TSTP Solution File: ITP191^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP191^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:52 EDT 2024

% Result   : Theorem 17.63s 5.31s
% Output   : Refutation 18.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  553
% Syntax   : Number of formulae    :  910 ( 434 unt; 198 typ;   0 def)
%            Number of atoms       : 1936 ( 723 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 8791 ( 193   ~;   1   |; 129   &;7584   @)
%                                         (   0 <=>; 884  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg)
%            Number of types       :   52 (  51 usr)
%            Number of type conns  :  383 ( 383   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  151 ( 147 usr;  21 con; 0-5 aty)
%            Number of variables   : 2560 (  12   ^2493   !;  55   ?;2560   :)

% Comments : 
%------------------------------------------------------------------------------
thf(list_P431515740_pi_pi_type,type,
    list_P431515740_pi_pi: $tType ).

thf(set_Pr806375235ubject_type,type,
    set_Pr806375235ubject: $tType ).

thf(set_Pr1780909331reeRes_type,type,
    set_Pr1780909331reeRes: $tType ).

thf(produc1141751126_pi_pi_type,type,
    produc1141751126_pi_pi: $tType ).

thf(produc1359399907ubject_type,type,
    produc1359399907ubject: $tType ).

thf(produc355105483reeRes_type,type,
    produc355105483reeRes: $tType ).

thf(produc214645451ubject_type,type,
    produc214645451ubject: $tType ).

thf(produc1357834675reeRes_type,type,
    produc1357834675reeRes: $tType ).

thf(set_Pr1131282415pi_Rep_type,type,
    set_Pr1131282415pi_Rep: $tType ).

thf(produc971140967t_unit_type,type,
    produc971140967t_unit: $tType ).

thf(produc257012921pi_Rep_type,type,
    produc257012921pi_Rep: $tType ).

thf(produc1777919905pi_Rep_type,type,
    produc1777919905pi_Rep: $tType ).

thf(list_name_noption_pi_type,type,
    list_name_noption_pi: $tType ).

thf(list_P227219501e_name_type,type,
    list_P227219501e_name: $tType ).

thf(set_Pr443758855e_name_type,type,
    set_Pr443758855e_name: $tType ).

thf(produc1998742700t_name_type,type,
    produc1998742700t_name: $tType ).

thf(produc2052722628s_name_type,type,
    produc2052722628s_name: $tType ).

thf(produc140253050ect_pi_type,type,
    produc140253050ect_pi: $tType ).

thf(produc992857746Res_pi_type,type,
    produc992857746Res_pi: $tType ).

thf(set_Pr1834926343_pi_pi_type,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(produc135724498t_name_type,type,
    produc135724498t_name: $tType ).

thf(produc1212344719pi_Rep_type,type,
    produc1212344719pi_Rep: $tType ).

thf(produc546891580t_unit_type,type,
    produc546891580t_unit: $tType ).

thf(produc738223008nit_pi_type,type,
    produc738223008nit_pi: $tType ).

thf(produc1028309998t_unit_type,type,
    produc1028309998t_unit: $tType ).

thf(produc367475239e_name_type,type,
    produc367475239e_name: $tType ).

thf(product_prod_pi_name_type,type,
    product_prod_pi_name: $tType ).

thf(product_prod_name_pi_type,type,
    product_prod_name_pi: $tType ).

thf(product_prod_pi_pi_type,type,
    product_prod_pi_pi: $tType ).

thf(list_Late_subject_type,type,
    list_Late_subject: $tType ).

thf(list_Late_freeRes_type,type,
    list_Late_freeRes: $tType ).

thf(set_Late_subject_type,type,
    set_Late_subject: $tType ).

thf(set_Late_freeRes_type,type,
    set_Late_freeRes: $tType ).

thf(list_Product_unit_type,type,
    list_Product_unit: $tType ).

thf(list_pi_Rep_type,type,
    list_pi_Rep: $tType ).

thf(late_residual_Rep_type,type,
    late_residual_Rep: $tType ).

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

thf(late_subject_Rep_type,type,
    late_subject_Rep: $tType ).

thf(late_freeRes_Rep_type,type,
    late_freeRes_Rep: $tType ).

thf(set_pi_Rep_type,type,
    set_pi_Rep: $tType ).

thf(list_name_type,type,
    list_name: $tType ).

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

thf(list_pi_type,type,
    list_pi: $tType ).

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

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

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

thf(set_pi_type,type,
    set_pi: $tType ).

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

thf(pi_Rep_type,type,
    pi_Rep: $tType ).

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

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

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

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

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

thf(swap_name_type,type,
    swap_name: produc367475239e_name > name > name ).

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

thf(defaul1399868459t_unit_type,type,
    defaul1399868459t_unit: product_unit ).

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

thf(if_pi_type,type,
    if_pi: $o > pi > pi > pi ).

thf(if_pi_Rep_type,type,
    if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).

thf(if_Late_freeRes_type,type,
    if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).

thf(if_Late_subject_type,type,
    if_Late_subject: $o > late_subject > late_subject > late_subject ).

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

thf(late_TauR_type,type,
    late_TauR: late_freeRes ).

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

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

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

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

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

thf(cons_name_noption_pi_type,type,
    cons_name_noption_pi: ( name > noption_pi ) > list_name_noption_pi > list_name_noption_pi ).

thf(cons_name_type,type,
    cons_name: name > list_name > list_name ).

thf(cons_pi_type,type,
    cons_pi: pi > list_pi > list_pi ).

thf(cons_pi_Rep_type,type,
    cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).

thf(cons_Late_freeRes_type,type,
    cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).

thf(cons_Late_subject_type,type,
    cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).

thf(cons_P1213805021e_name_type,type,
    cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).

thf(cons_P749510156_pi_pi_type,type,
    cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi ).

thf(cons_Product_unit_type,type,
    cons_Product_unit: product_unit > list_Product_unit > list_Product_unit ).

thf(nil_Pr743626285e_name_type,type,
    nil_Pr743626285e_name: list_P227219501e_name ).

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

thf(fresh_543891186ion_pi_type,type,
    fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).

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

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

thf(fresh_name_pi_Rep_type,type,
    fresh_name_pi_Rep: name > pi_Rep > $o ).

thf(fresh_1641682979reeRes_type,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(fresh_81631222sidual_type,type,
    fresh_81631222sidual: name > late_residual > $o ).

thf(fresh_717452603ubject_type,type,
    fresh_717452603ubject: name > late_subject > $o ).

thf(fresh_1135477378ion_pi_type,type,
    fresh_1135477378ion_pi: name > list_name_noption_pi > $o ).

thf(fresh_name_list_name_type,type,
    fresh_name_list_name: name > list_name > $o ).

thf(fresh_name_list_pi_type,type,
    fresh_name_list_pi: name > list_pi > $o ).

thf(fresh_922791155e_name_type,type,
    fresh_922791155e_name: name > list_P227219501e_name > $o ).

thf(fresh_1958133282_pi_pi_type,type,
    fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o ).

thf(fresh_1732817625t_unit_type,type,
    fresh_1732817625t_unit: name > list_Product_unit > $o ).

thf(fresh_441084397e_name_type,type,
    fresh_441084397e_name: name > produc367475239e_name > $o ).

thf(fresh_93646139ame_pi_type,type,
    fresh_93646139ame_pi: name > product_prod_name_pi > $o ).

thf(fresh_1376661020_pi_pi_type,type,
    fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).

thf(fresh_90540034t_unit_type,type,
    fresh_90540034t_unit: name > produc546891580t_unit > $o ).

thf(fresh_261416607i_name_type,type,
    fresh_261416607i_name: name > product_prod_pi_name > $o ).

thf(fresh_1627595501_pi_pi_type,type,
    fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).

thf(fresh_997779380t_unit_type,type,
    fresh_997779380t_unit: name > produc1028309998t_unit > $o ).

thf(fresh_1826856600t_name_type,type,
    fresh_1826856600t_name: name > produc135724498t_name > $o ).

thf(fresh_707692390nit_pi_type,type,
    fresh_707692390nit_pi: name > produc738223008nit_pi > $o ).

thf(fresh_994967853t_unit_type,type,
    fresh_994967853t_unit: name > produc971140967t_unit > $o ).

thf(fresh_1143631827t_unit_type,type,
    fresh_1143631827t_unit: name > product_unit > $o ).

thf(perm_n382765978reeRes_type,type,
    perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).

thf(perm_n1387060402ubject_type,type,
    perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).

thf(perm_n1667196784ion_pi_type,type,
    perm_n1667196784ion_pi: list_P227219501e_name > ( name > noption_pi ) > name > noption_pi ).

thf(perm_n1333244520reeRes_type,type,
    perm_n1333244520reeRes: list_P227219501e_name > ( pi > late_freeRes ) > pi > late_freeRes ).

thf(perm_n190055296ubject_type,type,
    perm_n190055296ubject: list_P227219501e_name > ( pi > late_subject ) > pi > late_subject ).

thf(perm_n1841560599reeRes_type,type,
    perm_n1841560599reeRes: list_P227219501e_name > ( pi_Rep > late_freeRes ) > pi_Rep > late_freeRes ).

thf(perm_n698371375ubject_type,type,
    perm_n698371375ubject: list_P227219501e_name > ( pi_Rep > late_subject ) > pi_Rep > late_subject ).

thf(perm_n1446290985reeRes_type,type,
    perm_n1446290985reeRes: list_P227219501e_name > ( late_freeRes > late_freeRes ) > late_freeRes > late_freeRes ).

thf(perm_n303101761ubject_type,type,
    perm_n303101761ubject: list_P227219501e_name > ( late_freeRes > late_subject ) > late_freeRes > late_subject ).

thf(perm_n443561793reeRes_type,type,
    perm_n443561793reeRes: list_P227219501e_name > ( late_subject > late_freeRes ) > late_subject > late_freeRes ).

thf(perm_n1447856217ubject_type,type,
    perm_n1447856217ubject: list_P227219501e_name > ( late_subject > late_subject ) > late_subject > late_subject ).

thf(perm_name_o_type,type,
    perm_name_o: list_P227219501e_name > $o > $o ).

thf(perm_name_name_type,type,
    perm_name_name: list_P227219501e_name > name > name ).

thf(perm_name_pi_type,type,
    perm_name_pi: list_P227219501e_name > pi > pi ).

thf(perm_name_pi_Rep_type,type,
    perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep ).

thf(perm_n336613537reeRes_type,type,
    perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes ).

thf(perm_n1938283068es_Rep_type,type,
    perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep ).

thf(perm_n414416632sidual_type,type,
    perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).

thf(perm_n890803237al_Rep_type,type,
    perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep ).

thf(perm_n1559866809ubject_type,type,
    perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject ).

thf(perm_n697952036ct_Rep_type,type,
    perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep ).

thf(perm_name_list_name_type,type,
    perm_name_list_name: list_P227219501e_name > list_name > list_name ).

thf(perm_name_list_pi_type,type,
    perm_name_list_pi: list_P227219501e_name > list_pi > list_pi ).

thf(perm_n729617823pi_Rep_type,type,
    perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).

thf(perm_n808352945reeRes_type,type,
    perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).

thf(perm_n1812647369ubject_type,type,
    perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).

thf(perm_n1160739829e_name_type,type,
    perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).

thf(perm_n1255502110_pi_pi_type,type,
    perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).

thf(perm_n1415585007_pi_pi_type,type,
    perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).

thf(perm_n258463228s_name_type,type,
    perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).

thf(perm_n1211707594Res_pi_type,type,
    perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).

thf(perm_n840427369pi_Rep_type,type,
    perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).

thf(perm_n169932155reeRes_type,type,
    perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).

thf(perm_n1174226579ubject_type,type,
    perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).

thf(perm_n204483300t_name_type,type,
    perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).

thf(perm_n359102898ect_pi_type,type,
    perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).

thf(perm_n1467004033pi_Rep_type,type,
    perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).

thf(perm_n1314686611reeRes_type,type,
    perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).

thf(perm_n171497387ubject_type,type,
    perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).

thf(perm_n1960409557t_unit_type,type,
    perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit ).

thf(perm_name_set_name_type,type,
    perm_name_set_name: list_P227219501e_name > set_name > set_name ).

thf(perm_name_set_pi_type,type,
    perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).

thf(perm_name_set_pi_Rep_type,type,
    perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).

thf(perm_n1555914327reeRes_type,type,
    perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).

thf(perm_n412725103ubject_type,type,
    perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).

thf(perm_n675238095_pi_pi_type,type,
    perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).

thf(swap_name2_type,type,
    swap_name2: produc367475239e_name > name > name ).

thf(produc1570949143e_name_type,type,
    produc1570949143e_name: name > name > produc367475239e_name ).

thf(product_Pair_name_pi_type,type,
    product_Pair_name_pi: name > pi > product_prod_name_pi ).

thf(produc235456326_pi_pi_type,type,
    produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).

thf(produc1785453612t_unit_type,type,
    produc1785453612t_unit: name > product_unit > produc546891580t_unit ).

thf(product_Pair_pi_name_type,type,
    product_Pair_pi_name: pi > name > product_prod_pi_name ).

thf(product_Pair_pi_pi_type,type,
    product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).

thf(produc1831798878t_unit_type,type,
    produc1831798878t_unit: pi > product_unit > produc1028309998t_unit ).

thf(produc1701355766s_name_type,type,
    produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).

thf(produc1177552196Res_pi_type,type,
    produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).

thf(produc216486617pi_Rep_type,type,
    produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).

thf(produc1244821099reeRes_type,type,
    produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).

thf(produc320590723ubject_type,type,
    produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).

thf(produc1647375838t_name_type,type,
    produc1647375838t_name: late_subject > name > produc1998742700t_name ).

thf(produc324947500ect_pi_type,type,
    produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).

thf(produc843063281pi_Rep_type,type,
    produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).

thf(produc242091907reeRes_type,type,
    produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).

thf(produc1465345179ubject_type,type,
    produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).

thf(produc421428802t_name_type,type,
    produc421428802t_name: product_unit > name > produc135724498t_name ).

thf(produc1806354576nit_pi_type,type,
    produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi ).

thf(produc1076565719t_unit_type,type,
    produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).

thf(product_Unity_type,type,
    product_Unity: product_unit ).

thf(eqvt_name_type,type,
    eqvt_name: set_Pr443758855e_name > $o ).

thf(eqvt_pi_type,type,
    eqvt_pi: set_Pr1834926343_pi_pi > $o ).

thf(collec1051790738_pi_pi_type,type,
    collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).

thf(strong2129052853vative_type,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(strong743114133lation_type,type,
    strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).

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

thf(member_pi_type,type,
    member_pi: pi > set_pi > $o ).

thf(member_pi_Rep_type,type,
    member_pi_Rep: pi_Rep > set_pi_Rep > $o ).

thf(member_Late_freeRes_type,type,
    member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).

thf(member_Late_subject_type,type,
    member_Late_subject: late_subject > set_Late_subject > $o ).

thf(member695284560e_name_type,type,
    member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).

thf(member558706512_pi_pi_type,type,
    member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(p_type,type,
    p: pi ).

thf(pq_type,type,
    pq: pi ).

thf(p2_type,type,
    p2: pi ).

thf(q_type,type,
    q: pi ).

thf(q2_type,type,
    q2: pi ).

thf(rel_type,type,
    rel: set_Pr1834926343_pi_pi ).

thf(aa_type,type,
    aa: late_subject ).

thf(ab_type,type,
    ab: name ).

thf(b_type,type,
    b: name ).

thf(c_type,type,
    c: name ).

thf(x_type,type,
    x: name ).

thf(xPQ_type,type,
    xPQ: pi ).

thf(y_type,type,
    y: name ).

thf(ya_type,type,
    ya: name ).

thf(333,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Late__Semantics_Osubject_Oinject_I2_J) ).

thf(1665,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(295,axiom,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_1641682979reeRes @ A @ B )
     => ( ( fresh_1641682979reeRes @ C @ B )
       => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_perm__fresh__fresh) ).

thf(1501,plain,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_1641682979reeRes @ A @ B )
     => ( ( fresh_1641682979reeRes @ C @ B )
       => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(83,axiom,
    ! [A: name,B: name,C: list_name] :
      ( ( fresh_name_list_name @ A @ ( cons_name @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_list_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_fresh__list__cons) ).

thf(629,plain,
    ! [A: name,B: name,C: list_name] :
      ( ( fresh_name_list_name @ A @ ( cons_name @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_list_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(286,axiom,
    ! [A: list_P227219501e_name > $o] :
      ( ! [B: list_P227219501e_name] : ( A @ B )
     => ( A @ nil_Pr743626285e_name ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_allE__Nil) ).

thf(1469,plain,
    ! [A: list_P227219501e_name > $o] :
      ( ! [B: list_P227219501e_name] : ( A @ B )
     => ( A @ nil_Pr743626285e_name ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(5,axiom,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__OfreeRes_T) ).

thf(365,plain,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(310,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( ( fresh_name_pi @ C @ A )
           => ( ( fresh_717452603ubject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_transitions_OResB) ).

thf(1559,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( ( fresh_name_pi @ C @ A )
           => ( ( fresh_717452603ubject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(165,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_name__id) ).

thf(909,plain,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(53,axiom,
    ! [A: name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_pi_Rep @ A @ C )
       => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_fresh__perm__app) ).

thf(518,plain,
    ! [A: name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_pi_Rep @ A @ C )
       => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(180,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_pi_Odistinct_I85_J) ).

thf(962,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(173,axiom,
    ! [A: late_subject_Rep] :
      ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_subject__perm__empty) ).

thf(941,plain,
    ! [A: late_subject_Rep] :
      ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(129,axiom,
    ! [A: list_P227219501e_name,B: product_prod_pi_pi,C: set_Pr1834926343_pi_pi] :
      ( ( perm_name_o @ A @ ( member558706512_pi_pi @ B @ C ) )
      = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_in__eqvt) ).

thf(777,plain,
    ! [A: list_P227219501e_name,B: product_prod_pi_pi,C: set_Pr1834926343_pi_pi] :
      ( ( perm_name_o @ A @ ( member558706512_pi_pi @ B @ C ) )
      = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(341,axiom,
    ! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
          ( ( fresh_1376661020_pi_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_residual_Ostrong__inducts) ).

thf(1686,plain,
    ! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
          ( ( fresh_1376661020_pi_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(222,axiom,
    ! [A: name,B: name > noption_pi,C: name] :
      ( ( fresh_543891186ion_pi @ A @ B )
     => ( ( fresh_543891186ion_pi @ C @ B )
       => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_perm__fresh__fresh) ).

thf(1158,plain,
    ! [A: name,B: name > noption_pi,C: name] :
      ( ( fresh_543891186ion_pi @ A @ B )
     => ( ( fresh_543891186ion_pi @ C @ B )
       => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(246,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
            ( ( ( par @ A @ B )
              = ( par @ F @ J ) )
           => ( ( ( late_BoundR @ C @ D @ E )
                = ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
             => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
               => ( ( fresh_name_pi @ H @ F )
                 => ( ( fresh_name_pi @ H @ J )
                   => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
              ( ( ( par @ A @ B )
                = ( par @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_name_pi @ H @ J )
                   => ( ( fresh_name_pi @ H @ F )
                     => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_parCasesB_H) ).

thf(1290,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
            ( ( ( par @ A @ B )
              = ( par @ F @ J ) )
           => ( ( ( late_BoundR @ C @ D @ E )
                = ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
             => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
               => ( ( fresh_name_pi @ H @ F )
                 => ( ( fresh_name_pi @ H @ J )
                   => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
              ( ( ( par @ A @ B )
                = ( par @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_name_pi @ H @ J )
                   => ( ( fresh_name_pi @ H @ F )
                     => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(197,axiom,
    ! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_residual_Odistinct_I1_J) ).

thf(1068,plain,
    ! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(279,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_pi_Odistinct_I55_J) ).

thf(1443,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(218,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: list_P227219501e_name] :
      ( ( eqvt_pi @ A )
     => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ B @ C ) @ A )
       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ D @ B ) @ ( perm_name_pi @ D @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_eqvtRelI) ).

thf(1142,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: list_P227219501e_name] :
      ( ( eqvt_pi @ A )
     => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ B @ C ) @ A )
       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ D @ B ) @ ( perm_name_pi @ D @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(91,axiom,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_InputS @ B ) )
      = ( late_InputS @ ( perm_name_name @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_subject_Operm_I1_J) ).

thf(655,plain,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_InputS @ B ) )
      = ( late_InputS @ ( perm_name_name @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(317,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
      ( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
     => ( ! [D: pi,E: pi,F: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
       => ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_parSym) ).

thf(1596,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
      ( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
     => ( ! [D: pi,E: pi,F: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
       => ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(266,axiom,
    fresh_name_pi @ ya @ q,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_cComm1_Ohyps_I4_J) ).

thf(1406,plain,
    fresh_name_pi @ ya @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(294,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( res @ A @ D ) @ B @ C )
          = ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_simps_I9_J) ).

thf(1497,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( res @ A @ D ) @ B @ C )
          = ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(200,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_1641682979reeRes @ D @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_freshFreeDerivative_I1_J) ).

thf(1078,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_1641682979reeRes @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(12,axiom,
    ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_fresh__unit) ).

thf(384,plain,
    ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(47,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Late__Semantics1_OfreeRes_Oinject) ).

thf(500,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(242,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( input @ C @ D @ B )
        = ( input @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_alphaInput) ).

thf(1275,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( input @ C @ D @ B )
        = ( input @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(38,axiom,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1627595501_pi_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_fresh__prod) ).

thf(472,plain,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1627595501_pi_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(327,axiom,
    ab != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cOpen_Ohyps_I2_J) ).

thf(1640,plain,
    ab != x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(249,axiom,
    ( strong743114133lation
    = ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
          ( ! [D: late_subject,E: name,F: pi] :
              ( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
                & ( fresh_name_pi @ E @ A ) )
             => ? [G: pi] :
                  ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
                  & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
          & ! [D: late_freeRes,E: pi] :
              ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
             => ? [F: pi] :
                  ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_simulation__def) ).

thf(1354,plain,
    ( strong743114133lation
    = ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
          ( ! [D: late_subject,E: name,F: pi] :
              ( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
                & ( fresh_name_pi @ E @ A ) )
             => ? [G: pi] :
                  ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
                  & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
          & ! [D: late_freeRes,E: pi] :
              ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
             => ? [F: pi] :
                  ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(19,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_eq__eqvt) ).

thf(404,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(162,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ B @ ( res @ A @ C ) ) @ ( res @ A @ ( par @ B @ C ) ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Res) ).

thf(898,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ B @ ( res @ A @ C ) ) @ ( res @ A @ ( par @ B @ C ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(213,axiom,
    ! [A: list_P227219501e_name,B: pi > late_freeRes,C: pi] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1333244520reeRes @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_perm__app) ).

thf(1127,plain,
    ! [A: list_P227219501e_name,B: pi > late_freeRes,C: pi] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1333244520reeRes @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(315,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subject_Ofresh_I2_J) ).

thf(1576,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(330,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( fresh_name_pi @ C @ B )
       => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_perm__fresh__fresh) ).

thf(1650,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( fresh_name_pi @ C @ B )
       => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(251,axiom,
    late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_cComm1_Ohyps_I2_J) ).

thf(1359,plain,
    late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(260,axiom,
    y != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062) ).

thf(1386,plain,
    y != x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(66,axiom,
    ! [A: list_P227219501e_name,B: name,C: late_subject] :
      ( ( perm_name_o @ A @ ( fresh_717452603ubject @ B @ C ) )
      = ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_fresh__eqvt) ).

thf(565,plain,
    ! [A: list_P227219501e_name,B: name,C: late_subject] :
      ( ( perm_name_o @ A @ ( fresh_717452603ubject @ B @ C ) )
      = ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(300,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_simCasesCont) ).

thf(1518,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(14,axiom,
    ! [A: name,B: list_P227219501e_name,C: name] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_name @ A @ C )
       => ( fresh_name_name @ A @ ( perm_name_name @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_fresh__perm__app) ).

thf(389,plain,
    ! [A: name,B: list_P227219501e_name,C: name] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_name @ A @ C )
       => ( fresh_name_name @ A @ ( perm_name_name @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(245,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_fresh__prodD_I1_J) ).

thf(1287,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(274,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Late__Semantics_OComm1) ).

thf(1430,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(113,axiom,
    ! [A: list_P227219501e_name,B: name,C: set_name] :
      ( ( perm_name_o @ A @ ( member_name @ B @ C ) )
      = ( member_name @ ( perm_name_name @ A @ B ) @ ( perm_name_set_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_in__eqvt) ).

thf(719,plain,
    ! [A: list_P227219501e_name,B: name,C: set_name] :
      ( ( perm_name_o @ A @ ( member_name @ B @ C ) )
      = ( member_name @ ( perm_name_name @ A @ B ) @ ( perm_name_set_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(8,axiom,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi____Rep_T) ).

thf(372,plain,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(81,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( ( perm_n336613537reeRes @ A @ B )
        = ( perm_n336613537reeRes @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_perm__bij) ).

thf(619,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( ( perm_n336613537reeRes @ A @ B )
        = ( perm_n336613537reeRes @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(122,axiom,
    ! [A: list_P227219501e_name,B: name,C: name > noption_pi] :
      ( ( perm_name_o @ A @ ( fresh_543891186ion_pi @ B @ C ) )
      = ( fresh_543891186ion_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1667196784ion_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_fresh__eqvt) ).

thf(751,plain,
    ! [A: list_P227219501e_name,B: name,C: name > noption_pi] :
      ( ( perm_name_o @ A @ ( fresh_543891186ion_pi @ B @ C ) )
      = ( fresh_543891186ion_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1667196784ion_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(243,axiom,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_717452603ubject @ A @ B )
     => ( ( fresh_717452603ubject @ C @ B )
       => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_perm__fresh__fresh) ).

thf(1279,plain,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_717452603ubject @ A @ B )
     => ( ( fresh_717452603ubject @ C @ B )
       => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(1,conjecture,
    ? [A: pi] :
      ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ A ) )
      & ( strong2129052853vative @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ? [A: pi] :
        ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ A ) )
        & ( strong2129052853vative @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(357,plain,
    ~ ? [A: pi] :
        ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ A ) )
        & ( strong2129052853vative @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(284,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_name__swap__bij) ).

thf(1462,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(64,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes > late_subject,C: late_freeRes] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n303101761ubject @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_perm__app) ).

thf(559,plain,
    ! [A: list_P227219501e_name,B: late_freeRes > late_subject,C: late_freeRes] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n303101761ubject @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(356,axiom,
    ! [A: list_P227219501e_name,B: name,C: name,D: pi] :
      ( ( perm_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( input @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_pi_Operm_I4_J) ).

thf(1800,plain,
    ! [A: list_P227219501e_name,B: name,C: name,D: pi] :
      ( ( perm_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( input @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(86,axiom,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi_T) ).

thf(638,plain,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(299,axiom,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subject_Oexhaust) ).

thf(1514,plain,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(346,axiom,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: name,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ F ) )
           => ! [I: pi] :
                ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
               => ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
                 => ( G = H ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
              ( ( ( res @ A @ B )
                = ( res @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_717452603ubject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh_name_pi @ H @ F )
                       => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_resCasesB_H) ).

thf(1704,plain,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: name,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ F ) )
           => ! [I: pi] :
                ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
               => ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
                 => ( G = H ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
              ( ( ( res @ A @ B )
                = ( res @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_717452603ubject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh_name_pi @ H @ F )
                       => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(247,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( B != C )
       => ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Open) ).

thf(1347,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( B != C )
       => ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(23,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_n1559866809ubject @ A @ B )
        = ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_eq__eqvt) ).

thf(416,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_n1559866809ubject @ A @ B )
        = ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(292,axiom,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( late_BoundOutputS @ ( perm_name_name @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_subject_Operm_I2_J) ).

thf(1489,plain,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( late_BoundOutputS @ ( perm_name_name @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(39,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_perm__compose) ).

thf(475,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(285,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( fresh_name_pi @ C @ A )
             => ( ( fresh_name_pi @ C @ E )
               => ( ( F != B )
                 => ( ( fresh_name_pi @ F @ D )
                   => ( ( C != B )
                     => ( ( fresh_name_pi @ C @ G )
                       => ( ( F != C )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_transitions_OClose2) ).

thf(1465,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( fresh_name_pi @ C @ A )
             => ( ( fresh_name_pi @ C @ E )
               => ( ( F != B )
                 => ( ( fresh_name_pi @ F @ D )
                   => ( ( C != B )
                     => ( ( fresh_name_pi @ C @ G )
                       => ( ( F != C )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(133,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_n336613537reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( late_OutputR @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_freeRes_Operm_I1_J) ).

thf(789,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_n336613537reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( late_OutputR @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(281,axiom,
    ( ( late_OutputR @ ab @ x )
    = late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cComm1_Ohyps_I9_J) ).

thf(1450,plain,
    ( ( late_OutputR @ ab @ x )
    = late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(74,axiom,
    ! [A: list_P227219501e_name,B: $o,C: late_freeRes,D: late_freeRes] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
          = ( perm_n336613537reeRes @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
          = ( perm_n336613537reeRes @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_if__eqvt) ).

thf(591,plain,
    ! [A: list_P227219501e_name,B: $o,C: late_freeRes,D: late_freeRes] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
          = ( perm_n336613537reeRes @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
          = ( perm_n336613537reeRes @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(208,axiom,
    ! [A: name,B: pi_Rep,C: name] :
      ( ( fresh_name_pi_Rep @ A @ B )
     => ( ( fresh_name_pi_Rep @ C @ B )
       => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_perm__fresh__fresh) ).

thf(1109,plain,
    ! [A: name,B: pi_Rep,C: name] :
      ( ( fresh_name_pi_Rep @ A @ B )
     => ( ( fresh_name_pi_Rep @ C @ B )
       => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(181,axiom,
    fresh_name_pi @ y @ q,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062) ).

thf(966,plain,
    fresh_name_pi @ y @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(244,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_forget) ).

thf(1283,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(41,axiom,
    ! [A: name,B: product_unit,C: pi] :
      ( ( fresh_707692390nit_pi @ A @ ( produc1806354576nit_pi @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_fresh__prod) ).

thf(480,plain,
    ! [A: name,B: product_unit,C: pi] :
      ( ( fresh_707692390nit_pi @ A @ ( produc1806354576nit_pi @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(339,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Late__Semantics_OPar1B) ).

thf(1682,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(216,axiom,
    ! [A: set_Pr443758855e_name,B: list_P227219501e_name,C: name,D: name] :
      ( ( eqvt_name @ A )
     => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ B @ C ) @ ( perm_name_name @ B @ D ) ) @ A )
       => ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_eqvtRelE) ).

thf(1136,plain,
    ! [A: set_Pr443758855e_name,B: list_P227219501e_name,C: name,D: name] :
      ( ( eqvt_name @ A )
     => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ B @ C ) @ ( perm_name_name @ B @ D ) ) @ A )
       => ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(221,axiom,
    ! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
      ( ! [D: late_subject,E: name,F: pi] :
          ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
         => ( ( fresh_name_pi @ E @ B )
           => ? [G: pi] :
                ( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
                & ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
     => ( ! [D: late_freeRes,E: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
           => ? [F: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
                & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
       => ( strong743114133lation @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_simCases) ).

thf(1151,plain,
    ! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
      ( ! [D: late_subject,E: name,F: pi] :
          ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
         => ( ( fresh_name_pi @ E @ B )
           => ? [G: pi] :
                ( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
                & ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
     => ( ! [D: late_freeRes,E: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
           => ? [F: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
                & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
       => ( strong743114133lation @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(171,axiom,
    fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Bound_Ohyps_I5_J) ).

thf(937,plain,
    fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(125,axiom,
    ! [A: name,B: name,C: product_unit] :
      ( ( fresh_90540034t_unit @ A @ ( produc1785453612t_unit @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_fresh__prod) ).

thf(766,plain,
    ! [A: name,B: name,C: product_unit] :
      ( ( fresh_90540034t_unit @ A @ ( produc1785453612t_unit @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(225,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_fresh__prodD_I2_J) ).

thf(1169,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(116,axiom,
    ! [A: list_P227219501e_name] :
      ( ( perm_n336613537reeRes @ A @ late_TauR )
      = late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_freeRes_Operm_I2_J) ).

thf(734,plain,
    ! [A: list_P227219501e_name] :
      ( ( perm_n336613537reeRes @ A @ late_TauR )
      = late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(280,axiom,
    ! [A: late_residual_Rep] :
      ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_residual__perm__empty) ).

thf(1447,plain,
    ! [A: late_residual_Rep] :
      ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(198,axiom,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_perm__swap_I2_J) ).

thf(1072,plain,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(128,axiom,
    ! [A: list_P227219501e_name,B: late_subject > late_subject,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n1447856217ubject @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_perm__app) ).

thf(774,plain,
    ! [A: list_P227219501e_name,B: late_subject > late_subject,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n1447856217ubject @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(301,axiom,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1143631827t_unit @ A @ B )
     => ( ( fresh_1143631827t_unit @ C @ B )
       => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_perm__fresh__fresh) ).

thf(1526,plain,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1143631827t_unit @ A @ B )
     => ( ( fresh_1143631827t_unit @ C @ B )
       => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(275,axiom,
    ! [A: late_subject > $o,B: late_subject] :
      ( ! [C: name] : ( A @ ( late_InputS @ C ) )
     => ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subject_Oinducts) ).

thf(1433,plain,
    ! [A: late_subject > $o,B: late_subject] :
      ( ! [C: name] : ( A @ ( late_InputS @ C ) )
     => ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(27,axiom,
    ! [A: name,B: produc1141751126_pi_pi,C: list_P431515740_pi_pi] :
      ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ B @ C ) )
      = ( ( fresh_1376661020_pi_pi @ A @ B )
        & ( fresh_1958133282_pi_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_fresh__list__cons) ).

thf(428,plain,
    ! [A: name,B: produc1141751126_pi_pi,C: list_P431515740_pi_pi] :
      ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ B @ C ) )
      = ( ( fresh_1376661020_pi_pi @ A @ B )
        & ( fresh_1958133282_pi_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(318,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ C @ D )
        = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B ) @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_renaming) ).

thf(1600,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ C @ D )
        = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B ) @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(56,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_n336613537reeRes @ A @ B )
        = ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_eq__eqvt) ).

thf(527,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_n336613537reeRes @ A @ B )
        = ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(345,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: produc1141751126_pi_pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1376661020_pi_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_simCasesCont) ).

thf(1696,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: produc1141751126_pi_pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1376661020_pi_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(319,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_fresh__prod) ).

thf(1604,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(99,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_cp__name__name1) ).

thf(678,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(342,axiom,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_name__swap__bij) ).

thf(1691,plain,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(93,axiom,
    ! [A: name,B: list_P227219501e_name,C: produc1141751126_pi_pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ A @ C )
       => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_fresh__perm__app) ).

thf(661,plain,
    ! [A: name,B: list_P227219501e_name,C: produc1141751126_pi_pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ A @ C )
       => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(61,axiom,
    ! [A: list_P227219501e_name,B: $o,C: name,D: name] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
          = ( perm_name_name @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
          = ( perm_name_name @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_if__eqvt) ).

thf(546,plain,
    ! [A: list_P227219501e_name,B: $o,C: name,D: name] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
          = ( perm_name_name @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
          = ( perm_name_name @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(138,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( perm_n169932155reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_perm__prod_Osimps) ).

thf(810,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( perm_n169932155reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(11,axiom,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi____Rep_T) ).

thf(381,plain,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(136,axiom,
    ! [A: $o,B: list_P227219501e_name,C: late_freeRes,D: late_freeRes] :
      ( ( A
       => ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
          = ( perm_n336613537reeRes @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
          = ( perm_n336613537reeRes @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_abs__fun__if) ).

thf(798,plain,
    ! [A: $o,B: list_P227219501e_name,C: late_freeRes,D: late_freeRes] :
      ( ( A
       => ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
          = ( perm_n336613537reeRes @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
          = ( perm_n336613537reeRes @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(51,axiom,
    ! [A: name,B: name > noption_pi,C: list_name_noption_pi] :
      ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ B @ C ) )
      = ( ( fresh_543891186ion_pi @ A @ B )
        & ( fresh_1135477378ion_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_fresh__list__cons) ).

thf(512,plain,
    ! [A: name,B: name > noption_pi,C: list_name_noption_pi] :
      ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ B @ C ) )
      = ( ( fresh_543891186ion_pi @ A @ B )
        & ( fresh_1135477378ion_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(30,axiom,
    ! [A: list_P227219501e_name,B: name,C: name > noption_pi] :
      ( ( fresh_543891186ion_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1667196784ion_pi @ A @ C ) )
      = ( fresh_543891186ion_pi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fresh__bij) ).

thf(439,plain,
    ! [A: list_P227219501e_name,B: name,C: name > noption_pi] :
      ( ( fresh_543891186ion_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1667196784ion_pi @ A @ C ) )
      = ( fresh_543891186ion_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(203,axiom,
    ! [A: set_Pr443758855e_name,B: name,C: name,D: list_P227219501e_name] :
      ( ( eqvt_name @ A )
     => ( ( member695284560e_name @ ( produc1570949143e_name @ B @ C ) @ A )
       => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ D @ B ) @ ( perm_name_name @ D @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_eqvtRelI) ).

thf(1091,plain,
    ! [A: set_Pr443758855e_name,B: name,C: name,D: list_P227219501e_name] :
      ( ( eqvt_name @ A )
     => ( ( member695284560e_name @ ( produc1570949143e_name @ B @ C ) @ A )
       => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ D @ B ) @ ( perm_name_name @ D @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(177,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_name__perm__compose) ).

thf(952,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(240,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_resSimCases) ).

thf(1255,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(75,axiom,
    ! [A: list_P227219501e_name,B: name > late_subject,C: name] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n1387060402ubject @ A @ B @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_perm__app) ).

thf(598,plain,
    ! [A: list_P227219501e_name,B: name > late_subject,C: name] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n1387060402ubject @ A @ B @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(15,axiom,
    ! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
      ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_mem__Collect__eq) ).

thf(392,plain,
    ! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
      ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(20,axiom,
    ! [A: name,B: pi,C: product_unit] :
      ( ( fresh_997779380t_unit @ A @ ( produc1831798878t_unit @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fresh__prod) ).

thf(407,plain,
    ! [A: name,B: pi,C: product_unit] :
      ( ( fresh_997779380t_unit @ A @ ( produc1831798878t_unit @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(237,axiom,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) )
      = ( fresh_name_pi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fresh__bij) ).

thf(1223,plain,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) )
      = ( fresh_name_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(161,axiom,
    ! [A: name,B: name,C: late_freeRes,D: name] :
      ( ( A != B )
     => ( ( fresh_1641682979reeRes @ B @ C )
       => ( ( fresh_1641682979reeRes @ A @ C )
         => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_fresh__aux) ).

thf(894,plain,
    ! [A: name,B: name,C: late_freeRes,D: name] :
      ( ( A != B )
     => ( ( fresh_1641682979reeRes @ B @ C )
       => ( ( fresh_1641682979reeRes @ A @ C )
         => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(212,axiom,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
       => ( ( fresh_name_pi @ E @ A )
         => ? [G: pi] :
              ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
              & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_simE_I1_J) ).

thf(1123,plain,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
       => ( ( fresh_name_pi @ E @ A )
         => ? [G: pi] :
              ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
              & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(152,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_name_pi @ A @ ( res @ B @ C ) )
      = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_pi_Ofresh_I9_J) ).

thf(862,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_name_pi @ A @ ( res @ B @ C ) )
      = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(313,axiom,
    fresh_name_pi @ ya @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_cComm1_Ohyps_I3_J) ).

thf(1570,plain,
    fresh_name_pi @ ya @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(337,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Late__Semantics_OComm2) ).

thf(1676,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(149,axiom,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_pt__name1) ).

thf(847,plain,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(157,axiom,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_717452603ubject @ A @ B )
     => ( ( fresh_717452603ubject @ C @ B )
       => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_name__fresh__fresh) ).

thf(879,plain,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_717452603ubject @ A @ B )
     => ( ( fresh_717452603ubject @ C @ B )
       => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(229,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_cp__name__name1) ).

thf(1178,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(144,axiom,
    ! [A: late_freeRes_Rep] :
      ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_freeRes__perm__empty) ).

thf(830,plain,
    ! [A: late_freeRes_Rep] :
      ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(353,axiom,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_name__calc_I2_J) ).

thf(1787,plain,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(232,axiom,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_name__swap) ).

thf(1210,plain,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(267,axiom,
    ! [A: produc367475239e_name,B: list_P227219501e_name,C: produc367475239e_name,D: list_P227219501e_name] :
      ( ( ( cons_P1213805021e_name @ A @ B )
        = ( cons_P1213805021e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_list_Oinject) ).

thf(1407,plain,
    ! [A: produc367475239e_name,B: list_P227219501e_name,C: produc367475239e_name,D: list_P227219501e_name] :
      ( ( ( cons_P1213805021e_name @ A @ B )
        = ( cons_P1213805021e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(262,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Late__Semantics1_Osubject_Oinject_I2_J) ).

thf(1392,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(110,axiom,
    ! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
      ( ( ( late_FreeR @ A @ B )
        = ( late_FreeR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_residual_Oinject_I2_J) ).

thf(710,plain,
    ! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
      ( ( ( late_FreeR @ A @ B )
        = ( late_FreeR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(35,axiom,
    ! [A: name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1641682979reeRes @ A @ C )
       => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_fresh__perm__app) ).

thf(456,plain,
    ! [A: name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1641682979reeRes @ A @ C )
       => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(185,axiom,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_residual_Ostrong__induct) ).

thf(974,plain,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(207,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ A )
       => ( ( fresh_name_pi @ C @ E )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_transitions_OPar1B) ).

thf(1106,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ A )
       => ( ( fresh_name_pi @ C @ E )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(265,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Late__Semantics_Osubject_Odistinct_I1_J) ).

thf(1402,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(106,axiom,
    ! [A: list_P227219501e_name,B: name,C: late_freeRes] :
      ( ( perm_name_o @ A @ ( fresh_1641682979reeRes @ B @ C ) )
      = ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_fresh__eqvt) ).

thf(697,plain,
    ! [A: list_P227219501e_name,B: name,C: late_freeRes] :
      ( ( perm_name_o @ A @ ( fresh_1641682979reeRes @ B @ C ) )
      = ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(350,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: list_P227219501e_name,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ B @ C ) @ ( perm_name_pi @ B @ D ) ) @ A )
       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_eqvtRelE) ).

thf(1772,plain,
    ! [A: set_Pr1834926343_pi_pi,B: list_P227219501e_name,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ B @ C ) @ ( perm_name_pi @ B @ D ) ) @ A )
       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(115,axiom,
    ! [A: $o,B: list_P227219501e_name,C: pi_Rep,D: pi_Rep] :
      ( ( A
       => ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
          = ( perm_name_pi_Rep @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
          = ( perm_name_pi_Rep @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_abs__fun__if) ).

thf(725,plain,
    ! [A: $o,B: list_P227219501e_name,C: pi_Rep,D: pi_Rep] :
      ( ( A
       => ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
          = ( perm_name_pi_Rep @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
          = ( perm_name_pi_Rep @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(335,axiom,
    fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Bound_Ohyps_I3_J) ).

thf(1672,plain,
    fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(194,axiom,
    ! [A: name,B: list_P227219501e_name,C: pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_pi @ A @ C )
       => ( fresh_name_pi @ A @ ( perm_name_pi @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fresh__perm__app) ).

thf(1006,plain,
    ! [A: name,B: list_P227219501e_name,C: pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_name_pi @ A @ C )
       => ( fresh_name_pi @ A @ ( perm_name_pi @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(78,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_perm__compose) ).

thf(610,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(131,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_name__perm__compose) ).

thf(783,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
      ( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
      = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(252,axiom,
    fresh_717452603ubject @ y @ aa,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Bound_Ohyps_I4_J) ).

thf(1360,plain,
    fresh_717452603ubject @ y @ aa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(248,axiom,
    ! [A: name,B: produc1141751126_pi_pi,C: name] :
      ( ( fresh_1376661020_pi_pi @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ C @ B )
       => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_name__fresh__fresh) ).

thf(1350,plain,
    ! [A: name,B: produc1141751126_pi_pi,C: name] :
      ( ( fresh_1376661020_pi_pi @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ C @ B )
       => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(119,axiom,
    ! [A: name,B: list_P227219501e_name,C: name > noption_pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_543891186ion_pi @ A @ C )
       => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_fresh__perm__app) ).

thf(742,plain,
    ! [A: name,B: list_P227219501e_name,C: name > noption_pi] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_543891186ion_pi @ A @ C )
       => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(70,axiom,
    ! [A: list_P227219501e_name,B: name,C: list_name] :
      ( ( perm_name_list_name @ A @ ( cons_name @ B @ C ) )
      = ( cons_name @ ( perm_name_name @ A @ B ) @ ( perm_name_list_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_cons__eqvt) ).

thf(578,plain,
    ! [A: list_P227219501e_name,B: name,C: list_name] :
      ( ( perm_name_list_name @ A @ ( cons_name @ B @ C ) )
      = ( cons_name @ ( perm_name_name @ A @ B ) @ ( perm_name_list_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(90,axiom,
    ! [A: pi_Rep,B: pi_Rep,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_pi_Rep @ C @ A )
        = ( perm_name_pi_Rep @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_pt__bij3) ).

thf(650,plain,
    ! [A: pi_Rep,B: pi_Rep,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_pi_Rep @ C @ A )
        = ( perm_name_pi_Rep @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(176,axiom,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1143631827t_unit @ A @ B )
     => ( ( fresh_1143631827t_unit @ C @ B )
       => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_name__fresh__fresh) ).

thf(948,plain,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1143631827t_unit @ A @ B )
     => ( ( fresh_1143631827t_unit @ C @ B )
       => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(312,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_name__swap__bij) ).

thf(1567,plain,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(43,axiom,
    ! [A: list_P227219501e_name,B: name,C: pi_Rep] :
      ( ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) )
      = ( fresh_name_pi_Rep @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_fresh__bij) ).

thf(488,plain,
    ! [A: list_P227219501e_name,B: name,C: pi_Rep] :
      ( ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) )
      = ( fresh_name_pi_Rep @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(253,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_perm__swap_I1_J) ).

thf(1361,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(58,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep,C: set_pi_Rep] :
      ( ( perm_name_o @ A @ ( member_pi_Rep @ B @ C ) )
      = ( member_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_name_set_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_in__eqvt) ).

thf(537,plain,
    ! [A: list_P227219501e_name,B: pi_Rep,C: set_pi_Rep] :
      ( ( perm_name_o @ A @ ( member_pi_Rep @ B @ C ) )
      = ( member_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_name_set_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(96,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_name_o @ A @ ( fresh_name_name @ B @ C ) )
      = ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_fresh__eqvt) ).

thf(669,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( perm_name_o @ A @ ( fresh_name_name @ B @ C ) )
      = ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(272,axiom,
    ! [A: name,B: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_name__id) ).

thf(1424,plain,
    ! [A: name,B: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(269,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_perm__swap_I1_J) ).

thf(1414,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(163,axiom,
    ! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
          ( ( fresh_1376661020_pi_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_residual_Ostrong__induct) ).

thf(901,plain,
    ! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
          ( ( fresh_1376661020_pi_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(102,axiom,
    ( eqvt_pi
    = ( ^ [A: set_Pr1834926343_pi_pi] :
        ! [B: product_prod_pi_pi,C: list_P227219501e_name] :
          ( ( member558706512_pi_pi @ B @ A )
         => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_eqvt__def) ).

thf(686,plain,
    ( eqvt_pi
    = ( ^ [A: set_Pr1834926343_pi_pi] :
        ! [B: product_prod_pi_pi,C: list_P227219501e_name] :
          ( ( member558706512_pi_pi @ B @ A )
         => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(199,axiom,
    ! [A: late_freeRes] :
      ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_pt__name1) ).

thf(1075,plain,
    ! [A: late_freeRes] :
      ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(82,axiom,
    ! [A: list_P227219501e_name,B: $o,C: pi_Rep,D: pi_Rep] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
          = ( perm_name_pi_Rep @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
          = ( perm_name_pi_Rep @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_if__eqvt) ).

thf(622,plain,
    ! [A: list_P227219501e_name,B: $o,C: pi_Rep,D: pi_Rep] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
          = ( perm_name_pi_Rep @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
          = ( perm_name_pi_Rep @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(52,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: list_Late_freeRes] :
      ( ( perm_n808352945reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
      = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n808352945reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_cons__eqvt) ).

thf(515,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: list_Late_freeRes] :
      ( ( perm_n808352945reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
      = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n808352945reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(334,axiom,
    ! [A: name,B: name,C: product_unit,D: name] :
      ( ( A != B )
     => ( ( fresh_1143631827t_unit @ B @ C )
       => ( ( fresh_1143631827t_unit @ A @ C )
         => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_fresh__aux) ).

thf(1668,plain,
    ! [A: name,B: name,C: product_unit,D: name] :
      ( ( A != B )
     => ( ( fresh_1143631827t_unit @ B @ C )
       => ( ( fresh_1143631827t_unit @ A @ C )
         => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(48,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: set_Late_subject] :
      ( ( perm_name_o @ A @ ( member_Late_subject @ B @ C ) )
      = ( member_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n412725103ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_in__eqvt) ).

thf(503,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: set_Late_subject] :
      ( ( perm_name_o @ A @ ( member_Late_subject @ B @ C ) )
      = ( member_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n412725103ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(89,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: name] :
      ( ( perm_n258463228s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( produc1701355766s_name @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_perm__prod_Osimps) ).

thf(647,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: name] :
      ( ( perm_n258463228s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( produc1701355766s_name @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(191,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_pi_Oinject_I7_J) ).

thf(997,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(302,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: pi] :
                ( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
               => ( F @ ( par @ G @ B ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( F @ ( par @ A @ G ) ) )
             => ( F @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_parCasesB) ).

thf(1530,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: pi] :
                ( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
               => ( F @ ( par @ G @ B ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( F @ ( par @ A @ G ) ) )
             => ( F @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(304,axiom,
    ! [A: name,B: name,C: pi,D: name] :
      ( ( A != B )
     => ( ( fresh_name_pi @ B @ C )
       => ( ( fresh_name_pi @ A @ C )
         => ( fresh_name_pi @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_fresh__aux) ).

thf(1539,plain,
    ! [A: name,B: name,C: pi,D: name] :
      ( ( A != B )
     => ( ( fresh_name_pi @ B @ C )
       => ( ( fresh_name_pi @ A @ C )
         => ( fresh_name_pi @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(134,axiom,
    ! [A: list_P227219501e_name,B: name,C: product_unit] :
      ( ( fresh_1143631827t_unit @ ( perm_name_name @ A @ B ) @ ( perm_n1960409557t_unit @ A @ C ) )
      = ( fresh_1143631827t_unit @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_fresh__bij) ).

thf(792,plain,
    ! [A: list_P227219501e_name,B: name,C: product_unit] :
      ( ( fresh_1143631827t_unit @ ( perm_name_name @ A @ B ) @ ( perm_n1960409557t_unit @ A @ C ) )
      = ( fresh_1143631827t_unit @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(344,axiom,
    late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Bound_Ohyps_I1_J) ).

thf(1695,plain,
    late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(311,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( A != C )
       => ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_fresh__fact1) ).

thf(1563,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( A != C )
       => ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(17,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_name__perm__compose) ).

thf(398,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(57,axiom,
    ! [A: list_P227219501e_name,B: $o,C: late_subject,D: late_subject] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
          = ( perm_n1559866809ubject @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
          = ( perm_n1559866809ubject @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_if__eqvt) ).

thf(530,plain,
    ! [A: list_P227219501e_name,B: $o,C: late_subject,D: late_subject] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
          = ( perm_n1559866809ubject @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
          = ( perm_n1559866809ubject @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(170,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_name @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_simCasesCont) ).

thf(926,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_name @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(202,axiom,
    ! [A: product_unit > late_residual > $o,B: product_unit,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: product_unit] :
          ( ( fresh_1143631827t_unit @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: product_unit] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_residual_Ostrong__inducts) ).

thf(1086,plain,
    ! [A: product_unit > late_residual > $o,B: product_unit,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: product_unit] :
          ( ( fresh_1143631827t_unit @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: product_unit] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(172,axiom,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_perm__swap_I1_J) ).

thf(938,plain,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(164,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
      ( ( strong2129052853vative @ A @ B @ C @ D @ E )
     => ( ( eqvt_pi @ E )
       => ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ ( perm_n1559866809ubject @ F @ C ) @ ( perm_name_name @ F @ D ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_derivativeEqvtI) ).

thf(906,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
      ( ( strong2129052853vative @ A @ B @ C @ D @ E )
     => ( ( eqvt_pi @ E )
       => ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ ( perm_n1559866809ubject @ F @ C ) @ ( perm_name_name @ F @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(298,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( fresh_name_pi @ F @ A )
             => ( ( fresh_name_pi @ F @ E )
               => ( ( C != B )
                 => ( ( fresh_name_pi @ C @ G )
                   => ( ( F != B )
                     => ( ( fresh_name_pi @ F @ D )
                       => ( ( C != F )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_transitions_OClose1) ).

thf(1510,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( fresh_name_pi @ F @ A )
             => ( ( fresh_name_pi @ F @ E )
               => ( ( C != B )
                 => ( ( fresh_name_pi @ C @ G )
                   => ( ( F != B )
                     => ( ( fresh_name_pi @ F @ D )
                       => ( ( C != F )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(26,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_perm__bij) ).

thf(425,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(235,axiom,
    ( aa
    = ( late_BoundOutputS @ ab ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cOpen_Ohyps_I3_J) ).

thf(1219,plain,
    ( aa
    = ( late_BoundOutputS @ ab ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(120,axiom,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_name__exists__fresh) ).

thf(745,plain,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(257,axiom,
    ! [A: name,B: produc1141751126_pi_pi,C: name] :
      ( ( fresh_1376661020_pi_pi @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ C @ B )
       => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_perm__fresh__fresh) ).

thf(1374,plain,
    ! [A: name,B: produc1141751126_pi_pi,C: name] :
      ( ( fresh_1376661020_pi_pi @ A @ B )
     => ( ( fresh_1376661020_pi_pi @ C @ B )
       => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(9,axiom,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__Osubject_T) ).

thf(375,plain,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(76,axiom,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
     => ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_fresh__prodD_I1_J) ).

thf(601,plain,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
     => ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(141,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_name_pi @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_freshFreeDerivative_I2_J) ).

thf(819,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_name_pi @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(65,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_cp__name__name1) ).

thf(562,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(105,axiom,
    ! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) )
      = ( fresh_1376661020_pi_pi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fresh__bij) ).

thf(694,plain,
    ! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) )
      = ( fresh_1376661020_pi_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(148,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_alphaRes) ).

thf(843,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(325,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_name @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_resSimCases) ).

thf(1620,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_name @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(179,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_fresh__fact2) ).

thf(958,plain,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(238,axiom,
    ! [A: name,B: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_name__id) ).

thf(1226,plain,
    ! [A: name,B: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(22,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fresh__prod) ).

thf(413,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(352,axiom,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_pt__name1) ).

thf(1784,plain,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(261,axiom,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( perm_name_o @ A @ ( fresh_name_pi @ B @ C ) )
      = ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_fresh__eqvt) ).

thf(1389,plain,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( perm_name_o @ A @ ( fresh_name_pi @ B @ C ) )
      = ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(156,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_name_name @ A @ B )
     => ( ( fresh_name_name @ C @ B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_name__fresh__fresh) ).

thf(875,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_name_name @ A @ B )
     => ( ( fresh_name_name @ C @ B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(143,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( fresh_name_pi @ C @ B )
       => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_name__fresh__fresh) ).

thf(826,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( fresh_name_pi @ C @ B )
       => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(87,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subject_Ofresh_I1_J) ).

thf(641,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(217,axiom,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_subst__identity) ).

thf(1139,plain,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(32,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_fresh__prodD_I2_J) ).

thf(445,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(68,axiom,
    ! [A: name,B: list_P227219501e_name,C: product_unit] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1143631827t_unit @ A @ C )
       => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_fresh__perm__app) ).

thf(572,plain,
    ! [A: name,B: list_P227219501e_name,C: product_unit] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_1143631827t_unit @ A @ C )
       => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(111,axiom,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Collect__mem__eq) ).

thf(713,plain,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(168,axiom,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_1641682979reeRes @ A @ B )
     => ( ( fresh_1641682979reeRes @ C @ B )
       => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_name__fresh__fresh) ).

thf(919,plain,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_1641682979reeRes @ A @ B )
     => ( ( fresh_1641682979reeRes @ C @ B )
       => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(175,axiom,
    eqvt_pi @ rel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_assms_I3_J) ).

thf(947,plain,
    eqvt_pi @ rel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(250,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_perm__swap_I1_J) ).

thf(1356,plain,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(59,axiom,
    ! [A: product_unit] :
      ~ ! [B: name] :
          ~ ( fresh_1143631827t_unit @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_name__exists__fresh) ).

thf(540,plain,
    ! [A: product_unit] :
      ~ ! [B: name] :
          ~ ( fresh_1143631827t_unit @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(97,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: pi_Rep] :
      ( ( perm_n1467004033pi_Rep @ A @ ( produc843063281pi_Rep @ B @ C ) )
      = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_perm__prod_Osimps) ).

thf(672,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: pi_Rep] :
      ( ( perm_n1467004033pi_Rep @ A @ ( produc843063281pi_Rep @ B @ C ) )
      = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(100,axiom,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi_T) ).

thf(681,plain,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(24,axiom,
    ! [A: product_unit] : ( A = product_Unity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_old_Ounit_Oexhaust) ).

thf(419,plain,
    ! [A: product_unit] : ( A = product_Unity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(189,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh_name_pi @ C @ A )
       => ( fresh_81631222sidual @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_freshResidual) ).

thf(990,plain,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh_name_pi @ C @ A )
       => ( fresh_81631222sidual @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(293,axiom,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_residual_Ostrong__induct) ).

thf(1492,plain,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(4,axiom,
    ! [A: name,B: name] :
      ( ( if_name @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Oname_T) ).

thf(362,plain,
    ! [A: name,B: name] :
      ( ( if_name @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(117,axiom,
    ! [A: produc1141751126_pi_pi] :
      ~ ! [B: name] :
          ~ ( fresh_1376661020_pi_pi @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_name__exists__fresh) ).

thf(737,plain,
    ! [A: produc1141751126_pi_pi] :
      ~ ! [B: name] :
          ~ ( fresh_1376661020_pi_pi @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(80,axiom,
    ! [A: list_P227219501e_name,B: name,C: pi_Rep] :
      ( ( perm_name_o @ A @ ( fresh_name_pi_Rep @ B @ C ) )
      = ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_fresh__eqvt) ).

thf(616,plain,
    ! [A: list_P227219501e_name,B: name,C: pi_Rep] :
      ( ( perm_name_o @ A @ ( fresh_name_pi_Rep @ B @ C ) )
      = ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(228,axiom,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ScopeExt) ).

thf(1175,plain,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(186,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_transitions_OInput) ).

thf(979,plain,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(77,axiom,
    ! [A: late_freeRes > $o,B: late_freeRes] :
      ( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
     => ( ( A @ late_TauR )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_freeRes_Oinducts) ).

thf(604,plain,
    ! [A: late_freeRes > $o,B: late_freeRes] :
      ( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
     => ( ( A @ late_TauR )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(50,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep,C: list_pi_Rep] :
      ( ( perm_n729617823pi_Rep @ A @ ( cons_pi_Rep @ B @ C ) )
      = ( cons_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_n729617823pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_cons__eqvt) ).

thf(509,plain,
    ! [A: list_P227219501e_name,B: pi_Rep,C: list_pi_Rep] :
      ( ( perm_n729617823pi_Rep @ A @ ( cons_pi_Rep @ B @ C ) )
      = ( cons_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_n729617823pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(29,axiom,
    ! [A: late_freeRes,B: late_freeRes,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n336613537reeRes @ C @ A )
        = ( perm_n336613537reeRes @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_pt__bij3) ).

thf(434,plain,
    ! [A: late_freeRes,B: late_freeRes,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n336613537reeRes @ C @ A )
        = ( perm_n336613537reeRes @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(314,axiom,
    ! [A: pi,B: pi,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_pi @ C @ A )
        = ( perm_name_pi @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_pt__bij3) ).

thf(1571,plain,
    ! [A: pi,B: pi,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_pi @ C @ A )
        = ( perm_name_pi @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(277,axiom,
    fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Bound_Ohyps_I2_J) ).

thf(1439,plain,
    fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(287,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_resTrans_I2_J) ).

thf(1471,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(45,axiom,
    ! [A: name,B: product_unit,C: list_Product_unit] :
      ( ( fresh_1732817625t_unit @ A @ ( cons_Product_unit @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_1732817625t_unit @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_fresh__list__cons) ).

thf(494,plain,
    ! [A: name,B: product_unit,C: list_Product_unit] :
      ( ( fresh_1732817625t_unit @ A @ ( cons_Product_unit @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_1732817625t_unit @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(140,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_name__swap) ).

thf(816,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(223,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( A != B )
     => ( ( fresh_name_name @ B @ C )
       => ( ( fresh_name_name @ A @ C )
         => ( fresh_name_name @ A @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_fresh__aux) ).

thf(1162,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( A != B )
     => ( ( fresh_name_name @ B @ C )
       => ( ( fresh_name_name @ A @ C )
         => ( fresh_name_name @ A @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(42,axiom,
    ! [A: name,B: name,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_name @ C @ A )
        = ( perm_name_name @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_pt__bij3) ).

thf(483,plain,
    ! [A: name,B: name,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_name @ C @ A )
        = ( perm_name_name @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(107,axiom,
    ! [A: late_subject,B: late_subject,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n1559866809ubject @ C @ A )
        = ( perm_n1559866809ubject @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_pt__bij3) ).

thf(700,plain,
    ! [A: late_subject,B: late_subject,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n1559866809ubject @ C @ A )
        = ( perm_n1559866809ubject @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(167,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( C != B )
             => ( ( C != F )
               => ( ( fresh_name_pi @ C @ G )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_transitions_OComm1) ).

thf(915,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( C != B )
             => ( ( C != F )
               => ( ( fresh_name_pi @ C @ G )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(259,axiom,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_residual_Ostrong__inducts) ).

thf(1381,plain,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(309,axiom,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_pi @ A @ B )
        = ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_eq__eqvt) ).

thf(1556,plain,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_pi @ A @ B )
        = ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(126,axiom,
    defaul1399868459t_unit = product_Unity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_default__unit__def) ).

thf(769,plain,
    defaul1399868459t_unit = product_Unity,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(187,axiom,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_pi__perm__empty) ).

thf(983,plain,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(288,axiom,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_name__swap) ).

thf(1474,plain,
    ! [A: name,B: name,C: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(233,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_inputBoundOutputTrans) ).

thf(1213,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(154,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_perm__compose) ).

thf(868,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
      ( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
      = ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(158,axiom,
    ! [A: name,B: pi,C: late_subject,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( late_BoundR @ C @ D @ B )
        = ( late_BoundR @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_alphaBoundResidual) ).

thf(883,plain,
    ! [A: name,B: pi,C: late_subject,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( late_BoundR @ C @ D @ B )
        = ( late_BoundR @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(188,axiom,
    ! [A: name,B: name,C: name > noption_pi,D: name] :
      ( ( A != B )
     => ( ( fresh_543891186ion_pi @ B @ C )
       => ( ( fresh_543891186ion_pi @ A @ C )
         => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_fresh__aux) ).

thf(986,plain,
    ! [A: name,B: name,C: name > noption_pi,D: name] :
      ( ( A != B )
     => ( ( fresh_543891186ion_pi @ B @ C )
       => ( ( fresh_543891186ion_pi @ A @ C )
         => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(209,axiom,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_resInputBoundOutputTrans) ).

thf(1113,plain,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(289,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_swap__simps_I2_J) ).

thf(1477,plain,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(254,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( res @ C @ B ) @ C @ A )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Agent_OsubstRes3) ).

thf(1364,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( res @ C @ B ) @ C @ A )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(206,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_name_name @ A @ B )
     => ( ( fresh_name_name @ C @ B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_perm__fresh__fresh) ).

thf(1102,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_name_name @ A @ B )
     => ( ( fresh_name_name @ C @ B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(28,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_perm__compose) ).

thf(431,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(343,axiom,
    fresh_1143631827t_unit @ ya @ product_Unity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_cComm1_Ohyps_I8_J) ).

thf(1694,plain,
    fresh_1143631827t_unit @ ya @ product_Unity,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(92,axiom,
    ! [A: list_P227219501e_name,B: late_subject > late_freeRes,C: late_subject] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n443561793reeRes @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_perm__app) ).

thf(658,plain,
    ! [A: list_P227219501e_name,B: late_subject > late_freeRes,C: late_subject] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n443561793reeRes @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(166,axiom,
    ! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_resInputFreeTrans) ).

thf(912,plain,
    ! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(54,axiom,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_Late__Semantics1_Osubject_Oinject_I1_J) ).

thf(521,plain,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(226,axiom,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_cOpen_Ohyps_I1_J) ).

thf(1171,plain,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(130,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_cp__name__name1) ).

thf(780,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(328,axiom,
    ! [A: late_subject] :
      ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_pt__name1) ).

thf(1643,plain,
    ! [A: late_subject] :
      ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(351,axiom,
    ! [A: $o,B: list_P227219501e_name,C: pi,D: pi] :
      ( ( A
       => ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
          = ( perm_name_pi @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
          = ( perm_name_pi @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_abs__fun__if) ).

thf(1775,plain,
    ! [A: $o,B: list_P227219501e_name,C: pi,D: pi] :
      ( ( A
       => ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
          = ( perm_name_pi @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
          = ( perm_name_pi @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(192,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: name,D: pi] :
      ( ( perm_n414416632sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( late_BoundR @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_residual_Operm_I1_J) ).

thf(1000,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: name,D: pi] :
      ( ( perm_n414416632sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( late_BoundR @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(114,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Late__Semantics_OfreeRes_Oinject) ).

thf(722,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(98,axiom,
    ! [A: list_P227219501e_name,B: name,C: late_freeRes] :
      ( ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) )
      = ( fresh_1641682979reeRes @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_fresh__bij) ).

thf(675,plain,
    ! [A: list_P227219501e_name,B: name,C: late_freeRes] :
      ( ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) )
      = ( fresh_1641682979reeRes @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(174,axiom,
    ya != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cComm1_Ohyps_I5_J) ).

thf(944,plain,
    ya != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(135,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) )
      = ( fresh_name_name @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fresh__bij) ).

thf(795,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) )
      = ( fresh_name_name @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(297,axiom,
    fresh_name_pi @ y @ ( par @ p @ q ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062) ).

thf(1509,plain,
    fresh_name_pi @ y @ ( par @ p @ q ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(201,axiom,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_residual_Ostrong__inducts) ).

thf(1081,plain,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(219,axiom,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( perm_name_pi @ A @ ( res @ B @ C ) )
      = ( res @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_pi_Operm_I9_J) ).

thf(1145,plain,
    ! [A: list_P227219501e_name,B: name,C: pi] :
      ( ( perm_name_pi @ A @ ( res @ B @ C ) )
      = ( res @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(123,axiom,
    ! [A: $o,B: list_P227219501e_name,C: late_subject,D: late_subject] :
      ( ( A
       => ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
          = ( perm_n1559866809ubject @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
          = ( perm_n1559866809ubject @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_abs__fun__if) ).

thf(754,plain,
    ! [A: $o,B: list_P227219501e_name,C: late_subject,D: late_subject] :
      ( ( A
       => ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
          = ( perm_n1559866809ubject @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
          = ( perm_n1559866809ubject @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(62,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_pi_Rep @ A @ B )
        = ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_eq__eqvt) ).

thf(553,plain,
    ! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
      ( ( perm_name_o @ A @ ( B = C ) )
      = ( ( perm_name_pi_Rep @ A @ B )
        = ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(146,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B )
        = ( subs @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_injPermSubst) ).

thf(836,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B )
        = ( subs @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(348,axiom,
    ! [A: name,B: name,C: name] :
      ( ( ( A = B )
       => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
          = C ) )
      & ( ( A != B )
       => ( ( ( C = B )
           => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
              = A ) )
          & ( ( C != B )
           => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_name__calc_I3_J) ).

thf(1758,plain,
    ! [A: name,B: name,C: name] :
      ( ( ( A = B )
       => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
          = C ) )
      & ( ( A != B )
       => ( ( ( C = B )
           => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
              = A ) )
          & ( ( C != B )
           => ( ( swap_name2 @ ( produc1570949143e_name @ A @ C ) @ B )
              = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(224,axiom,
    ! [A: late_residual > $o,B: late_residual] :
      ( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_residual_Oinducts) ).

thf(1166,plain,
    ! [A: late_residual > $o,B: late_residual] :
      ( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(183,axiom,
    ! [A: list_P227219501e_name,B: pi > late_subject,C: pi] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n190055296ubject @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_perm__app) ).

thf(968,plain,
    ! [A: list_P227219501e_name,B: pi > late_subject,C: pi] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n190055296ubject @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(230,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ! [E: pi,F: pi,G: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
     => ( ! [E: pi,F: pi,G: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ E @ F ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
       => ( ! [E: pi,F: pi,G: pi,H: name] :
              ( ( fresh_name_pi @ H @ E )
             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
         => ( ! [E: pi,F: pi,G: pi,H: name] :
                ( ( fresh_name_pi @ H @ G )
               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
           => ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_parAssocLeft) ).

thf(1181,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ! [E: pi,F: pi,G: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
     => ( ! [E: pi,F: pi,G: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ E @ F ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
       => ( ! [E: pi,F: pi,G: pi,H: name] :
              ( ( fresh_name_pi @ H @ E )
             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
         => ( ! [E: pi,F: pi,G: pi,H: name] :
                ( ( fresh_name_pi @ H @ G )
               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
           => ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(193,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_transitions_OPar2B) ).

thf(1003,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(159,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Late__Semantics_OResB) ).

thf(887,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(184,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_perm__swap_I2_J) ).

thf(971,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(255,axiom,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
       => ? [F: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
            & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_simE_I2_J) ).

thf(1368,plain,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
       => ? [F: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
            & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(291,axiom,
    ! [A: product_unit > late_residual > $o,B: product_unit,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: product_unit] :
          ( ( fresh_1143631827t_unit @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: product_unit] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_residual_Ostrong__induct) ).

thf(1484,plain,
    ! [A: product_unit > late_residual > $o,B: product_unit,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: product_unit] :
          ( ( fresh_1143631827t_unit @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: product_unit] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(190,axiom,
    ! [A: name,B: name,C: pi_Rep,D: name] :
      ( ( A != B )
     => ( ( fresh_name_pi_Rep @ B @ C )
       => ( ( fresh_name_pi_Rep @ A @ C )
         => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_fresh__aux) ).

thf(993,plain,
    ! [A: name,B: name,C: pi_Rep,D: name] :
      ( ( A != B )
     => ( ( fresh_name_pi_Rep @ B @ C )
       => ( ( fresh_name_pi_Rep @ A @ C )
         => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(108,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: set_Late_freeRes] :
      ( ( perm_name_o @ A @ ( member_Late_freeRes @ B @ C ) )
      = ( member_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1555914327reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_in__eqvt) ).

thf(705,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: set_Late_freeRes] :
      ( ( perm_name_o @ A @ ( member_Late_freeRes @ B @ C ) )
      = ( member_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1555914327reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(322,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Late__Semantics_OClose1) ).

thf(1611,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(354,axiom,
    ! [A: list_P227219501e_name,B: $o,C: pi,D: pi] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
          = ( perm_name_pi @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
          = ( perm_name_pi @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_if__eqvt) ).

thf(1790,plain,
    ! [A: list_P227219501e_name,B: $o,C: pi,D: pi] :
      ( ( ( perm_name_o @ A @ B )
       => ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
          = ( perm_name_pi @ A @ C ) ) )
      & ( ~ ( perm_name_o @ A @ B )
       => ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
          = ( perm_name_pi @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(72,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_fresh__prod) ).

thf(585,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(147,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
      ( ( perm_n414416632sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( late_FreeR @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_residual_Operm_I2_J) ).

thf(840,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
      ( ( perm_n414416632sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( late_FreeR @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(37,axiom,
    ! [A: $o,B: list_P227219501e_name,C: name,D: name] :
      ( ( A
       => ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
          = ( perm_name_name @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
          = ( perm_name_name @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_abs__fun__if) ).

thf(463,plain,
    ! [A: $o,B: list_P227219501e_name,C: name,D: name] :
      ( ( A
       => ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
          = ( perm_name_name @ B @ C ) ) )
      & ( ~ A
       => ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
          = ( perm_name_name @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(338,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
      ( ( strong2129052853vative @ A @ B @ C @ D @ E )
     => ( ( eqvt_pi @ E )
       => ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ C @ ( perm_name_name @ F @ D ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_derivativeEqvtI2) ).

thf(1679,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
      ( ( strong2129052853vative @ A @ B @ C @ D @ E )
     => ( ( eqvt_pi @ E )
       => ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ C @ ( perm_name_name @ F @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(3,axiom,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__OfreeRes_T) ).

thf(359,plain,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(282,axiom,
    ! [A: name,B: pi,C: late_freeRes,D: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ E ) )
           => ( ( ( late_FreeR @ C @ D )
                = ( late_FreeR @ F @ ( res @ H @ G ) ) )
             => ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
               => ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_resCasesF_H) ).

thf(1452,plain,
    ! [A: name,B: pi,C: late_freeRes,D: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ E ) )
           => ( ( ( late_FreeR @ C @ D )
                = ( late_FreeR @ F @ ( res @ H @ G ) ) )
             => ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
               => ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(326,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
      ( ( perm_n1211707594Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_perm__prod_Osimps) ).

thf(1637,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
      ( ( perm_n1211707594Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(214,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( subs @ ( res @ A @ B ) @ C @ A )
      = ( res @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3) ).

thf(1130,plain,
    ! [A: name,B: pi,C: name] :
      ( ( subs @ ( res @ A @ B ) @ C @ A )
      = ( res @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(316,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: product_unit] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1143631827t_unit @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_resSimCases) ).

thf(1579,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: product_unit] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1143631827t_unit @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(305,axiom,
    ! [A: name,B: name,C: list_P227219501e_name,D: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ C ) @ D )
      = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_name__calc_I1_J) ).

thf(1543,plain,
    ! [A: name,B: name,C: list_P227219501e_name,D: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ C ) @ D )
      = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(303,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Par2F) ).

thf(1536,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(79,axiom,
    ! [A: list_P227219501e_name,B: name > late_freeRes,C: name] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n382765978reeRes @ A @ B @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_perm__app) ).

thf(613,plain,
    ! [A: list_P227219501e_name,B: name > late_freeRes,C: name] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n382765978reeRes @ A @ B @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(236,axiom,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_freshRes) ).

thf(1221,plain,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(273,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_1641682979reeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ResF) ).

thf(1427,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_1641682979reeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(355,axiom,
    ! [A: pi,B: late_residual,C: list_P227219501e_name] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( perm_name_pi @ C @ A ) @ ( perm_n414416632sidual @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_eqvt) ).

thf(1797,plain,
    ! [A: pi,B: late_residual,C: list_P227219501e_name] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( perm_name_pi @ C @ A ) @ ( perm_n414416632sidual @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(256,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_Late__Semantics_OInput) ).

thf(1372,plain,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(241,axiom,
    ! [A: list_P227219501e_name,B: pi,C: set_pi] :
      ( ( perm_name_o @ A @ ( member_pi @ B @ C ) )
      = ( member_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_set_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_in__eqvt) ).

thf(1272,plain,
    ! [A: list_P227219501e_name,B: pi,C: set_pi] :
      ( ( perm_name_o @ A @ ( member_pi @ B @ C ) )
      = ( member_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_set_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(46,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes > late_freeRes,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1446290985reeRes @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_perm__app) ).

thf(497,plain,
    ! [A: list_P227219501e_name,B: late_freeRes > late_freeRes,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1446290985reeRes @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(324,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_perm__swap_I2_J) ).

thf(1617,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(204,axiom,
    ! [A: name,B: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_name__id) ).

thf(1094,plain,
    ! [A: name,B: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(13,axiom,
    ! [A: name,B: list_P227219501e_name,C: late_subject] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_717452603ubject @ A @ C )
       => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_fresh__perm__app) ).

thf(386,plain,
    ! [A: name,B: list_P227219501e_name,C: late_subject] :
      ( ( fresh_922791155e_name @ A @ B )
     => ( ( fresh_717452603ubject @ A @ C )
       => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(271,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_name__swap) ).

thf(1421,plain,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(34,axiom,
    ! [A: product_unit > $o,B: product_unit] :
      ( ( A @ product_Unity )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_old_Ounit_Oinducts) ).

thf(450,plain,
    ! [A: product_unit > $o,B: product_unit] :
      ( ( A @ product_Unity )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(283,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_perm__swap_I2_J) ).

thf(1459,plain,
    ! [A: name,B: name,C: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(63,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: list_Late_subject] :
      ( ( perm_n1812647369ubject @ A @ ( cons_Late_subject @ B @ C ) )
      = ( cons_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1812647369ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_cons__eqvt) ).

thf(556,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: list_Late_subject] :
      ( ( perm_n1812647369ubject @ A @ ( cons_Late_subject @ B @ C ) )
      = ( cons_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1812647369ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(340,axiom,
    fresh_name_pi @ x @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I1_J) ).

thf(1685,plain,
    fresh_name_pi @ x @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(308,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_name__swap) ).

thf(1553,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
      = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(103,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_name__perm__compose) ).

thf(688,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
      = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(331,axiom,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_name__swap__bij) ).

thf(1654,plain,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(231,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: produc1141751126_pi_pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1376661020_pi_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_resSimCases) ).

thf(1189,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: produc1141751126_pi_pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1376661020_pi_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(6,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Late____Semantics__Osubject_T) ).

thf(368,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(127,axiom,
    ! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
      ( ( perm_name_o @ A @ ( fresh_1376661020_pi_pi @ B @ C ) )
      = ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_fresh__eqvt) ).

thf(771,plain,
    ! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
      ( ( perm_name_o @ A @ ( fresh_1376661020_pi_pi @ B @ C ) )
      = ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(55,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
      ( ( ( perm_name_pi_Rep @ A @ B )
        = ( perm_name_pi_Rep @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_perm__bij) ).

thf(524,plain,
    ! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
      ( ( ( perm_name_pi_Rep @ A @ B )
        = ( perm_name_pi_Rep @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(71,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).

thf(581,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(234,axiom,
    ! [A: pi] :
      ( ( perm_name_pi @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_pt__name1) ).

thf(1216,plain,
    ! [A: pi] :
      ( ( perm_name_pi @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(160,axiom,
    ! [A: list_P227219501e_name,B: pi,C: name,D: name] :
      ( ( perm_name_pi @ A @ ( subs @ B @ C @ D ) )
      = ( subs @ ( perm_name_pi @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_name @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_eqvt__subs) ).

thf(891,plain,
    ! [A: list_P227219501e_name,B: pi,C: name,D: name] :
      ( ( perm_name_pi @ A @ ( subs @ B @ C @ D ) )
      = ( subs @ ( perm_name_pi @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_name @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(329,axiom,
    ! [A: name,B: pi_Rep,C: name] :
      ( ( fresh_name_pi_Rep @ A @ B )
     => ( ( fresh_name_pi_Rep @ C @ B )
       => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_name__fresh__fresh) ).

thf(1646,plain,
    ! [A: name,B: pi_Rep,C: name] :
      ( ( fresh_name_pi_Rep @ A @ B )
     => ( ( fresh_name_pi_Rep @ C @ B )
       => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(73,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_name__perm__compose) ).

thf(588,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
      = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(139,axiom,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_residual_Ofresh_I2_J) ).

thf(813,plain,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(121,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: name] :
      ( ( perm_n204483300t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( produc1647375838t_name @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_perm__prod_Osimps) ).

thf(748,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: name] :
      ( ( perm_n204483300t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( produc1647375838t_name @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(84,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_name__bij) ).

thf(632,plain,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(18,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: late_freeRes] :
      ( ( perm_n1314686611reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( produc242091907reeRes @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_perm__prod_Osimps) ).

thf(401,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: late_freeRes] :
      ( ( perm_n1314686611reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( produc242091907reeRes @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(132,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi_Rep] :
      ( ( perm_n840427369pi_Rep @ A @ ( produc216486617pi_Rep @ B @ C ) )
      = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_perm__prod_Osimps) ).

thf(786,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: pi_Rep] :
      ( ( perm_n840427369pi_Rep @ A @ ( produc216486617pi_Rep @ B @ C ) )
      = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(67,axiom,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_freeRes_Oexhaust) ).

thf(568,plain,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(10,axiom,
    ! [A: name,B: name] :
      ( ( if_name @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Oname_T) ).

thf(378,plain,
    ! [A: name,B: name] :
      ( ( if_name @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(95,axiom,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_freeRes_Ofresh_I2_J) ).

thf(667,plain,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(278,axiom,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ~ ( fresh_717452603ubject @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_inputIneqTrans) ).

thf(1440,plain,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ~ ( fresh_717452603ubject @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(40,axiom,
    ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_freshUnit) ).

thf(478,plain,
    ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(101,axiom,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
     => ( fresh_1627595501_pi_pi @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_fresh__prodD_I2_J) ).

thf(684,plain,
    ! [A: name,B: name,C: product_prod_pi_pi] :
      ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
     => ( fresh_1627595501_pi_pi @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(320,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_swap__simps_I1_J) ).

thf(1607,plain,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(124,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( ( perm_n1559866809ubject @ A @ B )
        = ( perm_n1559866809ubject @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_perm__bij) ).

thf(763,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( ( perm_n1559866809ubject @ A @ B )
        = ( perm_n1559866809ubject @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(112,axiom,
    ! [A: name,B: product_unit,C: product_unit] :
      ( ( fresh_994967853t_unit @ A @ ( produc1076565719t_unit @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_fresh__prod) ).

thf(716,plain,
    ! [A: name,B: product_unit,C: product_unit] :
      ( ( fresh_994967853t_unit @ A @ ( produc1076565719t_unit @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_1143631827t_unit @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(323,axiom,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( perm_name_pi @ A @ ( par @ B @ C ) )
      = ( par @ ( perm_name_pi @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pi_Operm_I8_J) ).

thf(1614,plain,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( perm_name_pi @ A @ ( par @ B @ C ) )
      = ( par @ ( perm_name_pi @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(210,axiom,
    ! [A: name,B: name > noption_pi,C: name] :
      ( ( fresh_543891186ion_pi @ A @ B )
     => ( ( fresh_543891186ion_pi @ C @ B )
       => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_name__fresh__fresh) ).

thf(1116,plain,
    ! [A: name,B: name > noption_pi,C: name] :
      ( ( fresh_543891186ion_pi @ A @ B )
     => ( ( fresh_543891186ion_pi @ C @ B )
       => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(215,axiom,
    ya != c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cComm1_Ohyps_I6_J) ).

thf(1133,plain,
    ya != c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(33,axiom,
    ! [A: list_P227219501e_name,B: name,C: product_unit] :
      ( ( perm_name_o @ A @ ( fresh_1143631827t_unit @ B @ C ) )
      = ( fresh_1143631827t_unit @ ( perm_name_name @ A @ B ) @ ( perm_n1960409557t_unit @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_fresh__eqvt) ).

thf(447,plain,
    ! [A: list_P227219501e_name,B: name,C: product_unit] :
      ( ( perm_name_o @ A @ ( fresh_1143631827t_unit @ B @ C ) )
      = ( fresh_1143631827t_unit @ ( perm_name_name @ A @ B ) @ ( perm_n1960409557t_unit @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(205,axiom,
    ! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ( ! [F: pi] :
            ( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
           => ( ( fresh_1641682979reeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_resCasesF) ).

thf(1097,plain,
    ! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ( ! [F: pi] :
            ( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
           => ( ( fresh_1641682979reeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(239,axiom,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( D != A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: name,H: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
               => ( ( G != A )
                 => ( ( C
                      = ( late_BoundOutputS @ G ) )
                   => ( F @ ( late_BoundOutputS @ G ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ H ) ) ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( ( fresh_717452603ubject @ A @ C )
                   => ( F @ C @ ( res @ A @ G ) ) ) )
             => ( F @ C @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_resCasesB) ).

thf(1229,plain,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( D != A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: name,H: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
               => ( ( G != A )
                 => ( ( C
                      = ( late_BoundOutputS @ G ) )
                   => ( F @ ( late_BoundOutputS @ G ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ H ) ) ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( ( fresh_717452603ubject @ A @ C )
                   => ( F @ C @ ( res @ A @ G ) ) ) )
             => ( F @ C @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(306,axiom,
    ! [A: name,B: name,C: produc1141751126_pi_pi,D: name] :
      ( ( A != B )
     => ( ( fresh_1376661020_pi_pi @ B @ C )
       => ( ( fresh_1376661020_pi_pi @ A @ C )
         => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_fresh__aux) ).

thf(1546,plain,
    ! [A: name,B: name,C: produc1141751126_pi_pi,D: name] :
      ( ( A != B )
     => ( ( fresh_1376661020_pi_pi @ B @ C )
       => ( ( fresh_1376661020_pi_pi @ A @ C )
         => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(263,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_pi_Odistinct_I57_J) ).

thf(1395,plain,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(151,axiom,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ( ( E != A )
       => ( ( E != B )
         => ( ( fresh_name_pi @ E @ C )
           => ( ( ( D
                  = ( late_InputS @ A ) )
               => ( ( F
                    = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) )
                 => ( G @ ( late_InputS @ A ) @ E @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) ) ) )
             => ( G @ D @ E @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_inputCases) ).

thf(854,plain,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ( ( E != A )
       => ( ( E != B )
         => ( ( fresh_name_pi @ E @ C )
           => ( ( ( D
                  = ( late_InputS @ A ) )
               => ( ( F
                    = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) )
                 => ( G @ ( late_InputS @ A ) @ E @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) ) ) )
             => ( G @ D @ E @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(25,axiom,
    ! [A: name,B: pi,C: list_pi] :
      ( ( fresh_name_list_pi @ A @ ( cons_pi @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_list_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_fresh__list__cons) ).

thf(422,plain,
    ! [A: name,B: pi,C: list_pi] :
      ( ( fresh_name_list_pi @ A @ ( cons_pi @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_list_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(347,axiom,
    fresh_name_pi @ ya @ q2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_cComm1_Ohyps_I7_J) ).

thf(1757,plain,
    fresh_name_pi @ ya @ q2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(145,axiom,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( ( perm_name_pi @ A @ B )
        = ( perm_name_pi @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_perm__bij) ).

thf(833,plain,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( ( perm_name_pi @ A @ B )
        = ( perm_name_pi @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(21,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep > late_subject,C: pi_Rep] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n698371375ubject @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_perm__app) ).

thf(410,plain,
    ! [A: list_P227219501e_name,B: pi_Rep > late_subject,C: pi_Rep] :
      ( ( perm_n1559866809ubject @ A @ ( B @ C ) )
      = ( perm_n698371375ubject @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(182,axiom,
    late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cComm1_Ohyps_I1_J) ).

thf(967,plain,
    late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(220,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Par1F) ).

thf(1148,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(336,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_inputFreeTrans) ).

thf(1673,plain,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(153,axiom,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( par @ A @ B ) @ C @ D )
      = ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_simps_I8_J) ).

thf(865,plain,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( par @ A @ B ) @ C @ D )
      = ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(290,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Late__Semantics1_Osubject_Odistinct_I1_J) ).

thf(1480,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(276,axiom,
    ! [A: list_P227219501e_name,B: pi,C: list_pi] :
      ( ( perm_name_list_pi @ A @ ( cons_pi @ B @ C ) )
      = ( cons_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_list_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_cons__eqvt) ).

thf(1436,plain,
    ! [A: list_P227219501e_name,B: pi,C: list_pi] :
      ( ( perm_name_list_pi @ A @ ( cons_pi @ B @ C ) )
      = ( cons_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_list_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(332,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: product_unit] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1143631827t_unit @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_simCasesCont) ).

thf(1657,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: product_unit] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1143631827t_unit @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(49,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( perm_n171497387ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( produc1465345179ubject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_perm__prod_Osimps) ).

thf(506,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( perm_n171497387ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( produc1465345179ubject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(137,axiom,
    ! [A: list_P227219501e_name,B: name,C: late_subject] :
      ( ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) )
      = ( fresh_717452603ubject @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_fresh__bij) ).

thf(807,plain,
    ! [A: list_P227219501e_name,B: name,C: late_subject] :
      ( ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) )
      = ( fresh_717452603ubject @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(94,axiom,
    ! [A: list_P227219501e_name,B: pi_Rep > late_freeRes,C: pi_Rep] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1841560599reeRes @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_perm__app) ).

thf(664,plain,
    ! [A: list_P227219501e_name,B: pi_Rep > late_freeRes,C: pi_Rep] :
      ( ( perm_n336613537reeRes @ A @ ( B @ C ) )
      = ( perm_n1841560599reeRes @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(85,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_freeRes_Ofresh_I1_J) ).

thf(635,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(196,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( par @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_pi_Ofresh_I8_J) ).

thf(1065,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( par @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(178,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: pi] :
      ( ( perm_n359102898ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_perm__prod_Osimps) ).

thf(955,plain,
    ! [A: list_P227219501e_name,B: late_subject,C: pi] :
      ( ( perm_n359102898ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(321,axiom,
    fresh_name_pi @ y @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062) ).

thf(1610,plain,
    fresh_name_pi @ y @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(227,axiom,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_perm__swap_I1_J) ).

thf(1172,plain,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(268,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_substRes2) ).

thf(1410,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(16,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_perm__compose) ).

thf(395,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(118,axiom,
    swap_name2 = swap_name,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_Agent_Oswap__name__def) ).

thf(740,plain,
    swap_name2 = swap_name,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(69,axiom,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_name__exists__fresh) ).

thf(575,plain,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(258,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Late__Semantics_OPar2B) ).

thf(1378,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(36,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J) ).

thf(459,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(142,axiom,
    ! [A: name,B: name,C: late_subject,D: name] :
      ( ( A != B )
     => ( ( fresh_717452603ubject @ B @ C )
       => ( ( fresh_717452603ubject @ A @ C )
         => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_fresh__aux) ).

thf(822,plain,
    ! [A: name,B: name,C: late_subject,D: name] :
      ( ( A != B )
     => ( ( fresh_717452603ubject @ B @ C )
       => ( ( fresh_717452603ubject @ A @ C )
         => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(150,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
        = ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_substTrans) ).

thf(850,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
        = ( subs @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(104,axiom,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1826856600t_name @ A @ ( produc421428802t_name @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_fresh__prod) ).

thf(691,plain,
    ! [A: name,B: product_unit,C: name] :
      ( ( fresh_1826856600t_name @ A @ ( produc421428802t_name @ B @ C ) )
      = ( ( fresh_1143631827t_unit @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(31,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_fresh__prodD_I1_J) ).

thf(442,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(155,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( ( E != C )
         => ( fresh_name_pi @ E @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_freshBoundDerivative_I2_J) ).

thf(871,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( ( E != C )
         => ( fresh_name_pi @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(211,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_name__swap__bij) ).

thf(1120,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(7,axiom,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__Osubject_T) ).

thf(369,plain,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(88,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_subject] :
      ( ( perm_n1174226579ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( produc320590723ubject @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_perm__prod_Osimps) ).

thf(644,plain,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_subject] :
      ( ( perm_n1174226579ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( produc320590723ubject @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(307,axiom,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_perm__swap_I2_J) ).

thf(1550,plain,
    ! [A: name,B: name,C: pi_Rep] :
      ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(296,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( F != B )
             => ( ( F != C )
               => ( ( fresh_name_pi @ F @ D )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_transitions_OComm2) ).

thf(1505,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( F != B )
             => ( ( F != C )
               => ( ( fresh_name_pi @ F @ D )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(264,axiom,
    ! [A: name,B: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_name__id) ).

thf(1399,plain,
    ! [A: name,B: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(195,axiom,
    ! [A: name,B: pi,C: late_residual] :
      ( ( late_transitions @ ( res @ A @ B ) @ C )
     => ( ! [D: pi,E: name,F: name] :
            ( ( ( res @ A @ B )
              = ( res @ F @ D ) )
           => ! [G: pi] :
                ( ( C
                  = ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
               => ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
                 => ( E = F ) ) ) )
       => ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
              ( ( ( res @ A @ B )
                = ( res @ H @ D ) )
             => ( ( C
                  = ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
               => ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh_name_pi @ F @ D )
                       => ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
         => ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
                ( ( ( res @ A @ B )
                  = ( res @ G @ D ) )
               => ( ( C
                    = ( late_FreeR @ E @ ( res @ G @ F ) ) )
                 => ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
                   => ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_resCases_H) ).

thf(1009,plain,
    ! [A: name,B: pi,C: late_residual] :
      ( ( late_transitions @ ( res @ A @ B ) @ C )
     => ( ! [D: pi,E: name,F: name] :
            ( ( ( res @ A @ B )
              = ( res @ F @ D ) )
           => ! [G: pi] :
                ( ( C
                  = ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
               => ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
                 => ( E = F ) ) ) )
       => ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
              ( ( ( res @ A @ B )
                = ( res @ H @ D ) )
             => ( ( C
                  = ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
               => ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh_name_pi @ F @ D )
                       => ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
         => ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
                ( ( ( res @ A @ B )
                  = ( res @ G @ D ) )
               => ( ( C
                    = ( late_FreeR @ E @ ( res @ G @ F ) ) )
                 => ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
                   => ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(169,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( fresh_717452603ubject @ E @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_freshBoundDerivative_I1_J) ).

thf(923,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( fresh_717452603ubject @ E @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(60,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_fresh__prod) ).

thf(543,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(349,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ E )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Late__Semantics_OClose2) ).

thf(1769,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ E )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(44,axiom,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_cp__name__name1) ).

thf(491,plain,
    ! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
      ( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
      = ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(109,axiom,
    ( fresh_name_name
    = ( != @ name ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_name__fresh) ).

thf(708,plain,
    ( fresh_name_name
    = ( ^ [A: name,B: name] : ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(270,axiom,
    ! [A: name,B: name,C: name] :
      ( ( A != B )
     => ( ( C != B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_swap__simps_I3_J) ).

thf(1417,plain,
    ! [A: name,B: name,C: name] :
      ( ( A != B )
     => ( ( C != B )
       => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(1805,plain,
    $false,
    inference(e,[status(thm)],[1665,1501,629,1469,365,1559,909,518,962,941,777,1686,1158,1290,1068,1443,1142,655,1596,1406,1497,1078,384,500,1275,472,1640,1354,404,898,1127,1576,1650,1359,1386,565,1518,389,1287,1430,719,372,619,751,1279,357,1462,559,1800,638,1514,1704,1347,416,1489,475,1465,789,1450,591,1109,966,1283,480,1682,1136,1151,937,766,1169,734,1447,1072,774,1526,1433,428,1600,527,1696,1604,678,1691,661,546,810,381,798,512,439,1091,952,1255,598,392,407,1223,894,1123,862,1570,1676,847,879,1178,830,1787,1210,1407,1392,710,456,974,1106,1402,697,1772,725,1672,1006,610,783,1360,1350,742,578,650,948,1567,488,1361,537,669,1424,1414,901,686,1075,622,515,1668,503,647,997,1530,1539,792,1695,1563,398,530,926,1086,938,906,1510,425,1219,745,1374,375,601,819,562,694,843,1620,958,1226,413,1784,1389,875,826,641,1139,445,572,713,919,947,1356,540,672,681,419,990,1492,362,737,616,1175,979,604,509,434,1571,1439,1471,494,816,1162,483,700,915,1381,1556,769,983,1474,1213,868,883,986,1113,1477,1364,1102,431,1694,658,912,521,1171,780,1643,1775,1000,722,675,944,795,1509,1081,1145,754,553,836,1758,1166,968,1181,1003,887,971,1368,1484,993,705,1611,1790,585,840,463,1679,359,1452,1637,1130,1579,1543,1536,613,1221,1427,1797,1372,1272,497,1617,1094,386,1421,450,1459,556,1685,1553,688,1654,1189,368,771,524,581,1216,891,1646,588,813,748,632,401,786,568,378,667,1440,478,684,1607,763,716,1614,1116,1133,447,1097,1229,1546,1395,854,422,1757,833,410,967,1148,1673,865,1480,1436,1657,506,807,664,635,1065,955,1610,1172,1410,395,740,575,1378,459,822,850,691,442,871,1120,369,644,1550,1505,1399,1009,923,543,1769,491,708,1417]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : ITP191^1 : TPTP v8.2.0. Released v7.5.0.
% 0.15/0.17  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n015.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Sat May 18 18:46:54 EDT 2024
% 0.16/0.39  % CPUTime  : 
% 0.98/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.02/1.15  % [INFO] 	 Parsing done (257ms). 
% 2.02/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.73/1.39  % [INFO] 	 eprover registered as external prover. 
% 2.73/1.39  % [INFO] 	 cvc4 registered as external prover. 
% 2.73/1.39  % [INFO] 	 Scanning for conjecture ... 
% 3.08/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 361 axioms. Running axiom selection ... 
% 3.29/1.63  % [INFO] 	 Axiom selection finished. Selected 354 axioms (removed 7 axioms). 
% 4.40/1.85  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.40/1.87  % [INFO] 	 Type checking passed. 
% 4.40/1.87  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 5.64/2.19  % [INFO] 	 [Domain constraints] Detected constraint on product_unit 
% 5.64/2.19  % [INFO] 	 [Domain constraints] dom(product_unit) ⊆ {product_Unity} 
% 5.90/2.27  % [INFO] 	 [Domain constraints] Detected constraint on product_unit 
% 5.90/2.27  % [INFO] 	 [Domain constraints] dom(product_unit) ⊆ {product_Unity} 
% 17.63/5.30  % External prover 'e' found a proof!
% 17.63/5.30  % [INFO] 	 Killing All external provers ... 
% 17.63/5.30  % Time passed: 4754ms (effective reasoning time: 4134ms)
% 17.63/5.30  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.63/5.31  % Axioms used in derivation (354): help_If_2_1_If_001t__Agent__Opi_T, fact_65_name__fresh__fresh, fact_19_perm__swap_I1_J, fact_230_residual_Ostrong__induct, help_If_1_1_If_001t__Agent__Oname_T, fact_62_name__fresh__fresh, fact_152_in__eqvt, fact_119_cp__name__name1, fact_338_inputBoundOutputTrans, fact_108_swap__simps_I1_J, fact_123_cp__name__name1, fact_57_perm__fresh__fresh, fact_88_fresh__eqvt, fact_26_name__swap, fact_16_perm__swap_I1_J, fact_260_abs__fun__if, fact_113_fresh__aux, fact_114_fresh__aux, fact_209_resCases_H, fact_252_fresh__list__cons, fact_124_name__perm__compose, fact_40_pt__name1, fact_190_residual_Operm_I2_J, fact_321_Late__Semantics1_Osubject_Oinject_I2_J, fact_282_fresh__prodD_I2_J, fact_286_if__eqvt, fact_70_fresh__perm__app, fact_73_fresh__perm__app, fact_303_simCasesCont, fact_328_inputCases, fact_42_pt__name1, fact_255_Bound_Ohyps_I5_J, fact_35_name__swap__bij, fact_183_Late__Semantics_OfreeRes_Oinject, fact_323_Late__Semantics1_OfreeRes_Oinject, fact_80_name__exists__fresh, fact_241_fresh__prod, fact_332_pi_Odistinct_I55_J, fact_64_name__fresh__fresh, fact_41_pt__name1, fact_312_eqvtRelE, fact_10_cComm1_Ohyps_I4_J, fact_266_pt__bij3, fact_101_forget, fact_11_cComm1_Ohyps_I7_J, fact_43_pt__name1, fact_153_in__eqvt, fact_85_fresh__eqvt, fact_158_eq__eqvt, fact_109_swap__simps_I2_J, fact_29_name__swap, fact_272_perm__prod_Osimps, fact_156_eq__eqvt, fact_99_fresh__fact2, fact_314_parSym, fact_258_freshUnit, fact_256_name__fresh, fact_313_eqvtRelE, fact_115_fresh__aux, fact_9_cComm1_Ohyps_I3_J, fact_207_transitions_OPar1B, fact_231_freshFreeDerivative_I2_J, fact_197_name__bij, fact_234_parCasesB, fact_188_residual_Ofresh_I2_J, fact_227_residual_Ostrong__induct, fact_285_fresh__prodD_I1_J, fact_318_simE_I1_J, fact_316_eqvt__def, fact_276_perm__prod_Osimps, fact_225_residual_Ostrong__inducts, fact_214_eqvt, fact_116_fresh__aux, fact_90_fresh__bij, fact_120_cp__name__name1, fact_320_simulation__def, fact_66_name__fresh__fresh, fact_295_cons__eqvt, fact_128_name__perm__compose, fact_54_perm__fresh__fresh, fact_284_fresh__prodD_I1_J, fact_334_inputFreeTrans, fact_228_residual_Ostrong__induct, fact_185_freeRes_Ofresh_I2_J, fact_294_cons__eqvt, fact_151_in__eqvt, fact_139_perm__app, fact_145_perm__app, fact_339_Late__Semantics_OInput, fact_146_perm__app, fact_141_perm__app, fact_257_fresh__unit, fact_127_name__perm__compose, fact_270_perm__prod_Osimps, fact_263_abs__fun__if, fact_166_perm__swap_I2_J, fact_121_cp__name__name1, fact_161_alphaRes, fact_104_Collect__mem__eq, fact_300_simCasesCont, fact_203_freshFreeDerivative_I1_J, fact_131_perm__compose, fact_75_fresh__perm__app, fact_22_name__id, fact_172_Late__Semantics_OClose2, fact_84_fresh__eqvt, fact_287_if__eqvt, fact_331_pi_Odistinct_I57_J, fact_36_cOpen_Ohyps_I1_J, fact_210_residual_Oinject_I2_J, fact_343_alphaInput, fact_98_freshRes, fact_133_perm__compose, fact_307_eqvtRelI, fact_110_swap__simps_I3_J, fact_106_substRes2, fact_181_residual__perm__empty, fact_291_cons__eqvt, fact_72_fresh__perm__app, fact_226_residual_Ostrong__inducts, fact_342_resInputBoundOutputTrans, fact_105_Agent_OsubstRes3, fact_130_perm__compose, fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_245_fresh__prod, fact_205_transitions_OResB, fact_150_in__eqvt, fact_7_Bound_Ohyps_I1_J, fact_17_perm__swap_I1_J, fact_102_name__calc_I2_J, fact_333_resTrans_I2_J, fact_299_resSimCases, fact_61_name__fresh__fresh, fact_55_perm__fresh__fresh, fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062, fact_163_renaming, fact_269_pt__bij3, fact_326_subject_Oexhaust, fact_329_list_Oinject, fact_5_assms_I3_J, fact_349_pi_Ofresh_I9_J, fact_23_name__id, fact_213_residual_Oinducts, fact_69_Bound_Ohyps_I4_J, fact_97_fresh__bij, fact_3_cComm1_Ohyps_I6_J, fact_199_resCasesF, fact_206_parCasesB_H, fact_25_name__id, fact_179_freeRes__perm__empty, fact_292_cons__eqvt, fact_243_fresh__prod, fact_112_fresh__aux, fact_38_simps_I8_J, fact_33_name__swap__bij, fact_221_Par2F, fact_296_resSimCases, fact_140_perm__app, help_If_1_1_If_001t__Late____Semantics__OfreeRes_T, fact_265_pt__bij3, fact_281_fresh__prodD_I2_J, fact_218_subject_Oinducts, fact_348_Agent_Oswap__name__def, fact_233_Late__Semantics_OPar2B, fact_249_ScopeExt, fact_71_fresh__perm__app, fact_347_name__calc_I3_J, fact_254_fresh__list__cons, help_If_1_1_If_001t__Agent__Opi____Rep_T, help_If_2_1_If_001t__Late____Semantics__OfreeRes_T, fact_242_fresh__prod, fact_193_subject_Operm_I2_J, fact_138_perm__bij, fact_96_fresh__bij, fact_290_if__eqvt, fact_297_resSimCases, help_If_1_1_If_001t__Late____Semantics__Osubject_T, fact_132_perm__compose, fact_198_freshResidual, fact_20_perm__swap_I1_J, fact_67_name__fresh__fresh, fact_279_perm__prod_Osimps, fact_47_subst__identity, fact_100_fresh__fact1, fact_0_cComm1_Ohyps_I5_J, fact_165_perm__swap_I2_J, fact_154_in__eqvt, fact_250_fresh__list__cons, fact_235_Open, fact_315_simE_I2_J, fact_322_Late__Semantics1_Osubject_Oinject_I1_J, help_If_2_1_If_001t__Late____Semantics__Osubject_T, fact_160_pi_Oinject_I7_J, fact_317_parAssocLeft, fact_327_Late__Semantics1_Osubject_Odistinct_I1_J, fact_142_perm__app, fact_2_cOpen_Ohyps_I2_J, fact_302_simCasesCont, fact_237_derivativeEqvtI, fact_136_perm__bij, fact_280_fresh__prodD_I2_J, fact_229_residual_Ostrong__induct, fact_50__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062, fact_1_cComm1_Ohyps_I9_J, fact_147_perm__app, fact_261_abs__fun__if, fact_79_name__exists__fresh, fact_191_freeRes_Operm_I1_J, fact_192_subject_Operm_I1_J, fact_155_eq__eqvt, fact_246_fresh__prod, fact_173_Late__Semantics_OClose1, fact_162_injPermSubst, fact_4_cOpen_Ohyps_I3_J, fact_293_cons__eqvt, fact_298_resSimCases, fact_52_pi_Operm_I9_J, fact_267_pt__bij3, fact_134_perm__bij, fact_169_perm__swap_I2_J, fact_308_eqvtRelI, fact_32_name__swap__bij, fact_86_fresh__eqvt, fact_21_name__id, fact_268_pt__bij3, fact_83_fresh__eqvt, fact_283_fresh__prodD_I1_J, fact_340_transitions_OInput, fact_201_ResF, fact_194_subject_Ofresh_I2_J, fact_45_cComm1_Ohyps_I2_J, fact_170_transitions_OClose2, fact_219_resCasesB, fact_220_Par1F, fact_335_resInputFreeTrans, fact_27_name__swap, fact_336_old_Ounit_Oinducts, fact_215_freeRes_Oinducts, fact_107_eqvt__subs, fact_117_fresh__aux, fact_174_transitions_OComm2, fact_168_perm__swap_I2_J, fact_224_residual_Ostrong__inducts, fact_159_eq__eqvt, fact_202_Late__Semantics_OResB, fact_196_residual_Operm_I1_J, fact_76_fresh__perm__app, fact_176_Late__Semantics_OComm2, fact_39_simps_I9_J, fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_157_eq__eqvt, fact_30_name__swap, fact_259_allE__Nil, fact_288_if__eqvt, fact_14_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3, fact_208_transitions_OPar2B, fact_275_perm__prod_Osimps, fact_46__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062, fact_81_name__exists__fresh, fact_8_assms_I1_J, fact_18_perm__swap_I1_J, fact_63_name__fresh__fresh, help_If_2_1_If_001t__Agent__Opi____Rep_T, fact_264_abs__fun__if, fact_337_old_Ounit_Oexhaust, fact_240_fresh__prod, fact_13_Bound_Ohyps_I2_J, fact_53_perm__fresh__fresh, fact_325_freeRes_Oexhaust, fact_189_substTrans, fact_236_derivativeEqvtI2, fact_248_Res, help_If_1_1_If_001t__Agent__Opi_T, fact_44_pt__name1, fact_15_cComm1_Ohyps_I1_J, fact_289_if__eqvt, fact_143_perm__app, fact_223_residual_Ostrong__inducts, fact_94_fresh__bij, fact_122_cp__name__name1, fact_232_Late__Semantics_OPar1B, fact_12_Bound_Ohyps_I3_J, fact_330_pi_Operm_I4_J, fact_319_simCases, fact_74_fresh__perm__app, fact_144_perm__app, fact_211_resCasesB_H, fact_148_perm__app, fact_49__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062, fact_58_perm__fresh__fresh, fact_271_perm__prod_Osimps, fact_68_name__fresh__fresh, fact_77_fresh__perm__app, fact_239_fresh__prod, fact_277_perm__prod_Osimps, fact_195_subject_Ofresh_I1_J, fact_184_Late__Semantics_Osubject_Oinject_I2_J, help_If_3_1_If_001t__Late____Semantics__Osubject_T, fact_126_name__perm__compose, fact_344_default__unit__def, fact_125_name__perm__compose, fact_56_perm__fresh__fresh, fact_180_subject__perm__empty, fact_28_name__swap, fact_78_name__exists__fresh, fact_129_perm__compose, fact_91_fresh__bij, fact_274_perm__prod_Osimps, fact_82_fresh__eqvt, fact_93_fresh__bij, fact_244_fresh__prod, fact_212_residual_Odistinct_I1_J, fact_253_fresh__list__cons, fact_164_pi_Odistinct_I85_J, fact_262_abs__fun__if, fact_149_in__eqvt, fact_95_fresh__bij, fact_346_name__calc_I1_J, fact_89_fresh__eqvt, fact_186_freeRes_Operm_I2_J, fact_175_transitions_OComm1, fact_341_inputIneqTrans, fact_222_freshBoundDerivative_I2_J, fact_238_fresh__prod, fact_34_name__swap__bij, fact_135_perm__bij, fact_301_simCasesCont, fact_37_pi_Operm_I8_J, fact_278_perm__prod_Osimps, fact_24_name__id, fact_167_perm__swap_I2_J, fact_137_perm__bij, fact_60_perm__fresh__fresh, fact_92_fresh__bij, fact_217_Late__Semantics_Osubject_Odistinct_I1_J, fact_51_pi_Ofresh_I8_J, fact_177_Late__Semantics_OComm1, fact_31_name__swap__bij, fact_59_perm__fresh__fresh, fact_251_fresh__list__cons, fact_103_mem__Collect__eq, fact_204_freshBoundDerivative_I1_J, fact_273_perm__prod_Osimps, fact_111_fresh__aux, fact_87_fresh__eqvt, fact_48_pi__perm__empty, fact_187_cComm1_Ohyps_I8_J, fact_200_resCasesF_H, fact_171_transitions_OClose1, fact_118_fresh__aux, fact_247_fresh__prod, fact_178_alphaBoundResidual, fact_182_freeRes_Ofresh_I1_J, help_If_2_1_If_001t__Agent__Oname_T
% 17.63/5.31  % No. of inferences in proof: 712
% 17.63/5.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4754 ms resp. 4134 ms w/o parsing
% 18.94/5.53  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.94/5.53  % [INFO] 	 Killing All external provers ... 
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