_name__fresh__abs,axiom,
    ! [B: name,A: name,X: late_subject] :
      ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
      = ( ( B = A )
        | ( fresh_717452603ubject @ B @ X ) ) ) ).

% name_fresh_abs
thf(fact_143_name__fresh__abs,axiom,
    ! [B: name,A: name,X: late_freeRes] :
      ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
      = ( ( B = A )
        | ( fresh_1641682979reeRes @ B @ X ) ) ) ).

% name_fresh_abs
thf(fact_144_name__fresh__abs,axiom,
    ! [B: name,A: name,X: name] :
      ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
      = ( ( B = A )
        | ( fresh_name_name @ B @ X ) ) ) ).

% name_fresh_abs
thf(fact_145_name__fresh__abs,axiom,
    ! [B: name,A: name,X: pi] :
      ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
      = ( ( B = A )
        | ( fresh_name_pi @ B @ X ) ) ) ).

% name_fresh_abs
thf(fact_146_abs__fresh_I1_J,axiom,
    ! [B: name,A: name,X: late_subject] :
      ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
      = ( ( B = A )
        | ( fresh_717452603ubject @ B @ X ) ) ) ).

% abs_fresh(1)
thf(fact_147_abs__fresh_I1_J,axiom,
    ! [B: name,A: name,X: late_freeRes] :
      ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
      = ( ( B = A )
        | ( fresh_1641682979reeRes @ B @ X ) ) ) ).

% abs_fresh(1)
thf(fact_148_abs__fresh_I1_J,axiom,
    ! [B: name,A: name,X: name] :
      ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
      = ( ( B = A )
        | ( fresh_name_name @ B @ X ) ) ) ).

% abs_fresh(1)
thf(fact_149_abs__fresh_I1_J,axiom,
    ! [B: name,A: name,X: pi] :
      ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
      = ( ( B = A )
        | ( fresh_name_pi @ B @ X ) ) ) ).

% abs_fresh(1)
thf(fact_150_pi_Oinject_I3_J,axiom,
    ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
      ( ( ( input @ X32 @ X1 @ X2 )
        = ( input @ Y32 @ Y1 @ Y2 ) )
      = ( ( X32 = Y32 )
        & ( ( abs_fun_name_pi @ X1 @ X2 )
          = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).

% pi.inject(3)
thf(fact_151_simps_I5_J,axiom,
    ! [A: name,B: name,P: pi,C: name,D: name] :
      ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
      = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).

% simps(5)
thf(fact_152_simps_I6_J,axiom,
    ! [A: name,B: name,P: pi,C: name,D: name] :
      ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
      = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).

% simps(6)
thf(fact_153_pi_Ofresh_I5_J,axiom,
    ! [A: name,X32: name,X2: name,X1: pi] :
      ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
      = ( ( fresh_name_name @ A @ X32 )
        & ( fresh_name_name @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% pi.fresh(5)
thf(fact_154_pi_Ofresh_I6_J,axiom,
    ! [A: name,X32: name,X2: name,X1: pi] :
      ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
      = ( ( fresh_name_name @ A @ X32 )
        & ( fresh_name_name @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% pi.fresh(6)
thf(fact_155_matchCases,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
      ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
     => ( ( ( late_transitions @ P @ Rs )
         => ( ( A = B )
           => ( F @ A @ A ) ) )
       => ( F @ A @ B ) ) ) ).

% matchCases
thf(fact_156_matchTrans,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
     => ( A = B ) ) ).

% matchTrans
thf(fact_157_matchCases_H,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
     => ~ ! [P3: pi] :
            ( ( ( B = A )
              & ( P = P3 ) )
           => ~ ( late_transitions @ P3 @ Rs ) ) ) ).

% matchCases'
thf(fact_158_mismatchCases,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
      ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
     => ( ( ( late_transitions @ P @ Rs )
         => ( ( A != B )
           => ( F @ A @ B ) ) )
       => ( F @ A @ B ) ) ) ).

% mismatchCases
thf(fact_159_mismatchTrans,axiom,
    ! [A: name,P: pi,Rs: late_residual] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).

% mismatchTrans
thf(fact_160_mismatchCases_H,axiom,
    ! [A: name,B: name,P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
     => ~ ! [P3: pi,A3: name,B2: name] :
            ( ( ( A = A3 )
              & ( B = B2 )
              & ( P = P3 ) )
           => ( ( late_transitions @ P3 @ Rs )
             => ( A3 = B2 ) ) ) ) ).

% mismatchCases'
thf(fact_161_Match,axiom,
    ! [P: pi,Rs: late_residual,B: name] :
      ( ( late_transitions @ P @ Rs )
     => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).

% Match
thf(fact_162_Mismatch,axiom,
    ! [P: pi,Rs: late_residual,A: name,B: name] :
      ( ( late_transitions @ P @ Rs )
     => ( ( A != B )
       => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).

% Mismatch
thf(fact_163_pi_Odistinct_I73_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( mismatch @ Name12 @ Name23 @ Pi2 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(73)
thf(fact_164_pi_Odistinct_I65_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( match @ Name12 @ Name23 @ Pi2 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(65)
thf(fact_165_pi_Odistinct_I75_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
      ( ( mismatch @ Name12 @ Name23 @ Pi2 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(75)
thf(fact_166_pi_Odistinct_I67_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name3: name,Pi3: pi] :
      ( ( match @ Name12 @ Name23 @ Pi2 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(67)
thf(fact_167_pi_Odistinct_I61_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( match @ Name12 @ Name23 @ Pi2 )
     != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(61)
thf(fact_168_pi_Oinject_I4_J,axiom,
    ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
      ( ( ( match @ X32 @ X2 @ X1 )
        = ( match @ Y32 @ Y2 @ Y1 ) )
      = ( ( X32 = Y32 )
        & ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% pi.inject(4)
thf(fact_169_pi_Oinject_I5_J,axiom,
    ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
      ( ( ( mismatch @ X32 @ X2 @ X1 )
        = ( mismatch @ Y32 @ Y2 @ Y1 ) )
      = ( ( X32 = Y32 )
        & ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% pi.inject(5)
thf(fact_170_pi_Odistinct_I49_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( match @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(49)
thf(fact_171_pi_Odistinct_I51_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(51)
thf(fact_172_pi_Odistinct_I23_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( match @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(23)
thf(fact_173_pi_Odistinct_I25_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(25)
thf(fact_174_pi_Odistinct_I39_J,axiom,
    ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( tau @ Pi2 )
     != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(39)
thf(fact_175_pi_Odistinct_I37_J,axiom,
    ! [Pi2: pi,Name13: name,Name24: name,Pi3: pi] :
      ( ( tau @ Pi2 )
     != ( match @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(37)
thf(fact_176_abs__fun__eq1,axiom,
    ! [A: name,X: name,Y: name] :
      ( ( ( abs_fun_name_name @ A @ X )
        = ( abs_fun_name_name @ A @ Y ) )
      = ( X = Y ) ) ).

% abs_fun_eq1
thf(fact_177_abs__fun__eq1,axiom,
    ! [A: name,X: late_freeRes,Y: late_freeRes] :
      ( ( ( abs_fu681348580reeRes @ A @ X )
        = ( abs_fu681348580reeRes @ A @ Y ) )
      = ( X = Y ) ) ).

% abs_fun_eq1
thf(fact_178_abs__fun__eq1,axiom,
    ! [A: name,X: late_subject,Y: late_subject] :
      ( ( ( abs_fu1904601852ubject @ A @ X )
        = ( abs_fu1904601852ubject @ A @ Y ) )
      = ( X = Y ) ) ).

% abs_fun_eq1
thf(fact_179_abs__fun__eq1,axiom,
    ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
      ( ( ( abs_fu1614711987ion_pi @ A @ X )
        = ( abs_fu1614711987ion_pi @ A @ Y ) )
      = ( X = Y ) ) ).

% abs_fun_eq1
thf(fact_180_abs__fun__eq1,axiom,
    ! [A: name,X: pi,Y: pi] :
      ( ( ( abs_fun_name_pi @ A @ X )
        = ( abs_fun_name_pi @ A @ Y ) )
      = ( X = Y ) ) ).

% abs_fun_eq1
thf(fact_181_pi_Ostrong__inducts,axiom,
    ! [P: late_subject > pi > $o,Z: late_subject,Pi2: pi] :
      ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
            ( ! [Za: late_subject] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: late_subject] :
              ( ! [Za: late_subject] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                ( ( fresh_717452603ubject @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: late_subject] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                  ( ! [Za: late_subject] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                    ( ! [Za: late_subject] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
                      ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
                     => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
                        ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
                       => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: late_subject] :
                          ( ( fresh_717452603ubject @ Name @ Z2 )
                         => ( ! [Za: late_subject] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: late_subject] :
                            ( ! [Za: late_subject] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_inducts
thf(fact_182_pi_Ostrong__inducts,axiom,
    ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi2: pi] :
      ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
            ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: late_freeRes] :
              ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                ( ( fresh_1641682979reeRes @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                  ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
                     => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ Name @ Z2 )
                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: late_freeRes] :
                            ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_inducts
thf(fact_183_pi_Ostrong__inducts,axiom,
    ! [P: name > pi > $o,Z: name,Pi2: pi] :
      ( ! [Z2: name] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
            ( ! [Za: name] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: name] :
              ( ! [Za: name] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                ( ( fresh_name_name @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: name] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                  ( ! [Za: name] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                    ( ! [Za: name] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
                      ( ! [Za: name] : ( P @ Za @ Pi13 )
                     => ( ! [Za: name] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
                        ( ! [Za: name] : ( P @ Za @ Pi13 )
                       => ( ! [Za: name] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: name] :
                          ( ( fresh_name_name @ Name @ Z2 )
                         => ( ! [Za: name] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: name] :
                            ( ! [Za: name] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_inducts
thf(fact_184_pi_Ostrong__inducts,axiom,
    ! [P: pi > pi > $o,Z: pi,Pi2: pi] :
      ( ! [Z2: pi] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
            ( ! [Za: pi] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: pi] :
              ( ! [Za: pi] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                ( ( fresh_name_pi @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: pi] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                  ( ! [Za: pi] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                    ( ! [Za: pi] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
                      ( ! [Za: pi] : ( P @ Za @ Pi13 )
                     => ( ! [Za: pi] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
                       => ( ! [Za: pi] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: pi] :
                          ( ( fresh_name_pi @ Name @ Z2 )
                         => ( ! [Za: pi] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: pi] :
                            ( ! [Za: pi] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_inducts
thf(fact_185_pi_Ostrong__induct,axiom,
    ! [P: late_subject > pi > $o,Z: late_subject,Pi2: pi] :
      ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
            ( ! [Za: late_subject] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: late_subject] :
              ( ! [Za: late_subject] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                ( ( fresh_717452603ubject @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: late_subject] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                  ( ! [Za: late_subject] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_subject] :
                    ( ! [Za: late_subject] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
                      ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
                     => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
                        ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
                       => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: late_subject] :
                          ( ( fresh_717452603ubject @ Name @ Z2 )
                         => ( ! [Za: late_subject] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: late_subject] :
                            ( ! [Za: late_subject] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_induct
thf(fact_186_pi_Ostrong__induct,axiom,
    ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi2: pi] :
      ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
            ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: late_freeRes] :
              ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                ( ( fresh_1641682979reeRes @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                  ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: late_freeRes] :
                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
                     => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ Name @ Z2 )
                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: late_freeRes] :
                            ( ! [Za: late_freeRes] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_induct
thf(fact_187_pi_Ostrong__induct,axiom,
    ! [P: name > pi > $o,Z: name,Pi2: pi] :
      ( ! [Z2: name] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
            ( ! [Za: name] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: name] :
              ( ! [Za: name] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                ( ( fresh_name_name @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: name] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                  ( ! [Za: name] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: name] :
                    ( ! [Za: name] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
                      ( ! [Za: name] : ( P @ Za @ Pi13 )
                     => ( ! [Za: name] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
                        ( ! [Za: name] : ( P @ Za @ Pi13 )
                       => ( ! [Za: name] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: name] :
                          ( ( fresh_name_name @ Name @ Z2 )
                         => ( ! [Za: name] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: name] :
                            ( ! [Za: name] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_induct
thf(fact_188_pi_Ostrong__induct,axiom,
    ! [P: pi > pi > $o,Z: pi,Pi2: pi] :
      ( ! [Z2: pi] : ( P @ Z2 @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
            ( ! [Za: pi] : ( P @ Za @ Pi )
           => ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi,Z2: pi] :
              ( ! [Za: pi] : ( P @ Za @ Pi )
             => ( P @ Z2 @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                ( ( fresh_name_pi @ Name22 @ Z2 )
               => ( ( fresh_name_name @ Name22 @ Name1 )
                 => ( ! [Za: pi] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi ) ) ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                  ( ! [Za: pi] : ( P @ Za @ Pi )
                 => ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi,Z2: pi] :
                    ( ! [Za: pi] : ( P @ Za @ Pi )
                   => ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
                      ( ! [Za: pi] : ( P @ Za @ Pi13 )
                     => ( ! [Za: pi] : ( P @ Za @ Pi24 )
                       => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
                       => ( ! [Za: pi] : ( P @ Za @ Pi24 )
                         => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi,Z2: pi] :
                          ( ( fresh_name_pi @ Name @ Z2 )
                         => ( ! [Za: pi] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( res @ Name @ Pi ) ) ) )
                     => ( ! [Pi: pi,Z2: pi] :
                            ( ! [Za: pi] : ( P @ Za @ Pi )
                           => ( P @ Z2 @ ( bang @ Pi ) ) )
                       => ( P @ Z @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.strong_induct
thf(fact_189_pi_Ofresh_I10_J,axiom,
    ! [A: name,X1: pi] :
      ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
      = ( fresh_name_pi @ A @ X1 ) ) ).

% pi.fresh(10)
thf(fact_190_pi_Ofresh_I7_J,axiom,
    ! [A: name,X2: pi,X1: pi] :
      ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
      = ( ( fresh_name_pi @ A @ X2 )
        & ( fresh_name_pi @ A @ X1 ) ) ) ).

% pi.fresh(7)
thf(fact_191_simps_I10_J,axiom,
    ! [P: pi,C: name,D: name] :
      ( ( subs @ ( bang @ P ) @ C @ D )
      = ( bang @ ( subs @ P @ C @ D ) ) ) ).

% simps(10)
thf(fact_192_pi_Ofresh_I1_J,axiom,
    ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).

% pi.fresh(1)
thf(fact_193_simps_I7_J,axiom,
    ! [P: pi,Q: pi,C: name,D: name] :
      ( ( subs @ ( sum @ P @ Q ) @ C @ D )
      = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).

% simps(7)
thf(fact_194_simps_I1_J,axiom,
    ! [C: name,D: name] :
      ( ( subs @ piNil @ C @ D )
      = piNil ) ).

% simps(1)
thf(fact_195_pi_Odistinct_I59_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(59)
thf(fact_196_pi_Odistinct_I33_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(33)
thf(fact_197_sumCases,axiom,
    ! [P: pi,Q: pi,Rs: late_residual] :
      ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
     => ( ~ ( late_transitions @ P @ Rs )
       => ( late_transitions @ Q @ Rs ) ) ) ).

% sumCases
thf(fact_198_sumCases_H,axiom,
    ! [P: pi,Q: pi,Rs: late_residual] :
      ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
     => ( ~ ( late_transitions @ P @ Rs )
       => ( late_transitions @ Q @ Rs ) ) ) ).

% sumCases'
thf(fact_199_Sum1,axiom,
    ! [P: pi,Rs: late_residual,Q: pi] :
      ( ( late_transitions @ P @ Rs )
     => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).

% Sum1
thf(fact_200_Sum2,axiom,
    ! [Q: pi,Rs: late_residual,P: pi] :
      ( ( late_transitions @ Q @ Rs )
     => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).

% Sum2
thf(fact_201_pi_Odistinct_I47_J,axiom,
    ! [Pi2: pi,Pi3: pi] :
      ( ( tau @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(47)
thf(fact_202_pi_Odistinct_I79_J,axiom,
    ! [Pi12: pi,Pi23: pi,Pi1: pi,Pi22: pi] :
      ( ( sum @ Pi12 @ Pi23 )
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(79)
thf(fact_203_pi_Odistinct_I81_J,axiom,
    ! [Pi12: pi,Pi23: pi,Name3: name,Pi3: pi] :
      ( ( sum @ Pi12 @ Pi23 )
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(81)
thf(fact_204_pi_Odistinct_I53_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( input @ Name12 @ Name23 @ Pi2 )
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(53)
thf(fact_205_pi_Odistinct_I27_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( output @ Name12 @ Name23 @ Pi2 )
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(27)
thf(fact_206_pi_Odistinct_I41_J,axiom,
    ! [Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( tau @ Pi2 )
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(41)
thf(fact_207_nilCases_H,axiom,
    ! [Rs: late_residual] :
      ~ ( late_transitions @ piNil @ Rs ) ).

% nilCases'
thf(fact_208_zeroTrans,axiom,
    ! [Rs: late_residual] :
      ~ ( late_transitions @ piNil @ Rs ) ).

% zeroTrans
thf(fact_209_pi_Odistinct_I13_J,axiom,
    ! [Pi1: pi,Pi22: pi] :
      ( piNil
     != ( par @ Pi1 @ Pi22 ) ) ).

% pi.distinct(13)
thf(fact_210_pi_Odistinct_I15_J,axiom,
    ! [Name3: name,Pi3: pi] :
      ( piNil
     != ( res @ Name3 @ Pi3 ) ) ).

% pi.distinct(15)
thf(fact_211_pi_Odistinct_I11_J,axiom,
    ! [Pi1: pi,Pi22: pi] :
      ( piNil
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(11)
thf(fact_212_pi_Odistinct_I17_J,axiom,
    ! [Pi3: pi] :
      ( piNil
     != ( bang @ Pi3 ) ) ).

% pi.distinct(17)
thf(fact_213_pi_Odistinct_I83_J,axiom,
    ! [Pi12: pi,Pi23: pi,Pi3: pi] :
      ( ( sum @ Pi12 @ Pi23 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(83)
thf(fact_214_pi_Oinject_I6_J,axiom,
    ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
      ( ( ( sum @ X2 @ X1 )
        = ( sum @ Y2 @ Y1 ) )
      = ( ( X2 = Y2 )
        & ( X1 = Y1 ) ) ) ).

% pi.inject(6)
thf(fact_215_pi_Oinject_I9_J,axiom,
    ! [X1: pi,Y1: pi] :
      ( ( ( bang @ X1 )
        = ( bang @ Y1 ) )
      = ( X1 = Y1 ) ) ).

% pi.inject(9)
thf(fact_216_pi_Odistinct_I89_J,axiom,
    ! [Name2: name,Pi2: pi,Pi3: pi] :
      ( ( res @ Name2 @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(89)
thf(fact_217_pi_Odistinct_I87_J,axiom,
    ! [Pi12: pi,Pi23: pi,Pi3: pi] :
      ( ( par @ Pi12 @ Pi23 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(87)
thf(fact_218_pi_Odistinct_I3_J,axiom,
    ! [Pi3: pi] :
      ( piNil
     != ( tau @ Pi3 ) ) ).

% pi.distinct(3)
thf(fact_219_pi_Odistinct_I1_J,axiom,
    ! [Name13: name,Name24: name,Pi3: pi] :
      ( piNil
     != ( output @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(1)
thf(fact_220_pi_Odistinct_I5_J,axiom,
    ! [Name13: name,Name24: name,Pi3: pi] :
      ( piNil
     != ( input @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(5)
thf(fact_221_pi_Odistinct_I77_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
      ( ( mismatch @ Name12 @ Name23 @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(77)
thf(fact_222_pi_Odistinct_I71_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( mismatch @ Name12 @ Name23 @ Pi2 )
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(71)
thf(fact_223_pi_Odistinct_I69_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi3: pi] :
      ( ( match @ Name12 @ Name23 @ Pi2 )
     != ( bang @ Pi3 ) ) ).

% pi.distinct(69)
thf(fact_224_pi_Odistinct_I63_J,axiom,
    ! [Name12: name,Name23: name,Pi2: pi,Pi1: pi,Pi22: pi] :
      ( ( match @ Name12 @ Name23 @ Pi2 )
     != ( sum @ Pi1 @ Pi22 ) ) ).

% pi.distinct(63)
thf(fact_225_pi_Odistinct_I9_J,axiom,
    ! [Name13: name,Name24: name,Pi3: pi] :
      ( piNil
     != ( mismatch @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(9)
thf(fact_226_pi_Odistinct_I7_J,axiom,
    ! [Name13: name,Name24: name,Pi3: pi] :
      ( piNil
     != ( match @ Name13 @ Name24 @ Pi3 ) ) ).

% pi.distinct(7)
thf(fact_227_Bang,axiom,
    ! [P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
     => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).

% Bang
thf(fact_228_bangCases,axiom,
    ! [P: pi,Rs: late_residual] :
      ( ( late_transitions @ ( bang @ P ) @ Rs )
     => ~ ! [P3: pi] :
            ( ( ( bang @ P )
              = ( bang @ P3 ) )
           => ~ ( late_transitions @ ( par @ P3 @ ( bang @ P3 ) ) @ Rs ) ) ) ).

% bangCases
thf(fact_229_resZeroTrans,axiom,
    ! [X: name,Rs: late_residual] :
      ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).

% resZeroTrans
thf(fact_230_pi_Oinducts,axiom,
    ! [P: pi > $o,Pi2: pi] :
      ( ( P @ piNil )
     => ( ! [Name1: name,Name22: name,Pi: pi] :
            ( ( P @ Pi )
           => ( P @ ( output @ Name1 @ Name22 @ Pi ) ) )
       => ( ! [Pi: pi] :
              ( ( P @ Pi )
             => ( P @ ( tau @ Pi ) ) )
         => ( ! [Name1: name,Name22: name,Pi: pi] :
                ( ( P @ Pi )
               => ( P @ ( input @ Name1 @ Name22 @ Pi ) ) )
           => ( ! [Name1: name,Name22: name,Pi: pi] :
                  ( ( P @ Pi )
                 => ( P @ ( match @ Name1 @ Name22 @ Pi ) ) )
             => ( ! [Name1: name,Name22: name,Pi: pi] :
                    ( ( P @ Pi )
                   => ( P @ ( mismatch @ Name1 @ Name22 @ Pi ) ) )
               => ( ! [Pi13: pi,Pi24: pi] :
                      ( ( P @ Pi13 )
                     => ( ( P @ Pi24 )
                       => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
                 => ( ! [Pi13: pi,Pi24: pi] :
                        ( ( P @ Pi13 )
                       => ( ( P @ Pi24 )
                         => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
                   => ( ! [Name: name,Pi: pi] :
                          ( ( P @ Pi )
                         => ( P @ ( res @ Name @ Pi ) ) )
                     => ( ! [Pi: pi] :
                            ( ( P @ Pi )
                           => ( P @ ( bang @ Pi ) ) )
                       => ( P @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% pi.inducts
thf(fact_231_aux2,axiom,
    ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).

% aux2
thf(fact_232_bangPred_Ocases,axiom,
    ! [A1: pi,A22: pi] :
      ( ( late_bangPred @ A1 @ A22 )
     => ( ( A22
         != ( bang @ A1 ) )
       => ( A22
          = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).

% bangPred.cases
thf(fact_233_bangPred_Osimps,axiom,
    ( late_bangPred
    = ( ^ [A12: pi,A23: pi] :
          ( ? [P5: pi] :
              ( ( A12 = P5 )
              & ( A23
                = ( bang @ P5 ) ) )
          | ? [P5: pi] :
              ( ( A12 = P5 )
              & ( A23
                = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).

% bangPred.simps
thf(fact_234_aux1,axiom,
    ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).

% aux1
thf(fact_235_bangPred_Oinducts,axiom,
    ! [X1: pi,X2: pi,P: pi > pi > $o] :
      ( ( late_bangPred @ X1 @ X2 )
     => ( ! [P3: pi] : ( P @ P3 @ ( bang @ P3 ) )
       => ( ! [P3: pi] : ( P @ P3 @ ( par @ P3 @ ( bang @ P3 ) ) )
         => ( P @ X1 @ X2 ) ) ) ) ).

% bangPred.inducts
thf(fact_236_subs__def,axiom,
    ( subs
    = ( ^ [X3: pi,C3: name,D2: name] :
          ( pi_rec_pi @ piNil
          @ ^ [A4: name,B3: name,P5: pi] : ( output @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
          @ ^ [P5: pi] : tau
          @ ^ [A4: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A4 @ C3 @ D2 ) @ Y5 )
          @ ^ [A4: name,B3: name,P5: pi] : ( match @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
          @ ^ [A4: name,B3: name,P5: pi] : ( mismatch @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
          @ ^ [P5: pi,Q5: pi] : sum
          @ ^ [P5: pi,Q5: pi] : par
          @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
          @ ^ [P5: pi] : bang
          @ X3 ) ) ) ).

% subs_def
thf(fact_237_abs__fresh_I2_J,axiom,
    ! [X: late_subject,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
     => ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
        = ( ( B = A )
          | ( fresh_717452603ubject @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_238_abs__fresh_I2_J,axiom,
    ! [X: late_freeRes,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
     => ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
        = ( ( B = A )
          | ( fresh_1641682979reeRes @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_239_abs__fresh_I2_J,axiom,
    ! [X: name,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_name_name @ X ) )
     => ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
        = ( ( B = A )
          | ( fresh_name_name @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_240_abs__fresh_I2_J,axiom,
    ! [X: pi,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_pi_name @ X ) )
     => ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
        = ( ( B = A )
          | ( fresh_name_pi @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_241_abs__fresh_I2_J,axiom,
    ! [X: name > noption_pi,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
     => ( ( fresh_92802872ion_pi @ B @ ( abs_fu1614711987ion_pi @ A @ X ) )
        = ( ( B = A )
          | ( fresh_543891186ion_pi @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_242_abs__fresh_I2_J,axiom,
    ! [X: name > noption_Late_subject,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
     => ( ( fresh_600418535ubject @ B @ ( abs_fu1705804544ubject @ A @ X ) )
        = ( ( B = A )
          | ( fresh_728038529ubject @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_243_abs__fresh_I2_J,axiom,
    ! [X: name > noption_Late_freeRes,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
     => ( ( fresh_1215331279reeRes @ B @ ( abs_fu1763130856reeRes @ A @ X ) )
        = ( ( B = A )
          | ( fresh_785364841reeRes @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_244_abs__fresh_I2_J,axiom,
    ! [X: name > noption_name,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
     => ( ( fresh_1742414570n_name @ B @ ( abs_fu1394407909n_name @ A @ X ) )
        = ( ( B = A )
          | ( fresh_1093033124n_name @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_245_abs__fresh_I2_J,axiom,
    ! [X: name > noptio354675977ion_pi,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_n1003758744i_name @ X ) )
     => ( ( fresh_1575363742ion_pi @ B @ ( abs_fu446471607ion_pi @ A @ X ) )
        = ( ( B = A )
          | ( fresh_92802872ion_pi @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_246_abs__fresh_I2_J,axiom,
    ! [X: late_freeRes > pi > name > noption_pi,B: name,A: name] :
      ( ( finite_finite_name @ ( supp_L635439693i_name @ X ) )
     => ( ( fresh_481208489ion_pi @ B @ ( abs_fu1682643010ion_pi @ A @ X ) )
        = ( ( B = A )
          | ( fresh_7927363ion_pi @ B @ X ) ) ) ) ).

% abs_fresh(2)
thf(fact_247_exists__fresh_H,axiom,
    ! [X: late_subject] :
      ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
     => ? [C2: name] : ( fresh_717452603ubject @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_248_exists__fresh_H,axiom,
    ! [X: late_freeRes] :
      ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
     => ? [C2: name] : ( fresh_1641682979reeRes @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_249_exists__fresh_H,axiom,
    ! [X: name] :
      ( ( finite_finite_name @ ( supp_name_name @ X ) )
     => ? [C2: name] : ( fresh_name_name @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_250_exists__fresh_H,axiom,
    ! [X: pi] :
      ( ( finite_finite_name @ ( supp_pi_name @ X ) )
     => ? [C2: name] : ( fresh_name_pi @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_251_exists__fresh_H,axiom,
    ! [X: name > noption_pi] :
      ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
     => ? [C2: name] : ( fresh_543891186ion_pi @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_252_exists__fresh_H,axiom,
    ! [X: name > noption_Late_subject] :
      ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
     => ? [C2: name] : ( fresh_728038529ubject @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_253_exists__fresh_H,axiom,
    ! [X: name > noption_Late_freeRes] :
      ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
     => ? [C2: name] : ( fresh_785364841reeRes @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_254_exists__fresh_H,axiom,
    ! [X: name > noption_name] :
      ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
     => ? [C2: name] : ( fresh_1093033124n_name @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_255_exists__fresh_H,axiom,
    ! [X: name > noptio354675977ion_pi] :
      ( ( finite_finite_name @ ( supp_n1003758744i_name @ X ) )
     => ? [C2: name] : ( fresh_92802872ion_pi @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_256_exists__fresh_H,axiom,
    ! [X: late_freeRes > pi > name > noption_pi] :
      ( ( finite_finite_name @ ( supp_L635439693i_name @ X ) )
     => ? [C2: name] : ( fresh_7927363ion_pi @ C2 @ X ) ) ).

% exists_fresh'
thf(fact_257_exists__fresh,axiom,
    ! [X: late_subject] :
      ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_717452603ubject @ C2 @ X ) ) ).

% exists_fresh
thf(fact_258_exists__fresh,axiom,
    ! [X: late_freeRes] :
      ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_1641682979reeRes @ C2 @ X ) ) ).

% exists_fresh
thf(fact_259_exists__fresh,axiom,
    ! [X: name] :
      ( ( finite_finite_name @ ( supp_name_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_name_name @ C2 @ X ) ) ).

% exists_fresh
thf(fact_260_exists__fresh,axiom,
    ! [X: pi] :
      ( ( finite_finite_name @ ( supp_pi_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_name_pi @ C2 @ X ) ) ).

% exists_fresh
thf(fact_261_exists__fresh,axiom,
    ! [X: name > noption_pi] :
      ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_543891186ion_pi @ C2 @ X ) ) ).

% exists_fresh
thf(fact_262_exists__fresh,axiom,
    ! [X: name > noption_Late_subject] :
      ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_728038529ubject @ C2 @ X ) ) ).

% exists_fresh
thf(fact_263_exists__fresh,axiom,
    ! [X: name > noption_Late_freeRes] :
      ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_785364841reeRes @ C2 @ X ) ) ).

% exists_fresh
thf(fact_264_exists__fresh,axiom,
    ! [X: name > noption_name] :
      ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_1093033124n_name @ C2 @ X ) ) ).

% exists_fresh
thf(fact_265_exists__fresh,axiom,
    ! [X: name > noptio354675977ion_pi] :
      ( ( finite_finite_name @ ( supp_n1003758744i_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_92802872ion_pi @ C2 @ X ) ) ).

% exists_fresh
thf(fact_266_exists__fresh,axiom,
    ! [X: late_freeRes > pi > name > noption_pi] :
      ( ( finite_finite_name @ ( supp_L635439693i_name @ X ) )
     => ~ ! [C2: name] :
            ~ ( fresh_7927363ion_pi @ C2 @ X ) ) ).

% exists_fresh
thf(fact_267_supp__fresh__iff,axiom,
    ( supp_n1630792207t_name
    = ( ^ [X3: name > noption_Late_subject] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_728038529ubject @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_268_supp__fresh__iff,axiom,
    ( supp_n252280103s_name
    = ( ^ [X3: name > noption_Late_freeRes] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_785364841reeRes @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_269_supp__fresh__iff,axiom,
    ( supp_n352473082e_name
    = ( ^ [X3: name > noption_name] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_1093033124n_name @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_270_supp__fresh__iff,axiom,
    ( supp_n1003758744i_name
    = ( ^ [X3: name > noptio354675977ion_pi] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_92802872ion_pi @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_271_supp__fresh__iff,axiom,
    ( supp_L1174290467t_name
    = ( ^ [X3: late_subject] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_717452603ubject @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_272_supp__fresh__iff,axiom,
    ( supp_L1228270395s_name
    = ( ^ [X3: late_freeRes] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_1641682979reeRes @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_273_supp__fresh__iff,axiom,
    ( supp_name_name
    = ( ^ [X3: name] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_name_name @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_274_supp__fresh__iff,axiom,
    ( supp_pi_name
    = ( ^ [X3: pi] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_name_pi @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_275_supp__fresh__iff,axiom,
    ( supp_n468628396i_name
    = ( ^ [X3: name > noption_pi] :
          ( collect_name
          @ ^ [A4: name] :
              ~ ( fresh_543891186ion_pi @ A4 @ X3 ) ) ) ) ).

% supp_fresh_iff
thf(fact_276_fresh__def,axiom,
    ( fresh_717452603ubject
    = ( ^ [A4: name,X3: late_subject] :
          ~ ( member_name @ A4 @ ( supp_L1174290467t_name @ X3 ) ) ) ) ).

% fresh_def
thf(fact_277_fresh__def,axiom,
    ( fresh_1641682979reeRes
    = ( ^ [A4: name,X3: late_freeRes] :
          ~ ( member_name @ A4 @ ( supp_L1228270395s_name @ X3 ) ) ) ) ).

% fresh_def
thf(fact_278_fresh__def,axiom,
    ( fresh_name_name
    = ( ^ [A4: name,X3: name] :
          ~ ( member_name @ A4 @ ( supp_name_name @ X3 ) ) ) ) ).

% fresh_def
thf(fact_279_fresh__def,axiom,
    ( fresh_name_pi
    = ( ^ [A4: name,X3: pi] :
          ~ ( member_name @ A4 @ ( supp_pi_name @ X3 ) ) ) ) ).

% fresh_def
thf(fact_280_fresh__def,axiom,
    ( fresh_543891186ion_pi
    = ( ^ [A4: name,X3: name > noption_pi] :
          ~ ( member_name @ A4 @ ( supp_n468628396i_name @ X3 ) ) ) ) ).

% fresh_def
thf(fact_281_pi_Osupp_I9_J,axiom,
    ! [X1: name,X2: pi] :
      ( ( supp_pi_name @ ( res @ X1 @ X2 ) )
      = ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).

% pi.supp(9)
thf(fact_282_pi_Osupp_I3_J,axiom,
    ! [X1: pi] :
      ( ( supp_pi_name @ ( tau @ X1 ) )
      = ( supp_pi_name @ X1 ) ) ).

% pi.supp(3)
thf(fact_283_subject_Osupp_I2_J,axiom,
    ! [X1: name] :
      ( ( supp_L1174290467t_name @ ( late_BoundOutputS @ X1 ) )
      = ( supp_name_name @ X1 ) ) ).

% subject.supp(2)
thf(fact_284_subject_Osupp_I1_J,axiom,
    ! [X1: name] :
      ( ( supp_L1174290467t_name @ ( late_InputS @ X1 ) )
      = ( supp_name_name @ X1 ) ) ).

% subject.supp(1)
thf(fact_285_pi_Osupp_I10_J,axiom,
    ! [X1: pi] :
      ( ( supp_pi_name @ ( bang @ X1 ) )
      = ( supp_pi_name @ X1 ) ) ).

% pi.supp(10)
thf(fact_286_fs__name1,axiom,
    ! [X: late_subject] : ( finite_finite_name @ ( supp_L1174290467t_name @ X ) ) ).

% fs_name1
thf(fact_287_fs__name1,axiom,
    ! [X: late_freeRes] : ( finite_finite_name @ ( supp_L1228270395s_name @ X ) ) ).

% fs_name1
thf(fact_288_fs__name1,axiom,
    ! [X: name] : ( finite_finite_name @ ( supp_name_name @ X ) ) ).

% fs_name1
thf(fact_289_fs__name1,axiom,
    ! [X: pi] : ( finite_finite_name @ ( supp_pi_name @ X ) ) ).

% fs_name1
thf(fact_290_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_291_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_292_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_293_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_294_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_295_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_296_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_297_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_298_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_299_residual_Orecs_I2_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi2 ) )
                  = ( F2 @ FreeRes3 @ Pi2 ) ) ) ) ) ) ) ) ).

% residual.recs(2)
thf(fact_300_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_795910143ubject @ Name2 @ F1 )
                 => ( ( fresh_198785932ubject @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_301_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_660367079reeRes @ Name2 @ F1 )
                 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_302_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_621211324i_name @ Name2 @ F1 )
                 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_303_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
                 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_304_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_795910143ubject @ Name2 @ F1 )
                 => ( ( fresh_198785932ubject @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_305_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_660367079reeRes @ Name2 @ F1 )
                 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_306_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_621211324i_name @ Name2 @ F1 )
                 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_307_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
                 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_308_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_795910143ubject @ Name2 @ F1 )
                 => ( ( fresh_198785932ubject @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_309_residual_Orecs_I1_J,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,Name2: name,Subject2: late_subject,Pi2: pi] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name,X33: pi] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                         => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ( ( fresh_660367079reeRes @ Name2 @ F1 )
                 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
                   => ( ( fresh_717452603ubject @ Name2 @ Subject2 )
                     => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject2 @ Name2 @ Pi2 ) )
                        = ( F1 @ Subject2 @ Name2 @ Pi2 ) ) ) ) ) ) ) ) ) ) ) ).

% residual.recs(1)
thf(fact_310_residual_Orec__fresh,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X: late_residual,Y: late_subject,A: name] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y )
         => ( ! [Y6: late_subject] :
                ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y6 )
               => ( Y6 = Y ) )
           => ( ( fresh_81631222sidual @ A @ X )
             => ( ( fresh_795910143ubject @ A @ F1 )
               => ( ( fresh_198785932ubject @ A @ F2 )
                 => ( fresh_717452603ubject @ A @ Y ) ) ) ) ) ) ) ) ).

% residual.rec_fresh
thf(fact_311_residual_Orec__fresh,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X: late_residual,Y: late_freeRes,A: name] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y )
         => ( ! [Y6: late_freeRes] :
                ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y6 )
               => ( Y6 = Y ) )
           => ( ( fresh_81631222sidual @ A @ X )
             => ( ( fresh_660367079reeRes @ A @ F1 )
               => ( ( fresh_256112244reeRes @ A @ F2 )
                 => ( fresh_1641682979reeRes @ A @ Y ) ) ) ) ) ) ) ) ).

% residual.rec_fresh
thf(fact_312_residual_Orec__fresh,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X: late_residual,Y: name,A: name] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y )
         => ( ! [Y6: name] :
                ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y6 )
               => ( Y6 = Y ) )
           => ( ( fresh_81631222sidual @ A @ X )
             => ( ( fresh_621211324i_name @ A @ F1 )
               => ( ( fresh_1030632537i_name @ A @ F2 )
                 => ( fresh_name_name @ A @ Y ) ) ) ) ) ) ) ) ).

% residual.rec_fresh
thf(fact_313_residual_Orec__fresh,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X: late_residual,Y: pi,A: name] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y )
         => ( ! [Y6: pi] :
                ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y6 )
               => ( Y6 = Y ) )
           => ( ( fresh_81631222sidual @ A @ X )
             => ( ( fresh_1438126218_pi_pi @ A @ F1 )
               => ( ( fresh_1011532071_pi_pi @ A @ F2 )
                 => ( fresh_name_pi @ A @ Y ) ) ) ) ) ) ) ) ).

% residual.rec_fresh
thf(fact_314_residual_Orec__fresh,axiom,
    ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X: late_residual,Y: name > noption_pi,A: name] :
      ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
       => ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y )
         => ( ! [Y6: name > noption_pi] :
                ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y6 )
               => ( Y6 = Y ) )
           => ( ( fresh_81631222sidual @ A @ X )
             => ( ( fresh_747777846ion_pi @ A @ F1 )
               => ( ( fresh_7927363ion_pi @ A @ F2 )
                 => ( fresh_543891186ion_pi @ A @ Y ) ) ) ) ) ) ) ) ).

% residual.rec_fresh
thf(fact_315_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_subject] :
                    ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_subject] :
                        ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_316_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_freeRes] :
                    ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_freeRes] :
                        ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_317_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: name] :
                    ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: name] :
                        ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_318_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_717452603ubject @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: pi] :
                    ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: pi] :
                        ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_319_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_subject] :
                    ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_subject] :
                        ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_320_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_freeRes] :
                    ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_freeRes] :
                        ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_321_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_621211324i_name @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_name_name @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: name] :
                    ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: name] :
                        ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_322_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_1641682979reeRes @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_name_pi @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: pi] :
                    ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: pi] :
                        ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_323_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_795910143ubject @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_717452603ubject @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_subject] :
                    ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_subject] :
                        ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_324_residual_Orec__unique,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,X: late_residual] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
         => ( ! [X13: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X13 @ X22 @ X33 ) )
           => ( ! [X13: late_freeRes,X22: pi] : ( P @ ( F2 @ X13 @ X22 ) )
             => ( ! [X13: late_subject,X22: name] :
                    ( ( fresh_660367079reeRes @ X22 @ F1 )
                   => ( ( fresh_717452603ubject @ X22 @ X13 )
                     => ( ( fresh_name_name @ X22 @ Z )
                       => ! [X33: pi] :
                            ( ( P @ ( F1 @ X13 @ X22 @ X33 ) )
                           => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X13 @ X22 @ X33 ) ) ) ) ) )
               => ? [X4: late_freeRes] :
                    ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
                    & ! [Y7: late_freeRes] :
                        ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
                       => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).

% residual.rec_unique
thf(fact_325_residual_Orec__fin__supp,axiom,
    ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X1: late_residual,Y1: late_subject] :
      ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
       => ( ( late_r689718217ubject @ F1 @ F2 @ X1 @ Y1 )
         => ( finite_finite_name @ ( supp_L1174290467t_name @ Y1 ) ) ) ) ) ).

% residual.rec_fin_supp
thf(fact_326_residual_Orec__fin__supp,axiom,
    ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X1: late_residual,Y1: late_freeRes] :
      ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
       => ( ( late_r1613948593reeRes @ F1 @ F2 @ X1 @ Y1 )
         => ( finite_finite_name @ ( supp_L1228270395s_name @ Y1 ) ) ) ) ) ).

% residual.rec_fin_supp
thf(fact_327_residual_Orec__fin__supp,axiom,
    ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X1: late_residual,Y1: name] :
      ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
       => ( ( late_r1742481968t_name @ F1 @ F2 @ X1 @ Y1 )
         => ( finite_finite_name @ ( supp_name_name @ Y1 ) ) ) ) ) ).

% residual.rec_fin_supp
thf(fact_328_residual_Orec__fin__supp,axiom,
    ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X1: late_residual,Y1: pi] :
      ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
       => ( ( late_r1261898622set_pi @ F1 @ F2 @ X1 @ Y1 )
         => ( finite_finite_name @ ( supp_pi_name @ Y1 ) ) ) ) ) ).

% residual.rec_fin_supp
thf(fact_329_residual_Orec__fin__supp,axiom,
    ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X1: late_residual,Y1: name > noption_pi] :
      ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
       => ( ( late_r750878080ion_pi @ F1 @ F2 @ X1 @ Y1 )
         => ( finite_finite_name @ ( supp_n468628396i_name @ Y1 ) ) ) ) ) ).

% residual.rec_fin_supp
thf(fact_330_pi_Osupp_I4_J,axiom,
    ! [X32: name,X1: name,X2: pi] :
      ( ( supp_pi_name @ ( input @ X32 @ X1 @ X2 ) )
      = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).

% pi.supp(4)
thf(fact_331_residual_Osupp_I1_J,axiom,
    ! [X32: late_subject,X1: name,X2: pi] :
      ( ( supp_L1174042202l_name @ ( late_BoundR @ X32 @ X1 @ X2 ) )
      = ( sup_sup_set_name @ ( supp_L1174290467t_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).

% residual.supp(1)
thf(fact_332_pi_Osupp_I7_J,axiom,
    ! [X2: pi,X1: pi] :
      ( ( supp_pi_name @ ( sum @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).

% pi.supp(7)
thf(fact_333_pi_Osupp_I8_J,axiom,
    ! [X2: pi,X1: pi] :
      ( ( supp_pi_name @ ( par @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).

% pi.supp(8)
thf(fact_334_freeRes_Osupp_I1_J,axiom,
    ! [X2: name,X1: name] :
      ( ( supp_L1228270395s_name @ ( late_OutputR @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_name_name @ X1 ) ) ) ).

% freeRes.supp(1)
thf(fact_335_residual_Osupp_I2_J,axiom,
    ! [X2: late_freeRes,X1: pi] :
      ( ( supp_L1174042202l_name @ ( late_FreeR @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_L1228270395s_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).

% residual.supp(2)
thf(fact_336_pi_Osupp_I2_J,axiom,
    ! [X32: name,X2: name,X1: pi] :
      ( ( supp_pi_name @ ( output @ X32 @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ) ).

% pi.supp(2)
thf(fact_337_pi_Osupp_I6_J,axiom,
    ! [X32: name,X2: name,X1: pi] :
      ( ( supp_pi_name @ ( mismatch @ X32 @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ) ).

% pi.supp(6)
thf(fact_338_pi_Osupp_I5_J,axiom,
    ! [X32: name,X2: name,X1: pi] :
      ( ( supp_pi_name @ ( match @ X32 @ X2 @ X1 ) )
      = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ) ).

% pi.supp(5)
thf(fact_339_pi_Orec__fin__supp,axiom,
    ! [F1: late_subject,F2: name > name > pi > late_subject > late_subject,F3: pi > late_subject > late_subject,F4: name > name > pi > late_subject > late_subject,F5: name > name > pi > late_subject > late_subject,F6: name > name > pi > late_subject > late_subject,F7: pi > pi > late_subject > late_subject > late_subject,F8: pi > pi > late_subject > late_subject > late_subject,F9: name > pi > late_subject > late_subject,F10: pi > late_subject > late_subject,X1: pi,Y1: late_subject] :
      ( ( finite_finite_name @ ( supp_L1174290467t_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_n200783964t_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_p742701746t_name @ F3 ) )
         => ( ( finite_finite_name @ ( supp_n200783964t_name @ F4 ) )
           => ( ( finite_finite_name @ ( supp_n200783964t_name @ F5 ) )
             => ( ( finite_finite_name @ ( supp_n200783964t_name @ F6 ) )
               => ( ( finite_finite_name @ ( supp_p1221108749t_name @ F7 ) )
                 => ( ( finite_finite_name @ ( supp_p1221108749t_name @ F8 ) )
                   => ( ( finite_finite_name @ ( supp_n122125407t_name @ F9 ) )
                     => ( ( finite_finite_name @ ( supp_p742701746t_name @ F10 ) )
                       => ( ( pi_rec232630607ubject @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
                         => ( finite_finite_name @ ( supp_L1174290467t_name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% pi.rec_fin_supp
thf(fact_340_pi_Orec__fin__supp,axiom,
    ! [F1: late_freeRes,F2: name > name > pi > late_freeRes > late_freeRes,F3: pi > late_freeRes > late_freeRes,F4: name > name > pi > late_freeRes > late_freeRes,F5: name > name > pi > late_freeRes > late_freeRes,F6: name > name > pi > late_freeRes > late_freeRes,F7: pi > pi > late_freeRes > late_freeRes > late_freeRes,F8: pi > pi > late_freeRes > late_freeRes > late_freeRes,F9: name > pi > late_freeRes > late_freeRes,F10: pi > late_freeRes > late_freeRes,X1: pi,Y1: late_freeRes] :
      ( ( finite_finite_name @ ( supp_L1228270395s_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_n337505932s_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_p71246050s_name @ F3 ) )
         => ( ( finite_finite_name @ ( supp_n337505932s_name @ F4 ) )
           => ( ( finite_finite_name @ ( supp_n337505932s_name @ F5 ) )
             => ( ( finite_finite_name @ ( supp_n337505932s_name @ F6 ) )
               => ( ( finite_finite_name @ ( supp_p1358344533s_name @ F7 ) )
                 => ( ( finite_finite_name @ ( supp_p1358344533s_name @ F8 ) )
                   => ( ( finite_finite_name @ ( supp_n1410452111s_name @ F9 ) )
                     => ( ( finite_finite_name @ ( supp_p71246050s_name @ F10 ) )
                       => ( ( pi_rec1156860983reeRes @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
                         => ( finite_finite_name @ ( supp_L1228270395s_name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% pi.rec_fin_supp
thf(fact_341_pi_Orec__fin__supp,axiom,
    ! [F1: name,F2: name > name > pi > name > name,F3: pi > name > name,F4: name > name > pi > name > name,F5: name > name > pi > name > name,F6: name > name > pi > name > name,F7: pi > pi > name > name > name,F8: pi > pi > name > name > name,F9: name > pi > name > name,F10: pi > name > name,X1: pi,Y1: name] :
      ( ( finite_finite_name @ ( supp_name_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_n612431512e_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_p1239856366e_name @ F3 ) )
         => ( ( finite_finite_name @ ( supp_n612431512e_name @ F4 ) )
           => ( ( finite_finite_name @ ( supp_n612431512e_name @ F5 ) )
             => ( ( finite_finite_name @ ( supp_n612431512e_name @ F6 ) )
               => ( ( finite_finite_name @ ( supp_p1618090470e_name @ F7 ) )
                 => ( ( finite_finite_name @ ( supp_p1618090470e_name @ F8 ) )
                   => ( ( finite_finite_name @ ( supp_n116460699e_name @ F9 ) )
                     => ( ( finite_finite_name @ ( supp_p1239856366e_name @ F10 ) )
                       => ( ( pi_rec_set_name @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
                         => ( finite_finite_name @ ( supp_name_name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% pi.rec_fin_supp
thf(fact_342_pi_Orec__fin__supp,axiom,
    ! [F1: pi,F2: name > name > pi > pi > pi,F3: pi > pi > pi,F4: name > name > pi > pi > pi,F5: name > name > pi > pi > pi,F6: name > name > pi > pi > pi,F7: pi > pi > pi > pi > pi,F8: pi > pi > pi > pi > pi,F9: name > pi > pi > pi,F10: pi > pi > pi,X1: pi,Y1: pi] :
      ( ( finite_finite_name @ ( supp_pi_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_n1977765016i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ F3 ) )
         => ( ( finite_finite_name @ ( supp_n1977765016i_name @ F4 ) )
           => ( ( finite_finite_name @ ( supp_n1977765016i_name @ F5 ) )
             => ( ( finite_finite_name @ ( supp_n1977765016i_name @ F6 ) )
               => ( ( finite_finite_name @ ( supp_p812767768i_name @ F7 ) )
                 => ( ( finite_finite_name @ ( supp_p812767768i_name @ F8 ) )
                   => ( ( finite_finite_name @ ( supp_n96533147i_name @ F9 ) )
                     => ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ F10 ) )
                       => ( ( pi_rec_set_pi @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
                         => ( finite_finite_name @ ( supp_pi_name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% pi.rec_fin_supp
thf(fact_343_pi_Orec__fin__supp,axiom,
    ! [F1: name > noption_pi,F2: name > name > pi > ( name > noption_pi ) > name > noption_pi,F3: pi > ( name > noption_pi ) > name > noption_pi,F4: name > name > pi > ( name > noption_pi ) > name > noption_pi,F5: name > name > pi > ( name > noption_pi ) > name > noption_pi,F6: name > name > pi > ( name > noption_pi ) > name > noption_pi,F7: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,F8: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,F9: name > pi > ( name > noption_pi ) > name > noption_pi,F10: pi > ( name > noption_pi ) > name > noption_pi,X1: pi,Y1: name > noption_pi] :
      ( ( finite_finite_name @ ( supp_n468628396i_name @ F1 ) )
     => ( ( finite_finite_name @ ( supp_n1987783534i_name @ F2 ) )
       => ( ( finite_finite_name @ ( supp_p1320058820i_name @ F3 ) )
         => ( ( finite_finite_name @ ( supp_n1987783534i_name @ F4 ) )
           => ( ( finite_finite_name @ ( supp_n1987783534i_name @ F5 ) )
             => ( ( finite_finite_name @ ( supp_n1987783534i_name @ F6 ) )
               => ( ( finite_finite_name @ ( supp_p1592910632i_name @ F7 ) )
                 => ( ( finite_finite_name @ ( supp_p1592910632i_name @ F8 ) )
                   => ( ( finite_finite_name @ ( supp_n52582513i_name @ F9 ) )
                     => ( ( finite_finite_name @ ( supp_p1320058820i_name @ F10 ) )
                       => ( ( pi_rec802206470ion_pi @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ F8 @ F9 @ F10 @ X1 @ Y1 )
                         => ( finite_finite_name @ ( supp_n468628396i_name @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% pi.rec_fin_supp
thf(fact_344_supports__fresh,axiom,
    ! [S: set_name,X: late_subject,A: name] :
      ( ( suppor632428453ubject @ S @ X )
     => ( ( finite_finite_name @ S )
       => ( ~ ( member_name @ A @ S )
         => ( fresh_717452603ubject @ A @ X ) ) ) ) ).

% supports_fresh
thf(fact_345_supports__fresh,axiom,
    ! [S: set_name,X: late_freeRes,A: name] :
      ( ( suppor1556658829reeRes @ S @ X )
     => ( ( finite_finite_name @ S )
       => ( ~ ( member_name @ A @ S )
         => ( fresh_1641682979reeRes @ A @ X ) ) ) ) ).

% supports_fresh
thf(fact_346_supports__fresh,axiom,
    ! [S: set_name,X: name,A: name] :
      ( ( supports_name_name @ S @ X )
     => ( ( finite_finite_name @ S )
       => ( ~ ( member_name @ A @ S )
         => ( fresh_name_name @ A @ X ) ) ) ) ).

% supports_fresh
thf(fact_347_supports__fresh,axiom,
    ! [S: set_name,X: pi,A: name] :
      ( ( supports_name_pi @ S @ X )
     => ( ( finite_finite_name @ S )
       => ( ~ ( member_name @ A @ S )
         => ( fresh_name_pi @ A @ X ) ) ) ) ).

% supports_fresh
thf(fact_348_supports__fresh,axiom,
    ! [S: set_name,X: name > noption_pi,A: name] :
      ( ( suppor1289515356ion_pi @ S @ X )
     => ( ( finite_finite_name @ S )
       => ( ~ ( member_name @ A @ S )
         => ( fresh_543891186ion_pi @ A @ X ) ) ) ) ).

% supports_fresh

% Helper facts (3)
thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
    ! [X: name,Y: name] :
      ( ( if_name @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
    ! [X: name,Y: name] :
      ( ( if_name @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ).

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