TSTP Solution File: ITP190^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP190^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 30.04s 8.13s
% Output   : Refutation 30.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  538
% Syntax   : Number of formulae    :  900 ( 451 unt; 178 typ;   0 def)
%            Number of atoms       : 1713 ( 811 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 7899 ( 255   ~;   1   |; 100   &;6791   @)
%                                         (   0 <=>; 752  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg)
%            Number of types       :   41 (  40 usr)
%            Number of type conns  :  434 ( 434   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  142 ( 138 usr;  19 con; 0-5 aty)
%            Number of variables   : 2523 (  10   ^2489   !;  24   ?;2523   :)

% Comments : 
%------------------------------------------------------------------------------
thf(produc1872410278e_name_type,type,
    produc1872410278e_name: $tType ).

thf(produc890461031e_name_type,type,
    produc890461031e_name: $tType ).

thf(list_l1406151091e_name_type,type,
    list_l1406151091e_name: $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(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(produc1998742700t_name_type,type,
    produc1998742700t_name: $tType ).

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

thf(produc865358760ubject_type,type,
    produc865358760ubject: $tType ).

thf(produc2008547984reeRes_type,type,
    produc2008547984reeRes: $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(produc367475239e_name_type,type,
    produc367475239e_name: $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_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(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(name_prm_name_type,type,
    name_prm_name: list_P227219501e_name > name > name ).

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

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

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_l798145763e_name_type,type,
    cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name ).

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

thf(nil_li29751603e_name_type,type,
    nil_li29751603e_name: list_l1406151091e_name ).

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_1981651763reeRes_type,type,
    fresh_1981651763reeRes: name > list_Late_freeRes > $o ).

thf(fresh_838462539ubject_type,type,
    fresh_838462539ubject: name > list_Late_subject > $o ).

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

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

thf(fresh_1963366730reeRes_type,type,
    fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).

thf(fresh_820177506ubject_type,type,
    fresh_820177506ubject: name > produc865358760ubject > $o ).

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

thf(fresh_2007541374s_name_type,type,
    fresh_2007541374s_name: name > produc2052722628s_name > $o ).

thf(fresh_1847501388Res_pi_type,type,
    fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).

thf(fresh_493808761reeRes_type,type,
    fresh_493808761reeRes: name > produc1357834675reeRes > $o ).

thf(fresh_1498103185ubject_type,type,
    fresh_1498103185ubject: name > produc214645451ubject > $o ).

thf(fresh_1953561446t_name_type,type,
    fresh_1953561446t_name: name > produc1998742700t_name > $o ).

thf(fresh_994896692ect_pi_type,type,
    fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).

thf(fresh_1638563217reeRes_type,type,
    fresh_1638563217reeRes: name > produc355105483reeRes > $o ).

thf(fresh_495373993ubject_type,type,
    fresh_495373993ubject: name > produc1359399907ubject > $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_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_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(produc1069608854e_name_type,type,
    produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).

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

thf(produc1531804426reeRes_type,type,
    produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).

thf(produc607574050ubject_type,type,
    produc607574050ubject: name > late_subject > produc865358760ubject ).

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

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(produc208131031e_name_type,type,
    produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).

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

thf(p_type,type,
    p: pi ).

thf(p2_type,type,
    p2: pi ).

thf(pxQ_type,type,
    pxQ: pi ).

thf(q_type,type,
    q: pi ).

thf(q2_type,type,
    q2: pi ).

thf(q_a_type,type,
    q_a: pi ).

thf(rel_type,type,
    rel: set_Pr1834926343_pi_pi ).

thf(alpha_type,type,
    alpha: late_freeRes ).

thf(aa_type,type,
    aa: name ).

thf(b_type,type,
    b: name ).

thf(x_type,type,
    x: name ).

thf(y_type,type,
    y: name ).

thf(z_type,type,
    z: name ).

thf(160,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/sandbox/benchmark/theBenchmark.p',fact_310_inputCases) ).

thf(892,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)],[160]) ).

thf(333,axiom,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_residual_Ostrong__induct) ).

thf(1665,plain,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(78,axiom,
    perm_name_name = name_prm_name,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_Agent_Oname__prm__name__def) ).

thf(629,plain,
    perm_name_name = name_prm_name,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(185,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/sandbox/benchmark/theBenchmark.p',fact_198_resCasesF_H) ).

thf(1024,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)],[185]) ).

thf(117,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Late__Semantics_Osubject_Odistinct_I1_J) ).

thf(760,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(324,axiom,
    z != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062) ).

thf(1633,plain,
    z != x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(36,axiom,
    swap_name2 = swap_name,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Agent_Oswap__name__def) ).

thf(479,plain,
    swap_name2 = swap_name,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(342,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/sandbox/benchmark/theBenchmark.p',fact_196_transitions_OResB) ).

thf(1729,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)],[342]) ).

thf(145,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/sandbox/benchmark/theBenchmark.p',fact_255_perm__prod_Osimps) ).

thf(846,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)],[145]) ).

thf(186,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/sandbox/benchmark/theBenchmark.p',fact_275_alphaInput) ).

thf(1031,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)],[186]) ).

thf(251,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/sandbox/benchmark/theBenchmark.p',fact_289_transitions_OInput) ).

thf(1315,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)],[251]) ).

thf(37,axiom,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Late__Semantics1_Osubject_Oinject_I1_J) ).

thf(481,plain,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(348,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/sandbox/benchmark/theBenchmark.p',fact_308_resInputFreeTrans) ).

thf(1750,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)],[348]) ).

thf(48,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/sandbox/benchmark/theBenchmark.p',fact_258_perm__prod_Osimps) ).

thf(523,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)],[48]) ).

thf(313,axiom,
    ! [A: produc1872410278e_name] :
      ( ! [B: produc367475239e_name > produc367475239e_name > $o] :
          ( A
         != ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
     => ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: list_P227219501e_name] :
            ( A
           != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_sorted__wrt_Ocases) ).

thf(1596,plain,
    ! [A: produc1872410278e_name] :
      ( ! [B: produc367475239e_name > produc367475239e_name > $o] :
          ( A
         != ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
     => ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: list_P227219501e_name] :
            ( A
           != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(198,axiom,
    y != aa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cClose1_Ohyps_I5_J) ).

thf(1068,plain,
    y != aa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(154,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/sandbox/benchmark/theBenchmark.p',fact_279_pi_Ofresh_I8_J) ).

thf(873,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)],[154]) ).

thf(312,axiom,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_residual_Ostrong__inducts) ).

thf(1591,plain,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

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

thf(379,plain,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(93,axiom,
    ! [A: name,B: name,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_name @ C @ A )
        = ( perm_name_name @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_pt__bij3) ).

thf(677,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)],[93]) ).

thf(286,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/sandbox/benchmark/theBenchmark.p',fact_112_fresh__aux) ).

thf(1437,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)],[286]) ).

thf(211,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/sandbox/benchmark/theBenchmark.p',fact_124_name__perm__compose) ).

thf(1173,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)],[211]) ).

thf(189,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/sandbox/benchmark/theBenchmark.p',fact_309_inputBoundOutputTrans) ).

thf(1041,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)],[189]) ).

thf(150,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/sandbox/benchmark/theBenchmark.p',fact_252_perm__prod_Osimps) ).

thf(861,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)],[150]) ).

thf(201,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/sandbox/benchmark/theBenchmark.p',fact_72_name__fresh__fresh) ).

thf(1078,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)],[201]) ).

thf(51,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/sandbox/benchmark/theBenchmark.p',fact_81_fresh__perm__app) ).

thf(533,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)],[51]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',fact_176_fresh__list__cons) ).

thf(550,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)],[56]) ).

thf(104,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Pair__inject) ).

thf(715,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(240,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/sandbox/benchmark/theBenchmark.p',fact_331_transitions_OComm2) ).

thf(1275,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)],[240]) ).

thf(34,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/sandbox/benchmark/theBenchmark.p',fact_94_fresh__bij) ).

thf(472,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)],[34]) ).

thf(229,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Late__Semantics_OfreeRes_Oinject) ).

thf(1233,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)],[229]) ).

thf(318,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/sandbox/benchmark/theBenchmark.p',fact_38_perm__swap_I2_J) ).

thf(1608,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)],[318]) ).

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

thf(385,plain,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(135,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/sandbox/benchmark/theBenchmark.p',fact_118_cp__name__name1) ).

thf(814,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)],[135]) ).

thf(254,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/sandbox/benchmark/theBenchmark.p',fact_191_pi_Operm_I9_J) ).

thf(1327,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)],[254]) ).

thf(351,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/sandbox/benchmark/theBenchmark.p',fact_202_residual_Odistinct_I1_J) ).

thf(1761,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)],[351]) ).

thf(259,axiom,
    ! [A: produc890461031e_name] :
      ( ! [B: list_P227219501e_name] :
          ( A
         != ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
     => ( ! [B: list_P227219501e_name] :
            ( A
           != ( produc208131031e_name @ B @ nil_Pr743626285e_name ) )
       => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( A
             != ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_shuffles_Ocases) ).

thf(1342,plain,
    ! [A: produc890461031e_name] :
      ( ! [B: list_P227219501e_name] :
          ( A
         != ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
     => ( ! [B: list_P227219501e_name] :
            ( A
           != ( produc208131031e_name @ B @ nil_Pr743626285e_name ) )
       => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( A
             != ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(178,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Late__Semantics1_OfreeRes_Oinject) ).

thf(1001,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)],[178]) ).

thf(274,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/sandbox/benchmark/theBenchmark.p',fact_26_name__swap__bij) ).

thf(1391,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)],[274]) ).

thf(102,axiom,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_fresh__prod) ).

thf(709,plain,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(158,axiom,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
     => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: list_P227219501e_name] :
            ( ( A @ F @ E )
           => ( A @ ( cons_P1213805021e_name @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_splice_Oinduct) ).

thf(885,plain,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
     => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: list_P227219501e_name] :
            ( ( A @ F @ E )
           => ( A @ ( cons_P1213805021e_name @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(315,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/sandbox/benchmark/theBenchmark.p',fact_276_name__calc_I1_J) ).

thf(1601,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)],[315]) ).

thf(61,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/sandbox/benchmark/theBenchmark.p',fact_248_abs__fun__if) ).

thf(565,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)],[61]) ).

thf(232,axiom,
    ! [A: list_P227219501e_name > $o] :
      ( ! [B: list_P227219501e_name] : ( A @ B )
     => ( A @ nil_Pr743626285e_name ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_allE__Nil) ).

thf(1243,plain,
    ! [A: list_P227219501e_name > $o] :
      ( ! [B: list_P227219501e_name] : ( A @ B )
     => ( A @ nil_Pr743626285e_name ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(358,axiom,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_residual_Ostrong__induct) ).

thf(1782,plain,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(124,axiom,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_fresh__prod) ).

thf(782,plain,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(287,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/sandbox/benchmark/theBenchmark.p',fact_129_perm__compose) ).

thf(1441,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)],[287]) ).

thf(361,axiom,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
      = ( ? [B: produc367475239e_name,C: list_P227219501e_name] :
            ( A
            = ( cons_P1213805021e_name @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_neq__Nil__conv) ).

thf(1792,plain,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
      = ( ? [B: produc367475239e_name,C: list_P227219501e_name] :
            ( A
            = ( cons_P1213805021e_name @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(332,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/sandbox/benchmark/theBenchmark.p',fact_220_residual_Ostrong__induct) ).

thf(1660,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)],[332]) ).

thf(125,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/sandbox/benchmark/theBenchmark.p',fact_319_substTrans) ).

thf(785,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)],[125]) ).

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

thf(372,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(255,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/sandbox/benchmark/theBenchmark.p',fact_256_perm__prod_Osimps) ).

thf(1330,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)],[255]) ).

thf(114,axiom,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi_T) ).

thf(751,plain,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(241,axiom,
    ! [A: produc367475239e_name,B: list_P227219501e_name] :
      ( nil_Pr743626285e_name
     != ( cons_P1213805021e_name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_list_Odistinct_I1_J) ).

thf(1279,plain,
    ! [A: produc367475239e_name,B: list_P227219501e_name] :
      ( nil_Pr743626285e_name
     != ( cons_P1213805021e_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(308,axiom,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
     => ( ! [B: produc367475239e_name] :
            ( A
           != ( cons_P1213805021e_name @ B @ nil_Pr743626285e_name ) )
       => ~ ! [B: produc367475239e_name,C: produc367475239e_name,D: list_P227219501e_name] :
              ( A
             != ( cons_P1213805021e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_remdups__adj_Ocases) ).

thf(1577,plain,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
     => ( ! [B: produc367475239e_name] :
            ( A
           != ( cons_P1213805021e_name @ B @ nil_Pr743626285e_name ) )
       => ~ ! [B: produc367475239e_name,C: produc367475239e_name,D: list_P227219501e_name] :
              ( A
             != ( cons_P1213805021e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(54,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/sandbox/benchmark/theBenchmark.p',fact_235_if__eqvt) ).

thf(542,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)],[54]) ).

thf(136,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Late__Semantics1_Osubject_Odistinct_I1_J) ).

thf(817,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(59,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/sandbox/benchmark/theBenchmark.p',fact_137_perm__app) ).

thf(559,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)],[59]) ).

thf(271,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/sandbox/benchmark/theBenchmark.p',fact_12_perm__swap_I1_J) ).

thf(1379,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)],[271]) ).

thf(261,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/sandbox/benchmark/theBenchmark.p',fact_306_transitions_OPar1B) ).

thf(1347,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)],[261]) ).

thf(120,axiom,
    ! [A: name,B: late_freeRes,C: list_Late_freeRes] :
      ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1981651763reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_fresh__list__cons) ).

thf(770,plain,
    ! [A: name,B: late_freeRes,C: list_Late_freeRes] :
      ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1981651763reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(355,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_swap__simps_I1_J) ).

thf(1773,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)],[355]) ).

thf(252,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/sandbox/benchmark/theBenchmark.p',fact_197_resCasesF) ).

thf(1319,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)],[252]) ).

thf(153,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/sandbox/benchmark/theBenchmark.p',fact_145_in__eqvt) ).

thf(870,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)],[153]) ).

thf(35,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pi_Odistinct_I55_J) ).

thf(475,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)],[35]) ).

thf(126,axiom,
    ! [A: name,B: late_subject,C: list_Late_subject] :
      ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_838462539ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_fresh__list__cons) ).

thf(789,plain,
    ! [A: name,B: late_subject,C: list_Late_subject] :
      ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_838462539ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(269,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_name__id) ).

thf(1373,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)],[269]) ).

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

thf(376,plain,
    ! [A: pi_Rep,B: pi_Rep] :
      ( ( if_pi_Rep @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(141,axiom,
    ! [A: name,B: late_subject,C: late_freeRes] :
      ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_fresh__prod) ).

thf(834,plain,
    ! [A: name,B: late_subject,C: late_freeRes] :
      ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(62,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/sandbox/benchmark/theBenchmark.p',fact_89_fresh__eqvt) ).

thf(574,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)],[62]) ).

thf(309,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/sandbox/benchmark/theBenchmark.p',fact_330_Late__Semantics_OComm2) ).

thf(1581,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)],[309]) ).

thf(242,axiom,
    fresh_name_pi @ z @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_cClose1_Ohyps_I8_J) ).

thf(1283,plain,
    fresh_name_pi @ z @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(192,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/sandbox/benchmark/theBenchmark.p',fact_13_perm__swap_I1_J) ).

thf(1051,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)],[192]) ).

thf(137,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/sandbox/benchmark/theBenchmark.p',fact_88_fresh__eqvt) ).

thf(821,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)],[137]) ).

thf(170,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/sandbox/benchmark/theBenchmark.p',fact_109_fresh__aux) ).

thf(981,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)],[170]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',fact_132_perm__bij) ).

thf(397,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)],[15]) ).

thf(80,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_old_Oprod_Oinject) ).

thf(634,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(109,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/sandbox/benchmark/theBenchmark.p',fact_185_cons__eqvt) ).

thf(734,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)],[109]) ).

thf(275,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/sandbox/benchmark/theBenchmark.p',fact_210_Open) ).

thf(1394,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)],[275]) ).

thf(295,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/sandbox/benchmark/theBenchmark.p',fact_332_transitions_OComm1) ).

thf(1526,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)],[295]) ).

thf(177,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/sandbox/benchmark/theBenchmark.p',fact_36_perm__swap_I2_J) ).

thf(998,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)],[177]) ).

thf(173,axiom,
    ! [A: produc367475239e_name] :
      ~ ! [B: name,C: name] :
          ( A
         != ( produc1570949143e_name @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_old_Oprod_Oexhaust) ).

thf(988,plain,
    ! [A: produc367475239e_name] :
      ~ ! [B: name,C: name] :
          ( A
         != ( produc1570949143e_name @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(284,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/sandbox/benchmark/theBenchmark.p',fact_150_in__eqvt) ).

thf(1433,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)],[284]) ).

thf(314,axiom,
    late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_cClose1_Ohyps_I1_J) ).

thf(1600,plain,
    late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(146,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/sandbox/benchmark/theBenchmark.p',fact_254_perm__prod_Osimps) ).

thf(849,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)],[146]) ).

thf(24,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/sandbox/benchmark/theBenchmark.p',fact_115_cp__name__name1) ).

thf(428,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)],[24]) ).

thf(219,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/sandbox/benchmark/theBenchmark.p',fact_215_residual_Ostrong__inducts) ).

thf(1201,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)],[219]) ).

thf(329,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/sandbox/benchmark/theBenchmark.p',fact_188_residual_Ofresh_I2_J) ).

thf(1651,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)],[329]) ).

thf(316,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/sandbox/benchmark/theBenchmark.p',fact_186_cons__eqvt) ).

thf(1604,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)],[316]) ).

thf(220,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/sandbox/benchmark/theBenchmark.p',fact_144_perm__app) ).

thf(1206,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)],[220]) ).

thf(50,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/sandbox/benchmark/theBenchmark.p',fact_317_simps_I9_J) ).

thf(529,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)],[50]) ).

thf(87,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/sandbox/benchmark/theBenchmark.p',fact_149_in__eqvt) ).

thf(661,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)],[87]) ).

thf(128,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/sandbox/benchmark/theBenchmark.p',fact_91_fresh__eqvt) ).

thf(793,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)],[128]) ).

thf(168,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/sandbox/benchmark/theBenchmark.p',fact_209_resCasesB_H) ).

thf(925,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)],[168]) ).

thf(248,axiom,
    ! [A: name,B: name] :
      ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_swap__simps_I2_J) ).

thf(1306,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)],[248]) ).

thf(206,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/sandbox/benchmark/theBenchmark.p',fact_62_perm__fresh__fresh) ).

thf(1153,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)],[206]) ).

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

thf(366,plain,
    ! [A: name,B: name] :
      ( ( if_name @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(344,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/sandbox/benchmark/theBenchmark.p',fact_326_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3) ).

thf(1736,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)],[344]) ).

thf(325,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/sandbox/benchmark/theBenchmark.p',fact_25_name__swap__bij) ).

thf(1636,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)],[325]) ).

thf(191,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/sandbox/benchmark/theBenchmark.p',fact_64_perm__fresh__fresh) ).

thf(1047,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)],[191]) ).

thf(208,axiom,
    ! [A: late_freeRes_Rep] :
      ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_freeRes__perm__empty) ).

thf(1163,plain,
    ! [A: late_freeRes_Rep] :
      ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(340,axiom,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_name__calc_I2_J) ).

thf(1723,plain,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(184,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_old_Oprod_Oinject) ).

thf(1021,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(236,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_fresh__prodD_I1_J) ).

thf(1255,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)],[236]) ).

thf(68,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/sandbox/benchmark/theBenchmark.p',fact_294_subject_Oinducts) ).

thf(598,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)],[68]) ).

thf(98,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/sandbox/benchmark/theBenchmark.p',fact_177_fresh__list__cons) ).

thf(693,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)],[98]) ).

thf(268,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/sandbox/benchmark/theBenchmark.p',fact_325_eqvt__subs) ).

thf(1370,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)],[268]) ).

thf(305,axiom,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_pi__perm__empty) ).

thf(1560,plain,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(38,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/sandbox/benchmark/theBenchmark.p',fact_76_fresh__perm__app) ).

thf(484,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)],[38]) ).

thf(156,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Res) ).

thf(879,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(336,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/sandbox/benchmark/theBenchmark.p',fact_203_residual_Oinducts) ).

thf(1687,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)],[336]) ).

thf(321,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/sandbox/benchmark/theBenchmark.p',fact_139_perm__app) ).

thf(1624,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)],[321]) ).

thf(65,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/sandbox/benchmark/theBenchmark.p',fact_154_eq__eqvt) ).

thf(583,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)],[65]) ).

thf(159,axiom,
    ! [A: list_P227219501e_name,B: pi,C: pi] :
      ( ( ( perm_name_pi @ A @ B )
        = ( perm_name_pi @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_perm__bij) ).

thf(889,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)],[159]) ).

thf(359,axiom,
    aa = b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062) ).

thf(1787,plain,
    aa = b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(116,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/sandbox/benchmark/theBenchmark.p',fact_79_fresh__perm__app) ).

thf(757,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)],[116]) ).

thf(181,axiom,
    y != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).

thf(1012,plain,
    y != x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(147,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_pi_Oinject_I7_J) ).

thf(852,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)],[147]) ).

thf(26,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_fresh__prod) ).

thf(435,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(94,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/sandbox/benchmark/theBenchmark.p',fact_147_in__eqvt) ).

thf(682,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)],[94]) ).

thf(217,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/sandbox/benchmark/theBenchmark.p',fact_300_inputIneqTrans) ).

thf(1195,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)],[217]) ).

thf(262,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/sandbox/benchmark/theBenchmark.p',fact_28_name__swap__bij) ).

thf(1350,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)],[262]) ).

thf(203,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/sandbox/benchmark/theBenchmark.p',fact_11_perm__swap_I1_J) ).

thf(1089,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)],[203]) ).

thf(84,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/sandbox/benchmark/theBenchmark.p',fact_125_perm__compose) ).

thf(650,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)],[84]) ).

thf(297,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/sandbox/benchmark/theBenchmark.p',fact_37_perm__swap_I2_J) ).

thf(1534,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)],[297]) ).

thf(227,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/sandbox/benchmark/theBenchmark.p',fact_23_name__swap) ).

thf(1227,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)],[227]) ).

thf(106,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/sandbox/benchmark/theBenchmark.p',fact_136_perm__app) ).

thf(725,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)],[106]) ).

thf(17,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/sandbox/benchmark/theBenchmark.p',fact_148_in__eqvt) ).

thf(403,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)],[17]) ).

thf(282,axiom,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_freeRes_Oexhaust) ).

thf(1425,plain,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(299,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/sandbox/benchmark/theBenchmark.p',fact_61_residual_Operm_I2_J) ).

thf(1540,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)],[299]) ).

thf(12,axiom,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_name__exists__fresh) ).

thf(388,plain,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(72,axiom,
    ! [A: late_subject] :
      ~ ! [B: name] :
          ~ ( fresh_717452603ubject @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_name__exists__fresh) ).

thf(610,plain,
    ! [A: late_subject] :
      ~ ! [B: name] :
          ~ ( fresh_717452603ubject @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(276,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Pair__inject) ).

thf(1397,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(202,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/sandbox/benchmark/theBenchmark.p',fact_239_if__eqvt) ).

thf(1082,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)],[202]) ).

thf(265,axiom,
    ! [A: name,B: pi] :
      ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_name__id) ).

thf(1361,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)],[265]) ).

thf(345,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/sandbox/benchmark/theBenchmark.p',fact_216_residual_Ostrong__inducts) ).

thf(1739,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)],[345]) ).

thf(200,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/sandbox/benchmark/theBenchmark.p',fact_27_name__swap__bij) ).

thf(1075,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)],[200]) ).

thf(49,axiom,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( late_BoundOutputS @ ( perm_name_name @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_subject_Operm_I2_J) ).

thf(526,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)],[49]) ).

thf(290,axiom,
    ! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name )
     => ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
            ( ( A @ D )
           => ( A @ ( cons_P1213805021e_name @ C @ D ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_list_Oinducts) ).

thf(1446,plain,
    ! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name )
     => ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
            ( ( A @ D )
           => ( A @ ( cons_P1213805021e_name @ C @ D ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(346,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/sandbox/benchmark/theBenchmark.p',fact_301_inputFreeTrans) ).

thf(1744,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)],[346]) ).

thf(101,axiom,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_ScopeExt) ).

thf(706,plain,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(81,axiom,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi_T) ).

thf(637,plain,
    ! [A: pi,B: pi] :
      ( ( if_pi @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(310,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/sandbox/benchmark/theBenchmark.p',fact_69_name__fresh__fresh) ).

thf(1584,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)],[310]) ).

thf(142,axiom,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_freeRes_Ofresh_I2_J) ).

thf(837,plain,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(253,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/sandbox/benchmark/theBenchmark.p',fact_29_name__swap__bij) ).

thf(1324,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)],[253]) ).

thf(234,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/sandbox/benchmark/theBenchmark.p',fact_105_freshFreeDerivative_I2_J) ).

thf(1249,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)],[234]) ).

thf(245,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/sandbox/benchmark/theBenchmark.p',fact_307_transitions_OPar2B) ).

thf(1297,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)],[245]) ).

thf(216,axiom,
    ! [A: late_freeRes] :
      ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_pt__name1) ).

thf(1192,plain,
    ! [A: late_freeRes] :
      ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(164,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/sandbox/benchmark/theBenchmark.p',fact_303_Late__Semantics_OPar2B) ).

thf(911,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)],[164]) ).

thf(283,axiom,
    ! [A: produc367475239e_name,B: list_P227219501e_name] :
      ( ( cons_P1213805021e_name @ A @ B )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_not__Cons__self2) ).

thf(1429,plain,
    ! [A: produc367475239e_name,B: list_P227219501e_name] :
      ( ( cons_P1213805021e_name @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(339,axiom,
    ! [A: pi] :
      ( ( perm_name_pi @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_pt__name1) ).

thf(1720,plain,
    ! [A: pi] :
      ( ( perm_name_pi @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(123,axiom,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_old_Oprod_Oinducts) ).

thf(779,plain,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(322,axiom,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_pt__name1) ).

thf(1627,plain,
    ! [A: name] :
      ( ( perm_name_name @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(83,axiom,
    ! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
      ( ( ( perm_n1559866809ubject @ A @ B )
        = ( perm_n1559866809ubject @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_perm__bij) ).

thf(647,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)],[83]) ).

thf(356,axiom,
    ! [A: name,B: late_subject] :
      ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_name__id) ).

thf(1776,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)],[356]) ).

thf(311,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/sandbox/benchmark/theBenchmark.p',fact_311_resInputBoundOutputTrans) ).

thf(1588,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)],[311]) ).

thf(171,axiom,
    late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Free_Ohyps) ).

thf(985,plain,
    late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(296,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/sandbox/benchmark/theBenchmark.p',fact_68_name__fresh__fresh) ).

thf(1530,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)],[296]) ).

thf(291,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/sandbox/benchmark/theBenchmark.p',fact_340_simCases) ).

thf(1456,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)],[291]) ).

thf(272,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/sandbox/benchmark/theBenchmark.p',fact_119_cp__name__name1) ).

thf(1382,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)],[272]) ).

thf(256,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
     => ( fresh_name_name @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_fresh__prodD_I2_J) ).

thf(1333,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)],[256]) ).

thf(127,axiom,
    eqvt_pi @ rel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_EqvtRel) ).

thf(792,plain,
    eqvt_pi @ rel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(357,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/sandbox/benchmark/theBenchmark.p',fact_200_freshBoundDerivative_I1_J) ).

thf(1779,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)],[357]) ).

thf(132,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/sandbox/benchmark/theBenchmark.p',fact_138_perm__app) ).

thf(805,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)],[132]) ).

thf(306,axiom,
    ! [A: late_subject] :
      ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pt__name1) ).

thf(1563,plain,
    ! [A: late_subject] :
      ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(193,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/sandbox/benchmark/theBenchmark.p',fact_73_name__fresh__fresh) ).

thf(1054,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)],[193]) ).

thf(210,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/sandbox/benchmark/theBenchmark.p',fact_155_eq__eqvt) ).

thf(1170,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)],[210]) ).

thf(187,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/sandbox/benchmark/theBenchmark.p',fact_167_list_Oinject) ).

thf(1035,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)],[187]) ).

thf(92,axiom,
    ! [A: name,B: late_subject,C: pi] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_fresh__prod) ).

thf(674,plain,
    ! [A: name,B: late_subject,C: pi] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(293,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/sandbox/benchmark/theBenchmark.p',fact_305_parCasesB_H) ).

thf(1466,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)],[293]) ).

thf(199,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/sandbox/benchmark/theBenchmark.p',fact_250_alphaRes) ).

thf(1071,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)],[199]) ).

thf(121,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/sandbox/benchmark/theBenchmark.p',fact_127_perm__compose) ).

thf(773,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)],[121]) ).

thf(66,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/sandbox/benchmark/theBenchmark.p',fact_345_parAssocLeft) ).

thf(586,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)],[66]) ).

thf(20,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/sandbox/benchmark/theBenchmark.p',fact_238_if__eqvt) ).

thf(412,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)],[20]) ).

thf(23,axiom,
    ! [A: list_P227219501e_name,B: name] :
      ( ( perm_n1559866809ubject @ A @ ( late_InputS @ B ) )
      = ( late_InputS @ ( perm_name_name @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_subject_Operm_I1_J) ).

thf(425,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)],[23]) ).

thf(45,axiom,
    ! [A: name,B: late_freeRes,C: late_subject] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_fresh__prod) ).

thf(513,plain,
    ! [A: name,B: late_freeRes,C: late_subject] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(347,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/sandbox/benchmark/theBenchmark.p',fact_17_name__id) ).

thf(1747,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)],[347]) ).

thf(69,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/sandbox/benchmark/theBenchmark.p',fact_135_perm__app) ).

thf(601,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)],[69]) ).

thf(224,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Late__Semantics_OInput) ).

thf(1219,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)],[224]) ).

thf(138,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/sandbox/benchmark/theBenchmark.p',fact_344_parSym) ).

thf(824,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)],[138]) ).

thf(144,axiom,
    ! [A: late_freeRes] :
      ~ ! [B: name] :
          ~ ( fresh_1641682979reeRes @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_name__exists__fresh) ).

thf(843,plain,
    ! [A: late_freeRes] :
      ~ ! [B: name] :
          ~ ( fresh_1641682979reeRes @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(63,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/sandbox/benchmark/theBenchmark.p',fact_96_fresh__bij) ).

thf(577,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)],[63]) ).

thf(226,axiom,
    fresh_name_pi @ x @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_assms_I1_J) ).

thf(1226,plain,
    fresh_name_pi @ x @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(60,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_fresh__prod) ).

thf(562,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(162,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/sandbox/benchmark/theBenchmark.p',fact_297_Par1F) ).

thf(904,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)],[162]) ).

thf(13,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/sandbox/benchmark/theBenchmark.p',fact_121_name__perm__compose) ).

thf(391,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)],[13]) ).

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

thf(382,plain,
    ! [A: name,B: name] :
      ( ( if_name @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(250,axiom,
    ! [A: name,B: late_freeRes] :
      ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_name__id) ).

thf(1312,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)],[250]) ).

thf(42,axiom,
    ! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
      ( ( ( perm_n336613537reeRes @ A @ B )
        = ( perm_n336613537reeRes @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_perm__bij) ).

thf(498,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)],[42]) ).

thf(343,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/sandbox/benchmark/theBenchmark.p',fact_40_perm__swap_I2_J) ).

thf(1733,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)],[343]) ).

thf(194,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/sandbox/benchmark/theBenchmark.p',fact_329_Late__Semantics_OComm1) ).

thf(1058,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)],[194]) ).

thf(231,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/sandbox/benchmark/theBenchmark.p',fact_67_perm__fresh__fresh) ).

thf(1239,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)],[231]) ).

thf(204,axiom,
    ! [A: list_P227219501e_name,B: produc367475239e_name,C: list_P227219501e_name] :
      ( ( A
        = ( cons_P1213805021e_name @ B @ C ) )
     => ( A != nil_Pr743626285e_name ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_list_OdiscI) ).

thf(1092,plain,
    ! [A: list_P227219501e_name,B: produc367475239e_name,C: list_P227219501e_name] :
      ( ( A
        = ( cons_P1213805021e_name @ B @ C ) )
     => ( A != nil_Pr743626285e_name ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(352,axiom,
    fresh_name_pi @ z @ p2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_cClose1_Ohyps_I11_J) ).

thf(1765,plain,
    fresh_name_pi @ z @ p2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(237,axiom,
    z != aa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cClose1_Ohyps_I10_J) ).

thf(1258,plain,
    z != aa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(221,axiom,
    ! [A: produc890461031e_name] :
      ( ! [B: list_P227219501e_name] :
          ( A
         != ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
     => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
            ( A
           != ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_splice_Ocases) ).

thf(1209,plain,
    ! [A: produc890461031e_name] :
      ( ! [B: list_P227219501e_name] :
          ( A
         != ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
     => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
            ( A
           != ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(140,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/sandbox/benchmark/theBenchmark.p',fact_86_fresh__eqvt) ).

thf(831,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)],[140]) ).

thf(278,axiom,
    ! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
      ( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
     => ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: list_P227219501e_name] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_P1213805021e_name @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_sorted__wrt_Oinduct) ).

thf(1408,plain,
    ! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
      ( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
     => ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: list_P227219501e_name] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_P1213805021e_name @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(21,axiom,
    ! [A: name,B: late_subject,C: late_subject] :
      ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_fresh__prod) ).

thf(419,plain,
    ! [A: name,B: late_subject,C: late_subject] :
      ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(176,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/sandbox/benchmark/theBenchmark.p',fact_339_simulation__def) ).

thf(996,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)],[176]) ).

thf(1,conjecture,
    late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(362,plain,
    ~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(110,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Late__Semantics1_Osubject_Oinject_I2_J) ).

thf(737,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(74,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/sandbox/benchmark/theBenchmark.p',fact_242_pt__bij3) ).

thf(616,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)],[74]) ).

thf(337,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/sandbox/benchmark/theBenchmark.p',fact_111_fresh__aux) ).

thf(1690,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)],[337]) ).

thf(270,axiom,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_pt__name1) ).

thf(1376,plain,
    ! [A: pi_Rep] :
      ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(118,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/sandbox/benchmark/theBenchmark.p',fact_152_eq__eqvt) ).

thf(764,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)],[118]) ).

thf(70,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Late__Semantics_Osubject_Oinject_I2_J) ).

thf(604,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(161,axiom,
    ! [A: produc1872410278e_name] :
      ( ! [B: produc367475239e_name > produc367475239e_name > $o] :
          ( A
         != ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
     => ( ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name] :
            ( A
           != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) ) )
       => ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( A
             != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_successively_Ocases) ).

thf(900,plain,
    ! [A: produc1872410278e_name] :
      ( ! [B: produc367475239e_name > produc367475239e_name > $o] :
          ( A
         != ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
     => ( ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name] :
            ( A
           != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) ) )
       => ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( A
             != ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

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/sandbox/benchmark/theBenchmark.p',fact_253_perm__prod_Osimps) ).

thf(406,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(134,axiom,
    ! [A: name,B: late_freeRes,C: late_freeRes] :
      ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_fresh__prod) ).

thf(811,plain,
    ! [A: name,B: late_freeRes,C: late_freeRes] :
      ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(41,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_substRes2) ).

thf(494,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)],[41]) ).

thf(79,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/sandbox/benchmark/theBenchmark.p',fact_184_cons__eqvt) ).

thf(631,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)],[79]) ).

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 @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_Late__Semantics_OPar1B) ).

thf(1339,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)],[258]) ).

thf(323,axiom,
    ! [A: produc367475239e_name > $o,B: produc367475239e_name] :
      ( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_prod__cases) ).

thf(1630,plain,
    ! [A: produc367475239e_name > $o,B: produc367475239e_name] :
      ( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(67,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_forget) ).

thf(594,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)],[67]) ).

thf(130,axiom,
    alpha = late_TauR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_cClose1_Ohyps_I14_J) ).

thf(799,plain,
    alpha = late_TauR,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(75,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/sandbox/benchmark/theBenchmark.p',fact_78_fresh__perm__app) ).

thf(621,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)],[75]) ).

thf(47,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/sandbox/benchmark/theBenchmark.p',fact_87_fresh__eqvt) ).

thf(520,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)],[47]) ).

thf(77,axiom,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_fresh__prod) ).

thf(626,plain,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(149,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_name__bij) ).

thf(858,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)],[149]) ).

thf(304,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/sandbox/benchmark/theBenchmark.p',fact_193_residual_Operm_I1_J) ).

thf(1557,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)],[304]) ).

thf(244,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/sandbox/benchmark/theBenchmark.p',fact_110_fresh__aux) ).

thf(1293,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)],[244]) ).

thf(90,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/sandbox/benchmark/theBenchmark.p',fact_259_perm__prod_Osimps) ).

thf(668,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)],[90]) ).

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/sandbox/benchmark/theBenchmark.p',fact_181_fresh__prodD_I1_J) ).

thf(462,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(195,axiom,
    fresh_name_name @ z @ x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_cClose1_Ohyps_I13_J) ).

thf(1061,plain,
    fresh_name_name @ z @ x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(95,axiom,
    ! [A: product_prod_pi_pi] :
    ? [B: pi,C: pi] :
      ( A
      = ( product_Pair_pi_pi @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_surj__pair) ).

thf(685,plain,
    ! [A: product_prod_pi_pi] :
    ? [B: pi,C: pi] :
      ( A
      = ( product_Pair_pi_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(218,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/sandbox/benchmark/theBenchmark.p',fact_281_pi_Operm_I4_J) ).

thf(1198,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)],[218]) ).

thf(222,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/sandbox/benchmark/theBenchmark.p',fact_10_perm__swap_I1_J) ).

thf(1213,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)],[222]) ).

thf(289,axiom,
    fresh_name_pi @ z @ ( res @ x @ q ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_cClose1_Ohyps_I9_J) ).

thf(1445,plain,
    fresh_name_pi @ z @ ( res @ x @ q ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(327,axiom,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
     => ~ ! [B: produc367475239e_name,C: list_P227219501e_name] :
            ( A
           != ( cons_P1213805021e_name @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_list_Oexhaust) ).

thf(1643,plain,
    ! [A: list_P227219501e_name] :
      ( ( A != nil_Pr743626285e_name )
     => ~ ! [B: produc367475239e_name,C: list_P227219501e_name] :
            ( A
           != ( cons_P1213805021e_name @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(182,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/sandbox/benchmark/theBenchmark.p',fact_90_fresh__eqvt) ).

thf(1015,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)],[182]) ).

thf(212,axiom,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
     => ( ! [D: list_P227219501e_name] : ( A @ D @ nil_Pr743626285e_name )
       => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
              ( ( A @ E @ ( cons_P1213805021e_name @ F @ G ) )
             => ( ( A @ ( cons_P1213805021e_name @ D @ E ) @ G )
               => ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_shuffles_Oinduct) ).

thf(1176,plain,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
     => ( ! [D: list_P227219501e_name] : ( A @ D @ nil_Pr743626285e_name )
       => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
              ( ( A @ E @ ( cons_P1213805021e_name @ F @ G ) )
             => ( ( A @ ( cons_P1213805021e_name @ D @ E ) @ G )
               => ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(27,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/sandbox/benchmark/theBenchmark.p',fact_97_fresh__bij) ).

thf(438,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)],[27]) ).

thf(25,axiom,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subject_Oexhaust) ).

thf(431,plain,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(85,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/sandbox/benchmark/theBenchmark.p',fact_347_pi_Ofresh_I9_J) ).

thf(653,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)],[85]) ).

thf(190,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/sandbox/benchmark/theBenchmark.p',fact_41_eqvt) ).

thf(1044,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)],[190]) ).

thf(233,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/sandbox/benchmark/theBenchmark.p',fact_113_fresh__aux) ).

thf(1245,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)],[233]) ).

thf(14,axiom,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_prod__cases) ).

thf(394,plain,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(172,axiom,
    ( ( late_BoundOutputS @ aa )
    = ( late_BoundOutputS @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_cOpen_Ohyps_I3_J) ).

thf(986,plain,
    ( ( late_BoundOutputS @ aa )
    = ( late_BoundOutputS @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(341,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/sandbox/benchmark/theBenchmark.p',fact_222_freshFreeDerivative_I1_J) ).

thf(1726,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)],[341]) ).

thf(266,axiom,
    ! [A: late_subject_Rep] :
      ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subject__perm__empty) ).

thf(1364,plain,
    ! [A: late_subject_Rep] :
      ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(338,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/sandbox/benchmark/theBenchmark.p',fact_221_resCasesB) ).

thf(1694,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)],[338]) ).

thf(167,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/sandbox/benchmark/theBenchmark.p',fact_21_name__swap) ).

thf(922,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)],[167]) ).

thf(105,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/sandbox/benchmark/theBenchmark.p',fact_183_cons__eqvt) ).

thf(722,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)],[105]) ).

thf(40,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_fresh__fact2) ).

thf(490,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)],[40]) ).

thf(281,axiom,
    ! [A: pi,B: pi,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_name_pi @ C @ A )
        = ( perm_name_pi @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_pt__bij3) ).

thf(1420,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)],[281]) ).

thf(39,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/sandbox/benchmark/theBenchmark.p',fact_128_perm__compose) ).

thf(487,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)],[39]) ).

thf(113,axiom,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_freshRes) ).

thf(749,plain,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(46,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/sandbox/benchmark/theBenchmark.p',fact_323_Agent_OsubstRes3) ).

thf(516,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)],[46]) ).

thf(183,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/sandbox/benchmark/theBenchmark.p',fact_22_name__swap) ).

thf(1018,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)],[183]) ).

thf(115,axiom,
    ! [A: list_P227219501e_name] :
      ( ( perm_n336613537reeRes @ A @ late_TauR )
      = late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_freeRes_Operm_I2_J) ).

thf(754,plain,
    ! [A: list_P227219501e_name] :
      ( ( perm_n336613537reeRes @ A @ late_TauR )
      = late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(57,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/sandbox/benchmark/theBenchmark.p',fact_151_eq__eqvt) ).

thf(553,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)],[57]) ).

thf(213,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/sandbox/benchmark/theBenchmark.p',fact_313_Late__Semantics_OClose2) ).

thf(1181,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)],[213]) ).

thf(350,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/sandbox/benchmark/theBenchmark.p',fact_312_Late__Semantics_OClose1) ).

thf(1758,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)],[350]) ).

thf(209,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/sandbox/benchmark/theBenchmark.p',fact_63_perm__fresh__fresh) ).

thf(1166,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)],[209]) ).

thf(122,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/sandbox/benchmark/theBenchmark.p',fact_123_name__perm__compose) ).

thf(776,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)],[122]) ).

thf(103,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/sandbox/benchmark/theBenchmark.p',fact_140_perm__app) ).

thf(712,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)],[103]) ).

thf(97,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/sandbox/benchmark/theBenchmark.p',fact_122_name__perm__compose) ).

thf(690,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)],[97]) ).

thf(82,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/sandbox/benchmark/theBenchmark.p',fact_236_if__eqvt) ).

thf(640,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)],[82]) ).

thf(319,axiom,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
     => ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ ( cons_P1213805021e_name @ D @ E ) @ nil_Pr743626285e_name )
       => ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ D @ E ) )
         => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
                ( ( A @ E @ G )
               => ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_list__induct2_H) ).

thf(1611,plain,
    ! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
     => ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ ( cons_P1213805021e_name @ D @ E ) @ nil_Pr743626285e_name )
       => ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ D @ E ) )
         => ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
                ( ( A @ E @ G )
               => ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(307,axiom,
    ! [A: name,B: name,C: name] :
      ( ( ( A = B )
       => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
          = C ) )
      & ( ( A != B )
       => ( ( ( C = B )
           => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
              = A ) )
          & ( ( C != B )
           => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_swap__name_Osimps) ).

thf(1566,plain,
    ! [A: name,B: name,C: name] :
      ( ( ( A = B )
       => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
          = C ) )
      & ( ( A != B )
       => ( ( ( C = B )
           => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
              = A ) )
          & ( ( C != B )
           => ( ( swap_name @ ( produc1570949143e_name @ A @ C ) @ B )
              = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(328,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/sandbox/benchmark/theBenchmark.p',fact_66_perm__fresh__fresh) ).

thf(1647,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)],[328]) ).

thf(235,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/sandbox/benchmark/theBenchmark.p',fact_98_fresh__bij) ).

thf(1252,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)],[235]) ).

thf(349,axiom,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_residual_Ostrong__inducts) ).

thf(1753,plain,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(175,axiom,
    b != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cOpen_Ohyps_I2_J) ).

thf(993,plain,
    b != x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(64,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/sandbox/benchmark/theBenchmark.p',fact_175_fresh__list__cons) ).

thf(580,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)],[64]) ).

thf(148,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/sandbox/benchmark/theBenchmark.p',fact_92_mem__Collect__eq) ).

thf(855,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)],[148]) ).

thf(19,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/sandbox/benchmark/theBenchmark.p',fact_318_simps_I8_J) ).

thf(409,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)],[19]) ).

thf(228,axiom,
    ! [A: produc367475239e_name > $o,B: produc367475239e_name] :
      ( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_old_Oprod_Oinducts) ).

thf(1230,plain,
    ! [A: produc367475239e_name > $o,B: produc367475239e_name] :
      ( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(246,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/sandbox/benchmark/theBenchmark.p',fact_156_residual_Oinject_I2_J) ).

thf(1300,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)],[246]) ).

thf(215,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/sandbox/benchmark/theBenchmark.p',fact_195_Late__Semantics_OResB) ).

thf(1188,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)],[215]) ).

thf(28,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/sandbox/benchmark/theBenchmark.p',fact_245_abs__fun__if) ).

thf(441,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)],[28]) ).

thf(188,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/sandbox/benchmark/theBenchmark.p',fact_189_freeRes_Ofresh_I1_J) ).

thf(1038,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)],[188]) ).

thf(133,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/sandbox/benchmark/theBenchmark.p',fact_143_perm__app) ).

thf(808,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)],[133]) ).

thf(163,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/sandbox/benchmark/theBenchmark.p',fact_212_freshBoundDerivative_I2_J) ).

thf(907,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)],[163]) ).

thf(277,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/sandbox/benchmark/theBenchmark.p',fact_314_transitions_OClose1) ).

thf(1404,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)],[277]) ).

thf(112,axiom,
    ! [A: late_subject,B: late_subject,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n1559866809ubject @ C @ A )
        = ( perm_n1559866809ubject @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_pt__bij3) ).

thf(744,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)],[112]) ).

thf(86,axiom,
    ! [A: late_freeRes,B: late_freeRes,C: list_P227219501e_name] :
      ( ( A = B )
     => ( ( perm_n336613537reeRes @ C @ A )
        = ( perm_n336613537reeRes @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_pt__bij3) ).

thf(656,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)],[86]) ).

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/sandbox/benchmark/theBenchmark.p',fact_117_cp__name__name1) ).

thf(613,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(263,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/sandbox/benchmark/theBenchmark.p',fact_108_swap__simps_I3_J) ).

thf(1353,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)],[263]) ).

thf(151,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_subject_Ofresh_I1_J) ).

thf(864,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(169,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_resTrans_I2_J) ).

thf(978,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)],[169]) ).

thf(334,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/sandbox/benchmark/theBenchmark.p',fact_20_name__swap) ).

thf(1670,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)],[334]) ).

thf(180,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/sandbox/benchmark/theBenchmark.p',fact_251_alphaBoundResidual) ).

thf(1008,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)],[180]) ).

thf(239,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/sandbox/benchmark/theBenchmark.p',fact_39_perm__swap_I2_J) ).

thf(1272,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)],[239]) ).

thf(155,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/sandbox/benchmark/theBenchmark.p',fact_153_eq__eqvt) ).

thf(876,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)],[155]) ).

thf(300,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_prod_Oinject) ).

thf(1543,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( produc1570949143e_name @ A @ B )
        = ( produc1570949143e_name @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(353,axiom,
    ! [A: late_residual_Rep] :
      ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_residual__perm__empty) ).

thf(1766,plain,
    ! [A: late_residual_Rep] :
      ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(225,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/sandbox/benchmark/theBenchmark.p',fact_219_residual_Ostrong__induct) ).

thf(1221,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)],[225]) ).

thf(243,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/sandbox/benchmark/theBenchmark.p',fact_249_abs__fun__if) ).

thf(1284,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)],[243]) ).

thf(32,axiom,
    ! [A: product_prod_pi_pi] :
      ~ ! [B: pi,C: pi] :
          ( A
         != ( product_Pair_pi_pi @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_old_Oprod_Oexhaust) ).

thf(465,plain,
    ! [A: product_prod_pi_pi] :
      ~ ! [B: pi,C: pi] :
          ( A
         != ( product_Pair_pi_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',fact_247_abs__fun__if) ).

thf(450,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)],[29]) ).

thf(53,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_subject_Ofresh_I2_J) ).

thf(539,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(303,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/sandbox/benchmark/theBenchmark.p',fact_337_simE_I2_J) ).

thf(1553,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)],[303]) ).

thf(91,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/sandbox/benchmark/theBenchmark.p',fact_146_in__eqvt) ).

thf(671,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)],[91]) ).

thf(207,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/sandbox/benchmark/theBenchmark.p',fact_304_parCasesB) ).

thf(1157,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)],[207]) ).

thf(96,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/sandbox/benchmark/theBenchmark.p',fact_179_fresh__prodD_I2_J) ).

thf(688,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)],[96]) ).

thf(223,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh_name_pi @ C @ A )
       => ( fresh_81631222sidual @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_freshResidual) ).

thf(1216,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)],[223]) ).

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

thf(363,plain,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(58,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/sandbox/benchmark/theBenchmark.p',fact_260_perm__prod_Osimps) ).

thf(556,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)],[58]) ).

thf(330,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/sandbox/benchmark/theBenchmark.p',fact_24_name__swap) ).

thf(1654,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)],[330]) ).

thf(279,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/sandbox/benchmark/theBenchmark.p',fact_327_renaming) ).

thf(1412,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)],[279]) ).

thf(100,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/sandbox/benchmark/theBenchmark.p',fact_237_if__eqvt) ).

thf(699,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)],[100]) ).

thf(273,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/sandbox/benchmark/theBenchmark.p',fact_102_freeRes_Oinducts) ).

thf(1385,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)],[273]) ).

thf(326,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/sandbox/benchmark/theBenchmark.p',fact_65_perm__fresh__fresh) ).

thf(1639,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)],[326]) ).

thf(196,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/sandbox/benchmark/theBenchmark.p',fact_346_derivativeEqvtI) ).

thf(1062,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)],[196]) ).

thf(294,axiom,
    ! [A: produc367475239e_name] :
    ? [B: name,C: name] :
      ( A
      = ( produc1570949143e_name @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_surj__pair) ).

thf(1523,plain,
    ! [A: produc367475239e_name] :
    ? [B: name,C: name] :
      ( A
      = ( produc1570949143e_name @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(108,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/sandbox/benchmark/theBenchmark.p',fact_126_perm__compose) ).

thf(731,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)],[108]) ).

thf(165,axiom,
    ! [A: list_l1406151091e_name] :
      ( ( A != nil_li29751603e_name )
     => ( ! [B: list_l1406151091e_name] :
            ( A
           != ( cons_l798145763e_name @ nil_Pr743626285e_name @ B ) )
       => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_l1406151091e_name] :
              ( A
             != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_transpose_Ocases) ).

thf(914,plain,
    ! [A: list_l1406151091e_name] :
      ( ( A != nil_li29751603e_name )
     => ( ! [B: list_l1406151091e_name] :
            ( A
           != ( cons_l798145763e_name @ nil_Pr743626285e_name @ B ) )
       => ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_l1406151091e_name] :
              ( A
             != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(44,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/sandbox/benchmark/theBenchmark.p',fact_257_perm__prod_Osimps) ).

thf(510,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)],[44]) ).

thf(89,axiom,
    fresh_name_pi @ y @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_cClose1_Ohyps_I3_J) ).

thf(667,plain,
    fresh_name_pi @ y @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(317,axiom,
    fresh_name_pi @ z @ q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062) ).

thf(1607,plain,
    fresh_name_pi @ z @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(249,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/sandbox/benchmark/theBenchmark.p',fact_296_Par2F) ).

thf(1309,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)],[249]) ).

thf(52,axiom,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_name__exists__fresh) ).

thf(536,plain,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(55,axiom,
    fresh_name_pi @ y @ q2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_cClose1_Ohyps_I7_J) ).

thf(549,plain,
    fresh_name_pi @ y @ q2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(288,axiom,
    fresh_name_name @ y @ x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_cClose1_Ohyps_I12_J) ).

thf(1444,plain,
    fresh_name_name @ y @ x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(205,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/sandbox/benchmark/theBenchmark.p',fact_204_resCases_H) ).

thf(1097,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)],[205]) ).

thf(301,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/sandbox/benchmark/theBenchmark.p',fact_328_injPermSubst) ).

thf(1546,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)],[301]) ).

thf(247,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/sandbox/benchmark/theBenchmark.p',fact_261_perm__prod_Osimps) ).

thf(1303,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)],[247]) ).

thf(335,axiom,
    ! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name )
     => ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
       => ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( ( A @ E )
             => ( ( A @ ( cons_P1213805021e_name @ D @ E ) )
               => ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_induct__list012) ).

thf(1673,plain,
    ! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
      ( ( A @ nil_Pr743626285e_name )
     => ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
       => ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
              ( ( A @ E )
             => ( ( A @ ( cons_P1213805021e_name @ D @ E ) )
               => ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(22,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/sandbox/benchmark/theBenchmark.p',fact_142_perm__app) ).

thf(422,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)],[22]) ).

thf(152,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/sandbox/benchmark/theBenchmark.p',fact_95_fresh__bij) ).

thf(867,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)],[152]) ).

thf(7,axiom,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__Osubject_T) ).

thf(373,plain,
    ! [A: late_subject,B: late_subject] :
      ( ( if_Late_subject @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(285,axiom,
    late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cOpen_Ohyps_I1_J) ).

thf(1436,plain,
    late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(331,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/sandbox/benchmark/theBenchmark.p',fact_199_ResF) ).

thf(1657,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)],[331]) ).

thf(257,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/sandbox/benchmark/theBenchmark.p',fact_338_simE_I1_J) ).

thf(1335,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)],[257]) ).

thf(119,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/sandbox/benchmark/theBenchmark.p',fact_120_name__perm__compose) ).

thf(767,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)],[119]) ).

thf(16,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_pi_Ofresh_I4_J) ).

thf(400,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(139,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/sandbox/benchmark/theBenchmark.p',fact_116_cp__name__name1) ).

thf(828,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)],[139]) ).

thf(197,axiom,
    y != z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cClose1_Ohyps_I6_J) ).

thf(1065,plain,
    y != z,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(99,axiom,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Collect__mem__eq) ).

thf(696,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)],[99]) ).

thf(260,axiom,
    late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_cClose1_Ohyps_I2_J) ).

thf(1346,plain,
    late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(129,axiom,
    ! [A: list_P227219501e_name,B: name,C: name] :
      ( ( ( perm_name_name @ A @ B )
        = ( perm_name_name @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_perm__bij) ).

thf(796,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)],[129]) ).

thf(166,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/sandbox/benchmark/theBenchmark.p',fact_70_name__fresh__fresh) ).

thf(918,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)],[166]) ).

thf(131,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_pi_Odistinct_I85_J) ).

thf(801,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(360,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/sandbox/benchmark/theBenchmark.p',fact_55_freeRes_Operm_I1_J) ).

thf(1789,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)],[360]) ).

thf(88,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/sandbox/benchmark/theBenchmark.p',fact_77_fresh__perm__app) ).

thf(664,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)],[88]) ).

thf(230,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/sandbox/benchmark/theBenchmark.p',fact_14_perm__swap_I1_J) ).

thf(1236,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)],[230]) ).

thf(238,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/sandbox/benchmark/theBenchmark.p',fact_298_name__calc_I3_J) ).

thf(1261,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)],[238]) ).

thf(298,axiom,
    ! [A: produc367475239e_name,B: list_P227219501e_name,C: name] :
      ( ( name_prm_name @ ( cons_P1213805021e_name @ A @ B ) @ C )
      = ( swap_name @ A @ ( name_prm_name @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_name__prm__name_Osimps_I2_J) ).

thf(1537,plain,
    ! [A: produc367475239e_name,B: list_P227219501e_name,C: name] :
      ( ( name_prm_name @ ( cons_P1213805021e_name @ A @ B ) @ C )
      = ( swap_name @ A @ ( name_prm_name @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(302,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/sandbox/benchmark/theBenchmark.p',fact_342_derivativeEqvtI2) ).

thf(1550,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)],[302]) ).

thf(174,axiom,
    fresh_name_pi @ y @ ( res @ x @ q ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_cClose1_Ohyps_I4_J) ).

thf(992,plain,
    fresh_name_pi @ y @ ( res @ x @ q ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(179,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/sandbox/benchmark/theBenchmark.p',fact_71_name__fresh__fresh) ).

thf(1004,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)],[179]) ).

thf(320,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/sandbox/benchmark/theBenchmark.p',fact_280_pi_Operm_I8_J) ).

thf(1621,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)],[320]) ).

thf(43,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/sandbox/benchmark/theBenchmark.p',fact_246_abs__fun__if) ).

thf(501,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)],[43]) ).

thf(76,axiom,
    ( fresh_name_name
    = ( != @ name ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_name__fresh) ).

thf(624,plain,
    ( fresh_name_name
    = ( ^ [A: name,B: name] : ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(143,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_pi_Odistinct_I57_J) ).

thf(839,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)],[143]) ).

thf(107,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/sandbox/benchmark/theBenchmark.p',fact_99_fresh__bij) ).

thf(728,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)],[107]) ).

thf(111,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/sandbox/benchmark/theBenchmark.p',fact_321_fresh__fact1) ).

thf(740,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)],[111]) ).

thf(264,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Late__Semantics_OfreeRes_Odistinct_I1_J) ).

thf(1357,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(30,axiom,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_subst__identity) ).

thf(459,plain,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

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

thf(369,plain,
    ! [A: late_freeRes,B: late_freeRes] :
      ( ( if_Late_freeRes @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(71,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/sandbox/benchmark/theBenchmark.p',fact_141_perm__app) ).

thf(607,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)],[71]) ).

thf(214,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).

thf(1184,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(292,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/sandbox/benchmark/theBenchmark.p',fact_80_fresh__perm__app) ).

thf(1463,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)],[292]) ).

thf(280,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/sandbox/benchmark/theBenchmark.p',fact_114_fresh__aux) ).

thf(1416,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)],[280]) ).

thf(354,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/sandbox/benchmark/theBenchmark.p',fact_333_transitions_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 @ 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)],[354]) ).

thf(157,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/sandbox/benchmark/theBenchmark.p',fact_182_cons__eqvt) ).

thf(882,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)],[157]) ).

thf(33,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_prod_Oinject) ).

thf(469,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(267,axiom,
    ! [A: name] :
      ( ( name_prm_name @ nil_Pr743626285e_name @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_name__prm__name_Osimps_I1_J) ).

thf(1367,plain,
    ! [A: name] :
      ( ( name_prm_name @ nil_Pr743626285e_name @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1813,plain,
    $false,
    inference(cvc4,[status(thm)],[892,1665,629,1024,760,1633,479,1729,846,1031,1315,481,1750,523,1596,1068,873,1591,379,677,1437,1173,1041,861,1078,533,550,715,1275,472,1233,1608,385,814,1327,1761,1342,1001,1391,709,885,1601,565,1243,1782,782,1441,1792,1660,785,372,1330,751,1279,1577,542,817,559,1379,1347,770,1773,1319,870,475,789,1373,376,834,574,1581,1283,1051,821,981,397,634,734,1394,1526,998,988,1433,1600,849,428,1201,1651,1604,1206,529,661,793,925,1306,1153,366,1736,1636,1047,1163,1723,1021,1255,598,693,1370,1560,484,879,1687,1624,583,889,1787,757,1012,852,435,682,1195,1350,1089,650,1534,1227,725,403,1425,1540,388,610,1397,1082,1361,1739,1075,526,1446,1744,706,637,1584,837,1324,1249,1297,1192,911,1429,1720,779,1627,647,1776,1588,985,1530,1456,1382,1333,792,1779,805,1563,1054,1170,1035,674,1466,1071,773,586,412,425,513,1747,601,1219,824,843,577,1226,562,904,391,382,1312,498,1733,1058,1239,1092,1765,1258,1209,831,1408,419,996,362,737,616,1690,1376,764,604,900,406,811,494,631,1339,1630,594,799,621,520,626,858,1557,1293,668,462,1061,685,1198,1213,1445,1643,1015,1176,438,431,653,1044,1245,394,986,1726,1364,1694,922,722,490,1420,487,749,516,1018,754,553,1181,1758,1166,776,712,690,640,1611,1566,1647,1252,1753,993,580,855,409,1230,1300,1188,441,1038,808,907,1404,744,656,613,1353,864,978,1670,1008,1272,876,1543,1766,1221,1284,465,450,539,1553,671,1157,688,1216,363,556,1654,1412,699,1385,1639,1062,1523,731,914,510,667,1607,1309,536,549,1444,1097,1546,1303,1673,422,867,373,1436,1657,1335,767,400,828,1065,696,1346,796,918,801,1789,664,1236,1261,1537,1550,992,1004,1621,501,624,839,728,740,1357,459,369,607,1184,1463,1416,1769,882,469,1367]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : ITP190^1 : TPTP v8.2.0. Released v7.5.0.
% 0.18/0.18  % Command  : run_Leo-III %s %d
% 0.19/0.40  % Computer : n022.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit : 300
% 0.19/0.40  % WCLimit  : 300
% 0.19/0.40  % DateTime : Sat May 18 16:32:53 EDT 2024
% 0.19/0.40  % CPUTime  : 
% 1.11/1.02  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.17/1.34  % [INFO] 	 Parsing done (321ms). 
% 2.17/1.35  % [INFO] 	 Running in sequential loop mode. 
% 3.01/1.62  % [INFO] 	 eprover registered as external prover. 
% 3.01/1.62  % [INFO] 	 cvc4 registered as external prover. 
% 3.01/1.63  % [INFO] 	 Scanning for conjecture ... 
% 3.46/1.76  % [INFO] 	 Found a conjecture (or negated_conjecture) and 360 axioms. Running axiom selection ... 
% 3.76/1.90  % [INFO] 	 Axiom selection finished. Selected 359 axioms (removed 1 axioms). 
% 4.78/2.13  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.78/2.16  % [INFO] 	 Type checking passed. 
% 4.92/2.16  % [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 ... 
% 30.04/8.12  % External prover 'cvc4' found a proof!
% 30.04/8.12  % [INFO] 	 Killing All external provers ... 
% 30.04/8.12  % Time passed: 7545ms (effective reasoning time: 6766ms)
% 30.04/8.12  % 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)>
% 30.04/8.13  % Axioms used in derivation (359): fact_241_pt__bij3, help_If_2_1_If_001t__Agent__Opi_T, help_If_1_1_If_001t__Agent__Oname_T, fact_88_fresh__eqvt, fact_236_if__eqvt, fact_332_transitions_OComm1, fact_119_cp__name__name1, fact_92_mem__Collect__eq, fact_295_subject_Oexhaust, fact_189_freeRes_Ofresh_I1_J, fact_176_fresh__list__cons, fact_162_fresh__prod, fact_113_fresh__aux, fact_179_fresh__prodD_I2_J, fact_232_old_Oprod_Oinducts, fact_246_abs__fun__if, fact_298_name__calc_I3_J, fact_114_fresh__aux, fact_262_list_Odistinct_I1_J, fact_54_pi__perm__empty, fact_168_old_Oprod_Oinject, fact_124_name__perm__compose, fact_326_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3, fact_167_list_Oinject, fact_292_Late__Semantics_Osubject_Odistinct_I1_J, fact_44_Late__Semantics1_OfreeRes_Oinject, fact_271_transpose_Ocases, fact_106_swap__simps_I1_J, fact_279_pi_Ofresh_I8_J, fact_152_eq__eqvt, fact_159_fresh__prod, fact_186_cons__eqvt, fact_323_Agent_OsubstRes3, fact_314_transitions_OClose1, fact_45_cClose1_Ohyps_I11_J, fact_260_perm__prod_Osimps, fact_8_cClose1_Ohyps_I14_J, fact_243_pt__bij3, fact_108_swap__simps_I3_J, fact_132_perm__bij, fact_9_cClose1_Ohyps_I13_J, fact_10_perm__swap_I1_J, fact_344_parSym, fact_259_perm__prod_Osimps, fact_214_residual_Ostrong__inducts, fact_337_simE_I2_J, fact_60_name__fresh, fact_30_pt__name1, fact_346_derivativeEqvtI, fact_251_alphaBoundResidual, fact_0__092_060open_062a_A_061_Ab_092_060close_062, fact_35__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, fact_258_perm__prod_Osimps, fact_23_name__swap, fact_145_in__eqvt, fact_38_perm__swap_I2_J, fact_320_forget, fact_121_name__perm__compose, fact_82_name__exists__fresh, fact_59_freeRes_Operm_I2_J, fact_90_fresh__eqvt, fact_34_pt__name1, fact_272_remdups__adj_Ocases, fact_202_residual_Odistinct_I1_J, fact_73_name__fresh__fresh, fact_26_name__swap__bij, fact_269_induct__list012, fact_135_perm__app, fact_188_residual_Ofresh_I2_J, fact_43_Late__Semantics_OfreeRes_Oinject, fact_196_transitions_OResB, fact_249_abs__fun__if, fact_348_pi_Ofresh_I4_J, fact_239_if__eqvt, fact_325_eqvt__subs, fact_53_freeRes__perm__empty, fact_27_name__swap__bij, fact_139_perm__app, fact_78_fresh__perm__app, fact_125_perm__compose, fact_141_perm__app, fact_194_name__bij, fact_36_perm__swap_I2_J, fact_203_residual_Oinducts, fact_156_residual_Oinject_I2_J, fact_238_if__eqvt, fact_220_residual_Ostrong__induct, fact_245_abs__fun__if, fact_93_Collect__mem__eq, fact_191_pi_Operm_I9_J, fact_192_cClose1_Ohyps_I1_J, fact_317_simps_I9_J, fact_79_fresh__perm__app, fact_221_resCasesB, fact_28_name__swap__bij, fact_115_cp__name__name1, fact_222_freshFreeDerivative_I1_J, fact_104_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_277_Late__Semantics1_Osubject_Oinject_I1_J, fact_244_pt__bij3, fact_29_name__swap__bij, fact_233_not__Cons__self2, fact_339_simulation__def, fact_150_in__eqvt, fact_187_freeRes_Ofresh_I2_J, fact_138_perm__app, fact_151_eq__eqvt, fact_287_pi_Oinject_I7_J, fact_302_Late__Semantics_OPar1B, fact_62_perm__fresh__fresh, fact_327_renaming, fact_63_perm__fresh__fresh, fact_97_fresh__bij, fact_231_old_Oprod_Oinducts, fact_112_fresh__aux, fact_223_surj__pair, fact_11_perm__swap_I1_J, fact_107_swap__simps_I2_J, fact_105_freshFreeDerivative_I2_J, help_If_1_1_If_001t__Late____Semantics__OfreeRes_T, fact_157_fresh__prod, fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062, fact_140_perm__app, fact_48_assms_I1_J, fact_19_name__id, fact_284_ScopeExt, fact_257_perm__prod_Osimps, fact_201_freshRes, fact_197_resCasesF, fact_248_abs__fun__if, fact_290_Late__Semantics_OInput, fact_205_sorted__wrt_Ocases, fact_319_substTrans, fact_31_pt__name1, fact_267_list__induct2_H, help_If_2_1_If_001t__Late____Semantics__OfreeRes_T, fact_42__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062, fact_96_fresh__bij, fact_33_pt__name1, fact_199_ResF, fact_338_simE_I1_J, help_If_1_1_If_001t__Agent__Opi____Rep_T, fact_130_perm__bij, fact_66_perm__fresh__fresh, fact_37_perm__swap_I2_J, fact_211_freshResidual, fact_304_parCasesB, fact_254_perm__prod_Osimps, fact_122_name__perm__compose, help_If_1_1_If_001t__Late____Semantics__Osubject_T, fact_213_residual_Ostrong__inducts, fact_133_perm__bij, fact_136_perm__app, fact_32_pt__name1, fact_250_alphaRes, fact_165_fresh__prod, fact_219_residual_Ostrong__induct, fact_55_freeRes_Operm_I1_J, fact_146_in__eqvt, fact_52_subject__perm__empty, fact_334_Agent_Oswap__name__def, fact_16_name__id, fact_324_substRes2, fact_61_residual_Operm_I2_J, fact_20_name__swap, help_If_2_1_If_001t__Late____Semantics__Osubject_T, fact_225_prod__cases, fact_120_name__perm__compose, fact_313_Late__Semantics_OClose2, fact_252_perm__prod_Osimps, fact_347_pi_Ofresh_I9_J, fact_210_Open, fact_190_subject_Ofresh_I2_J, fact_72_name__fresh__fresh, fact_142_perm__app, fact_256_perm__prod_Osimps, fact_282_subject_Ofresh_I1_J, fact_21_name__swap, fact_13_perm__swap_I1_J, fact_116_cp__name__name1, fact_155_eq__eqvt, fact_268_splice_Oinduct, fact_183_cons__eqvt, fact_285_Res, fact_275_alphaInput, fact_100_name__calc_I2_J, fact_101_freeRes_Oexhaust, fact_134_perm__bij, fact_109_fresh__aux, fact_174_fresh__list__cons, fact_117_cp__name__name1, fact_12_perm__swap_I1_J, fact_86_fresh__eqvt, fact_84_name__exists__fresh, fact_229_old_Oprod_Oexhaust, fact_280_pi_Operm_I8_J, fact_307_transitions_OPar2B, fact_330_Late__Semantics_OComm2, fact_131_perm__bij, fact_103_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_164_fresh__prod, fact_215_residual_Ostrong__inducts, fact_85_name__exists__fresh, fact_291_pi_Odistinct_I57_J, fact_170_prod_Oinject, fact_266_neq__Nil__conv, fact_230_old_Oprod_Oexhaust, fact_6_cOpen_Ohyps_I1_J, fact_273_sorted__wrt_Oinduct, fact_283_subject_Operm_I1_J, fact_309_inputBoundOutputTrans, fact_158_fresh__prod, fact_335_swap__name_Osimps, fact_311_resInputBoundOutputTrans, fact_172_cClose1_Ohyps_I2_J, fact_56_subject_Operm_I2_J, fact_299_resTrans_I2_J, fact_80_fresh__perm__app, fact_147_in__eqvt, fact_173_fresh__list__cons, fact_310_inputCases, fact_15_name__id, fact_312_Late__Semantics_OClose1, fact_200_freshBoundDerivative_I1_J, fact_76_fresh__perm__app, fact_217_residual_Ostrong__induct, fact_276_name__calc_I1_J, fact_2_cClose1_Ohyps_I10_J, fact_178_fresh__prodD_I2_J, fact_24_name__swap, fact_69_name__fresh__fresh, fact_57_Late__Semantics_Osubject_Oinject_I2_J, fact_318_simps_I8_J, fact_322_fresh__fact2, fact_50_cClose1_Ohyps_I3_J, fact_316_subst__identity, fact_7_cOpen_Ohyps_I3_J, fact_4_cClose1_Ohyps_I5_J, fact_294_subject_Oinducts, fact_198_resCasesF_H, fact_81_fresh__perm__app, fact_253_perm__prod_Osimps, fact_182_cons__eqvt, fact_270_shuffles_Oinduct, fact_305_parCasesB_H, fact_1_cOpen_Ohyps_I2_J, fact_51_residual__perm__empty, fact_163_fresh__prod, fact_315_EqvtRel, help_If_2_1_If_001t__Agent__Opi____Rep_T, fact_169_old_Oprod_Oinject, fact_161_fresh__prod, fact_118_cp__name__name1, fact_207_splice_Ocases, fact_181_fresh__prodD_I1_J, fact_153_eq__eqvt, fact_166_fresh__prod, fact_40_perm__swap_I2_J, fact_204_resCases_H, fact_99_fresh__bij, fact_212_freshBoundDerivative_I2_J, fact_94_fresh__bij, fact_110_fresh__aux, fact_300_inputIneqTrans, help_If_1_1_If_001t__Agent__Opi_T, fact_25_name__swap__bij, fact_234_allE__Nil, fact_265_list_Oinducts, fact_127_perm__compose, fact_345_parAssocLeft, fact_58_Late__Semantics1_Osubject_Oinject_I2_J, fact_39_perm__swap_I2_J, fact_102_freeRes_Oinducts, fact_143_perm__app, fact_171_prod_Oinject, fact_41_eqvt, fact_286_pi_Odistinct_I55_J, fact_340_simCases, fact_185_cons__eqvt, fact_281_pi_Operm_I4_J, fact_218_residual_Ostrong__induct, fact_144_perm__app, fact_301_inputFreeTrans, fact_68_name__fresh__fresh, fact_77_fresh__perm__app, fact_148_in__eqvt, fact_71_name__fresh__fresh, help_If_3_1_If_001t__Late____Semantics__Osubject_T, fact_3_cClose1_Ohyps_I6_J, fact_154_eq__eqvt, fact_128_perm__compose, fact_255_perm__prod_Osimps, fact_75_cClose1_Ohyps_I4_J, fact_341_name__prm__name_Osimps_I1_J, fact_17_name__id, fact_228_Pair__inject, fact_274_Free_Ohyps, fact_343_Agent_Oname__prm__name__def, fact_224_surj__pair, fact_331_transitions_OComm2, fact_18_name__id, fact_64_perm__fresh__fresh, fact_226_prod__cases, fact_14_perm__swap_I1_J, fact_22_name__swap, fact_129_perm__compose, fact_306_transitions_OPar1B, fact_342_derivativeEqvtI2, fact_137_perm__app, fact_83_name__exists__fresh, fact_216_residual_Ostrong__inducts, fact_227_Pair__inject, fact_237_if__eqvt, fact_293_Late__Semantics1_Osubject_Odistinct_I1_J, fact_296_Par2F, fact_336_name__prm__name_Osimps_I2_J, fact_46_cClose1_Ohyps_I7_J, fact_235_if__eqvt, fact_308_resInputFreeTrans, fact_264_list_Oexhaust, fact_240_pt__bij3, fact_89_fresh__eqvt, fact_321_fresh__fact1, fact_149_in__eqvt, fact_209_resCasesB_H, fact_95_fresh__bij, fact_206_successively_Ocases, fact_49_cClose1_Ohyps_I8_J, fact_175_fresh__list__cons, fact_297_Par1F, fact_208_shuffles_Ocases, fact_195_Late__Semantics_OResB, fact_126_perm__compose, fact_263_list_OdiscI, fact_288_pi_Odistinct_I85_J, fact_70_name__fresh__fresh, fact_289_transitions_OInput, fact_98_fresh__bij, fact_261_perm__prod_Osimps, fact_247_abs__fun__if, fact_177_fresh__list__cons, fact_180_fresh__prodD_I1_J, fact_328_injPermSubst, fact_184_cons__eqvt, fact_303_Late__Semantics_OPar2B, fact_67_perm__fresh__fresh, fact_123_name__perm__compose, fact_74_cClose1_Ohyps_I9_J, fact_333_transitions_OClose2, fact_91_fresh__eqvt, fact_65_perm__fresh__fresh, fact_329_Late__Semantics_OComm1, fact_111_fresh__aux, fact_160_fresh__prod, help_If_2_1_If_001t__Agent__Oname_T, fact_47_cClose1_Ohyps_I12_J, fact_242_pt__bij3, fact_87_fresh__eqvt, fact_193_residual_Operm_I1_J
% 30.04/8.13  % No. of inferences in proof: 722
% 30.04/8.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7545 ms resp. 6766 ms w/o parsing
% 30.95/8.39  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.95/8.39  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------