DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP188^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n025.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 : Wed Feb 25 08:56:16 AM UTC 2026

% Result   : Theorem 27.82s 5.44s
% Output   : Refutation 27.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   52 (  48 unt;   0 typ;   0 def)
%            Number of atoms       :  162 (  52 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  622 (   7   ~;   0   |;   0   &; 569   @)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :   26 (  25 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  83 usr;  14 con; 0-5 aty)
%                                         (  24  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   69 (  30   ^;  39   !;   0   ?;  69   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    pi: $tType ).

thf(type_def_7,type,
    name: $tType ).

thf(type_def_8,type,
    late_freeRes: $tType ).

thf(type_def_9,type,
    late_subject: $tType ).

thf(type_def_10,type,
    late_residual: $tType ).

thf(type_def_11,type,
    noption_name: $tType ).

thf(type_def_12,type,
    noption_pi: $tType ).

thf(type_def_13,type,
    noption_Late_freeRes: $tType ).

thf(type_def_14,type,
    produc1141751126_pi_pi: $tType ).

thf(type_def_15,type,
    noptio1575811931_pi_pi: $tType ).

thf(type_def_16,type,
    produc1462499409ion_pi: $tType ).

thf(type_def_17,type,
    produc405342261i_name: $tType ).

thf(type_def_18,type,
    produc629157763_pi_pi: $tType ).

thf(type_def_19,type,
    produc1834551554reeRes: $tType ).

thf(type_def_20,type,
    produc53907987_pi_pi: $tType ).

thf(type_def_21,type,
    produc367475239e_name: $tType ).

thf(type_def_22,type,
    product_prod_name_pi: $tType ).

thf(type_def_23,type,
    produc2008547984reeRes: $tType ).

thf(type_def_24,type,
    product_prod_pi_name: $tType ).

thf(type_def_25,type,
    product_prod_pi_pi: $tType ).

thf(type_def_26,type,
    produc649380958reeRes: $tType ).

thf(type_def_27,type,
    produc2052722628s_name: $tType ).

thf(type_def_28,type,
    produc992857746Res_pi: $tType ).

thf(type_def_29,type,
    produc1357834675reeRes: $tType ).

thf(type_def_30,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(func_def_0,type,
    produc53907987_pi_pi: $tType ).

thf(func_def_1,type,
    produc1462499409ion_pi: $tType ).

thf(func_def_2,type,
    noptio1575811931_pi_pi: $tType ).

thf(func_def_3,type,
    produc1834551554reeRes: $tType ).

thf(func_def_4,type,
    produc405342261i_name: $tType ).

thf(func_def_5,type,
    produc629157763_pi_pi: $tType ).

thf(func_def_6,type,
    produc1141751126_pi_pi: $tType ).

thf(func_def_7,type,
    produc1357834675reeRes: $tType ).

thf(func_def_8,type,
    produc2052722628s_name: $tType ).

thf(func_def_9,type,
    produc2008547984reeRes: $tType ).

thf(func_def_10,type,
    produc992857746Res_pi: $tType ).

thf(func_def_11,type,
    produc649380958reeRes: $tType ).

thf(func_def_12,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(func_def_13,type,
    produc367475239e_name: $tType ).

thf(func_def_14,type,
    product_prod_pi_name: $tType ).

thf(func_def_15,type,
    product_prod_name_pi: $tType ).

thf(func_def_16,type,
    product_prod_pi_pi: $tType ).

thf(func_def_17,type,
    noption_Late_freeRes: $tType ).

thf(func_def_18,type,
    noption_name: $tType ).

thf(func_def_19,type,
    noption_pi: $tType ).

thf(func_def_20,type,
    late_residual: $tType ).

thf(func_def_21,type,
    late_subject: $tType ).

thf(func_def_22,type,
    late_freeRes: $tType ).

thf(func_def_23,type,
    name: $tType ).

thf(func_def_24,type,
    pi: $tType ).

thf(func_def_25,type,
    bang: pi > pi ).

thf(func_def_26,type,
    input: name > name > pi > pi ).

thf(func_def_27,type,
    match: name > name > pi > pi ).

thf(func_def_28,type,
    mismatch: name > name > pi > pi ).

thf(func_def_29,type,
    output: name > name > pi > pi ).

thf(func_def_30,type,
    par: pi > pi > pi ).

thf(func_def_31,type,
    piNil: pi ).

thf(func_def_32,type,
    res: name > pi > pi ).

thf(func_def_33,type,
    sum: pi > pi > pi ).

thf(func_def_34,type,
    tau: pi > pi ).

thf(func_def_35,type,
    subs: pi > name > name > pi ).

thf(func_def_36,type,
    subst_name: name > name > name > name ).

thf(func_def_37,type,
    if_name: $o > name > name > name ).

thf(func_def_38,type,
    late_OutputR: name > name > late_freeRes ).

thf(func_def_39,type,
    late_TauR: late_freeRes ).

thf(func_def_40,type,
    late_BoundR: late_subject > name > pi > late_residual ).

thf(func_def_41,type,
    late_FreeR: late_freeRes > pi > late_residual ).

thf(func_def_42,type,
    late_BoundOutputS: name > late_subject ).

thf(func_def_43,type,
    late_InputS: name > late_subject ).

thf(func_def_44,type,
    late_transitions: pi > late_residual > $o ).

thf(func_def_45,type,
    abs_fun_name_name: name > name > name > noption_name ).

thf(func_def_46,type,
    abs_fun_name_pi: name > pi > name > noption_pi ).

thf(func_def_47,type,
    abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).

thf(func_def_48,type,
    abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).

thf(func_def_49,type,
    fresh_1093033124n_name: name > ( name > noption_name ) > $o ).

thf(func_def_50,type,
    fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).

thf(func_def_51,type,
    fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).

thf(func_def_52,type,
    fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).

thf(func_def_53,type,
    fresh_name_name: name > name > $o ).

thf(func_def_54,type,
    fresh_name_pi: name > pi > $o ).

thf(func_def_55,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(func_def_56,type,
    fresh_81631222sidual: name > late_residual > $o ).

thf(func_def_57,type,
    fresh_717452603ubject: name > late_subject > $o ).

thf(func_def_58,type,
    fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).

thf(func_def_59,type,
    fresh_453496559i_name: name > produc405342261i_name > $o ).

thf(func_def_60,type,
    fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).

thf(func_def_61,type,
    fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).

thf(func_def_62,type,
    fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o ).

thf(func_def_63,type,
    fresh_441084397e_name: name > produc367475239e_name > $o ).

thf(func_def_64,type,
    fresh_93646139ame_pi: name > product_prod_name_pi > $o ).

thf(func_def_65,type,
    fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).

thf(func_def_66,type,
    fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).

thf(func_def_67,type,
    fresh_261416607i_name: name > product_prod_pi_name > $o ).

thf(func_def_68,type,
    fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).

thf(func_def_69,type,
    fresh_1504024600reeRes: name > produc649380958reeRes > $o ).

thf(func_def_70,type,
    fresh_2007541374s_name: name > produc2052722628s_name > $o ).

thf(func_def_71,type,
    fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).

thf(func_def_72,type,
    fresh_493808761reeRes: name > produc1357834675reeRes > $o ).

thf(func_def_73,type,
    produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).

thf(func_def_74,type,
    produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).

thf(func_def_75,type,
    produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).

thf(func_def_76,type,
    produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).

thf(func_def_77,type,
    produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).

thf(func_def_78,type,
    produc1570949143e_name: name > name > produc367475239e_name ).

thf(func_def_79,type,
    product_Pair_name_pi: name > pi > product_prod_name_pi ).

thf(func_def_80,type,
    produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).

thf(func_def_81,type,
    produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).

thf(func_def_82,type,
    product_Pair_pi_name: pi > name > product_prod_pi_name ).

thf(func_def_83,type,
    product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).

thf(func_def_84,type,
    produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).

thf(func_def_85,type,
    produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).

thf(func_def_86,type,
    produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).

thf(func_def_87,type,
    produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).

thf(func_def_88,type,
    eqvt_pi: set_Pr1834926343_pi_pi > $o ).

thf(func_def_89,type,
    collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).

thf(func_def_90,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(func_def_91,type,
    strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).

thf(func_def_92,type,
    member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(func_def_93,type,
    p: pi ).

thf(func_def_94,type,
    p2: pi ).

thf(func_def_95,type,
    pxQ: pi ).

thf(func_def_96,type,
    q: pi ).

thf(func_def_97,type,
    rel: set_Pr1834926343_pi_pi ).

thf(func_def_98,type,
    aa: late_subject ).

thf(func_def_99,type,
    u: name ).

thf(func_def_100,type,
    x: name ).

thf(func_def_101,type,
    y: name ).

thf(func_def_126,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_127,type,
    sK2: product_prod_pi_pi > pi ).

thf(func_def_128,type,
    sK3: product_prod_pi_pi > pi ).

thf(func_def_129,type,
    sK4: ( product_prod_pi_pi > $o ) > pi ).

thf(func_def_130,type,
    sK5: name > name ).

thf(func_def_131,type,
    sK6: ( product_prod_pi_pi > $o ) > pi ).

thf(f2806,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[f2805]) ).

thf(f2805,plain,
    $false = $true,
    inference(boolean_simplification,[status(thm)],[f2804]) ).

thf(f2804,plain,
    ( $true = ( ~ $true ) ),
    inference(forward_demodulation,[status(thm)],[f2801,f1183]) ).

thf(f1183,plain,
    ( ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f746]) ).

thf(f746,plain,
    ( ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f745]) ).

thf(f745,plain,
    fresh_name_pi @ x @ ( subs @ p2 @ y @ u ),
    inference(rectify,[status(thm)],[f4]) ).

thf(f4,axiom,
    fresh_name_pi @ x @ ( subs @ p2 @ y @ u ),
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062) ).

thf(f2801,plain,
    ( $true
    = ( ~ ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) ) ) ),
    inference(boolean_simplification,[status(thm)],[f2764]) ).

thf(f2764,plain,
    ( ( ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) )
     => $false )
    = $true ),
    inference(superposition,[status(thm)],[f2736,f1972]) ).

thf(f1972,plain,
    ( $false
    = ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ q ) ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( res @ x @ q ) ) ) @ rel ) ),
    inference(forward_demodulation,[status(thm)],[f1963,f1961]) ).

thf(f1961,plain,
    ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
    = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ q ) ) ),
    inference(backward_demodulation,[status(thm)],[f1066,f1949]) ).

thf(f1949,plain,
    ! [X0: name] :
      ( q
      = ( subs @ q @ y @ X0 ) ),
    inference(equality_proxy_clausification,[status(thm)],[f1912]) ).

thf(f1912,plain,
    ! [X0: name] :
      ( $true
      = ( ( subs @ q @ y @ X0 )
        = q ) ),
    inference(boolean_simplification,[status(thm)],[f1900]) ).

thf(f1900,plain,
    ! [X0: name] :
      ( ( $true
       => ( ( subs @ q @ y @ X0 )
          = q ) )
      = $true ),
    inference(superposition,[status(thm)],[f1880,f1150]) ).

thf(f1150,plain,
    ( ( fresh_name_pi @ y @ q )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f449]) ).

thf(f449,plain,
    ( ( fresh_name_pi @ y @ q )
    = $true ),
    inference(fool_elimination,[status(thm)],[f448]) ).

thf(f448,plain,
    fresh_name_pi @ y @ q,
    inference(rectify,[status(thm)],[f7]) ).

thf(f7,axiom,
    fresh_name_pi @ y @ q,
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062) ).

thf(f1880,plain,
    ! [X2: pi,X3: name,X1: name] :
      ( $true
      = ( ( fresh_name_pi @ X3 @ X2 )
       => ( ( subs @ X2 @ X3 @ X1 )
          = X2 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f1877]) ).

thf(f1877,plain,
    ! [X2: pi,X3: name,X1: name] :
      ( $true
      = ( ^ [Y0: name] :
            ( ( fresh_name_pi @ Y0 @ X2 )
           => ( ( subs @ X2 @ Y0 @ X1 )
              = X2 ) )
        @ X3 ) ),
    inference(pi_clausification,[status(thm)],[f1863]) ).

thf(f1863,plain,
    ! [X2: pi,X1: name] :
      ( $true
      = ( !! @ name
        @ ^ [Y0: name] :
            ( ( fresh_name_pi @ Y0 @ X2 )
           => ( ( subs @ X2 @ Y0 @ X1 )
              = X2 ) ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f1860]) ).

thf(f1860,plain,
    ! [X2: pi,X1: name] :
      ( ( ^ [Y0: pi] :
            ( !! @ name
            @ ^ [Y1: name] :
                ( ( fresh_name_pi @ Y1 @ Y0 )
               => ( ( subs @ Y0 @ Y1 @ X1 )
                  = Y0 ) ) )
        @ X2 )
      = $true ),
    inference(pi_clausification,[status(thm)],[f1849]) ).

thf(f1849,plain,
    ! [X1: name] :
      ( ( !! @ pi
        @ ^ [Y0: pi] :
            ( !! @ name
            @ ^ [Y1: name] :
                ( ( fresh_name_pi @ Y1 @ Y0 )
               => ( ( subs @ Y0 @ Y1 @ X1 )
                  = Y0 ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[status(thm)],[f1844]) ).

thf(f1844,plain,
    ! [X1: name] :
      ( $true
      = ( ^ [Y0: name] :
            ( !! @ pi
            @ ^ [Y1: pi] :
                ( !! @ name
                @ ^ [Y2: name] :
                    ( ( fresh_name_pi @ Y2 @ Y1 )
                   => ( ( subs @ Y1 @ Y2 @ Y0 )
                      = Y1 ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[status(thm)],[f1189]) ).

thf(f1189,plain,
    ( ( !! @ name
      @ ^ [Y0: name] :
          ( !! @ pi
          @ ^ [Y1: pi] :
              ( !! @ name
              @ ^ [Y2: name] :
                  ( ( fresh_name_pi @ Y2 @ Y1 )
                 => ( ( subs @ Y1 @ Y2 @ Y0 )
                    = Y1 ) ) ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f403]) ).

thf(f403,plain,
    ( ( !! @ name
      @ ^ [Y0: name] :
          ( !! @ pi
          @ ^ [Y1: pi] :
              ( !! @ name
              @ ^ [Y2: name] :
                  ( ( fresh_name_pi @ Y2 @ Y1 )
                 => ( ( subs @ Y1 @ Y2 @ Y0 )
                    = Y1 ) ) ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f402]) ).

thf(f402,plain,
    ! [X0: name,X1: pi,X2: name] :
      ( ( fresh_name_pi @ X0 @ X1 )
     => ( ( subs @ X1 @ X0 @ X2 )
        = X1 ) ),
    inference(rectify,[status(thm)],[f48]) ).

thf(f48,axiom,
    ! [X9: name,X4: pi,X14: name] :
      ( ( fresh_name_pi @ X9 @ X4 )
     => ( ( subs @ X4 @ X9 @ X14 )
        = X4 ) ),
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_47_forget) ).

thf(f1066,plain,
    ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
    = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f876]) ).

thf(f876,plain,
    ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
    = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ),
    inference(fool_elimination,[status(thm)],[f6]) ).

thf(f6,axiom,
    ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
    = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062) ).

thf(f1963,plain,
    ( $false
    = ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( res @ x @ q ) ) ) @ rel ) ),
    inference(backward_demodulation,[status(thm)],[f1465,f1949]) ).

thf(f1465,plain,
    ( $false
    = ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( res @ x @ ( subs @ q @ y @ u ) ) ) ) @ rel ) ),
    inference(not_proxy_clausification,[status(thm)],[f1464]) ).

thf(f1464,plain,
    ( ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( res @ x @ ( subs @ q @ y @ u ) ) ) ) @ rel ) )
    = $true ),
    inference(backward_demodulation,[status(thm)],[f1350,f1095]) ).

thf(f1095,plain,
    ( ( subs @ ( res @ x @ q ) @ y @ u )
    = ( res @ x @ ( subs @ q @ y @ u ) ) ),
    inference(cnf_transformation,[status(thm)],[f720]) ).

thf(f720,plain,
    ( ( subs @ ( res @ x @ q ) @ y @ u )
    = ( res @ x @ ( subs @ q @ y @ u ) ) ),
    inference(fool_elimination,[status(thm)],[f2]) ).

thf(f2,axiom,
    ( ( subs @ ( res @ x @ q ) @ y @ u )
    = ( res @ x @ ( subs @ q @ y @ u ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062) ).

thf(f1350,plain,
    ( $true
    = ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ) ) ),
    inference(cnf_transformation,[status(thm)],[f740]) ).

thf(f740,plain,
    ( $true
    = ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ) ) ),
    inference(fool_elimination,[status(thm)],[f739]) ).

thf(f739,plain,
    ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ),
    inference(rectify,[status(thm)],[f340]) ).

thf(f340,negated_conjecture,
    ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ),
    inference(negated_conjecture,[status(cth)],[f339]) ).

thf(f339,conjecture,
    member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel,
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',conj_0) ).

thf(f2736,plain,
    ! [X2: pi,X3: pi,X1: name] :
      ( $true
      = ( ( fresh_name_pi @ X1 @ X2 )
       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X1 @ ( par @ X2 @ X3 ) ) @ ( par @ X2 @ ( res @ X1 @ X3 ) ) ) @ rel ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f2731]) ).

thf(f2731,plain,
    ! [X2: pi,X3: pi,X1: name] :
      ( ( ^ [Y0: pi] :
            ( ( fresh_name_pi @ X1 @ X2 )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X1 @ ( par @ X2 @ Y0 ) ) @ ( par @ X2 @ ( res @ X1 @ Y0 ) ) ) @ rel ) )
        @ X3 )
      = $true ),
    inference(pi_clausification,[status(thm)],[f2692]) ).

thf(f2692,plain,
    ! [X2: pi,X1: name] :
      ( ( !! @ pi
        @ ^ [Y0: pi] :
            ( ( fresh_name_pi @ X1 @ X2 )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X1 @ ( par @ X2 @ Y0 ) ) @ ( par @ X2 @ ( res @ X1 @ Y0 ) ) ) @ rel ) ) )
      = $true ),
    inference(beta_eta_normalization,[status(thm)],[f2683]) ).

thf(f2683,plain,
    ! [X2: pi,X1: name] :
      ( ( ^ [Y0: pi] :
            ( !! @ pi
            @ ^ [Y1: pi] :
                ( ( fresh_name_pi @ X1 @ Y0 )
               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X1 @ ( par @ Y0 @ Y1 ) ) @ ( par @ Y0 @ ( res @ X1 @ Y1 ) ) ) @ rel ) ) )
        @ X2 )
      = $true ),
    inference(pi_clausification,[status(thm)],[f2671]) ).

thf(f2671,plain,
    ! [X1: name] :
      ( ( !! @ pi
        @ ^ [Y0: pi] :
            ( !! @ pi
            @ ^ [Y1: pi] :
                ( ( fresh_name_pi @ X1 @ Y0 )
               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X1 @ ( par @ Y0 @ Y1 ) ) @ ( par @ Y0 @ ( res @ X1 @ Y1 ) ) ) @ rel ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[status(thm)],[f2668]) ).

thf(f2668,plain,
    ! [X1: name] :
      ( $true
      = ( ^ [Y0: name] :
            ( !! @ pi
            @ ^ [Y1: pi] :
                ( !! @ pi
                @ ^ [Y2: pi] :
                    ( ( fresh_name_pi @ Y0 @ Y1 )
                   => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y0 @ ( par @ Y1 @ Y2 ) ) @ ( par @ Y1 @ ( res @ Y0 @ Y2 ) ) ) @ rel ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[status(thm)],[f1062]) ).

thf(f1062,plain,
    ( $true
    = ( !! @ name
      @ ^ [Y0: name] :
          ( !! @ pi
          @ ^ [Y1: pi] :
              ( !! @ pi
              @ ^ [Y2: pi] :
                  ( ( fresh_name_pi @ Y0 @ Y1 )
                 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y0 @ ( par @ Y1 @ Y2 ) ) @ ( par @ Y1 @ ( res @ Y0 @ Y2 ) ) ) @ rel ) ) ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f995]) ).

thf(f995,plain,
    ( $true
    = ( !! @ name
      @ ^ [Y0: name] :
          ( !! @ pi
          @ ^ [Y1: pi] :
              ( !! @ pi
              @ ^ [Y2: pi] :
                  ( ( fresh_name_pi @ Y0 @ Y1 )
                 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y0 @ ( par @ Y1 @ Y2 ) ) @ ( par @ Y1 @ ( res @ Y0 @ Y2 ) ) ) @ rel ) ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f994]) ).

thf(f994,plain,
    ! [X0: pi,X1: pi,X2: name] :
      ( ( fresh_name_pi @ X2 @ X1 )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X2 @ ( par @ X1 @ X0 ) ) @ ( par @ X1 @ ( res @ X2 @ X0 ) ) ) @ rel ) ),
    inference(rectify,[status(thm)],[f9]) ).

thf(f9,axiom,
    ! [X2: pi,X1: pi,X0: name] :
      ( ( fresh_name_pi @ X0 @ X1 )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X0 @ ( par @ X1 @ X2 ) ) @ ( par @ X1 @ ( res @ X0 @ X2 ) ) ) @ rel ) ),
    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_8_Res) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ITP188^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.12  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32  % Computer : n025.cluster.edu
% 0.15/0.32  % Model    : x86_64 x86_64
% 0.15/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32  % Memory   : 8042.1875MB
% 0.15/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32  % CPULimit : 300
% 0.15/0.32  % WCLimit  : 300
% 0.15/0.32  % DateTime : Tue Feb 24 08:29:27 EST 2026
% 0.15/0.32  % CPUTime  : 
% 0.15/0.32  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.44  ---- Original DTF file ---
% 0.27/0.44  thf(spec,logic,$$dhol).
% 0.27/0.44  %------------------------------------------------------------------------------
% 0.27/0.44  % File     : ITP188^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.44  % Domain   : Interactive Theorem Proving
% 0.27/0.44  % Problem  : Sledgehammer Strong_Late_Sim_SC problem prob_690__3415376_1
% 0.27/0.44  % Version  : Especial.
% 0.27/0.44  % English  :
% 0.27/0.44  
% 0.27/0.44  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.44  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.44  % Source   : [Des21]
% 0.27/0.44  % Names    : Strong_Late_Sim_SC/prob_690__3415376_1 [Des21]
% 0.27/0.44  
% 0.27/0.44  % Status   : Theorem
% 0.27/0.44  % Rating   : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.27/0.44  % Syntax   : Number of formulae    :  441 ( 202 unt; 102 typ;   0 def)
% 0.27/0.44  %            Number of atoms       :  901 ( 371 equ;   0 cnn)
% 0.27/0.44  %            Maximal formula atoms :   16 (   2 avg)
% 0.27/0.44  %            Number of connectives : 4374 ( 181   ~;  11   |;  83   &;3518   @)
% 0.27/0.44  %                                         (   0 <=>; 581  =>;   0  <=;   0 <~>)
% 0.27/0.44  %            Maximal formula depth :   27 (   9 avg)
% 0.27/0.44  %            Number of types       :   26 (  25 usr)
% 0.27/0.44  %            Number of type conns  :  294 ( 294   >;   0   *;   0   +;   0  <<)
% 0.27/0.44  %            Number of symbols     :   80 (  77 usr;  13 con; 0-5 aty)
% 0.27/0.44  %            Number of variables   : 1730 (   9   ^;1681   !;  40   ?;1730   :)
% 0.27/0.44  % SPC      : TH0_THM_EQU_NAR
% 0.27/0.44  
% 0.27/0.44  % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:00.397
% 0.27/0.44  %------------------------------------------------------------------------------
% 0.27/0.44  % Could-be-implicit typings (25)
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.27/0.44      produc53907987_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.27/0.44      produc1462499409ion_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.27/0.44      noptio1575811931_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      produc1834551554reeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.27/0.44      produc405342261i_name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.27/0.44      produc629157763_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.44      produc1141751126_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      produc1357834675reeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.27/0.44      produc2052722628s_name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      produc2008547984reeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.27/0.44      produc992857746Res_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      produc649380958reeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.44      set_Pr1834926343_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.27/0.44      produc367475239e_name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 0.27/0.44      product_prod_pi_name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 0.27/0.44      product_prod_name_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.44      product_prod_pi_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      noption_Late_freeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 0.27/0.44      noption_name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.27/0.44      noption_pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.27/0.44      late_residual: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.27/0.44      late_subject: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      late_freeRes: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Agent__Oname,type,
% 0.27/0.44      name: $tType ).
% 0.27/0.44  
% 0.27/0.44  thf(ty_n_t__Agent__Opi,type,
% 0.27/0.44      pi: $tType ).
% 0.27/0.44  
% 0.27/0.44  % Explicit typings (77)
% 0.27/0.44  thf(sy_c_Agent_Opi_OBang,type,
% 0.27/0.44      bang: pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OInput,type,
% 0.27/0.44      input: name > name > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OMatch,type,
% 0.27/0.44      match: name > name > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OMismatch,type,
% 0.27/0.44      mismatch: name > name > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OOutput,type,
% 0.27/0.44      output: name > name > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OPar,type,
% 0.27/0.44      par: pi > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OPiNil,type,
% 0.27/0.44      piNil: pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_ORes,type,
% 0.27/0.44      res: name > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OSum,type,
% 0.27/0.44      sum: pi > pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Opi_OTau,type,
% 0.27/0.44      tau: pi > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Osubs,type,
% 0.27/0.44      subs: pi > name > name > pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Agent_Osubst__name,type,
% 0.27/0.44      subst_name: name > name > name > name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_If_001t__Agent__Oname,type,
% 0.27/0.44      if_name: $o > name > name > name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.27/0.44      late_OutputR: name > name > late_freeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.27/0.44      late_TauR: late_freeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.27/0.44      late_BoundR: late_subject > name > pi > late_residual ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.27/0.44      late_FreeR: late_freeRes > pi > late_residual ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.27/0.44      late_BoundOutputS: name > late_subject ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.27/0.44      late_InputS: name > late_subject ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Late__Semantics_Otransitions,type,
% 0.27/0.44      late_transitions: pi > late_residual > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.27/0.44      abs_fun_name_name: name > name > name > noption_name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.27/0.44      abs_fun_name_pi: name > pi > name > noption_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.44      abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 0.27/0.44      fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.27/0.44      fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 0.27/0.44      fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J,type,
% 0.27/0.44      fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.27/0.44      fresh_name_name: name > name > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.27/0.44      fresh_name_pi: name > pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      fresh_1641682979reeRes: name > late_freeRes > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
% 0.27/0.44      fresh_81631222sidual: name > late_residual > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.27/0.44      fresh_717452603ubject: name > late_subject > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.27/0.44      fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.27/0.44      fresh_453496559i_name: name > produc405342261i_name > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.27/0.44      fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.27/0.44      fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.27/0.44      fresh_441084397e_name: name > produc367475239e_name > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 0.27/0.44      fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.44      fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 0.27/0.44      fresh_261416607i_name: name > product_prod_pi_name > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.44      fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      fresh_1504024600reeRes: name > produc649380958reeRes > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.27/0.44      fresh_2007541374s_name: name > produc2052722628s_name > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.27/0.44      fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.44      fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.27/0.44      produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
% 0.27/0.44      produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 0.27/0.44      produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.44      produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.27/0.44      produc1570949143e_name: name > name > produc367475239e_name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.27/0.44      product_Pair_name_pi: name > pi > product_prod_name_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.44      produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
% 0.27/0.44      product_Pair_pi_name: pi > name > product_prod_pi_name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.27/0.44      product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.27/0.44      produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.27/0.44      produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.44      produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.27/0.44      eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.44      collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.27/0.44      strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.27/0.44      strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.44      member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_P,type,
% 0.27/0.44      p: pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_P_H____,type,
% 0.27/0.44      p2: pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_PxQ____,type,
% 0.27/0.44      pxQ: pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_Q,type,
% 0.27/0.44      q: pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_Rel,type,
% 0.27/0.44      rel: set_Pr1834926343_pi_pi ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_aa____,type,
% 0.27/0.44      aa: late_subject ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_u____,type,
% 0.27/0.44      u: name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_x,type,
% 0.27/0.44      x: name ).
% 0.27/0.44  
% 0.27/0.44  thf(sy_v_y____,type,
% 0.27/0.44      y: name ).
% 0.27/0.44  
% 0.27/0.44  % Relevant facts (335)
% 0.27/0.44  thf(fact_0_False,axiom,
% 0.27/0.44      x != u ).
% 0.27/0.44  
% 0.27/0.44  % False
% 0.27/0.44  thf(fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062,axiom,
% 0.27/0.44      ( ( subs @ ( res @ x @ q ) @ y @ u )
% 0.27/0.44      = ( res @ x @ ( subs @ q @ y @ u ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open><\<nu>x>Q[y::=u] = <\<nu>x>Q[y::=u]\<close>
% 0.27/0.44  thf(fact_2__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.27/0.44      y != x ).
% 0.27/0.44  
% 0.27/0.44  % \<open>y \<noteq> x\<close>
% 0.27/0.44  thf(fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062,axiom,
% 0.27/0.44      fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open>x \<sharp> P'[y::=u]\<close>
% 0.27/0.44  thf(fact_4_EqvtRel,axiom,
% 0.27/0.44      eqvt_pi @ rel ).
% 0.27/0.44  
% 0.27/0.44  % EqvtRel
% 0.27/0.44  thf(fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062,axiom,
% 0.27/0.44      ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
% 0.27/0.44      = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open><\<nu>x>(P' \<parallel> Q)[y::=u] = <\<nu>x>(P'[y::=u] \<parallel> Q[y::=u])\<close>
% 0.27/0.44  thf(fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.27/0.44      fresh_name_pi @ y @ q ).
% 0.27/0.44  
% 0.27/0.44  % \<open>y \<sharp> Q\<close>
% 0.27/0.44  thf(fact_7__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 0.27/0.44      fresh_name_pi @ x @ p2 ).
% 0.27/0.44  
% 0.27/0.44  % \<open>x \<sharp> P'\<close>
% 0.27/0.44  thf(fact_8_Res,axiom,
% 0.27/0.44      ! [Y: name,R: pi,S: pi] :
% 0.27/0.44        ( ( fresh_name_pi @ Y @ R )
% 0.27/0.44       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Res
% 0.27/0.44  thf(fact_9_ScopeExt,axiom,
% 0.27/0.44      ! [Y: name,R: pi,Z: name,S: pi] :
% 0.27/0.44        ( ( fresh_name_pi @ Y @ R )
% 0.27/0.44       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) ).
% 0.27/0.44  
% 0.27/0.44  % ScopeExt
% 0.27/0.44  thf(fact_10__092_060open_062y_A_092_060sharp_062_A_060_092_060nu_062x_062Q_092_060close_062,axiom,
% 0.27/0.44      fresh_name_pi @ y @ ( res @ x @ q ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open>y \<sharp> <\<nu>x>Q\<close>
% 0.27/0.44  thf(fact_11_assms_I1_J,axiom,
% 0.27/0.44      fresh_name_pi @ x @ p ).
% 0.27/0.44  
% 0.27/0.44  % assms(1)
% 0.27/0.44  thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 0.27/0.44      fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Bound.hyps(3)
% 0.27/0.44  thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 0.27/0.44      fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Bound.hyps(2)
% 0.27/0.44  thf(fact_14_simps_I8_J,axiom,
% 0.27/0.44      ! [P: pi,Q: pi,C: name,D: name] :
% 0.27/0.44        ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.27/0.44        = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % simps(8)
% 0.27/0.44  thf(fact_15_simps_I9_J,axiom,
% 0.27/0.44      ! [X: name,C: name,D: name,P: pi] :
% 0.27/0.44        ( ( X != C )
% 0.27/0.44       => ( ( X != D )
% 0.27/0.44         => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.27/0.44            = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % simps(9)
% 0.27/0.44  thf(fact_16_subst__identity,axiom,
% 0.27/0.44      ! [P: pi,A: name] :
% 0.27/0.44        ( ( subs @ P @ A @ A )
% 0.27/0.44        = P ) ).
% 0.27/0.44  
% 0.27/0.44  % subst_identity
% 0.27/0.44  thf(fact_17_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 0.27/0.44        ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.27/0.44          = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_18_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
% 0.27/0.44        ( ( ( produc1275980869_pi_pi @ X1 @ X2 )
% 0.27/0.44          = ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_19_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 0.27/0.44        ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.27/0.44          = ( produc540578151i_name @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_20_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 0.27/0.44        ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.27/0.44          = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_21_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 0.27/0.44        ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.27/0.44          = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_22_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.27/0.44        ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.27/0.44          = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_23_prod_Oinject,axiom,
% 0.27/0.44      ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 0.27/0.44        ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 0.27/0.44          = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 0.27/0.44        = ( ( X1 = Y1 )
% 0.27/0.44          & ( X2 = Y2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod.inject
% 0.27/0.44  thf(fact_24_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.27/0.44        ( ( ( produc1505598906reeRes @ A @ B )
% 0.27/0.44          = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_25_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.27/0.44        ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.27/0.44          = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_26_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.27/0.44        ( ( ( produc540578151i_name @ A @ B )
% 0.27/0.44          = ( produc540578151i_name @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_27_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.27/0.44        ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.27/0.44          = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_28_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.27/0.44        ( ( ( produc1342893193ion_pi @ A @ B )
% 0.27/0.44          = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_29_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.27/0.44        ( ( ( product_Pair_pi_pi @ A @ B )
% 0.27/0.44          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_30_old_Oprod_Oinject,axiom,
% 0.27/0.44      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.27/0.44        ( ( ( produc235456326_pi_pi @ A @ B )
% 0.27/0.44          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.27/0.44        = ( ( A = A2 )
% 0.27/0.44          & ( B = B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inject
% 0.27/0.44  thf(fact_31_pi_Odistinct_I85_J,axiom,
% 0.27/0.44      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.27/0.44        ( ( par @ Pi1 @ Pi2 )
% 0.27/0.44       != ( res @ Name @ Pi ) ) ).
% 0.27/0.44  
% 0.27/0.44  % pi.distinct(85)
% 0.27/0.44  thf(fact_32__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.27/0.44      fresh_name_pi @ y @ p ).
% 0.27/0.44  
% 0.27/0.44  % \<open>y \<sharp> P\<close>
% 0.27/0.44  thf(fact_33_Bound_Ohyps_I5_J,axiom,
% 0.27/0.44      fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Bound.hyps(5)
% 0.27/0.44  thf(fact_34_parSym,axiom,
% 0.27/0.44      ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.27/0.44        ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.27/0.44       => ( ! [R2: pi,S2: pi,X3: name] :
% 0.27/0.44              ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 0.27/0.44             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
% 0.27/0.44         => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % parSym
% 0.27/0.44  thf(fact_35_substRes2,axiom,
% 0.27/0.44      ! [B: name,P: pi,A: name] :
% 0.27/0.44        ( ( fresh_name_pi @ B @ P )
% 0.27/0.44       => ( ( res @ A @ P )
% 0.27/0.44          = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % substRes2
% 0.27/0.44  thf(fact_36_Agent_OsubstRes3,axiom,
% 0.27/0.44      ! [B: name,P: pi,A: name] :
% 0.27/0.44        ( ( fresh_name_pi @ B @ P )
% 0.27/0.44       => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.27/0.44          = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Agent.substRes3
% 0.27/0.44  thf(fact_37_Bound_Ohyps_I4_J,axiom,
% 0.27/0.44      fresh_717452603ubject @ y @ aa ).
% 0.27/0.44  
% 0.27/0.44  % Bound.hyps(4)
% 0.27/0.44  thf(fact_38__092_060open_062x_A_092_060sharp_062_Aa_092_060close_062,axiom,
% 0.27/0.44      fresh_717452603ubject @ x @ aa ).
% 0.27/0.44  
% 0.27/0.44  % \<open>x \<sharp> a\<close>
% 0.27/0.44  thf(fact_39_pi_Ofresh_I8_J,axiom,
% 0.27/0.44      ! [A: name,X2: pi,X1: pi] :
% 0.27/0.44        ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.27/0.44        = ( ( fresh_name_pi @ A @ X2 )
% 0.27/0.44          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % pi.fresh(8)
% 0.27/0.44  thf(fact_40_name__exists__fresh,axiom,
% 0.27/0.44      ! [X: late_freeRes] :
% 0.27/0.44        ~ ! [C2: name] :
% 0.27/0.44            ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 0.27/0.44  
% 0.27/0.44  % name_exists_fresh
% 0.27/0.44  thf(fact_41_name__exists__fresh,axiom,
% 0.27/0.44      ! [X: produc1141751126_pi_pi] :
% 0.27/0.44        ~ ! [C2: name] :
% 0.27/0.44            ~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% 0.27/0.44  
% 0.27/0.44  % name_exists_fresh
% 0.27/0.44  thf(fact_42_name__exists__fresh,axiom,
% 0.27/0.44      ! [X: name] :
% 0.27/0.44        ~ ! [C2: name] :
% 0.27/0.44            ~ ( fresh_name_name @ C2 @ X ) ).
% 0.27/0.44  
% 0.27/0.44  % name_exists_fresh
% 0.27/0.44  thf(fact_43_name__exists__fresh,axiom,
% 0.27/0.44      ! [X: pi] :
% 0.27/0.44        ~ ! [C2: name] :
% 0.27/0.44            ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.27/0.44  
% 0.27/0.44  % name_exists_fresh
% 0.27/0.44  thf(fact_44_freshRes,axiom,
% 0.27/0.44      ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.27/0.44  
% 0.27/0.44  % freshRes
% 0.27/0.44  thf(fact_45_fresh__fact2,axiom,
% 0.27/0.44      ! [A: name,B: name,P: pi] :
% 0.27/0.44        ( ( A != B )
% 0.27/0.44       => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_fact2
% 0.27/0.44  thf(fact_46_fresh__fact1,axiom,
% 0.27/0.44      ! [A: name,P: pi,C: name,B: name] :
% 0.27/0.44        ( ( fresh_name_pi @ A @ P )
% 0.27/0.44       => ( ( A != C )
% 0.27/0.44         => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_fact1
% 0.27/0.44  thf(fact_47_forget,axiom,
% 0.27/0.44      ! [A: name,P: pi,B: name] :
% 0.27/0.44        ( ( fresh_name_pi @ A @ P )
% 0.27/0.44       => ( ( subs @ P @ A @ B )
% 0.27/0.44          = P ) ) ).
% 0.27/0.44  
% 0.27/0.44  % forget
% 0.27/0.44  thf(fact_48_parAssocLeft,axiom,
% 0.27/0.44      ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.27/0.44        ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 0.27/0.44       => ( ! [S2: pi,T: pi,X3: name] :
% 0.27/0.44              ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 0.27/0.44             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ S2 ) @ ( res @ X3 @ T ) ) @ Rel ) )
% 0.27/0.44         => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 0.27/0.44                ( ( fresh_name_pi @ X3 @ S2 )
% 0.27/0.44               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X3 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.27/0.44           => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 0.27/0.44                  ( ( fresh_name_pi @ X3 @ U )
% 0.27/0.44                 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X3 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X3 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.27/0.44             => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % parAssocLeft
% 0.27/0.44  thf(fact_49_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_50_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_51_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_52_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_53_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_54_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.27/0.44        ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.27/0.44      ! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 0.27/0.44        ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ Prod ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.inducts
% 0.27/0.44  thf(fact_56_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc1834551554reeRes] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_57_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc53907987_pi_pi] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_58_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc405342261i_name] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: name] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_59_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc629157763_pi_pi] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_60_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc1462499409ion_pi] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_61_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: product_prod_pi_pi] :
% 0.27/0.44        ~ ! [A3: pi,B3: pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_62_old_Oprod_Oexhaust,axiom,
% 0.27/0.44      ! [Y: produc1141751126_pi_pi] :
% 0.27/0.44        ~ ! [A3: name,B3: product_prod_pi_pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % old.prod.exhaust
% 0.27/0.44  thf(fact_63_prod__induct4,axiom,
% 0.27/0.44      ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) )
% 0.27/0.44       => ( P @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_induct4
% 0.27/0.44  thf(fact_64_prod__induct3,axiom,
% 0.27/0.44      ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) )
% 0.27/0.44       => ( P @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_induct3
% 0.27/0.44  thf(fact_65_prod__induct3,axiom,
% 0.27/0.44      ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 0.27/0.44        ( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
% 0.27/0.44       => ( P @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_induct3
% 0.27/0.44  thf(fact_66_prod__cases4,axiom,
% 0.27/0.44      ! [Y: produc53907987_pi_pi] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases4
% 0.27/0.44  thf(fact_67_mem__Collect__eq,axiom,
% 0.27/0.44      ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.27/0.44        ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.27/0.44        = ( P @ A ) ) ).
% 0.27/0.44  
% 0.27/0.44  % mem_Collect_eq
% 0.27/0.44  thf(fact_68_Collect__mem__eq,axiom,
% 0.27/0.44      ! [A4: set_Pr1834926343_pi_pi] :
% 0.27/0.44        ( ( collec1051790738_pi_pi
% 0.27/0.44          @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
% 0.27/0.44        = A4 ) ).
% 0.27/0.44  
% 0.27/0.44  % Collect_mem_eq
% 0.27/0.44  thf(fact_69_Collect__cong,axiom,
% 0.27/0.44      ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.27/0.44        ( ! [X3: product_prod_pi_pi] :
% 0.27/0.44            ( ( P @ X3 )
% 0.27/0.44            = ( Q @ X3 ) )
% 0.27/0.44       => ( ( collec1051790738_pi_pi @ P )
% 0.27/0.44          = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Collect_cong
% 0.27/0.44  thf(fact_70_prod__cases3,axiom,
% 0.27/0.44      ! [Y: produc53907987_pi_pi] :
% 0.27/0.44        ~ ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases3
% 0.27/0.44  thf(fact_71_prod__cases3,axiom,
% 0.27/0.44      ! [Y: produc1141751126_pi_pi] :
% 0.27/0.44        ~ ! [A3: name,B3: pi,C2: pi] :
% 0.27/0.44            ( Y
% 0.27/0.44           != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases3
% 0.27/0.44  thf(fact_72_Pair__inject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.27/0.44        ( ( ( produc1505598906reeRes @ A @ B )
% 0.27/0.44          = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_73_Pair__inject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.27/0.44        ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.27/0.44          = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_74_Pair__inject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.27/0.44        ( ( ( produc540578151i_name @ A @ B )
% 0.27/0.44          = ( produc540578151i_name @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_75_Pair__inject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.27/0.44        ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.27/0.44          = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_76_Pair__inject,axiom,
% 0.27/0.44      ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.27/0.44        ( ( ( produc1342893193ion_pi @ A @ B )
% 0.27/0.44          = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_77_Pair__inject,axiom,
% 0.27/0.44      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.27/0.44        ( ( ( product_Pair_pi_pi @ A @ B )
% 0.27/0.44          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_78_Pair__inject,axiom,
% 0.27/0.44      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.27/0.44        ( ( ( produc235456326_pi_pi @ A @ B )
% 0.27/0.44          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.27/0.44       => ~ ( ( A = A2 )
% 0.27/0.44           => ( B != B2 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Pair_inject
% 0.27/0.44  thf(fact_79_prod__cases,axiom,
% 0.27/0.44      ! [P: produc1834551554reeRes > $o,P2: produc1834551554reeRes] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_80_prod__cases,axiom,
% 0.27/0.44      ! [P: produc53907987_pi_pi > $o,P2: produc53907987_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_81_prod__cases,axiom,
% 0.27/0.44      ! [P: produc405342261i_name > $o,P2: produc405342261i_name] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_82_prod__cases,axiom,
% 0.27/0.44      ! [P: produc629157763_pi_pi > $o,P2: produc629157763_pi_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_83_prod__cases,axiom,
% 0.27/0.44      ! [P: produc1462499409ion_pi > $o,P2: produc1462499409ion_pi] :
% 0.27/0.44        ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_84_prod__cases,axiom,
% 0.27/0.44      ! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
% 0.27/0.44        ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_85_prod__cases,axiom,
% 0.27/0.44      ! [P: produc1141751126_pi_pi > $o,P2: produc1141751126_pi_pi] :
% 0.27/0.44        ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.27/0.44       => ( P @ P2 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % prod_cases
% 0.27/0.44  thf(fact_86_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc1834551554reeRes] :
% 0.27/0.44      ? [X3: name > noption_pi,Y3: late_freeRes] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_87_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc53907987_pi_pi] :
% 0.27/0.44      ? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_88_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc405342261i_name] :
% 0.27/0.44      ? [X3: name > noption_pi,Y3: name] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc540578151i_name @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_89_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc629157763_pi_pi] :
% 0.27/0.44      ? [X3: name > noption_pi,Y3: pi] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_90_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc1462499409ion_pi] :
% 0.27/0.44      ? [X3: name > noption_pi,Y3: name > noption_pi] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_91_surj__pair,axiom,
% 0.27/0.44      ! [P2: product_prod_pi_pi] :
% 0.27/0.44      ? [X3: pi,Y3: pi] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_92_surj__pair,axiom,
% 0.27/0.44      ! [P2: produc1141751126_pi_pi] :
% 0.27/0.44      ? [X3: name,Y3: product_prod_pi_pi] :
% 0.27/0.44        ( P2
% 0.27/0.44        = ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% 0.27/0.44  
% 0.27/0.44  % surj_pair
% 0.27/0.44  thf(fact_93_pi_Oinject_I7_J,axiom,
% 0.27/0.44      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.27/0.44        ( ( ( par @ X2 @ X1 )
% 0.27/0.44          = ( par @ Y2 @ Y1 ) )
% 0.27/0.44        = ( ( X2 = Y2 )
% 0.27/0.44          & ( X1 = Y1 ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % pi.inject(7)
% 0.27/0.44  thf(fact_94_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.44        ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.44          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_95_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: late_freeRes,Y: name] :
% 0.27/0.44        ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.44          & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_96_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: late_freeRes,Y: pi] :
% 0.27/0.44        ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.44          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_97_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: late_freeRes] :
% 0.27/0.44        ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_name @ A @ X )
% 0.27/0.44          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_98_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: name] :
% 0.27/0.44        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_name @ A @ X )
% 0.27/0.44          & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_99_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: pi] :
% 0.27/0.44        ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_name @ A @ X )
% 0.27/0.44          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_100_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: pi,Y: late_freeRes] :
% 0.27/0.44        ( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_pi @ A @ X )
% 0.27/0.44          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_101_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: pi,Y: name] :
% 0.27/0.44        ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_pi @ A @ X )
% 0.27/0.44          & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_102_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: pi,Y: pi] :
% 0.27/0.44        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_pi @ A @ X )
% 0.27/0.44          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_103_fresh__prod,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.44        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.44        = ( ( fresh_name_name @ A @ X )
% 0.27/0.44          & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prod
% 0.27/0.44  thf(fact_104_substTrans,axiom,
% 0.27/0.44      ! [B: name,P: pi,A: name,C: name] :
% 0.27/0.44        ( ( fresh_name_pi @ B @ P )
% 0.27/0.44       => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.27/0.44          = ( subs @ P @ A @ C ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % substTrans
% 0.27/0.44  thf(fact_105_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.27/0.44        ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_106_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.27/0.44        ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_107_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: name] :
% 0.27/0.44        ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_108_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: pi] :
% 0.27/0.44        ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_109_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.27/0.44        ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_110_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: pi,Y: pi] :
% 0.27/0.44        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_name_pi @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_111_fresh__prodD_I1_J,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.44        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(1)
% 0.27/0.44  thf(fact_112_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.27/0.44        ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.27/0.44       => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_113_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.27/0.44        ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_114_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: name] :
% 0.27/0.44        ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.27/0.44       => ( fresh_name_name @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_115_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: pi] :
% 0.27/0.44        ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_name_pi @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_116_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.27/0.44        ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_117_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: pi,Y: pi] :
% 0.27/0.44        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_name_pi @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_118_fresh__prodD_I2_J,axiom,
% 0.27/0.44      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.44        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.44       => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 0.27/0.44  
% 0.27/0.44  % fresh_prodD(2)
% 0.27/0.44  thf(fact_119_Bound_Ohyps_I1_J,axiom,
% 0.27/0.44      late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ aa @ y @ pxQ ) ).
% 0.27/0.44  
% 0.27/0.44  % Bound.hyps(1)
% 0.27/0.44  thf(fact_120__092_060open_062_060_092_060nu_062x_062_IP_A_092_060parallel_062_AQ_J_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_A_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_092_060close_062,axiom,
% 0.27/0.44      late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ ( res @ x @ ( par @ p2 @ q ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open><\<nu>x>(P \<parallel> Q) \<longmapsto> a\<guillemotleft>y\<guillemotright> \<prec> <\<nu>x>(P' \<parallel> Q)\<close>
% 0.27/0.44  thf(fact_121_cPar1_Ohyps,axiom,
% 0.27/0.44      late_transitions @ p @ ( late_BoundR @ aa @ y @ p2 ) ).
% 0.27/0.44  
% 0.27/0.44  % cPar1.hyps
% 0.27/0.44  thf(fact_122__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 0.27/0.44      late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ aa @ y @ ( par @ p2 @ q ) ) ).
% 0.27/0.44  
% 0.27/0.44  % \<open>P \<parallel> Q \<longmapsto> a\<guillemotleft>y\<guillemotright> \<prec> P' \<parallel> Q\<close>
% 0.27/0.44  thf(fact_123_freshBoundDerivative_I2_J,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.44         => ( ( Y != X )
% 0.27/0.44           => ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % freshBoundDerivative(2)
% 0.27/0.44  thf(fact_124_freshResidual,axiom,
% 0.27/0.44      ! [P: pi,Rs: late_residual,X: name] :
% 0.27/0.44        ( ( late_transitions @ P @ Rs )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44         => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % freshResidual
% 0.27/0.44  thf(fact_125_parCasesB,axiom,
% 0.27/0.44      ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.27/0.44        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44         => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.44           => ( ! [P4: pi] :
% 0.27/0.44                  ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.44                 => ( Prop @ ( par @ P4 @ Q ) ) )
% 0.27/0.44             => ( ! [Q2: pi] :
% 0.27/0.44                    ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.27/0.44                   => ( Prop @ ( par @ P @ Q2 ) ) )
% 0.27/0.44               => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % parCasesB
% 0.27/0.44  thf(fact_126_Late__Semantics_OPar2B,axiom,
% 0.27/0.44      ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 0.27/0.44        ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Late_Semantics.Par2B
% 0.27/0.44  thf(fact_127_Late__Semantics_OPar1B,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.44         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Late_Semantics.Par1B
% 0.27/0.44  thf(fact_128_Late__Semantics_OResB,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_717452603ubject @ Y @ A )
% 0.27/0.44         => ( ( Y != X )
% 0.27/0.44           => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % Late_Semantics.ResB
% 0.27/0.44  thf(fact_129_freshBoundDerivative_I1_J,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.44         => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % freshBoundDerivative(1)
% 0.27/0.44  thf(fact_130_transitions_OResB,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_717452603ubject @ Y @ A )
% 0.27/0.44         => ( ( Y != X )
% 0.27/0.44           => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44             => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.44               => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % transitions.ResB
% 0.27/0.44  thf(fact_131_transitions_OPar2B,axiom,
% 0.27/0.44      ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 0.27/0.44        ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44         => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.44           => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.44             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % transitions.Par2B
% 0.27/0.44  thf(fact_132_transitions_OPar1B,axiom,
% 0.27/0.44      ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.27/0.44        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.44       => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44         => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.44           => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.44             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % transitions.Par1B
% 0.27/0.44  thf(fact_133_parCasesB_H,axiom,
% 0.27/0.44      ! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
% 0.27/0.44        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.27/0.44       => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Q4: pi] :
% 0.27/0.44              ( ( ( par @ P @ Q )
% 0.27/0.44                = ( par @ P5 @ Q4 ) )
% 0.27/0.44             => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.27/0.44                  = ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 0.27/0.44               => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.27/0.44                 => ( ( fresh_name_pi @ X3 @ P5 )
% 0.27/0.44                   => ( ( fresh_name_pi @ X3 @ Q4 )
% 0.27/0.44                     => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
% 0.27/0.44         => ~ ! [Q4: pi,A3: late_subject,X3: name,Q2: pi,P5: pi] :
% 0.27/0.44                ( ( ( par @ P @ Q )
% 0.27/0.44                  = ( par @ P5 @ Q4 ) )
% 0.27/0.44               => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.27/0.44                    = ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q2 ) ) )
% 0.27/0.44                 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.27/0.44                   => ( ( fresh_name_pi @ X3 @ P5 )
% 0.27/0.44                     => ( ( fresh_name_pi @ X3 @ Q4 )
% 0.27/0.44                       => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % parCasesB'
% 0.27/0.44  thf(fact_134_simE_I1_J,axiom,
% 0.27/0.44      ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q3: pi] :
% 0.27/0.44        ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.44       => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.27/0.44         => ( ( fresh_name_pi @ X @ P )
% 0.27/0.44           => ? [P4: pi] :
% 0.27/0.44                ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.44                & ( strong2129052853vative @ P4 @ Q3 @ A @ X @ Rel ) ) ) ) ) ).
% 0.27/0.44  
% 0.27/0.44  % simE(1)
% 0.27/0.44  thf(fact_135_simCasesCont,axiom,
% 0.27/0.44      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 0.27/0.44        ( ( eqvt_pi @ Rel )
% 0.27/0.44       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.27/0.45             => ( ( fresh_name_pi @ X3 @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ X3 @ Q )
% 0.27/0.45                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.27/0.45                   => ( ( fresh_1641682979reeRes @ X3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.27/0.45         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.27/0.45           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simCasesCont
% 0.27/0.45  thf(fact_136_simCasesCont,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.27/0.45             => ( ( fresh_name_pi @ X3 @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ X3 @ Q )
% 0.27/0.45                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.27/0.45                   => ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.27/0.45         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.27/0.45           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simCasesCont
% 0.27/0.45  thf(fact_137_simCasesCont,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.27/0.45             => ( ( fresh_name_pi @ X3 @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ X3 @ Q )
% 0.27/0.45                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.27/0.45                   => ( ( fresh_name_name @ X3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.27/0.45         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.27/0.45           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simCasesCont
% 0.27/0.45  thf(fact_138_simCasesCont,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 0.27/0.45             => ( ( fresh_name_pi @ X3 @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ X3 @ Q )
% 0.27/0.45                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.27/0.45                   => ( ( fresh_name_pi @ X3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.27/0.45         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.27/0.45           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simCasesCont
% 0.27/0.45  thf(fact_139_parZeroLeft,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.27/0.45        ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.27/0.45       => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % parZeroLeft
% 0.27/0.45  thf(fact_140_parZeroRight,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.27/0.45        ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.27/0.45       => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % parZeroRight
% 0.27/0.45  thf(fact_141_inputIneqTrans,axiom,
% 0.27/0.45      ! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.27/0.45       => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.27/0.45  
% 0.27/0.45  % inputIneqTrans
% 0.27/0.45  thf(fact_142_resTauBoundTrans,axiom,
% 0.27/0.45      ! [X: name,P: pi,A: late_subject,Y: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resTauBoundTrans
% 0.27/0.45  thf(fact_143_pi_Ofresh_I1_J,axiom,
% 0.27/0.45      ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(1)
% 0.27/0.45  thf(fact_144_pi_Ofresh_I3_J,axiom,
% 0.27/0.45      ! [A: name,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.27/0.45        = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(3)
% 0.27/0.45  thf(fact_145_simps_I1_J,axiom,
% 0.27/0.45      ! [C: name,D: name] :
% 0.27/0.45        ( ( subs @ piNil @ C @ D )
% 0.27/0.45        = piNil ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(1)
% 0.27/0.45  thf(fact_146_simps_I2_J,axiom,
% 0.27/0.45      ! [P: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( tau @ P ) @ C @ D )
% 0.27/0.45        = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(2)
% 0.27/0.45  thf(fact_147_residual_Ofresh_I2_J,axiom,
% 0.27/0.45      ! [A: name,X2: late_freeRes,X1: pi] :
% 0.27/0.45        ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.27/0.45          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.fresh(2)
% 0.27/0.45  thf(fact_148_inputFreeTrans,axiom,
% 0.27/0.45      ! [A: name,X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % inputFreeTrans
% 0.27/0.45  thf(fact_149_residual_Oinject_I2_J,axiom,
% 0.27/0.45      ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.27/0.45        ( ( ( late_FreeR @ X2 @ X1 )
% 0.27/0.45          = ( late_FreeR @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.inject(2)
% 0.27/0.45  thf(fact_150_nilSim_I2_J,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.27/0.45        ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % nilSim(2)
% 0.27/0.45  thf(fact_151_nilSim_I1_J,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.27/0.45        ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % nilSim(1)
% 0.27/0.45  thf(fact_152_pi_Odistinct_I3_J,axiom,
% 0.27/0.45      ! [Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( tau @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(3)
% 0.27/0.45  thf(fact_153_pi_Odistinct_I5_J,axiom,
% 0.27/0.45      ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(5)
% 0.27/0.45  thf(fact_154_pi_Odistinct_I35_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(35)
% 0.27/0.45  thf(fact_155_pi_Oinject_I2_J,axiom,
% 0.27/0.45      ! [X1: pi,Y1: pi] :
% 0.27/0.45        ( ( ( tau @ X1 )
% 0.27/0.45          = ( tau @ Y1 ) )
% 0.27/0.45        = ( X1 = Y1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(2)
% 0.27/0.45  thf(fact_156_resInputFreeTrans,axiom,
% 0.27/0.45      ! [X: name,A: name,Y: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resInputFreeTrans
% 0.27/0.45  thf(fact_157_residual_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [Subject: late_subject,Name3: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 0.27/0.45        ( ( late_BoundR @ Subject @ Name3 @ Pi3 )
% 0.27/0.45       != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.distinct(1)
% 0.27/0.45  thf(fact_158_residual_Oinducts,axiom,
% 0.27/0.45      ! [P: late_residual > $o,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.inducts
% 0.27/0.45  thf(fact_159_pi_Odistinct_I57_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(57)
% 0.27/0.45  thf(fact_160_pi_Odistinct_I55_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(55)
% 0.27/0.45  thf(fact_161_pi_Odistinct_I45_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(45)
% 0.27/0.45  thf(fact_162_pi_Odistinct_I43_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(43)
% 0.27/0.45  thf(fact_163_nilCases_H,axiom,
% 0.27/0.45      ! [Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ piNil @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % nilCases'
% 0.27/0.45  thf(fact_164_zeroTrans,axiom,
% 0.27/0.45      ! [Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ piNil @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % zeroTrans
% 0.27/0.45  thf(fact_165_pi_Odistinct_I15_J,axiom,
% 0.27/0.45      ! [Name: name,Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(15)
% 0.27/0.45  thf(fact_166_pi_Odistinct_I13_J,axiom,
% 0.27/0.45      ! [Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(13)
% 0.27/0.45  thf(fact_167_nilSimRight,axiom,
% 0.27/0.45      ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.27/0.45  
% 0.27/0.45  % nilSimRight
% 0.27/0.45  thf(fact_168_ResF,axiom,
% 0.27/0.45      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( ( fresh_1641682979reeRes @ Y @ Alpha2 )
% 0.27/0.45         => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % ResF
% 0.27/0.45  thf(fact_169_resCasesF_H,axiom,
% 0.27/0.45      ! [X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 0.27/0.45              ( ( ( res @ X @ P )
% 0.27/0.45                = ( res @ Y3 @ P5 ) )
% 0.27/0.45             => ( ( ( late_FreeR @ Alpha2 @ P3 )
% 0.27/0.45                  = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.45               => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.45                 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resCasesF'
% 0.27/0.45  thf(fact_170_resCasesF,axiom,
% 0.27/0.45      ! [X: name,P: pi,Alpha2: late_freeRes,XP: pi,F: pi > $o] :
% 0.27/0.45        ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ XP ) )
% 0.27/0.45       => ( ! [P4: pi] :
% 0.27/0.45              ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.27/0.45             => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.27/0.45               => ( F @ ( res @ X @ P4 ) ) ) )
% 0.27/0.45         => ( F @ XP ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resCasesF
% 0.27/0.45  thf(fact_171_Par1F,axiom,
% 0.27/0.45      ! [P: pi,Alpha2: late_freeRes,P3: pi,Q: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P3 @ Q ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Par1F
% 0.27/0.45  thf(fact_172_Par2F,axiom,
% 0.27/0.45      ! [Q: pi,Alpha2: late_freeRes,Q3: pi,P: pi] :
% 0.27/0.45        ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.27/0.45       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P @ Q3 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Par2F
% 0.27/0.45  thf(fact_173_freshFreeDerivative_I1_J,axiom,
% 0.27/0.45      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.45         => ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % freshFreeDerivative(1)
% 0.27/0.45  thf(fact_174_freshFreeDerivative_I2_J,axiom,
% 0.27/0.45      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.45         => ( fresh_name_pi @ Y @ P3 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % freshFreeDerivative(2)
% 0.27/0.45  thf(fact_175_simE_I2_J,axiom,
% 0.27/0.45      ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha2: late_freeRes,Q3: pi] :
% 0.27/0.45        ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.27/0.45         => ? [P4: pi] :
% 0.27/0.45              ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.27/0.45              & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q3 ) @ Rel ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simE(2)
% 0.27/0.45  thf(fact_176_resTrans_I2_J,axiom,
% 0.27/0.45      ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % resTrans(2)
% 0.27/0.45  thf(fact_177_simCases,axiom,
% 0.27/0.45      ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.27/0.45        ( ! [A3: late_subject,Y3: name,Q2: pi] :
% 0.27/0.45            ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.27/0.45           => ( ( fresh_name_pi @ Y3 @ P )
% 0.27/0.45             => ? [P6: pi] :
% 0.27/0.45                  ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.45                  & ( strong2129052853vative @ P6 @ Q2 @ A3 @ Y3 @ Rel ) ) ) )
% 0.27/0.45       => ( ! [Alpha: late_freeRes,Q2: pi] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45             => ? [P6: pi] :
% 0.27/0.45                  ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 0.27/0.45         => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simCases
% 0.27/0.45  thf(fact_178_simulation__def,axiom,
% 0.27/0.45      ( strong743114133lation
% 0.27/0.45      = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.27/0.45            ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.27/0.45                ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.27/0.45                  & ( fresh_name_pi @ X4 @ P7 ) )
% 0.27/0.45               => ? [P8: pi] :
% 0.27/0.45                    ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 0.27/0.45                    & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.27/0.45            & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.27/0.45                ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.27/0.45               => ? [P8: pi] :
% 0.27/0.45                    ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simulation_def
% 0.27/0.45  thf(fact_179_tauBoundTrans,axiom,
% 0.27/0.45      ! [P: pi,A: late_subject,X: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % tauBoundTrans
% 0.27/0.45  thf(fact_180_resZeroTrans,axiom,
% 0.27/0.45      ! [X: name,Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % resZeroTrans
% 0.27/0.45  thf(fact_181_residual_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_induct
% 0.27/0.45  thf(fact_182_residual_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_induct
% 0.27/0.45  thf(fact_183_residual_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 0.27/0.45            ( ( fresh_name_name @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_induct
% 0.27/0.45  thf(fact_184_residual_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 0.27/0.45            ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_induct
% 0.27/0.45  thf(fact_185_residual_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_inducts
% 0.27/0.45  thf(fact_186_residual_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_inducts
% 0.27/0.45  thf(fact_187_residual_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 0.27/0.45            ( ( fresh_name_name @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_inducts
% 0.27/0.45  thf(fact_188_residual_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.27/0.45        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 0.27/0.45            ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.27/0.45           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.27/0.45             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.45         => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.strong_inducts
% 0.27/0.45  thf(fact_189_resSimCases,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [Q2: pi,A3: name] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.27/0.45             => ( ( A3 != X )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.27/0.45         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.27/0.45               => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.45                 => ( ( X != Y3 )
% 0.27/0.45                   => ( ( fresh_1641682979reeRes @ Y3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.45           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.27/0.45                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.45                   => ? [P6: pi] :
% 0.27/0.45                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.27/0.45             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resSimCases
% 0.27/0.45  thf(fact_190_resSimCases,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [Q2: pi,A3: name] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.27/0.45             => ( ( A3 != X )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.27/0.45         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.27/0.45               => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.45                 => ( ( X != Y3 )
% 0.27/0.45                   => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.45           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.27/0.45                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.45                   => ? [P6: pi] :
% 0.27/0.45                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.27/0.45             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resSimCases
% 0.27/0.45  thf(fact_191_resSimCases,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [Q2: pi,A3: name] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.27/0.45             => ( ( A3 != X )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.27/0.45         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.27/0.45               => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.45                 => ( ( X != Y3 )
% 0.27/0.45                   => ( ( fresh_name_name @ Y3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.45           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.27/0.45                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.45                   => ? [P6: pi] :
% 0.27/0.45                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.27/0.45             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resSimCases
% 0.27/0.45  thf(fact_192_resSimCases,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.27/0.45        ( ( eqvt_pi @ Rel )
% 0.27/0.45       => ( ! [Q2: pi,A3: name] :
% 0.27/0.45              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 0.27/0.45             => ( ( A3 != X )
% 0.27/0.45               => ? [P6: pi] :
% 0.27/0.45                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.45                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 0.27/0.45         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 0.27/0.45                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 0.27/0.45               => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.45                 => ( ( X != Y3 )
% 0.27/0.45                   => ( ( fresh_name_pi @ Y3 @ C3 )
% 0.27/0.45                     => ? [P6: pi] :
% 0.27/0.45                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.45                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.45           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 0.27/0.45                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.45                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.45                   => ? [P6: pi] :
% 0.27/0.45                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 0.27/0.45                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 0.27/0.45             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resSimCases
% 0.27/0.45  thf(fact_193_resInputBoundOutputTrans,axiom,
% 0.27/0.45      ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resInputBoundOutputTrans
% 0.27/0.45  thf(fact_194_resTauOutputTrans,axiom,
% 0.27/0.45      ! [X: name,P: pi,A: name,B: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resTauOutputTrans
% 0.27/0.45  thf(fact_195_residual_Ofresh_I1_J,axiom,
% 0.27/0.45      ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 0.27/0.45        ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.27/0.45        = ( ( fresh_717452603ubject @ A @ X32 )
% 0.27/0.45          & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.fresh(1)
% 0.27/0.45  thf(fact_196_Tau,axiom,
% 0.27/0.45      ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Tau
% 0.27/0.45  thf(fact_197_tauCases_H,axiom,
% 0.27/0.45      ! [P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.27/0.45       => ~ ! [P5: pi] :
% 0.27/0.45              ( ( ( tau @ P )
% 0.27/0.45                = ( tau @ P5 ) )
% 0.27/0.45             => ( Rs
% 0.27/0.45               != ( late_FreeR @ late_TauR @ P5 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % tauCases'
% 0.27/0.45  thf(fact_198_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.27/0.45      ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.27/0.45        ( ( ( late_OutputR @ X2 @ X1 )
% 0.27/0.45          = ( late_OutputR @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.freeRes.inject
% 0.27/0.45  thf(fact_199_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.27/0.45      ! [X1: name,Y1: name] :
% 0.27/0.45        ( ( ( late_BoundOutputS @ X1 )
% 0.27/0.45          = ( late_BoundOutputS @ Y1 ) )
% 0.27/0.45        = ( X1 = Y1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.subject.inject(2)
% 0.27/0.45  thf(fact_200_subject_Ofresh_I2_J,axiom,
% 0.27/0.45      ! [A: name,X1: name] :
% 0.27/0.45        ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.45        = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % subject.fresh(2)
% 0.27/0.45  thf(fact_201_freeRes_Ofresh_I1_J,axiom,
% 0.27/0.45      ! [A: name,X2: name,X1: name] :
% 0.27/0.45        ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_name_name @ A @ X2 )
% 0.27/0.45          & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % freeRes.fresh(1)
% 0.27/0.45  thf(fact_202_freeRes_Ofresh_I2_J,axiom,
% 0.27/0.45      ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.27/0.45  
% 0.27/0.45  % freeRes.fresh(2)
% 0.27/0.45  thf(fact_203_pi_Ofresh_I9_J,axiom,
% 0.27/0.45      ! [A: name,X1: name,X2: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.27/0.45        = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(9)
% 0.27/0.45  thf(fact_204_pi_Ofresh_I4_J,axiom,
% 0.27/0.45      ! [A: name,X32: name,X1: name,X2: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.27/0.45        = ( ( fresh_name_name @ A @ X32 )
% 0.27/0.45          & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(4)
% 0.27/0.45  thf(fact_205_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name] :
% 0.27/0.45        ( ( late_OutputR @ Name12 @ Name22 )
% 0.27/0.45       != late_TauR ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.freeRes.distinct(1)
% 0.27/0.45  thf(fact_206_abs__fun__eq1,axiom,
% 0.27/0.45      ! [A: name,X: name,Y: name] :
% 0.27/0.45        ( ( ( abs_fun_name_name @ A @ X )
% 0.27/0.45          = ( abs_fun_name_name @ A @ Y ) )
% 0.27/0.45        = ( X = Y ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fun_eq1
% 0.27/0.45  thf(fact_207_abs__fun__eq1,axiom,
% 0.27/0.45      ! [A: name,X: produc1141751126_pi_pi,Y: produc1141751126_pi_pi] :
% 0.27/0.45        ( ( ( abs_fu385186459_pi_pi @ A @ X )
% 0.27/0.45          = ( abs_fu385186459_pi_pi @ A @ Y ) )
% 0.27/0.45        = ( X = Y ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fun_eq1
% 0.27/0.45  thf(fact_208_abs__fun__eq1,axiom,
% 0.27/0.45      ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.45        ( ( ( abs_fu681348580reeRes @ A @ X )
% 0.27/0.45          = ( abs_fu681348580reeRes @ A @ Y ) )
% 0.27/0.45        = ( X = Y ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fun_eq1
% 0.27/0.45  thf(fact_209_abs__fun__eq1,axiom,
% 0.27/0.45      ! [A: name,X: pi,Y: pi] :
% 0.27/0.45        ( ( ( abs_fun_name_pi @ A @ X )
% 0.27/0.45          = ( abs_fun_name_pi @ A @ Y ) )
% 0.27/0.45        = ( X = Y ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fun_eq1
% 0.27/0.45  thf(fact_210_freeRes_Oinducts,axiom,
% 0.27/0.45      ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.27/0.45        ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.27/0.45       => ( ( P @ late_TauR )
% 0.27/0.45         => ( P @ FreeRes3 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % freeRes.inducts
% 0.27/0.45  thf(fact_211_pi_Oinject_I8_J,axiom,
% 0.27/0.45      ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.27/0.45        ( ( ( res @ X1 @ X2 )
% 0.27/0.45          = ( res @ Y1 @ Y2 ) )
% 0.27/0.45        = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.27/0.45          = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(8)
% 0.27/0.45  thf(fact_212_residual_Oinject_I1_J,axiom,
% 0.27/0.45      ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.27/0.45        ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.27/0.45          = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.27/0.45        = ( ( X32 = Y32 )
% 0.27/0.45          & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.27/0.45            = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % residual.inject(1)
% 0.27/0.45  thf(fact_213_name__fresh__abs,axiom,
% 0.27/0.45      ! [B: name,A: name,X: late_freeRes] :
% 0.27/0.45        ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % name_fresh_abs
% 0.27/0.45  thf(fact_214_name__fresh__abs,axiom,
% 0.27/0.45      ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.45        ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % name_fresh_abs
% 0.27/0.45  thf(fact_215_name__fresh__abs,axiom,
% 0.27/0.45      ! [B: name,A: name,X: name] :
% 0.27/0.45        ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_name_name @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % name_fresh_abs
% 0.27/0.45  thf(fact_216_name__fresh__abs,axiom,
% 0.27/0.45      ! [B: name,A: name,X: pi] :
% 0.27/0.45        ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % name_fresh_abs
% 0.27/0.45  thf(fact_217_abs__fresh_I1_J,axiom,
% 0.27/0.45      ! [B: name,A: name,X: late_freeRes] :
% 0.27/0.45        ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fresh(1)
% 0.27/0.45  thf(fact_218_abs__fresh_I1_J,axiom,
% 0.27/0.45      ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.45        ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fresh(1)
% 0.27/0.45  thf(fact_219_abs__fresh_I1_J,axiom,
% 0.27/0.45      ! [B: name,A: name,X: name] :
% 0.27/0.45        ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_name_name @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fresh(1)
% 0.27/0.45  thf(fact_220_abs__fresh_I1_J,axiom,
% 0.27/0.45      ! [B: name,A: name,X: pi] :
% 0.27/0.45        ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.27/0.45        = ( ( B = A )
% 0.27/0.45          | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % abs_fresh(1)
% 0.27/0.45  thf(fact_221_pi_Oinject_I3_J,axiom,
% 0.27/0.45      ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.27/0.45        ( ( ( input @ X32 @ X1 @ X2 )
% 0.27/0.45          = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.27/0.45        = ( ( X32 = Y32 )
% 0.27/0.45          & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.27/0.45            = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(3)
% 0.27/0.45  thf(fact_222_Open,axiom,
% 0.27/0.45      ! [P: pi,A: name,B: name,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.45       => ( ( A != B )
% 0.27/0.45         => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Open
% 0.27/0.45  thf(fact_223_resCases_H,axiom,
% 0.27/0.45      ! [X: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.27/0.45       => ( ! [P5: pi,A3: name,B3: name] :
% 0.27/0.45              ( ( ( res @ X @ P )
% 0.27/0.45                = ( res @ B3 @ P5 ) )
% 0.27/0.45             => ! [P4: pi] :
% 0.27/0.45                  ( ( Rs
% 0.27/0.45                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 0.27/0.45                 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 0.27/0.45                   => ( A3 = B3 ) ) ) )
% 0.27/0.45         => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 0.27/0.45                ( ( ( res @ X @ P )
% 0.27/0.45                  = ( res @ Y3 @ P5 ) )
% 0.27/0.45               => ( ( Rs
% 0.27/0.45                    = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.45                 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.27/0.45                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.45                     => ( ( Y3 != X3 )
% 0.27/0.45                       => ( ( fresh_name_pi @ X3 @ P5 )
% 0.27/0.45                         => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
% 0.27/0.45           => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 0.27/0.45                  ( ( ( res @ X @ P )
% 0.27/0.45                    = ( res @ Y3 @ P5 ) )
% 0.27/0.45                 => ( ( Rs
% 0.27/0.45                      = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.45                   => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.45                     => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resCases'
% 0.27/0.45  thf(fact_224_resCasesB_H,axiom,
% 0.27/0.45      ! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
% 0.27/0.45       => ( ! [P5: pi,A3: name,B3: name] :
% 0.27/0.45              ( ( ( res @ X5 @ P )
% 0.27/0.45                = ( res @ B3 @ P5 ) )
% 0.27/0.45             => ! [P4: pi] :
% 0.27/0.45                  ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.27/0.45                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 0.27/0.45                 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 0.27/0.45                   => ( A3 = B3 ) ) ) )
% 0.27/0.45         => ~ ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 0.27/0.45                ( ( ( res @ X5 @ P )
% 0.27/0.45                  = ( res @ Y3 @ P5 ) )
% 0.27/0.45               => ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.27/0.45                    = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.45                 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 0.27/0.45                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.45                     => ( ( Y3 != X3 )
% 0.27/0.45                       => ( ( fresh_name_pi @ X3 @ P5 )
% 0.27/0.45                         => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resCasesB'
% 0.27/0.45  thf(fact_225_tauOutputTrans,axiom,
% 0.27/0.45      ! [P: pi,A: name,B: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % tauOutputTrans
% 0.27/0.45  thf(fact_226_inputBoundOutputTrans,axiom,
% 0.27/0.45      ! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % inputBoundOutputTrans
% 0.27/0.45  thf(fact_227_tauCases,axiom,
% 0.27/0.45      ! [P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.27/0.45        ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( ( ( Alpha2 = late_TauR )
% 0.27/0.45           => ( ( P = P3 )
% 0.27/0.45             => ( Prop @ late_TauR @ P ) ) )
% 0.27/0.45         => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % tauCases
% 0.27/0.45  thf(fact_228_transitions_OClose2,axiom,
% 0.27/0.45      ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ X @ P )
% 0.27/0.45           => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.45             => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.45                 => ( ( X != A )
% 0.27/0.45                   => ( ( fresh_name_pi @ X @ P3 )
% 0.27/0.45                     => ( ( Y != A )
% 0.27/0.45                       => ( ( fresh_name_pi @ Y @ Q3 )
% 0.27/0.45                         => ( ( X != Y )
% 0.27/0.45                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % transitions.Close2
% 0.27/0.45  thf(fact_229_transitions_OClose1,axiom,
% 0.27/0.45      ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ X @ P )
% 0.27/0.45           => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.45             => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.45               => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.45                 => ( ( X != A )
% 0.27/0.45                   => ( ( fresh_name_pi @ X @ Q3 )
% 0.27/0.45                     => ( ( Y != A )
% 0.27/0.45                       => ( ( fresh_name_pi @ Y @ P3 )
% 0.27/0.45                         => ( ( X != Y )
% 0.27/0.45                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % transitions.Close1
% 0.27/0.45  thf(fact_230_Late__Semantics_OClose2,axiom,
% 0.27/0.45      ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.45           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.Close2
% 0.27/0.45  thf(fact_231_Late__Semantics_OClose1,axiom,
% 0.27/0.45      ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.45           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.Close1
% 0.27/0.45  thf(fact_232_name__fresh,axiom,
% 0.27/0.45      ( fresh_name_name
% 0.27/0.45      = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % name_fresh
% 0.27/0.45  thf(fact_233_subject_Ofresh_I1_J,axiom,
% 0.27/0.45      ! [A: name,X1: name] :
% 0.27/0.45        ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.27/0.45        = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % subject.fresh(1)
% 0.27/0.45  thf(fact_234_subject_Oinducts,axiom,
% 0.27/0.45      ! [P: late_subject > $o,Subject: late_subject] :
% 0.27/0.45        ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.27/0.45       => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.27/0.45         => ( P @ Subject ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % subject.inducts
% 0.27/0.45  thf(fact_235_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [Name3: name,Name: name] :
% 0.27/0.45        ( ( late_InputS @ Name3 )
% 0.27/0.45       != ( late_BoundOutputS @ Name ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.subject.distinct(1)
% 0.27/0.45  thf(fact_236_Late__Semantics_OInput,axiom,
% 0.27/0.45      ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.Input
% 0.27/0.45  thf(fact_237_transitions_OInput,axiom,
% 0.27/0.45      ! [X: name,A: name,P: pi] :
% 0.27/0.45        ( ( X != A )
% 0.27/0.45       => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % transitions.Input
% 0.27/0.45  thf(fact_238_inputCases_H,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ~ ! [X3: name,A3: name,P5: pi] :
% 0.27/0.45              ( ( ( A = A3 )
% 0.27/0.45                & ( ( abs_fun_name_pi @ B @ P )
% 0.27/0.45                  = ( abs_fun_name_pi @ X3 @ P5 ) ) )
% 0.27/0.45             => ( ( Rs
% 0.27/0.45                  = ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P5 ) )
% 0.27/0.45               => ( X3 = A3 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % inputCases'
% 0.27/0.45  thf(fact_239_Late__Semantics_OComm1,axiom,
% 0.27/0.45      ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 0.27/0.45         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.Comm1
% 0.27/0.45  thf(fact_240_Late__Semantics_OComm2,axiom,
% 0.27/0.45      ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.27/0.45         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics.Comm2
% 0.27/0.45  thf(fact_241_transitions_OComm2,axiom,
% 0.27/0.45      ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ X @ P )
% 0.27/0.45           => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.45             => ( ( X != A )
% 0.27/0.45               => ( ( X != B )
% 0.27/0.45                 => ( ( fresh_name_pi @ X @ P3 )
% 0.27/0.45                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % transitions.Comm2
% 0.27/0.45  thf(fact_242_transitions_OComm1,axiom,
% 0.27/0.45      ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.45       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 0.27/0.45         => ( ( fresh_name_pi @ X @ P )
% 0.27/0.45           => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.45             => ( ( X != A )
% 0.27/0.45               => ( ( X != B )
% 0.27/0.45                 => ( ( fresh_name_pi @ X @ Q3 )
% 0.27/0.45                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % transitions.Comm1
% 0.27/0.45  thf(fact_243_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.27/0.45      ! [X1: name,Y1: name] :
% 0.27/0.45        ( ( ( late_InputS @ X1 )
% 0.27/0.45          = ( late_InputS @ Y1 ) )
% 0.27/0.45        = ( X1 = Y1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics1.subject.inject(1)
% 0.27/0.45  thf(fact_244_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.27/0.45      ! [X2: name,Y2: name] :
% 0.27/0.45        ( ( ( late_BoundOutputS @ X2 )
% 0.27/0.45          = ( late_BoundOutputS @ Y2 ) )
% 0.27/0.45        = ( X2 = Y2 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics1.subject.inject(2)
% 0.27/0.45  thf(fact_245_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.27/0.45      ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.27/0.45        ( ( ( late_OutputR @ X11 @ X12 )
% 0.27/0.45          = ( late_OutputR @ Y11 @ Y12 ) )
% 0.27/0.45        = ( ( X11 = Y11 )
% 0.27/0.45          & ( X12 = Y12 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics1.freeRes.inject
% 0.27/0.45  thf(fact_246_freeRes_Oexhaust,axiom,
% 0.27/0.45      ! [Y: late_freeRes] :
% 0.27/0.45        ( ! [X112: name,X122: name] :
% 0.27/0.45            ( Y
% 0.27/0.45           != ( late_OutputR @ X112 @ X122 ) )
% 0.27/0.45       => ( Y = late_TauR ) ) ).
% 0.27/0.45  
% 0.27/0.45  % freeRes.exhaust
% 0.27/0.45  thf(fact_247_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [X11: name,X12: name] :
% 0.27/0.45        ( ( late_OutputR @ X11 @ X12 )
% 0.27/0.45       != late_TauR ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics1.freeRes.distinct(1)
% 0.27/0.45  thf(fact_248_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [X1: name,X2: name] :
% 0.27/0.45        ( ( late_InputS @ X1 )
% 0.27/0.45       != ( late_BoundOutputS @ X2 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Late_Semantics1.subject.distinct(1)
% 0.27/0.45  thf(fact_249_subject_Oexhaust,axiom,
% 0.27/0.45      ! [Y: late_subject] :
% 0.27/0.45        ( ! [X13: name] :
% 0.27/0.45            ( Y
% 0.27/0.45           != ( late_InputS @ X13 ) )
% 0.27/0.45       => ~ ! [X22: name] :
% 0.27/0.45              ( Y
% 0.27/0.45             != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % subject.exhaust
% 0.27/0.45  thf(fact_250_resOutputTauTrans,axiom,
% 0.27/0.45      ! [X: name,A: name,B: name,P: pi,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resOutputTauTrans
% 0.27/0.45  thf(fact_251_resOutputInputTrans,axiom,
% 0.27/0.45      ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resOutputInputTrans
% 0.27/0.45  thf(fact_252_resOutputOutputTrans,axiom,
% 0.27/0.45      ! [X: name,A: name,P: pi,B: name,Y: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % resOutputOutputTrans
% 0.27/0.45  thf(fact_253_pi_Ofresh_I2_J,axiom,
% 0.27/0.45      ! [A: name,X32: name,X2: name,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_name_name @ A @ X32 )
% 0.27/0.45          & ( fresh_name_name @ A @ X2 )
% 0.27/0.45          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(2)
% 0.27/0.45  thf(fact_254_pi_Odistinct_I31_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(31)
% 0.27/0.45  thf(fact_255_pi_Odistinct_I29_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(29)
% 0.27/0.45  thf(fact_256_pi_Odistinct_I21_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(21)
% 0.27/0.45  thf(fact_257_pi_Odistinct_I1_J,axiom,
% 0.27/0.45      ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(1)
% 0.27/0.45  thf(fact_258_pi_Odistinct_I19_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( tau @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(19)
% 0.27/0.45  thf(fact_259_pi_Oinject_I1_J,axiom,
% 0.27/0.45      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.27/0.45        ( ( ( output @ X32 @ X2 @ X1 )
% 0.27/0.45          = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X32 = Y32 )
% 0.27/0.45          & ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(1)
% 0.27/0.45  thf(fact_260_resTrans_I1_J,axiom,
% 0.27/0.45      ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % resTrans(1)
% 0.27/0.45  thf(fact_261_outputBoundTrans,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,C: late_subject,X: name,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputBoundTrans
% 0.27/0.45  thf(fact_262_nilSim_I3_J,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.27/0.45        ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % nilSim(3)
% 0.27/0.45  thf(fact_263_outputCases,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.27/0.45        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ( ( ( Alpha2
% 0.27/0.45              = ( late_OutputR @ A @ B ) )
% 0.27/0.45           => ( ( P = P3 )
% 0.27/0.45             => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.27/0.45         => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputCases
% 0.27/0.45  thf(fact_264_outputCases_H,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ~ ! [A3: name,B3: name,P5: pi] :
% 0.27/0.45              ( ( ( A = A3 )
% 0.27/0.45                & ( B = B3 )
% 0.27/0.45                & ( P = P5 ) )
% 0.27/0.45             => ( Rs
% 0.27/0.45               != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputCases'
% 0.27/0.45  thf(fact_265_outputIneqTrans,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,C: name,D: name,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P3 ) )
% 0.27/0.45       => ~ ( ( A != C )
% 0.27/0.45            | ( B != D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputIneqTrans
% 0.27/0.45  thf(fact_266_Output,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Output
% 0.27/0.45  thf(fact_267_outputTauTrans,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,P3: pi] :
% 0.27/0.45        ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputTauTrans
% 0.27/0.45  thf(fact_268_outputFreshTrans,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 0.27/0.45        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.27/0.45       => ~ ( ( fresh_1641682979reeRes @ A @ Alpha2 )
% 0.27/0.45            | ( fresh_1641682979reeRes @ B @ Alpha2 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % outputFreshTrans
% 0.27/0.45  thf(fact_269_simps_I3_J,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 0.27/0.45        = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(3)
% 0.27/0.45  thf(fact_270_simps_I4_J,axiom,
% 0.27/0.45      ! [X: name,A: name,C: name,D: name,P: pi] :
% 0.27/0.45        ( ( X != A )
% 0.27/0.45       => ( ( X != C )
% 0.27/0.45         => ( ( X != D )
% 0.27/0.45           => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 0.27/0.45              = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(4)
% 0.27/0.45  thf(fact_271_substInput,axiom,
% 0.27/0.45      ! [X: name,B: name,C: name,A: name,P: pi] :
% 0.27/0.45        ( ( X != B )
% 0.27/0.45       => ( ( X != C )
% 0.27/0.45         => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 0.27/0.45            = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % substInput
% 0.27/0.45  thf(fact_272_subst__name__def,axiom,
% 0.27/0.45      ( subst_name
% 0.27/0.45      = ( ^ [A5: name,B4: name,C4: name] : ( if_name @ ( A5 = B4 ) @ C4 @ A5 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % subst_name_def
% 0.27/0.45  thf(fact_273_simps_I6_J,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 0.27/0.45        = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(6)
% 0.27/0.45  thf(fact_274_simps_I5_J,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 0.27/0.45        = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(5)
% 0.27/0.45  thf(fact_275_pi_Ofresh_I5_J,axiom,
% 0.27/0.45      ! [A: name,X32: name,X2: name,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_name_name @ A @ X32 )
% 0.27/0.45          & ( fresh_name_name @ A @ X2 )
% 0.27/0.45          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(5)
% 0.27/0.45  thf(fact_276_pi_Ofresh_I6_J,axiom,
% 0.27/0.45      ! [A: name,X32: name,X2: name,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_name_name @ A @ X32 )
% 0.27/0.45          & ( fresh_name_name @ A @ X2 )
% 0.27/0.45          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(6)
% 0.27/0.45  thf(fact_277_matchCases,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.27/0.45        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ( ( ( late_transitions @ P @ Rs )
% 0.27/0.45           => ( ( A = B )
% 0.27/0.45             => ( F @ A @ A ) ) )
% 0.27/0.45         => ( F @ A @ B ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % matchCases
% 0.27/0.45  thf(fact_278_matchTrans,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ( A = B ) ) ).
% 0.27/0.45  
% 0.27/0.45  % matchTrans
% 0.27/0.45  thf(fact_279_matchCases_H,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ~ ! [P5: pi] :
% 0.27/0.45              ( ( ( B = A )
% 0.27/0.45                & ( P = P5 ) )
% 0.27/0.45             => ~ ( late_transitions @ P5 @ Rs ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % matchCases'
% 0.27/0.45  thf(fact_280_mismatchCases,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.27/0.45        ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ( ( ( late_transitions @ P @ Rs )
% 0.27/0.45           => ( ( A != B )
% 0.27/0.45             => ( F @ A @ B ) ) )
% 0.27/0.45         => ( F @ A @ B ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % mismatchCases
% 0.27/0.45  thf(fact_281_mismatchTrans,axiom,
% 0.27/0.45      ! [A: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.27/0.45  
% 0.27/0.45  % mismatchTrans
% 0.27/0.45  thf(fact_282_mismatchCases_H,axiom,
% 0.27/0.45      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.27/0.45       => ~ ! [P5: pi,A3: name,B3: name] :
% 0.27/0.45              ( ( ( A = A3 )
% 0.27/0.45                & ( B = B3 )
% 0.27/0.45                & ( P = P5 ) )
% 0.27/0.45             => ( ( late_transitions @ P5 @ Rs )
% 0.27/0.45               => ( A3 = B3 ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % mismatchCases'
% 0.27/0.45  thf(fact_283_Match,axiom,
% 0.27/0.45      ! [P: pi,Rs: late_residual,B: name] :
% 0.27/0.45        ( ( late_transitions @ P @ Rs )
% 0.27/0.45       => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Match
% 0.27/0.45  thf(fact_284_Mismatch,axiom,
% 0.27/0.45      ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.27/0.45        ( ( late_transitions @ P @ Rs )
% 0.27/0.45       => ( ( A != B )
% 0.27/0.45         => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Mismatch
% 0.27/0.45  thf(fact_285_pi_Odistinct_I67_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(67)
% 0.27/0.45  thf(fact_286_pi_Odistinct_I75_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(75)
% 0.27/0.45  thf(fact_287_pi_Odistinct_I65_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(65)
% 0.27/0.45  thf(fact_288_pi_Odistinct_I73_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(73)
% 0.27/0.45  thf(fact_289_pi_Odistinct_I49_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(49)
% 0.27/0.45  thf(fact_290_pi_Odistinct_I51_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(51)
% 0.27/0.45  thf(fact_291_pi_Odistinct_I7_J,axiom,
% 0.27/0.45      ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(7)
% 0.27/0.45  thf(fact_292_pi_Odistinct_I9_J,axiom,
% 0.27/0.45      ! [Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(9)
% 0.27/0.45  thf(fact_293_pi_Odistinct_I37_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(37)
% 0.27/0.45  thf(fact_294_pi_Odistinct_I39_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(39)
% 0.27/0.45  thf(fact_295_pi_Oinject_I5_J,axiom,
% 0.27/0.45      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.27/0.45        ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.27/0.45          = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X32 = Y32 )
% 0.27/0.45          & ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(5)
% 0.27/0.45  thf(fact_296_pi_Oinject_I4_J,axiom,
% 0.27/0.45      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.27/0.45        ( ( ( match @ X32 @ X2 @ X1 )
% 0.27/0.45          = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X32 = Y32 )
% 0.27/0.45          & ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(4)
% 0.27/0.45  thf(fact_297_pi_Odistinct_I61_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(61)
% 0.27/0.45  thf(fact_298_pi_Odistinct_I23_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(23)
% 0.27/0.45  thf(fact_299_pi_Odistinct_I25_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(25)
% 0.27/0.45  thf(fact_300_matchNilLeft,axiom,
% 0.27/0.45      ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.27/0.45        ( ( A != B )
% 0.27/0.45       => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % matchNilLeft
% 0.27/0.45  thf(fact_301_mismatchNilLeft,axiom,
% 0.27/0.45      ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 0.27/0.45  
% 0.27/0.45  % mismatchNilLeft
% 0.27/0.45  thf(fact_302_pi_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                  ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.27/0.45                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.27/0.45                          ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_induct
% 0.27/0.45  thf(fact_303_pi_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                  ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                    ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                      ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                        ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                          ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_induct
% 0.27/0.45  thf(fact_304_pi_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: name] :
% 0.27/0.45                ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                  ( ( fresh_name_name @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                    ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                      ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.27/0.45                        ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.27/0.45                          ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 0.27/0.45                            ( ( fresh_name_name @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: name] :
% 0.27/0.45                              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_induct
% 0.27/0.45  thf(fact_305_pi_Ostrong__induct,axiom,
% 0.27/0.45      ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: pi] :
% 0.27/0.45                ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                  ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                    ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                      ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.27/0.45                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.27/0.45                          ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                            ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: pi] :
% 0.27/0.45                              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_induct
% 0.27/0.45  thf(fact_306_pi_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                  ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.27/0.45                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.27/0.45                          ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.27/0.45                              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_inducts
% 0.27/0.45  thf(fact_307_pi_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                  ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                    ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                      ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                        ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                          ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.45                              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_inducts
% 0.27/0.45  thf(fact_308_pi_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: name] :
% 0.27/0.45                ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                  ( ( fresh_name_name @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                    ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 0.27/0.45                      ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.27/0.45                        ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.27/0.45                          ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 0.27/0.45                            ( ( fresh_name_name @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: name] :
% 0.27/0.45                              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_inducts
% 0.27/0.45  thf(fact_309_pi_Ostrong__inducts,axiom,
% 0.27/0.45      ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.27/0.45        ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.27/0.45       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45         => ( ! [Pi4: pi,Z2: pi] :
% 0.27/0.45                ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.27/0.45           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                  ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.27/0.45                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.27/0.45                   => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 0.27/0.45             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                    ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                      ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 0.27/0.45                 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.27/0.45                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                       => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                   => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.27/0.45                          ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.27/0.45                         => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.27/0.45                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.27/0.45                     => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 0.27/0.45                            ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.27/0.45                           => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 0.27/0.45                       => ( ! [Pi4: pi,Z2: pi] :
% 0.27/0.45                              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.27/0.45                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.27/0.45                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.strong_inducts
% 0.27/0.45  thf(fact_310_pi_Ofresh_I10_J,axiom,
% 0.27/0.45      ! [A: name,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 0.27/0.45        = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(10)
% 0.27/0.45  thf(fact_311_pi_Ofresh_I7_J,axiom,
% 0.27/0.45      ! [A: name,X2: pi,X1: pi] :
% 0.27/0.45        ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.27/0.45        = ( ( fresh_name_pi @ A @ X2 )
% 0.27/0.45          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.fresh(7)
% 0.27/0.45  thf(fact_312_simps_I10_J,axiom,
% 0.27/0.45      ! [P: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( bang @ P ) @ C @ D )
% 0.27/0.45        = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(10)
% 0.27/0.45  thf(fact_313_simps_I7_J,axiom,
% 0.27/0.45      ! [P: pi,Q: pi,C: name,D: name] :
% 0.27/0.45        ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.27/0.45        = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % simps(7)
% 0.27/0.45  thf(fact_314_pi_Odistinct_I77_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(77)
% 0.27/0.45  thf(fact_315_pi_Odistinct_I71_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(71)
% 0.27/0.45  thf(fact_316_pi_Odistinct_I69_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(69)
% 0.27/0.45  thf(fact_317_pi_Odistinct_I63_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( match @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(63)
% 0.27/0.45  thf(fact_318_pi_Odistinct_I33_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(33)
% 0.27/0.45  thf(fact_319_pi_Odistinct_I27_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(27)
% 0.27/0.45  thf(fact_320_pi_Odistinct_I89_J,axiom,
% 0.27/0.45      ! [Name3: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( res @ Name3 @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(89)
% 0.27/0.45  thf(fact_321_pi_Odistinct_I87_J,axiom,
% 0.27/0.45      ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.27/0.45        ( ( par @ Pi1 @ Pi2 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(87)
% 0.27/0.45  thf(fact_322_pi_Odistinct_I59_J,axiom,
% 0.27/0.45      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(59)
% 0.27/0.45  thf(fact_323_pi_Odistinct_I17_J,axiom,
% 0.27/0.45      ! [Pi: pi] :
% 0.27/0.45        ( piNil
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(17)
% 0.27/0.45  thf(fact_324_Sum2,axiom,
% 0.27/0.45      ! [Q: pi,Rs: late_residual,P: pi] :
% 0.27/0.45        ( ( late_transitions @ Q @ Rs )
% 0.27/0.45       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Sum2
% 0.27/0.45  thf(fact_325_Sum1,axiom,
% 0.27/0.45      ! [P: pi,Rs: late_residual,Q: pi] :
% 0.27/0.45        ( ( late_transitions @ P @ Rs )
% 0.27/0.45       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.27/0.45  
% 0.27/0.45  % Sum1
% 0.27/0.45  thf(fact_326_sumCases_H,axiom,
% 0.27/0.45      ! [P: pi,Q: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.27/0.45       => ( ~ ( late_transitions @ P @ Rs )
% 0.27/0.45         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % sumCases'
% 0.27/0.45  thf(fact_327_sumCases,axiom,
% 0.27/0.45      ! [P: pi,Q: pi,Rs: late_residual] :
% 0.27/0.45        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.27/0.45       => ( ~ ( late_transitions @ P @ Rs )
% 0.27/0.45         => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % sumCases
% 0.27/0.45  thf(fact_328_pi_Odistinct_I47_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Pi: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(47)
% 0.27/0.45  thf(fact_329_pi_Odistinct_I81_J,axiom,
% 0.27/0.45      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.27/0.45        ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.45       != ( res @ Name @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(81)
% 0.27/0.45  thf(fact_330_pi_Odistinct_I79_J,axiom,
% 0.27/0.45      ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.45       != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(79)
% 0.27/0.45  thf(fact_331_pi_Odistinct_I83_J,axiom,
% 0.27/0.45      ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.27/0.45        ( ( sum @ Pi1 @ Pi2 )
% 0.27/0.45       != ( bang @ Pi ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(83)
% 0.27/0.45  thf(fact_332_pi_Oinject_I6_J,axiom,
% 0.27/0.45      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.27/0.45        ( ( ( sum @ X2 @ X1 )
% 0.27/0.45          = ( sum @ Y2 @ Y1 ) )
% 0.27/0.45        = ( ( X2 = Y2 )
% 0.27/0.45          & ( X1 = Y1 ) ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(6)
% 0.27/0.45  thf(fact_333_pi_Oinject_I9_J,axiom,
% 0.27/0.45      ! [X1: pi,Y1: pi] :
% 0.27/0.45        ( ( ( bang @ X1 )
% 0.27/0.45          = ( bang @ Y1 ) )
% 0.27/0.45        = ( X1 = Y1 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.inject(9)
% 0.27/0.45  thf(fact_334_pi_Odistinct_I41_J,axiom,
% 0.27/0.45      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.45        ( ( tau @ Pi3 )
% 0.27/0.45       != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.27/0.45  
% 0.27/0.45  % pi.distinct(41)
% 0.27/0.45  
% 0.27/0.45  % Helper facts (3)
% 0.27/0.45  thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.45      ! [P: $o] :
% 0.27/0.45        ( ( P = $true )
% 0.27/0.45        | ( P = $false ) ) ).
% 0.27/0.45  
% 0.27/0.45  thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.45      ! [X: name,Y: name] :
% 0.27/0.45        ( ( if_name @ $false @ X @ Y )
% 0.27/0.45        = Y ) ).
% 0.27/0.45  
% 0.27/0.45  thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.45      ! [X: name,Y: name] :
% 0.27/0.45        ( ( if_name @ $true @ X @ Y )
% 0.27/0.45        = X ) ).
% 0.27/0.45  
% 0.27/0.45  % Conjectures (1)
% 0.27/0.45  thf(conj_0,conjecture,
% 0.27/0.45      member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ).
% 0.27/0.45  
% 0.27/0.45  %------------------------------------------------------------------------------
% 0.27/0.45  ------------------------
% 3.67/1.79  ---- Embedded in THF ---
% 3.67/1.79  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.67/1.79  %%% Generated on Tue Feb 24 08:29:29 EST 2026
% 3.67/1.79  %%% using '$$dhol' embedding, version 1.3.0.
% 3.67/1.79  %%% Logic specification used:
% 3.67/1.79  %%% thf(spec, logic, $$dhol).
% 3.67/1.79  
% 3.67/1.79  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2DTF23404.p
% See solution above
% 3.67/1.80  ------------------------
% 3.83/1.86  ---- Cleaned THF ---
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.83/1.86      produc53907987_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 3.83/1.86      produc1462499409ion_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.83/1.86      noptio1575811931_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.86      produc1834551554reeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 3.83/1.86      produc405342261i_name: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 3.83/1.86      produc629157763_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.83/1.86      produc1141751126_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.86      produc1357834675reeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 3.83/1.86      produc2052722628s_name: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.86      produc2008547984reeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 3.83/1.86      produc992857746Res_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.86      produc649380958reeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.83/1.86      set_Pr1834926343_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 3.83/1.86      produc367475239e_name: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 3.83/1.86      product_prod_pi_name: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 3.83/1.86      product_prod_name_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.83/1.86      product_prod_pi_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 3.83/1.86      noption_Late_freeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 3.83/1.86      noption_name: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 3.83/1.86      noption_pi: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Late____Semantics__Oresidual,type,
% 3.83/1.86      late_residual: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Late____Semantics__Osubject,type,
% 3.83/1.86      late_subject: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 3.83/1.86      late_freeRes: $tType ).
% 3.83/1.86  
% 3.83/1.86  thf(ty_n_t__Agent__Oname,type,
% 3.83/1.86      name: $tType ).
% 3.83/1.87  
% 3.83/1.87  thf(ty_n_t__Agent__Opi,type,
% 3.83/1.87      pi: $tType ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OBang,type,
% 3.83/1.87      bang: pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OInput,type,
% 3.83/1.87      input: name > name > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OMatch,type,
% 3.83/1.87      match: name > name > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OMismatch,type,
% 3.83/1.87      mismatch: name > name > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OOutput,type,
% 3.83/1.87      output: name > name > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OPar,type,
% 3.83/1.87      par: pi > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OPiNil,type,
% 3.83/1.87      piNil: pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_ORes,type,
% 3.83/1.87      res: name > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OSum,type,
% 3.83/1.87      sum: pi > pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Opi_OTau,type,
% 3.83/1.87      tau: pi > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Osubs,type,
% 3.83/1.87      subs: pi > name > name > pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Agent_Osubst__name,type,
% 3.83/1.87      subst_name: name > name > name > name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_If_001t__Agent__Oname,type,
% 3.83/1.87      if_name: $o > name > name > name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 3.83/1.87      late_OutputR: name > name > late_freeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 3.83/1.87      late_TauR: late_freeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 3.83/1.87      late_BoundR: late_subject > name > pi > late_residual ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 3.83/1.87      late_FreeR: late_freeRes > pi > late_residual ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 3.83/1.87      late_BoundOutputS: name > late_subject ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 3.83/1.87      late_InputS: name > late_subject ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Late__Semantics_Otransitions,type,
% 3.83/1.87      late_transitions: pi > late_residual > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
% 3.83/1.87      abs_fun_name_name: name > name > name > noption_name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
% 3.83/1.87      abs_fun_name_pi: name > pi > name > noption_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.83/1.87      abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 3.83/1.87      fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 3.83/1.87      fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 3.83/1.87      fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J,type,
% 3.83/1.87      fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
% 3.83/1.87      fresh_name_name: name > name > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
% 3.83/1.87      fresh_name_pi: name > pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      fresh_1641682979reeRes: name > late_freeRes > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
% 3.83/1.87      fresh_81631222sidual: name > late_residual > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 3.83/1.87      fresh_717452603ubject: name > late_subject > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 3.83/1.87      fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 3.83/1.87      fresh_453496559i_name: name > produc405342261i_name > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 3.83/1.87      fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.87      fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 3.83/1.87      fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 3.83/1.87      fresh_441084397e_name: name > produc367475239e_name > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 3.83/1.87      fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.87      fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.83/1.87      fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 3.83/1.87      fresh_261416607i_name: name > product_prod_pi_name > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.83/1.87      fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.87      fresh_1504024600reeRes: name > produc649380958reeRes > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 3.83/1.87      fresh_2007541374s_name: name > produc2052722628s_name > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 3.83/1.87      fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 3.83/1.87      fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 3.83/1.87      produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
% 3.83/1.87      produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 3.83/1.87      produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 3.83/1.87      produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 3.83/1.87      produc1570949143e_name: name > name > produc367475239e_name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
% 3.83/1.87      product_Pair_name_pi: name > pi > product_prod_name_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.83/1.87      produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
% 3.83/1.87      product_Pair_pi_name: pi > name > product_prod_pi_name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 3.83/1.87      product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 3.83/1.87      produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 3.83/1.87      produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 3.83/1.87      produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 3.83/1.87      eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.83/1.87      collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 3.83/1.87      strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 3.83/1.87      strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.83/1.87      member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_P,type,
% 3.83/1.87      p: pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_P_H____,type,
% 3.83/1.87      p2: pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_PxQ____,type,
% 3.83/1.87      pxQ: pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_Q,type,
% 3.83/1.87      q: pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_Rel,type,
% 3.83/1.87      rel: set_Pr1834926343_pi_pi ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_aa____,type,
% 3.83/1.87      aa: late_subject ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_u____,type,
% 3.83/1.87      u: name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_x,type,
% 3.83/1.87      x: name ).
% 3.83/1.87  
% 3.83/1.87  thf(sy_v_y____,type,
% 3.83/1.87      y: name ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_0_False,axiom,
% 3.83/1.87      x != u ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062,axiom,
% 3.83/1.87      ( ( subs @ ( res @ x @ q ) @ y @ u )
% 3.83/1.87      = ( res @ x @ ( subs @ q @ y @ u ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_2__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 3.83/1.87      y != x ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062,axiom,
% 3.83/1.87      fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_4_EqvtRel,axiom,
% 3.83/1.87      eqvt_pi @ rel ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062,axiom,
% 3.83/1.87      ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
% 3.83/1.87      = ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 3.83/1.87      fresh_name_pi @ y @ q ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_7__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062,axiom,
% 3.83/1.87      fresh_name_pi @ x @ p2 ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_8_Res,axiom,
% 3.83/1.87      ! [Y: name,R: pi,S: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ Y @ R )
% 3.83/1.87       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_9_ScopeExt,axiom,
% 3.83/1.87      ! [Y: name,R: pi,Z: name,S: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ Y @ R )
% 3.83/1.87       => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_10__092_060open_062y_A_092_060sharp_062_A_060_092_060nu_062x_062Q_092_060close_062,axiom,
% 3.83/1.87      fresh_name_pi @ y @ ( res @ x @ q ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_11_assms_I1_J,axiom,
% 3.83/1.87      fresh_name_pi @ x @ p ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 3.83/1.87      fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 3.83/1.87      fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_14_simps_I8_J,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 3.83/1.87        = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_15_simps_I9_J,axiom,
% 3.83/1.87      ! [X: name,C: name,D: name,P: pi] :
% 3.83/1.87        ( ( X != C )
% 3.83/1.87       => ( ( X != D )
% 3.83/1.87         => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 3.83/1.87            = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_16_subst__identity,axiom,
% 3.83/1.87      ! [P: pi,A: name] :
% 3.83/1.87        ( ( subs @ P @ A @ A )
% 3.83/1.87        = P ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_17_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 3.83/1.87        ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 3.83/1.87          = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_18_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( ( produc1275980869_pi_pi @ X1 @ X2 )
% 3.83/1.87          = ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_19_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 3.83/1.87        ( ( ( produc540578151i_name @ X1 @ X2 )
% 3.83/1.87          = ( produc540578151i_name @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_20_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 3.83/1.87        ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 3.83/1.87          = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_21_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 3.83/1.87        ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 3.83/1.87          = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_22_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 3.83/1.87        ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 3.83/1.87          = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_23_prod_Oinject,axiom,
% 3.83/1.87      ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 3.83/1.87        ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 3.83/1.87          = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X1 = Y1 )
% 3.83/1.87          & ( X2 = Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_24_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 3.83/1.87        ( ( ( produc1505598906reeRes @ A @ B )
% 3.83/1.87          = ( produc1505598906reeRes @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_25_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( ( produc1275980869_pi_pi @ A @ B )
% 3.83/1.87          = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_26_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 3.83/1.87        ( ( ( produc540578151i_name @ A @ B )
% 3.83/1.87          = ( produc540578151i_name @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_27_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 3.83/1.87        ( ( ( produc1820286517_pi_pi @ A @ B )
% 3.83/1.87          = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_28_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 3.83/1.87        ( ( ( produc1342893193ion_pi @ A @ B )
% 3.83/1.87          = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_29_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 3.83/1.87        ( ( ( product_Pair_pi_pi @ A @ B )
% 3.83/1.87          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_30_old_Oprod_Oinject,axiom,
% 3.83/1.87      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 3.83/1.87        ( ( ( produc235456326_pi_pi @ A @ B )
% 3.83/1.87          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 3.83/1.87        = ( ( A = A2 )
% 3.83/1.87          & ( B = B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_31_pi_Odistinct_I85_J,axiom,
% 3.83/1.87      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( par @ Pi1 @ Pi2 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_32__092_060open_062y_A_092_060sharp_062_AP_092_060close_062,axiom,
% 3.83/1.87      fresh_name_pi @ y @ p ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_33_Bound_Ohyps_I5_J,axiom,
% 3.83/1.87      fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_34_parSym,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 3.83/1.87        ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 3.83/1.87       => ( ! [R2: pi,S2: pi,X3: name] :
% 3.83/1.87              ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 3.83/1.87             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
% 3.83/1.87         => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_35_substRes2,axiom,
% 3.83/1.87      ! [B: name,P: pi,A: name] :
% 3.83/1.87        ( ( fresh_name_pi @ B @ P )
% 3.83/1.87       => ( ( res @ A @ P )
% 3.83/1.87          = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_36_Agent_OsubstRes3,axiom,
% 3.83/1.87      ! [B: name,P: pi,A: name] :
% 3.83/1.87        ( ( fresh_name_pi @ B @ P )
% 3.83/1.87       => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 3.83/1.87          = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_37_Bound_Ohyps_I4_J,axiom,
% 3.83/1.87      fresh_717452603ubject @ y @ aa ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_38__092_060open_062x_A_092_060sharp_062_Aa_092_060close_062,axiom,
% 3.83/1.87      fresh_717452603ubject @ x @ aa ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_39_pi_Ofresh_I8_J,axiom,
% 3.83/1.87      ! [A: name,X2: pi,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_pi @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_40_name__exists__fresh,axiom,
% 3.83/1.87      ! [X: late_freeRes] :
% 3.83/1.87        ~ ! [C2: name] :
% 3.83/1.87            ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_41_name__exists__fresh,axiom,
% 3.83/1.87      ! [X: produc1141751126_pi_pi] :
% 3.83/1.87        ~ ! [C2: name] :
% 3.83/1.87            ~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_42_name__exists__fresh,axiom,
% 3.83/1.87      ! [X: name] :
% 3.83/1.87        ~ ! [C2: name] :
% 3.83/1.87            ~ ( fresh_name_name @ C2 @ X ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_43_name__exists__fresh,axiom,
% 3.83/1.87      ! [X: pi] :
% 3.83/1.87        ~ ! [C2: name] :
% 3.83/1.87            ~ ( fresh_name_pi @ C2 @ X ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_44_freshRes,axiom,
% 3.83/1.87      ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_45_fresh__fact2,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi] :
% 3.83/1.87        ( ( A != B )
% 3.83/1.87       => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_46_fresh__fact1,axiom,
% 3.83/1.87      ! [A: name,P: pi,C: name,B: name] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ P )
% 3.83/1.87       => ( ( A != C )
% 3.83/1.87         => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_47_forget,axiom,
% 3.83/1.87      ! [A: name,P: pi,B: name] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ P )
% 3.83/1.87       => ( ( subs @ P @ A @ B )
% 3.83/1.87          = P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_48_parAssocLeft,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 3.83/1.87        ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 3.83/1.87       => ( ! [S2: pi,T: pi,X3: name] :
% 3.83/1.87              ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 3.83/1.87             => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ S2 ) @ ( res @ X3 @ T ) ) @ Rel ) )
% 3.83/1.87         => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 3.83/1.87                ( ( fresh_name_pi @ X3 @ S2 )
% 3.83/1.87               => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X3 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 3.83/1.87           => ( ! [S2: pi,T: pi,U: pi,X3: name] :
% 3.83/1.87                  ( ( fresh_name_pi @ X3 @ U )
% 3.83/1.87                 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X3 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X3 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 3.83/1.87             => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_49_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_50_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_51_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_52_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_53_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_54_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 3.83/1.87        ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_55_old_Oprod_Oinducts,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 3.83/1.87        ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ Prod ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_56_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc1834551554reeRes] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_57_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc53907987_pi_pi] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_58_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc405342261i_name] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: name] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_59_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc629157763_pi_pi] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_60_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc1462499409ion_pi] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_61_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: product_prod_pi_pi] :
% 3.83/1.87        ~ ! [A3: pi,B3: pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_62_old_Oprod_Oexhaust,axiom,
% 3.83/1.87      ! [Y: produc1141751126_pi_pi] :
% 3.83/1.87        ~ ! [A3: name,B3: product_prod_pi_pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_63_prod__induct4,axiom,
% 3.83/1.87      ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) )
% 3.83/1.87       => ( P @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_64_prod__induct3,axiom,
% 3.83/1.87      ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) )
% 3.83/1.87       => ( P @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_65_prod__induct3,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 3.83/1.87        ( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
% 3.83/1.87       => ( P @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_66_prod__cases4,axiom,
% 3.83/1.87      ! [Y: produc53907987_pi_pi] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: name,C2: pi,D2: pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C2 @ D2 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_67_mem__Collect__eq,axiom,
% 3.83/1.87      ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 3.83/1.87        ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 3.83/1.87        = ( P @ A ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_68_Collect__mem__eq,axiom,
% 3.83/1.87      ! [A4: set_Pr1834926343_pi_pi] :
% 3.83/1.87        ( ( collec1051790738_pi_pi
% 3.83/1.87          @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
% 3.83/1.87        = A4 ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_69_Collect__cong,axiom,
% 3.83/1.87      ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 3.83/1.87        ( ! [X3: product_prod_pi_pi] :
% 3.83/1.87            ( ( P @ X3 )
% 3.83/1.87            = ( Q @ X3 ) )
% 3.83/1.87       => ( ( collec1051790738_pi_pi @ P )
% 3.83/1.87          = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_70_prod__cases3,axiom,
% 3.83/1.87      ! [Y: produc53907987_pi_pi] :
% 3.83/1.87        ~ ! [A3: name > noption_pi,B3: name,C2: product_prod_pi_pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_71_prod__cases3,axiom,
% 3.83/1.87      ! [Y: produc1141751126_pi_pi] :
% 3.83/1.87        ~ ! [A3: name,B3: pi,C2: pi] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_72_Pair__inject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 3.83/1.87        ( ( ( produc1505598906reeRes @ A @ B )
% 3.83/1.87          = ( produc1505598906reeRes @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_73_Pair__inject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( ( produc1275980869_pi_pi @ A @ B )
% 3.83/1.87          = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_74_Pair__inject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 3.83/1.87        ( ( ( produc540578151i_name @ A @ B )
% 3.83/1.87          = ( produc540578151i_name @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_75_Pair__inject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 3.83/1.87        ( ( ( produc1820286517_pi_pi @ A @ B )
% 3.83/1.87          = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_76_Pair__inject,axiom,
% 3.83/1.87      ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 3.83/1.87        ( ( ( produc1342893193ion_pi @ A @ B )
% 3.83/1.87          = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_77_Pair__inject,axiom,
% 3.83/1.87      ! [A: pi,B: pi,A2: pi,B2: pi] :
% 3.83/1.87        ( ( ( product_Pair_pi_pi @ A @ B )
% 3.83/1.87          = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_78_Pair__inject,axiom,
% 3.83/1.87      ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 3.83/1.87        ( ( ( produc235456326_pi_pi @ A @ B )
% 3.83/1.87          = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 3.83/1.87       => ~ ( ( A = A2 )
% 3.83/1.87           => ( B != B2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_79_prod__cases,axiom,
% 3.83/1.87      ! [P: produc1834551554reeRes > $o,P2: produc1834551554reeRes] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_80_prod__cases,axiom,
% 3.83/1.87      ! [P: produc53907987_pi_pi > $o,P2: produc53907987_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_81_prod__cases,axiom,
% 3.83/1.87      ! [P: produc405342261i_name > $o,P2: produc405342261i_name] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_82_prod__cases,axiom,
% 3.83/1.87      ! [P: produc629157763_pi_pi > $o,P2: produc629157763_pi_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_83_prod__cases,axiom,
% 3.83/1.87      ! [P: produc1462499409ion_pi > $o,P2: produc1462499409ion_pi] :
% 3.83/1.87        ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_84_prod__cases,axiom,
% 3.83/1.87      ! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
% 3.83/1.87        ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_85_prod__cases,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > $o,P2: produc1141751126_pi_pi] :
% 3.83/1.87        ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 3.83/1.87       => ( P @ P2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_86_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc1834551554reeRes] :
% 3.83/1.87      ? [X3: name > noption_pi,Y3: late_freeRes] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_87_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc53907987_pi_pi] :
% 3.83/1.87      ? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_88_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc405342261i_name] :
% 3.83/1.87      ? [X3: name > noption_pi,Y3: name] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc540578151i_name @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_89_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc629157763_pi_pi] :
% 3.83/1.87      ? [X3: name > noption_pi,Y3: pi] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_90_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc1462499409ion_pi] :
% 3.83/1.87      ? [X3: name > noption_pi,Y3: name > noption_pi] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_91_surj__pair,axiom,
% 3.83/1.87      ! [P2: product_prod_pi_pi] :
% 3.83/1.87      ? [X3: pi,Y3: pi] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_92_surj__pair,axiom,
% 3.83/1.87      ! [P2: produc1141751126_pi_pi] :
% 3.83/1.87      ? [X3: name,Y3: product_prod_pi_pi] :
% 3.83/1.87        ( P2
% 3.83/1.87        = ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_93_pi_Oinject_I7_J,axiom,
% 3.83/1.87      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.83/1.87        ( ( ( par @ X2 @ X1 )
% 3.83/1.87          = ( par @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_94_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 3.83/1.87        ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.83/1.87          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_95_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: late_freeRes,Y: name] :
% 3.83/1.87        ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.83/1.87          & ( fresh_name_name @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_96_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: late_freeRes,Y: pi] :
% 3.83/1.87        ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_1641682979reeRes @ A @ X )
% 3.83/1.87          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_97_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: late_freeRes] :
% 3.83/1.87        ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X )
% 3.83/1.87          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_98_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: name] :
% 3.83/1.87        ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X )
% 3.83/1.87          & ( fresh_name_name @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_99_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: pi] :
% 3.83/1.87        ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X )
% 3.83/1.87          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_100_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: late_freeRes] :
% 3.83/1.87        ( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_pi @ A @ X )
% 3.83/1.87          & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_101_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: name] :
% 3.83/1.87        ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_pi @ A @ X )
% 3.83/1.87          & ( fresh_name_name @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_102_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: pi] :
% 3.83/1.87        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_pi @ A @ X )
% 3.83/1.87          & ( fresh_name_pi @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_103_fresh__prod,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 3.83/1.87        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X )
% 3.83/1.87          & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_104_substTrans,axiom,
% 3.83/1.87      ! [B: name,P: pi,A: name,C: name] :
% 3.83/1.87        ( ( fresh_name_pi @ B @ P )
% 3.83/1.87       => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 3.83/1.87          = ( subs @ P @ A @ C ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_105_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 3.83/1.87        ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_106_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_107_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: name] :
% 3.83/1.87        ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_108_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: pi] :
% 3.83/1.87        ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_109_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 3.83/1.87        ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_110_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: pi] :
% 3.83/1.87        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_name_pi @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_111_fresh__prodD_I1_J,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 3.83/1.87        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_name_name @ A @ X ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_112_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 3.83/1.87        ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 3.83/1.87       => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_113_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_114_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: name] :
% 3.83/1.87        ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 3.83/1.87       => ( fresh_name_name @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_115_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: pi] :
% 3.83/1.87        ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_name_pi @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_116_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 3.83/1.87        ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_117_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: pi] :
% 3.83/1.87        ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_name_pi @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_118_fresh__prodD_I2_J,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: product_prod_pi_pi] :
% 3.83/1.87        ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 3.83/1.87       => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_119_Bound_Ohyps_I1_J,axiom,
% 3.83/1.87      late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ aa @ y @ pxQ ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_120__092_060open_062_060_092_060nu_062x_062_IP_A_092_060parallel_062_AQ_J_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_A_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_092_060close_062,axiom,
% 3.83/1.87      late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ ( res @ x @ ( par @ p2 @ q ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_121_cPar1_Ohyps,axiom,
% 3.83/1.87      late_transitions @ p @ ( late_BoundR @ aa @ y @ p2 ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_122__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062y_092_060guillemotright_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 3.83/1.87      late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ aa @ y @ ( par @ p2 @ q ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_123_freshBoundDerivative_I2_J,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87         => ( ( Y != X )
% 3.83/1.87           => ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_124_freshResidual,axiom,
% 3.83/1.87      ! [P: pi,Rs: late_residual,X: name] :
% 3.83/1.87        ( ( late_transitions @ P @ Rs )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87         => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_125_parCasesB,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 3.83/1.87        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87           => ( ! [P4: pi] :
% 3.83/1.87                  ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 3.83/1.87                 => ( Prop @ ( par @ P4 @ Q ) ) )
% 3.83/1.87             => ( ! [Q2: pi] :
% 3.83/1.87                    ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.83/1.87                   => ( Prop @ ( par @ P @ Q2 ) ) )
% 3.83/1.87               => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_126_Late__Semantics_OPar2B,axiom,
% 3.83/1.87      ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 3.83/1.87        ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_127_Late__Semantics_OPar1B,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87         => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_128_Late__Semantics_OResB,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_717452603ubject @ Y @ A )
% 3.83/1.87         => ( ( Y != X )
% 3.83/1.87           => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_129_freshBoundDerivative_I1_J,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87         => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_130_transitions_OResB,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_717452603ubject @ Y @ A )
% 3.83/1.87         => ( ( Y != X )
% 3.83/1.87           => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87             => ( ( fresh_717452603ubject @ X @ A )
% 3.83/1.87               => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_131_transitions_OPar2B,axiom,
% 3.83/1.87      ! [Q: pi,A: late_subject,X: name,Q3: pi,P: pi] :
% 3.83/1.87        ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87           => ( ( fresh_717452603ubject @ X @ A )
% 3.83/1.87             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q3 ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_132_transitions_OPar1B,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87           => ( ( fresh_717452603ubject @ X @ A )
% 3.83/1.87             => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_133_parCasesB_H,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 3.83/1.87       => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Q4: pi] :
% 3.83/1.87              ( ( ( par @ P @ Q )
% 3.83/1.87                = ( par @ P5 @ Q4 ) )
% 3.83/1.87             => ( ( ( late_BoundR @ B @ Y @ P3 )
% 3.83/1.87                  = ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 3.83/1.87               => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 3.83/1.87                 => ( ( fresh_name_pi @ X3 @ P5 )
% 3.83/1.87                   => ( ( fresh_name_pi @ X3 @ Q4 )
% 3.83/1.87                     => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
% 3.83/1.87         => ~ ! [Q4: pi,A3: late_subject,X3: name,Q2: pi,P5: pi] :
% 3.83/1.87                ( ( ( par @ P @ Q )
% 3.83/1.87                  = ( par @ P5 @ Q4 ) )
% 3.83/1.87               => ( ( ( late_BoundR @ B @ Y @ P3 )
% 3.83/1.87                    = ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q2 ) ) )
% 3.83/1.87                 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 3.83/1.87                   => ( ( fresh_name_pi @ X3 @ P5 )
% 3.83/1.87                     => ( ( fresh_name_pi @ X3 @ Q4 )
% 3.83/1.87                       => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_134_simE_I1_J,axiom,
% 3.83/1.87      ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q3: pi] :
% 3.83/1.87        ( ( strong743114133lation @ P @ Rel @ Q )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87           => ? [P4: pi] :
% 3.83/1.87                ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 3.83/1.87                & ( strong2129052853vative @ P4 @ Q3 @ A @ X @ Rel ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_135_simCasesCont,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 3.83/1.87             => ( ( fresh_name_pi @ X3 @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ X3 @ Q )
% 3.83/1.87                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 3.83/1.87                   => ( ( fresh_1641682979reeRes @ X3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 3.83/1.87         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 3.83/1.87           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_136_simCasesCont,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 3.83/1.87             => ( ( fresh_name_pi @ X3 @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ X3 @ Q )
% 3.83/1.87                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 3.83/1.87                   => ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 3.83/1.87         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 3.83/1.87           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_137_simCasesCont,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 3.83/1.87             => ( ( fresh_name_pi @ X3 @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ X3 @ Q )
% 3.83/1.87                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 3.83/1.87                   => ( ( fresh_name_name @ X3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 3.83/1.87         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 3.83/1.87           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_138_simCasesCont,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [A3: late_subject,X3: name,Q2: pi] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q2 ) )
% 3.83/1.87             => ( ( fresh_name_pi @ X3 @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ X3 @ Q )
% 3.83/1.87                 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 3.83/1.87                   => ( ( fresh_name_pi @ X3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ Q2 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 3.83/1.87         => ( ! [Alpha: late_freeRes,Q2: pi] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 3.83/1.87           => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_139_parZeroLeft,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.83/1.87        ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 3.83/1.87       => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_140_parZeroRight,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.83/1.87        ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 3.83/1.87       => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_141_inputIneqTrans,axiom,
% 3.83/1.87      ! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 3.83/1.87       => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_142_resTauBoundTrans,axiom,
% 3.83/1.87      ! [X: name,P: pi,A: late_subject,Y: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_143_pi_Ofresh_I1_J,axiom,
% 3.83/1.87      ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_144_pi_Ofresh_I3_J,axiom,
% 3.83/1.87      ! [A: name,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 3.83/1.87        = ( fresh_name_pi @ A @ X1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_145_simps_I1_J,axiom,
% 3.83/1.87      ! [C: name,D: name] :
% 3.83/1.87        ( ( subs @ piNil @ C @ D )
% 3.83/1.87        = piNil ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_146_simps_I2_J,axiom,
% 3.83/1.87      ! [P: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( tau @ P ) @ C @ D )
% 3.83/1.87        = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_147_residual_Ofresh_I2_J,axiom,
% 3.83/1.87      ! [A: name,X2: late_freeRes,X1: pi] :
% 3.83/1.87        ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_1641682979reeRes @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_148_inputFreeTrans,axiom,
% 3.83/1.87      ! [A: name,X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_149_residual_Oinject_I2_J,axiom,
% 3.83/1.87      ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 3.83/1.87        ( ( ( late_FreeR @ X2 @ X1 )
% 3.83/1.87          = ( late_FreeR @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_150_nilSim_I2_J,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 3.83/1.87        ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_151_nilSim_I1_J,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.83/1.87        ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_152_pi_Odistinct_I3_J,axiom,
% 3.83/1.87      ! [Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( tau @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_153_pi_Odistinct_I5_J,axiom,
% 3.83/1.87      ! [Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_154_pi_Odistinct_I35_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_155_pi_Oinject_I2_J,axiom,
% 3.83/1.87      ! [X1: pi,Y1: pi] :
% 3.83/1.87        ( ( ( tau @ X1 )
% 3.83/1.87          = ( tau @ Y1 ) )
% 3.83/1.87        = ( X1 = Y1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_156_resInputFreeTrans,axiom,
% 3.83/1.87      ! [X: name,A: name,Y: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha2 @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_157_residual_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [Subject: late_subject,Name3: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 3.83/1.87        ( ( late_BoundR @ Subject @ Name3 @ Pi3 )
% 3.83/1.87       != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_158_residual_Oinducts,axiom,
% 3.83/1.87      ! [P: late_residual > $o,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_159_pi_Odistinct_I57_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_160_pi_Odistinct_I55_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_161_pi_Odistinct_I45_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_162_pi_Odistinct_I43_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_163_nilCases_H,axiom,
% 3.83/1.87      ! [Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ piNil @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_164_zeroTrans,axiom,
% 3.83/1.87      ! [Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ piNil @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_165_pi_Odistinct_I15_J,axiom,
% 3.83/1.87      ! [Name: name,Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_166_pi_Odistinct_I13_J,axiom,
% 3.83/1.87      ! [Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_167_nilSimRight,axiom,
% 3.83/1.87      ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_168_ResF,axiom,
% 3.83/1.87      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( ( fresh_1641682979reeRes @ Y @ Alpha2 )
% 3.83/1.87         => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha2 @ ( res @ Y @ P3 ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_169_resCasesF_H,axiom,
% 3.83/1.87      ! [X: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 3.83/1.87              ( ( ( res @ X @ P )
% 3.83/1.87                = ( res @ Y3 @ P5 ) )
% 3.83/1.87             => ( ( ( late_FreeR @ Alpha2 @ P3 )
% 3.83/1.87                  = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 3.83/1.87               => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 3.83/1.87                 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_170_resCasesF,axiom,
% 3.83/1.87      ! [X: name,P: pi,Alpha2: late_freeRes,XP: pi,F: pi > $o] :
% 3.83/1.87        ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha2 @ XP ) )
% 3.83/1.87       => ( ! [P4: pi] :
% 3.83/1.87              ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 3.83/1.87             => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 3.83/1.87               => ( F @ ( res @ X @ P4 ) ) ) )
% 3.83/1.87         => ( F @ XP ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_171_Par1F,axiom,
% 3.83/1.87      ! [P: pi,Alpha2: late_freeRes,P3: pi,Q: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P3 @ Q ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_172_Par2F,axiom,
% 3.83/1.87      ! [Q: pi,Alpha2: late_freeRes,Q3: pi,P: pi] :
% 3.83/1.87        ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.83/1.87       => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha2 @ ( par @ P @ Q3 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_173_freshFreeDerivative_I1_J,axiom,
% 3.83/1.87      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87         => ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_174_freshFreeDerivative_I2_J,axiom,
% 3.83/1.87      ! [P: pi,Alpha2: late_freeRes,P3: pi,Y: name] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87         => ( fresh_name_pi @ Y @ P3 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_175_simE_I2_J,axiom,
% 3.83/1.87      ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha2: late_freeRes,Q3: pi] :
% 3.83/1.87        ( ( strong743114133lation @ P @ Rel @ Q )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.83/1.87         => ? [P4: pi] :
% 3.83/1.87              ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P4 ) )
% 3.83/1.87              & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q3 ) @ Rel ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_176_resTrans_I2_J,axiom,
% 3.83/1.87      ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_177_simCases,axiom,
% 3.83/1.87      ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 3.83/1.87        ( ! [A3: late_subject,Y3: name,Q2: pi] :
% 3.83/1.87            ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 3.83/1.87           => ( ( fresh_name_pi @ Y3 @ P )
% 3.83/1.87             => ? [P6: pi] :
% 3.83/1.87                  ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 3.83/1.87                  & ( strong2129052853vative @ P6 @ Q2 @ A3 @ Y3 @ Rel ) ) ) )
% 3.83/1.87       => ( ! [Alpha: late_freeRes,Q2: pi] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87             => ? [P6: pi] :
% 3.83/1.87                  ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) )
% 3.83/1.87         => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_178_simulation__def,axiom,
% 3.83/1.87      ( strong743114133lation
% 3.83/1.87      = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 3.83/1.87            ( ! [A5: late_subject,X4: name,Q6: pi] :
% 3.83/1.87                ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 3.83/1.87                  & ( fresh_name_pi @ X4 @ P7 ) )
% 3.83/1.87               => ? [P8: pi] :
% 3.83/1.87                    ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 3.83/1.87                    & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 3.83/1.87            & ! [Alpha3: late_freeRes,Q6: pi] :
% 3.83/1.87                ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 3.83/1.87               => ? [P8: pi] :
% 3.83/1.87                    ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_179_tauBoundTrans,axiom,
% 3.83/1.87      ! [P: pi,A: late_subject,X: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_180_resZeroTrans,axiom,
% 3.83/1.87      ! [X: name,Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_181_residual_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_182_residual_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_183_residual_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 3.83/1.87            ( ( fresh_name_name @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_184_residual_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 3.83/1.87            ( ( fresh_name_pi @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_185_residual_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_186_residual_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_187_residual_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: name] :
% 3.83/1.87            ( ( fresh_name_name @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_188_residual_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.83/1.87        ( ! [Subject2: late_subject,Name4: name,Pi4: pi,Z2: pi] :
% 3.83/1.87            ( ( fresh_name_pi @ Name4 @ Z2 )
% 3.83/1.87           => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 3.83/1.87             => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87       => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 3.83/1.87         => ( P @ Z @ Residual ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_189_resSimCases,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [Q2: pi,A3: name] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 3.83/1.87             => ( ( A3 != X )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 3.83/1.87         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 3.83/1.87               => ( ( fresh_717452603ubject @ X @ A3 )
% 3.83/1.87                 => ( ( X != Y3 )
% 3.83/1.87                   => ( ( fresh_1641682979reeRes @ Y3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 3.83/1.87           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 3.83/1.87                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.83/1.87                   => ? [P6: pi] :
% 3.83/1.87                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 3.83/1.87             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_190_resSimCases,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [Q2: pi,A3: name] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 3.83/1.87             => ( ( A3 != X )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 3.83/1.87         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 3.83/1.87               => ( ( fresh_717452603ubject @ X @ A3 )
% 3.83/1.87                 => ( ( X != Y3 )
% 3.83/1.87                   => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 3.83/1.87           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 3.83/1.87                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.83/1.87                   => ? [P6: pi] :
% 3.83/1.87                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 3.83/1.87             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_191_resSimCases,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [Q2: pi,A3: name] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 3.83/1.87             => ( ( A3 != X )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 3.83/1.87         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 3.83/1.87               => ( ( fresh_717452603ubject @ X @ A3 )
% 3.83/1.87                 => ( ( X != Y3 )
% 3.83/1.87                   => ( ( fresh_name_name @ Y3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 3.83/1.87           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 3.83/1.87                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.83/1.87                   => ? [P6: pi] :
% 3.83/1.87                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 3.83/1.87             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_192_resSimCases,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 3.83/1.87        ( ( eqvt_pi @ Rel )
% 3.83/1.87       => ( ! [Q2: pi,A3: name] :
% 3.83/1.87              ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q2 ) )
% 3.83/1.87             => ( ( A3 != X )
% 3.83/1.87               => ? [P6: pi] :
% 3.83/1.87                    ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 3.83/1.87                    & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q2 ) @ Rel ) ) ) )
% 3.83/1.87         => ( ! [Q2: pi,A3: late_subject,Y3: name] :
% 3.83/1.87                ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q2 ) )
% 3.83/1.87               => ( ( fresh_717452603ubject @ X @ A3 )
% 3.83/1.87                 => ( ( X != Y3 )
% 3.83/1.87                   => ( ( fresh_name_pi @ Y3 @ C3 )
% 3.83/1.87                     => ? [P6: pi] :
% 3.83/1.87                          ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 3.83/1.87                          & ( strong2129052853vative @ P6 @ ( res @ X @ Q2 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 3.83/1.87           => ( ! [Q2: pi,Alpha: late_freeRes] :
% 3.83/1.87                  ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.83/1.87                 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.83/1.87                   => ? [P6: pi] :
% 3.83/1.87                        ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P6 ) )
% 3.83/1.87                        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q2 ) ) @ Rel ) ) ) )
% 3.83/1.87             => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_193_resInputBoundOutputTrans,axiom,
% 3.83/1.87      ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_194_resTauOutputTrans,axiom,
% 3.83/1.87      ! [X: name,P: pi,A: name,B: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_195_residual_Ofresh_I1_J,axiom,
% 3.83/1.87      ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 3.83/1.87        ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.83/1.87        = ( ( fresh_717452603ubject @ A @ X32 )
% 3.83/1.87          & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_196_Tau,axiom,
% 3.83/1.87      ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_197_tauCases_H,axiom,
% 3.83/1.87      ! [P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( tau @ P ) @ Rs )
% 3.83/1.87       => ~ ! [P5: pi] :
% 3.83/1.87              ( ( ( tau @ P )
% 3.83/1.87                = ( tau @ P5 ) )
% 3.83/1.87             => ( Rs
% 3.83/1.87               != ( late_FreeR @ late_TauR @ P5 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_198_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.83/1.87      ! [X2: name,X1: name,Y2: name,Y1: name] :
% 3.83/1.87        ( ( ( late_OutputR @ X2 @ X1 )
% 3.83/1.87          = ( late_OutputR @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_199_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.83/1.87      ! [X1: name,Y1: name] :
% 3.83/1.87        ( ( ( late_BoundOutputS @ X1 )
% 3.83/1.87          = ( late_BoundOutputS @ Y1 ) )
% 3.83/1.87        = ( X1 = Y1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_200_subject_Ofresh_I2_J,axiom,
% 3.83/1.87      ! [A: name,X1: name] :
% 3.83/1.87        ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 3.83/1.87        = ( fresh_name_name @ A @ X1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_201_freeRes_Ofresh_I1_J,axiom,
% 3.83/1.87      ! [A: name,X2: name,X1: name] :
% 3.83/1.87        ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X2 )
% 3.83/1.87          & ( fresh_name_name @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_202_freeRes_Ofresh_I2_J,axiom,
% 3.83/1.87      ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_203_pi_Ofresh_I9_J,axiom,
% 3.83/1.87      ! [A: name,X1: name,X2: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 3.83/1.87        = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_204_pi_Ofresh_I4_J,axiom,
% 3.83/1.87      ! [A: name,X32: name,X1: name,X2: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X32 )
% 3.83/1.87          & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_205_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name] :
% 3.83/1.87        ( ( late_OutputR @ Name12 @ Name22 )
% 3.83/1.87       != late_TauR ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_206_abs__fun__eq1,axiom,
% 3.83/1.87      ! [A: name,X: name,Y: name] :
% 3.83/1.87        ( ( ( abs_fun_name_name @ A @ X )
% 3.83/1.87          = ( abs_fun_name_name @ A @ Y ) )
% 3.83/1.87        = ( X = Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_207_abs__fun__eq1,axiom,
% 3.83/1.87      ! [A: name,X: produc1141751126_pi_pi,Y: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( ( abs_fu385186459_pi_pi @ A @ X )
% 3.83/1.87          = ( abs_fu385186459_pi_pi @ A @ Y ) )
% 3.83/1.87        = ( X = Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_208_abs__fun__eq1,axiom,
% 3.83/1.87      ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 3.83/1.87        ( ( ( abs_fu681348580reeRes @ A @ X )
% 3.83/1.87          = ( abs_fu681348580reeRes @ A @ Y ) )
% 3.83/1.87        = ( X = Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_209_abs__fun__eq1,axiom,
% 3.83/1.87      ! [A: name,X: pi,Y: pi] :
% 3.83/1.87        ( ( ( abs_fun_name_pi @ A @ X )
% 3.83/1.87          = ( abs_fun_name_pi @ A @ Y ) )
% 3.83/1.87        = ( X = Y ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_210_freeRes_Oinducts,axiom,
% 3.83/1.87      ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 3.83/1.87        ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 3.83/1.87       => ( ( P @ late_TauR )
% 3.83/1.87         => ( P @ FreeRes3 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_211_pi_Oinject_I8_J,axiom,
% 3.83/1.87      ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 3.83/1.87        ( ( ( res @ X1 @ X2 )
% 3.83/1.87          = ( res @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.83/1.87          = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_212_residual_Oinject_I1_J,axiom,
% 3.83/1.87      ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 3.83/1.87        ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 3.83/1.87          = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X32 = Y32 )
% 3.83/1.87          & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.83/1.87            = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_213_name__fresh__abs,axiom,
% 3.83/1.87      ! [B: name,A: name,X: late_freeRes] :
% 3.83/1.87        ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_214_name__fresh__abs,axiom,
% 3.83/1.87      ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_215_name__fresh__abs,axiom,
% 3.83/1.87      ! [B: name,A: name,X: name] :
% 3.83/1.87        ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_name_name @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_216_name__fresh__abs,axiom,
% 3.83/1.87      ! [B: name,A: name,X: pi] :
% 3.83/1.87        ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_217_abs__fresh_I1_J,axiom,
% 3.83/1.87      ! [B: name,A: name,X: late_freeRes] :
% 3.83/1.87        ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_218_abs__fresh_I1_J,axiom,
% 3.83/1.87      ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 3.83/1.87        ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_219_abs__fresh_I1_J,axiom,
% 3.83/1.87      ! [B: name,A: name,X: name] :
% 3.83/1.87        ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_name_name @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_220_abs__fresh_I1_J,axiom,
% 3.83/1.87      ! [B: name,A: name,X: pi] :
% 3.83/1.87        ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.83/1.87        = ( ( B = A )
% 3.83/1.87          | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_221_pi_Oinject_I3_J,axiom,
% 3.83/1.87      ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 3.83/1.87        ( ( ( input @ X32 @ X1 @ X2 )
% 3.83/1.87          = ( input @ Y32 @ Y1 @ Y2 ) )
% 3.83/1.87        = ( ( X32 = Y32 )
% 3.83/1.87          & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.83/1.87            = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_222_Open,axiom,
% 3.83/1.87      ! [P: pi,A: name,B: name,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.83/1.87       => ( ( A != B )
% 3.83/1.87         => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_223_resCases_H,axiom,
% 3.83/1.87      ! [X: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 3.83/1.87       => ( ! [P5: pi,A3: name,B3: name] :
% 3.83/1.87              ( ( ( res @ X @ P )
% 3.83/1.87                = ( res @ B3 @ P5 ) )
% 3.83/1.87             => ! [P4: pi] :
% 3.83/1.87                  ( ( Rs
% 3.83/1.87                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 3.83/1.87                 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 3.83/1.87                   => ( A3 = B3 ) ) ) )
% 3.83/1.87         => ( ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 3.83/1.87                ( ( ( res @ X @ P )
% 3.83/1.87                  = ( res @ Y3 @ P5 ) )
% 3.83/1.87               => ( ( Rs
% 3.83/1.87                    = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 3.83/1.87                 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 3.83/1.87                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.83/1.87                     => ( ( Y3 != X3 )
% 3.83/1.87                       => ( ( fresh_name_pi @ X3 @ P5 )
% 3.83/1.87                         => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
% 3.83/1.87           => ~ ! [P5: pi,Alpha: late_freeRes,P4: pi,Y3: name] :
% 3.83/1.87                  ( ( ( res @ X @ P )
% 3.83/1.87                    = ( res @ Y3 @ P5 ) )
% 3.83/1.87                 => ( ( Rs
% 3.83/1.87                      = ( late_FreeR @ Alpha @ ( res @ Y3 @ P4 ) ) )
% 3.83/1.87                   => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha @ P4 ) )
% 3.83/1.87                     => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_224_resCasesB_H,axiom,
% 3.83/1.87      ! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
% 3.83/1.87       => ( ! [P5: pi,A3: name,B3: name] :
% 3.83/1.87              ( ( ( res @ X5 @ P )
% 3.83/1.87                = ( res @ B3 @ P5 ) )
% 3.83/1.87             => ! [P4: pi] :
% 3.83/1.87                  ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 3.83/1.87                    = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P4 ) )
% 3.83/1.87                 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) )
% 3.83/1.87                   => ( A3 = B3 ) ) ) )
% 3.83/1.87         => ~ ! [P5: pi,A3: late_subject,X3: name,P4: pi,Y3: name] :
% 3.83/1.87                ( ( ( res @ X5 @ P )
% 3.83/1.87                  = ( res @ Y3 @ P5 ) )
% 3.83/1.87               => ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 3.83/1.87                    = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P4 ) ) )
% 3.83/1.87                 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X3 @ P4 ) )
% 3.83/1.87                   => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.83/1.87                     => ( ( Y3 != X3 )
% 3.83/1.87                       => ( ( fresh_name_pi @ X3 @ P5 )
% 3.83/1.87                         => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_225_tauOutputTrans,axiom,
% 3.83/1.87      ! [P: pi,A: name,B: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_226_inputBoundOutputTrans,axiom,
% 3.83/1.87      ! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_227_tauCases,axiom,
% 3.83/1.87      ! [P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 3.83/1.87        ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( ( ( Alpha2 = late_TauR )
% 3.83/1.87           => ( ( P = P3 )
% 3.83/1.87             => ( Prop @ late_TauR @ P ) ) )
% 3.83/1.87         => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_228_transitions_OClose2,axiom,
% 3.83/1.87      ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87           => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87             => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ Y @ Q )
% 3.83/1.87                 => ( ( X != A )
% 3.83/1.87                   => ( ( fresh_name_pi @ X @ P3 )
% 3.83/1.87                     => ( ( Y != A )
% 3.83/1.87                       => ( ( fresh_name_pi @ Y @ Q3 )
% 3.83/1.87                         => ( ( X != Y )
% 3.83/1.87                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_229_transitions_OClose1,axiom,
% 3.83/1.87      ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87           => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87             => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87               => ( ( fresh_name_pi @ Y @ Q )
% 3.83/1.87                 => ( ( X != A )
% 3.83/1.87                   => ( ( fresh_name_pi @ X @ Q3 )
% 3.83/1.87                     => ( ( Y != A )
% 3.83/1.87                       => ( ( fresh_name_pi @ Y @ P3 )
% 3.83/1.87                         => ( ( X != Y )
% 3.83/1.87                           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_230_Late__Semantics_OClose2,axiom,
% 3.83/1.87      ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ Y @ Q )
% 3.83/1.87           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q3 @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_231_Late__Semantics_OClose1,axiom,
% 3.83/1.87      ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ Y @ P )
% 3.83/1.87           => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q3 ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_232_name__fresh,axiom,
% 3.83/1.87      ( fresh_name_name
% 3.83/1.87      = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_233_subject_Ofresh_I1_J,axiom,
% 3.83/1.87      ! [A: name,X1: name] :
% 3.83/1.87        ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 3.83/1.87        = ( fresh_name_name @ A @ X1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_234_subject_Oinducts,axiom,
% 3.83/1.87      ! [P: late_subject > $o,Subject: late_subject] :
% 3.83/1.87        ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 3.83/1.87       => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 3.83/1.87         => ( P @ Subject ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_235_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [Name3: name,Name: name] :
% 3.83/1.87        ( ( late_InputS @ Name3 )
% 3.83/1.87       != ( late_BoundOutputS @ Name ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_236_Late__Semantics_OInput,axiom,
% 3.83/1.87      ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_237_transitions_OInput,axiom,
% 3.83/1.87      ! [X: name,A: name,P: pi] :
% 3.83/1.87        ( ( X != A )
% 3.83/1.87       => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_238_inputCases_H,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ~ ! [X3: name,A3: name,P5: pi] :
% 3.83/1.87              ( ( ( A = A3 )
% 3.83/1.87                & ( ( abs_fun_name_pi @ B @ P )
% 3.83/1.87                  = ( abs_fun_name_pi @ X3 @ P5 ) ) )
% 3.83/1.87             => ( ( Rs
% 3.83/1.87                  = ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P5 ) )
% 3.83/1.87               => ( X3 = A3 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_239_Late__Semantics_OComm1,axiom,
% 3.83/1.87      ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 3.83/1.87         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_240_Late__Semantics_OComm2,axiom,
% 3.83/1.87      ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 3.83/1.87         => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_241_transitions_OComm2,axiom,
% 3.83/1.87      ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87           => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87             => ( ( X != A )
% 3.83/1.87               => ( ( X != B )
% 3.83/1.87                 => ( ( fresh_name_pi @ X @ P3 )
% 3.83/1.87                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q3 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_242_transitions_OComm1,axiom,
% 3.83/1.87      ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q3: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.83/1.87       => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q3 ) )
% 3.83/1.87         => ( ( fresh_name_pi @ X @ P )
% 3.83/1.87           => ( ( fresh_name_pi @ X @ Q )
% 3.83/1.87             => ( ( X != A )
% 3.83/1.87               => ( ( X != B )
% 3.83/1.87                 => ( ( fresh_name_pi @ X @ Q3 )
% 3.83/1.87                   => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q3 ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_243_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.83/1.87      ! [X1: name,Y1: name] :
% 3.83/1.87        ( ( ( late_InputS @ X1 )
% 3.83/1.87          = ( late_InputS @ Y1 ) )
% 3.83/1.87        = ( X1 = Y1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_244_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.83/1.87      ! [X2: name,Y2: name] :
% 3.83/1.87        ( ( ( late_BoundOutputS @ X2 )
% 3.83/1.87          = ( late_BoundOutputS @ Y2 ) )
% 3.83/1.87        = ( X2 = Y2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_245_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.83/1.87      ! [X11: name,X12: name,Y11: name,Y12: name] :
% 3.83/1.87        ( ( ( late_OutputR @ X11 @ X12 )
% 3.83/1.87          = ( late_OutputR @ Y11 @ Y12 ) )
% 3.83/1.87        = ( ( X11 = Y11 )
% 3.83/1.87          & ( X12 = Y12 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_246_freeRes_Oexhaust,axiom,
% 3.83/1.87      ! [Y: late_freeRes] :
% 3.83/1.87        ( ! [X112: name,X122: name] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( late_OutputR @ X112 @ X122 ) )
% 3.83/1.87       => ( Y = late_TauR ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_247_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [X11: name,X12: name] :
% 3.83/1.87        ( ( late_OutputR @ X11 @ X12 )
% 3.83/1.87       != late_TauR ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_248_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [X1: name,X2: name] :
% 3.83/1.87        ( ( late_InputS @ X1 )
% 3.83/1.87       != ( late_BoundOutputS @ X2 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_249_subject_Oexhaust,axiom,
% 3.83/1.87      ! [Y: late_subject] :
% 3.83/1.87        ( ! [X13: name] :
% 3.83/1.87            ( Y
% 3.83/1.87           != ( late_InputS @ X13 ) )
% 3.83/1.87       => ~ ! [X22: name] :
% 3.83/1.87              ( Y
% 3.83/1.87             != ( late_BoundOutputS @ X22 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_250_resOutputTauTrans,axiom,
% 3.83/1.87      ! [X: name,A: name,B: name,P: pi,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_251_resOutputInputTrans,axiom,
% 3.83/1.87      ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_252_resOutputOutputTrans,axiom,
% 3.83/1.87      ! [X: name,A: name,P: pi,B: name,Y: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_253_pi_Ofresh_I2_J,axiom,
% 3.83/1.87      ! [A: name,X32: name,X2: name,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X32 )
% 3.83/1.87          & ( fresh_name_name @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_254_pi_Odistinct_I31_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_255_pi_Odistinct_I29_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_256_pi_Odistinct_I21_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_257_pi_Odistinct_I1_J,axiom,
% 3.83/1.87      ! [Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_258_pi_Odistinct_I19_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( tau @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_259_pi_Oinject_I1_J,axiom,
% 3.83/1.87      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.83/1.87        ( ( ( output @ X32 @ X2 @ X1 )
% 3.83/1.87          = ( output @ Y32 @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X32 = Y32 )
% 3.83/1.87          & ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_260_resTrans_I1_J,axiom,
% 3.83/1.87      ! [X: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_261_outputBoundTrans,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,C: late_subject,X: name,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_262_nilSim_I3_J,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 3.83/1.87        ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_263_outputCases,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 3.83/1.87        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ( ( ( Alpha2
% 3.83/1.87              = ( late_OutputR @ A @ B ) )
% 3.83/1.87           => ( ( P = P3 )
% 3.83/1.87             => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 3.83/1.87         => ( Prop @ Alpha2 @ P3 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_264_outputCases_H,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ~ ! [A3: name,B3: name,P5: pi] :
% 3.83/1.87              ( ( ( A = A3 )
% 3.83/1.87                & ( B = B3 )
% 3.83/1.87                & ( P = P5 ) )
% 3.83/1.87             => ( Rs
% 3.83/1.87               != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_265_outputIneqTrans,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,C: name,D: name,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P3 ) )
% 3.83/1.87       => ~ ( ( A != C )
% 3.83/1.87            | ( B != D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_266_Output,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_267_outputTauTrans,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,P3: pi] :
% 3.83/1.87        ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_268_outputFreshTrans,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Alpha2: late_freeRes,P3: pi] :
% 3.83/1.87        ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.83/1.87       => ~ ( ( fresh_1641682979reeRes @ A @ Alpha2 )
% 3.83/1.87            | ( fresh_1641682979reeRes @ B @ Alpha2 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_269_simps_I3_J,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 3.83/1.87        = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_270_simps_I4_J,axiom,
% 3.83/1.87      ! [X: name,A: name,C: name,D: name,P: pi] :
% 3.83/1.87        ( ( X != A )
% 3.83/1.87       => ( ( X != C )
% 3.83/1.87         => ( ( X != D )
% 3.83/1.87           => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 3.83/1.87              = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_271_substInput,axiom,
% 3.83/1.87      ! [X: name,B: name,C: name,A: name,P: pi] :
% 3.83/1.87        ( ( X != B )
% 3.83/1.87       => ( ( X != C )
% 3.83/1.87         => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 3.83/1.87            = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_272_subst__name__def,axiom,
% 3.83/1.87      ( subst_name
% 3.83/1.87      = ( ^ [A5: name,B4: name,C4: name] : ( if_name @ ( A5 = B4 ) @ C4 @ A5 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_273_simps_I6_J,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 3.83/1.87        = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_274_simps_I5_J,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 3.83/1.87        = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_275_pi_Ofresh_I5_J,axiom,
% 3.83/1.87      ! [A: name,X32: name,X2: name,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X32 )
% 3.83/1.87          & ( fresh_name_name @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_276_pi_Ofresh_I6_J,axiom,
% 3.83/1.87      ! [A: name,X32: name,X2: name,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_name @ A @ X32 )
% 3.83/1.87          & ( fresh_name_name @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_277_matchCases,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.83/1.87        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ( ( ( late_transitions @ P @ Rs )
% 3.83/1.87           => ( ( A = B )
% 3.83/1.87             => ( F @ A @ A ) ) )
% 3.83/1.87         => ( F @ A @ B ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_278_matchTrans,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ( A = B ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_279_matchCases_H,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ~ ! [P5: pi] :
% 3.83/1.87              ( ( ( B = A )
% 3.83/1.87                & ( P = P5 ) )
% 3.83/1.87             => ~ ( late_transitions @ P5 @ Rs ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_280_mismatchCases,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.83/1.87        ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ( ( ( late_transitions @ P @ Rs )
% 3.83/1.87           => ( ( A != B )
% 3.83/1.87             => ( F @ A @ B ) ) )
% 3.83/1.87         => ( F @ A @ B ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_281_mismatchTrans,axiom,
% 3.83/1.87      ! [A: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_282_mismatchCases_H,axiom,
% 3.83/1.87      ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.83/1.87       => ~ ! [P5: pi,A3: name,B3: name] :
% 3.83/1.87              ( ( ( A = A3 )
% 3.83/1.87                & ( B = B3 )
% 3.83/1.87                & ( P = P5 ) )
% 3.83/1.87             => ( ( late_transitions @ P5 @ Rs )
% 3.83/1.87               => ( A3 = B3 ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_283_Match,axiom,
% 3.83/1.87      ! [P: pi,Rs: late_residual,B: name] :
% 3.83/1.87        ( ( late_transitions @ P @ Rs )
% 3.83/1.87       => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_284_Mismatch,axiom,
% 3.83/1.87      ! [P: pi,Rs: late_residual,A: name,B: name] :
% 3.83/1.87        ( ( late_transitions @ P @ Rs )
% 3.83/1.87       => ( ( A != B )
% 3.83/1.87         => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_285_pi_Odistinct_I67_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( match @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_286_pi_Odistinct_I75_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_287_pi_Odistinct_I65_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( match @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_288_pi_Odistinct_I73_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_289_pi_Odistinct_I49_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_290_pi_Odistinct_I51_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_291_pi_Odistinct_I7_J,axiom,
% 3.83/1.87      ! [Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_292_pi_Odistinct_I9_J,axiom,
% 3.83/1.87      ! [Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_293_pi_Odistinct_I37_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_294_pi_Odistinct_I39_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_295_pi_Oinject_I5_J,axiom,
% 3.83/1.87      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.83/1.87        ( ( ( mismatch @ X32 @ X2 @ X1 )
% 3.83/1.87          = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X32 = Y32 )
% 3.83/1.87          & ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_296_pi_Oinject_I4_J,axiom,
% 3.83/1.87      ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.83/1.87        ( ( ( match @ X32 @ X2 @ X1 )
% 3.83/1.87          = ( match @ Y32 @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X32 = Y32 )
% 3.83/1.87          & ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_297_pi_Odistinct_I61_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( match @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_298_pi_Odistinct_I23_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( match @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_299_pi_Odistinct_I25_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_300_matchNilLeft,axiom,
% 3.83/1.87      ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.83/1.87        ( ( A != B )
% 3.83/1.87       => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_301_mismatchNilLeft,axiom,
% 3.83/1.87      ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_302_pi_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                  ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.83/1.87                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.83/1.87                          ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_303_pi_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                  ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                    ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                      ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                        ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                          ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_304_pi_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: name] :
% 3.83/1.87                ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                  ( ( fresh_name_name @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                    ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                      ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.83/1.87                        ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.83/1.87                          ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 3.83/1.87                            ( ( fresh_name_name @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: name] :
% 3.83/1.87                              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_305_pi_Ostrong__induct,axiom,
% 3.83/1.87      ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: pi] :
% 3.83/1.87                ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                  ( ( fresh_name_pi @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                    ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                      ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.83/1.87                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.83/1.87                          ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                            ( ( fresh_name_pi @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: pi] :
% 3.83/1.87                              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_306_pi_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                  ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                    ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                      ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.83/1.87                        ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.83/1.87                          ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                            ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: late_freeRes] :
% 3.83/1.87                              ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_307_pi_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: produc1141751126_pi_pi > pi > $o,Z: produc1141751126_pi_pi,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: produc1141751126_pi_pi] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                  ( ( fresh_1376661020_pi_pi @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                    ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                      ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                        ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                          ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                            ( ( fresh_1376661020_pi_pi @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: produc1141751126_pi_pi] :
% 3.83/1.87                              ( ! [Za: produc1141751126_pi_pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_308_pi_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: name] :
% 3.83/1.87                ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                  ( ( fresh_name_name @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                    ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: name] :
% 3.83/1.87                      ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.83/1.87                        ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.83/1.87                          ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: name] :
% 3.83/1.87                            ( ( fresh_name_name @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: name] :
% 3.83/1.87                              ( ! [Za: name] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_309_pi_Ostrong__inducts,axiom,
% 3.83/1.87      ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 3.83/1.87        ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 3.83/1.87       => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87             => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87         => ( ! [Pi4: pi,Z2: pi] :
% 3.83/1.87                ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87               => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 3.83/1.87           => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                  ( ( fresh_name_pi @ Name23 @ Z2 )
% 3.83/1.87                 => ( ( fresh_name_name @ Name23 @ Name13 )
% 3.83/1.87                   => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi4 ) ) ) ) )
% 3.83/1.87             => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                    ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                   => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87               => ( ! [Name13: name,Name23: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                      ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                     => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi4 ) ) )
% 3.83/1.87                 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.83/1.87                        ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                       => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                         => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                   => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.83/1.87                          ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.83/1.87                         => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.83/1.87                           => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.83/1.87                     => ( ! [Name4: name,Pi4: pi,Z2: pi] :
% 3.83/1.87                            ( ( fresh_name_pi @ Name4 @ Z2 )
% 3.83/1.87                           => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( res @ Name4 @ Pi4 ) ) ) )
% 3.83/1.87                       => ( ! [Pi4: pi,Z2: pi] :
% 3.83/1.87                              ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 3.83/1.87                             => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 3.83/1.87                         => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_310_pi_Ofresh_I10_J,axiom,
% 3.83/1.87      ! [A: name,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 3.83/1.87        = ( fresh_name_pi @ A @ X1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_311_pi_Ofresh_I7_J,axiom,
% 3.83/1.87      ! [A: name,X2: pi,X1: pi] :
% 3.83/1.87        ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 3.83/1.87        = ( ( fresh_name_pi @ A @ X2 )
% 3.83/1.87          & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_312_simps_I10_J,axiom,
% 3.83/1.87      ! [P: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( bang @ P ) @ C @ D )
% 3.83/1.87        = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_313_simps_I7_J,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,C: name,D: name] :
% 3.83/1.87        ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 3.83/1.87        = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_314_pi_Odistinct_I77_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_315_pi_Odistinct_I71_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_316_pi_Odistinct_I69_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( match @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_317_pi_Odistinct_I63_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( match @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_318_pi_Odistinct_I33_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_319_pi_Odistinct_I27_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_320_pi_Odistinct_I89_J,axiom,
% 3.83/1.87      ! [Name3: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( res @ Name3 @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_321_pi_Odistinct_I87_J,axiom,
% 3.83/1.87      ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.83/1.87        ( ( par @ Pi1 @ Pi2 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_322_pi_Odistinct_I59_J,axiom,
% 3.83/1.87      ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_323_pi_Odistinct_I17_J,axiom,
% 3.83/1.87      ! [Pi: pi] :
% 3.83/1.87        ( piNil
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_324_Sum2,axiom,
% 3.83/1.87      ! [Q: pi,Rs: late_residual,P: pi] :
% 3.83/1.87        ( ( late_transitions @ Q @ Rs )
% 3.83/1.87       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_325_Sum1,axiom,
% 3.83/1.87      ! [P: pi,Rs: late_residual,Q: pi] :
% 3.83/1.87        ( ( late_transitions @ P @ Rs )
% 3.83/1.87       => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_326_sumCases_H,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.83/1.87       => ( ~ ( late_transitions @ P @ Rs )
% 3.83/1.87         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_327_sumCases,axiom,
% 3.83/1.87      ! [P: pi,Q: pi,Rs: late_residual] :
% 3.83/1.87        ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.83/1.87       => ( ~ ( late_transitions @ P @ Rs )
% 3.83/1.87         => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_328_pi_Odistinct_I47_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Pi: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_329_pi_Odistinct_I81_J,axiom,
% 3.83/1.87      ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.83/1.87        ( ( sum @ Pi1 @ Pi2 )
% 3.83/1.87       != ( res @ Name @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_330_pi_Odistinct_I79_J,axiom,
% 3.83/1.87      ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( sum @ Pi1 @ Pi2 )
% 3.83/1.87       != ( par @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_331_pi_Odistinct_I83_J,axiom,
% 3.83/1.87      ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.83/1.87        ( ( sum @ Pi1 @ Pi2 )
% 3.83/1.87       != ( bang @ Pi ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_332_pi_Oinject_I6_J,axiom,
% 3.83/1.87      ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.83/1.87        ( ( ( sum @ X2 @ X1 )
% 3.83/1.87          = ( sum @ Y2 @ Y1 ) )
% 3.83/1.87        = ( ( X2 = Y2 )
% 3.83/1.87          & ( X1 = Y1 ) ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_333_pi_Oinject_I9_J,axiom,
% 3.83/1.87      ! [X1: pi,Y1: pi] :
% 3.83/1.87        ( ( ( bang @ X1 )
% 3.83/1.87          = ( bang @ Y1 ) )
% 3.83/1.87        = ( X1 = Y1 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(fact_334_pi_Odistinct_I41_J,axiom,
% 3.83/1.87      ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.83/1.87        ( ( tau @ Pi3 )
% 3.83/1.87       != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 3.83/1.87      ! [P: $o] :
% 3.83/1.87        ( ( P = $true )
% 3.83/1.87        | ( P = $false ) ) ).
% 3.83/1.87  
% 3.83/1.87  thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 3.83/1.87      ! [X: name,Y: name] :
% 3.83/1.87        ( ( if_name @ $false @ X @ Y )
% 3.83/1.87        = Y ) ).
% 3.83/1.87  
% 3.83/1.87  thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 3.83/1.87      ! [X: name,Y: name] :
% 3.83/1.87        ( ( if_name @ $true @ X @ Y )
% 3.83/1.87        = X ) ).
% 3.83/1.87  
% 3.83/1.87  thf(conj_0,conjecture,
% 3.83/1.87      member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ).
% 3.83/1.87  ------------------------
% 3.90/1.93  % (23539)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/2Mi)
% 3.90/1.93  % (23536)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/4Mi)
% 3.90/1.93  % (23541)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/18Mi)
% 3.90/1.93  % (23540)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/275Mi)
% 3.90/1.93  % (23537)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/27Mi)
% 3.90/1.93  % (23538)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/2Mi)
% 3.90/1.93  % (23535)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/183Mi)
% 3.90/1.93  % (23538)Instruction limit reached!
% 3.90/1.93  % (23538)------------------------------
% 3.90/1.93  % (23538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.93  % (23538)Termination reason: Unknown
% 3.90/1.93  % (23538)Termination phase: shuffling
% 3.90/1.93  % (23539)Instruction limit reached!
% 3.90/1.93  % (23539)------------------------------
% 3.90/1.93  % (23539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.93  % (23539)Termination reason: Unknown
% 3.90/1.93  % (23539)Termination phase: shuffling
% 3.90/1.93  
% 3.90/1.93  % (23539)Memory used [KB]: 1535
% 3.90/1.93  % (23539)Time elapsed: 0.004 s
% 3.90/1.93  % (23539)Instructions burned: 3 (million)
% 3.90/1.93  % (23539)------------------------------
% 3.90/1.93  % (23539)------------------------------
% 3.90/1.93  
% 3.90/1.93  % (23538)Memory used [KB]: 1535
% 3.90/1.93  % (23538)Time elapsed: 0.004 s
% 3.90/1.93  % (23538)Instructions burned: 2 (million)
% 3.90/1.93  % (23538)------------------------------
% 3.90/1.93  % (23538)------------------------------
% 3.90/1.93  % (23536)Instruction limit reached!
% 3.90/1.93  % (23536)------------------------------
% 3.90/1.93  % (23536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.93  % (23536)Termination reason: Unknown
% 3.90/1.93  % (23536)Termination phase: shuffling
% 3.90/1.93  
% 3.90/1.93  % (23536)Memory used [KB]: 1663
% 3.90/1.93  % (23536)Time elapsed: 0.005 s
% 3.90/1.93  % (23536)Instructions burned: 4 (million)
% 3.90/1.93  % (23536)------------------------------
% 3.90/1.93  % (23536)------------------------------
% 3.90/1.94  % (23541)Instruction limit reached!
% 3.90/1.94  % (23541)------------------------------
% 3.90/1.94  % (23541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.94  % (23541)Termination reason: Unknown
% 3.90/1.94  % (23541)Termination phase: shuffling
% 3.90/1.94  
% 3.90/1.94  % (23541)Memory used [KB]: 1918
% 3.90/1.94  % (23541)Time elapsed: 0.012 s
% 3.90/1.94  % (23541)Instructions burned: 18 (million)
% 3.90/1.94  % (23541)------------------------------
% 3.90/1.94  % (23541)------------------------------
% 3.90/1.94  % (23537)Instruction limit reached!
% 3.90/1.94  % (23537)------------------------------
% 3.90/1.94  % (23537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.94  % (23537)Termination reason: Unknown
% 3.90/1.94  % (23537)Termination phase: shuffling
% 3.90/1.94  
% 3.90/1.94  % (23537)Memory used [KB]: 2046
% 3.90/1.94  % (23537)Time elapsed: 0.018 s
% 3.90/1.94  % (23537)Instructions burned: 28 (million)
% 3.90/1.94  % (23537)------------------------------
% 3.90/1.94  % (23537)------------------------------
% 3.90/1.95  % (23544)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/15Mi)
% 3.90/1.95  % (23543)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/37Mi)
% 3.90/1.95  % (23542)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/3Mi)
% 3.90/1.95  % (23542)Instruction limit reached!
% 3.90/1.95  % (23542)------------------------------
% 3.90/1.95  % (23542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.95  % (23542)Termination reason: Unknown
% 3.90/1.95  % (23542)Termination phase: shuffling
% 3.90/1.95  
% 3.90/1.95  % (23542)Memory used [KB]: 1535
% 3.90/1.95  % (23542)Time elapsed: 0.004 s
% 3.90/1.95  % (23542)Instructions burned: 4 (million)
% 3.90/1.95  % (23542)------------------------------
% 3.90/1.95  % (23542)------------------------------
% 3.90/1.95  % (23545)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/3Mi)
% 3.90/1.96  % (23544)Instruction limit reached!
% 3.90/1.96  % (23544)------------------------------
% 3.90/1.96  % (23544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.96  % (23544)Termination reason: Unknown
% 3.90/1.96  % (23544)Termination phase: shuffling
% 3.90/1.96  
% 3.90/1.96  % (23544)Memory used [KB]: 1791
% 3.90/1.96  % (23544)Time elapsed: 0.011 s
% 3.90/1.96  % (23544)Instructions burned: 16 (million)
% 3.90/1.96  % (23544)------------------------------
% 3.90/1.96  % (23544)------------------------------
% 3.90/1.96  % (23545)Instruction limit reached!
% 3.90/1.96  % (23545)------------------------------
% 3.90/1.96  % (23545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.96  % (23545)Termination reason: Unknown
% 3.90/1.96  % (23545)Termination phase: shuffling
% 3.90/1.96  
% 3.90/1.96  % (23545)Memory used [KB]: 1535
% 3.90/1.96  % (23545)Time elapsed: 0.004 s
% 3.90/1.96  % (23545)Instructions burned: 4 (million)
% 3.90/1.96  % (23545)------------------------------
% 3.90/1.96  % (23545)------------------------------
% 3.90/1.96  % (23547)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/1041Mi)
% 3.90/1.97  % (23543)Instruction limit reached!
% 3.90/1.97  % (23543)------------------------------
% 3.90/1.97  % (23543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.97  % (23543)Termination reason: Unknown
% 3.90/1.97  % (23543)Termination phase: shuffling
% 3.90/1.97  
% 3.90/1.97  % (23543)Memory used [KB]: 2302
% 3.90/1.97  % (23543)Time elapsed: 0.021 s
% 3.90/1.97  % (23543)Instructions burned: 38 (million)
% 3.90/1.97  % (23543)------------------------------
% 3.90/1.97  % (23543)------------------------------
% 3.90/1.97  % (23548)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/7Mi)
% 3.90/1.97  % (23548)Instruction limit reached!
% 3.90/1.97  % (23548)------------------------------
% 3.90/1.97  % (23548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.97  % (23548)Termination reason: Unknown
% 3.90/1.97  % (23548)Termination phase: shuffling
% 3.90/1.97  
% 3.90/1.97  % (23548)Memory used [KB]: 1663
% 3.90/1.97  % (23548)Time elapsed: 0.006 s
% 3.90/1.97  % (23548)Instructions burned: 7 (million)
% 3.90/1.97  % (23548)------------------------------
% 3.90/1.97  % (23548)------------------------------
% 3.90/1.98  % (23550)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/3Mi)
% 3.90/1.98  % (23549)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/16Mi)
% 3.90/1.98  % (23550)Instruction limit reached!
% 3.90/1.98  % (23550)------------------------------
% 3.90/1.98  % (23550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.98  % (23550)Termination reason: Unknown
% 3.90/1.98  % (23550)Termination phase: shuffling
% 3.90/1.98  
% 3.90/1.98  % (23550)Memory used [KB]: 1535
% 3.90/1.98  % (23550)Time elapsed: 0.004 s
% 3.90/1.98  % (23550)Instructions burned: 4 (million)
% 3.90/1.98  % (23550)------------------------------
% 3.90/1.98  % (23550)------------------------------
% 3.90/1.99  % (23549)Instruction limit reached!
% 3.90/1.99  % (23549)------------------------------
% 3.90/1.99  % (23549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.99  % (23549)Termination reason: Unknown
% 3.90/1.99  % (23549)Termination phase: shuffling
% 3.90/1.99  
% 3.90/1.99  % (23549)Memory used [KB]: 1791
% 3.90/1.99  % (23549)Time elapsed: 0.011 s
% 3.90/1.99  % (23551)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/3Mi)
% 3.90/1.99  % (23549)Instructions burned: 16 (million)
% 3.90/1.99  % (23549)------------------------------
% 3.90/1.99  % (23549)------------------------------
% 3.90/1.99  % (23551)Instruction limit reached!
% 3.90/1.99  % (23551)------------------------------
% 3.90/1.99  % (23551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/1.99  % (23551)Termination reason: Unknown
% 3.90/1.99  % (23551)Termination phase: shuffling
% 3.90/1.99  
% 3.90/1.99  % (23551)Memory used [KB]: 1535
% 3.90/1.99  % (23551)Time elapsed: 0.004 s
% 3.90/1.99  % (23551)Instructions burned: 4 (million)
% 3.90/1.99  % (23551)------------------------------
% 3.90/1.99  % (23551)------------------------------
% 3.90/1.99  % (23552)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/7Mi)
% 3.90/2.00  % (23552)Instruction limit reached!
% 3.90/2.00  % (23552)------------------------------
% 3.90/2.00  % (23552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.00  % (23552)Termination reason: Unknown
% 3.90/2.00  % (23552)Termination phase: shuffling
% 3.90/2.00  
% 3.90/2.00  % (23552)Memory used [KB]: 1663
% 3.90/2.00  % (23552)Time elapsed: 0.006 s
% 3.90/2.00  % (23552)Instructions burned: 7 (million)
% 3.90/2.00  % (23552)------------------------------
% 3.90/2.00  % (23552)------------------------------
% 3.90/2.00  % (23553)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2999ds/3Mi)
% 3.90/2.00  % (23553)Instruction limit reached!
% 3.90/2.00  % (23553)------------------------------
% 3.90/2.00  % (23553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.00  % (23553)Termination reason: Unknown
% 3.90/2.00  % (23553)Termination phase: shuffling
% 3.90/2.00  
% 3.90/2.00  % (23553)Memory used [KB]: 1535
% 3.90/2.00  % (23553)Time elapsed: 0.004 s
% 3.90/2.00  % (23553)Instructions burned: 3 (million)
% 3.90/2.00  % (23553)------------------------------
% 3.90/2.00  % (23553)------------------------------
% 3.90/2.00  % (23554)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/4Mi)
% 3.90/2.01  % (23540)Refutation not found, incomplete strategy
% 3.90/2.01  % (23540)------------------------------
% 3.90/2.01  % (23540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.01  % (23540)Termination reason: Refutation not found, incomplete strategy
% 3.90/2.01  
% 3.90/2.01  
% 3.90/2.01  % (23540)Memory used [KB]: 7675
% 3.90/2.01  % (23540)Time elapsed: 0.083 s
% 3.90/2.01  % (23540)Instructions burned: 145 (million)
% 3.90/2.01  % (23540)------------------------------
% 3.90/2.01  % (23540)------------------------------
% 3.90/2.01  % (23554)Instruction limit reached!
% 3.90/2.01  % (23554)------------------------------
% 3.90/2.01  % (23554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.01  % (23554)Termination reason: Unknown
% 3.90/2.01  % (23554)Termination phase: shuffling
% 3.90/2.01  
% 3.90/2.01  % (23554)Memory used [KB]: 1535
% 3.90/2.01  % (23554)Time elapsed: 0.004 s
% 3.90/2.01  % (23554)Instructions burned: 4 (million)
% 3.90/2.01  % (23554)------------------------------
% 3.90/2.01  % (23554)------------------------------
% 3.90/2.01  % (23555)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/18Mi)
% 3.90/2.02  % (23556)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/710Mi)
% 3.90/2.02  % (23555)Instruction limit reached!
% 3.90/2.02  % (23555)------------------------------
% 3.90/2.02  % (23555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.02  % (23555)Termination reason: Unknown
% 3.90/2.02  % (23555)Termination phase: shuffling
% 3.90/2.02  
% 3.90/2.02  % (23555)Memory used [KB]: 1918
% 3.90/2.02  % (23555)Time elapsed: 0.013 s
% 3.90/2.02  % (23555)Instructions burned: 19 (million)
% 3.90/2.02  % (23555)------------------------------
% 3.90/2.02  % (23555)------------------------------
% 3.90/2.02  % (23557)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/6Mi)
% 3.90/2.02  % (23535)Instruction limit reached!
% 3.90/2.02  % (23535)------------------------------
% 3.90/2.02  % (23535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.02  % (23535)Termination reason: Unknown
% 3.90/2.02  % (23535)Termination phase: Property scanning
% 3.90/2.02  
% 3.90/2.02  % (23535)Memory used [KB]: 3582
% 3.90/2.02  % (23535)Time elapsed: 0.097 s
% 3.90/2.02  % (23535)Instructions burned: 183 (million)
% 3.90/2.02  % (23535)------------------------------
% 3.90/2.02  % (23535)------------------------------
% 3.90/2.02  % (23557)Instruction limit reached!
% 3.90/2.02  % (23557)------------------------------
% 3.90/2.02  % (23557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.90/2.02  % (23557)Termination reason: Unknown
% 3.90/2.02  % (23557)Termination phase: shuffling
% 3.90/2.02  
% 3.90/2.02  % (23557)Memory used [KB]: 1663
% 3.90/2.02  % (23557)Time elapsed: 0.006 s
% 3.90/2.02  % (23557)Instructions burned: 7 (million)
% 3.90/2.02  % (23557)------------------------------
% 3.90/2.02  % (23557)------------------------------
% 3.90/2.03  % (23558)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/902Mi)
% 3.90/2.03  % (23559)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/21Mi)
% 4.67/2.04  % (23559)Instruction limit reached!
% 4.67/2.04  % (23559)------------------------------
% 4.67/2.04  % (23559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.04  % (23559)Termination reason: Unknown
% 4.67/2.04  % (23559)Termination phase: shuffling
% 4.67/2.04  
% 4.67/2.04  % (23559)Memory used [KB]: 1918
% 4.67/2.04  % (23559)Time elapsed: 0.014 s
% 4.67/2.04  % (23559)Instructions burned: 21 (million)
% 4.67/2.04  % (23559)------------------------------
% 4.67/2.04  % (23559)------------------------------
% 4.67/2.04  % (23560)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/5Mi)
% 4.67/2.04  % (23561)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/6Mi)
% 4.67/2.04  % (23560)Instruction limit reached!
% 4.67/2.04  % (23560)------------------------------
% 4.67/2.04  % (23560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.04  % (23560)Termination reason: Unknown
% 4.67/2.04  % (23560)Termination phase: shuffling
% 4.67/2.04  
% 4.67/2.04  % (23560)Memory used [KB]: 1663
% 4.67/2.04  % (23560)Time elapsed: 0.005 s
% 4.67/2.04  % (23560)Instructions burned: 5 (million)
% 4.67/2.04  % (23560)------------------------------
% 4.67/2.04  % (23560)------------------------------
% 4.67/2.04  % (23562)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/377Mi)
% 4.67/2.04  % (23561)Instruction limit reached!
% 4.67/2.04  % (23561)------------------------------
% 4.67/2.04  % (23561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.04  % (23561)Termination reason: Unknown
% 4.67/2.04  % (23561)Termination phase: shuffling
% 4.67/2.04  
% 4.67/2.04  % (23561)Memory used [KB]: 1663
% 4.67/2.04  % (23561)Time elapsed: 0.005 s
% 4.67/2.04  % (23561)Instructions burned: 6 (million)
% 4.67/2.04  % (23561)------------------------------
% 4.67/2.04  % (23561)------------------------------
% 4.67/2.06  % (23563)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/779Mi)
% 4.67/2.06  % (23564)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/19Mi)
% 4.67/2.06  % (23565)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23404 for (2998ds/879Mi)
% 4.67/2.07  % (23564)Instruction limit reached!
% 4.67/2.07  % (23564)------------------------------
% 4.67/2.07  % (23564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.07  % (23564)Termination reason: Unknown
% 4.67/2.07  % (23564)Termination phase: shuffling
% 4.67/2.07  
% 4.67/2.07  % (23564)Memory used [KB]: 2046
% 4.67/2.07  % (23564)Time elapsed: 0.012 s
% 4.67/2.07  % (23564)Instructions burned: 19 (million)
% 4.67/2.07  % (23564)------------------------------
% 4.67/2.07  % (23564)------------------------------
% 4.67/2.09  % (23566)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23404 for (2997ds/17Mi)
% 4.67/2.10  % (23566)Instruction limit reached!
% 4.67/2.10  % (23566)------------------------------
% 4.67/2.10  % (23566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.10  % (23566)Termination reason: Unknown
% 4.67/2.10  % (23566)Termination phase: shuffling
% 4.67/2.10  
% 4.67/2.10  % (23566)Memory used [KB]: 1918
% 4.67/2.10  % (23566)Time elapsed: 0.012 s
% 4.67/2.10  % (23566)Instructions burned: 18 (million)
% 4.67/2.10  % (23566)------------------------------
% 4.67/2.10  % (23566)------------------------------
% 4.67/2.12  % (23567)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2997ds/3Mi)
% 4.67/2.13  % (23567)Instruction limit reached!
% 4.67/2.13  % (23567)------------------------------
% 4.67/2.13  % (23567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.67/2.13  % (23567)Termination reason: Unknown
% 4.67/2.13  % (23567)Termination phase: shuffling
% 4.67/2.13  
% 4.67/2.13  % (23567)Memory used [KB]: 1535
% 4.67/2.13  % (23567)Time elapsed: 0.005 s
% 4.67/2.13  % (23567)Instructions burned: 4 (million)
% 4.67/2.13  % (23567)------------------------------
% 4.67/2.13  % (23567)------------------------------
% 4.93/2.15  % (23568)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23404 for (2997ds/30Mi)
% 4.93/2.17  % (23568)Instruction limit reached!
% 4.93/2.17  % (23568)------------------------------
% 4.93/2.17  % (23568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.17  % (23568)Termination reason: Unknown
% 4.93/2.17  % (23568)Termination phase: shuffling
% 4.93/2.17  
% 4.93/2.17  % (23568)Memory used [KB]: 2046
% 4.93/2.17  % (23568)Time elapsed: 0.019 s
% 4.93/2.17  % (23568)Instructions burned: 31 (million)
% 4.93/2.17  % (23568)------------------------------
% 4.93/2.17  % (23568)------------------------------
% 4.93/2.19  % (23569)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23404 for (2997ds/127Mi)
% 4.93/2.19  % (23558)Refutation not found, incomplete strategy
% 4.93/2.19  % (23558)------------------------------
% 4.93/2.19  % (23558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.19  % (23558)Termination reason: Refutation not found, incomplete strategy
% 4.93/2.19  
% 4.93/2.19  
% 4.93/2.19  % (23558)Memory used [KB]: 9466
% 4.93/2.19  % (23558)Time elapsed: 0.168 s
% 4.93/2.19  % (23558)Instructions burned: 302 (million)
% 4.93/2.19  % (23558)------------------------------
% 4.93/2.19  % (23558)------------------------------
% 5.22/2.22  % (23570)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23404 for (2996ds/100Mi)
% 5.22/2.24  % (23562)Instruction limit reached!
% 5.22/2.24  % (23562)------------------------------
% 5.22/2.24  % (23562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.22/2.24  % (23562)Termination reason: Unknown
% 5.22/2.24  % (23562)Termination phase: Saturation
% 5.22/2.24  
% 5.22/2.24  % (23562)Memory used [KB]: 9083
% 5.22/2.24  % (23562)Time elapsed: 0.200 s
% 5.22/2.24  % (23562)Instructions burned: 377 (million)
% 5.22/2.24  % (23562)------------------------------
% 5.22/2.24  % (23562)------------------------------
% 5.22/2.26  % (23569)Instruction limit reached!
% 5.22/2.26  % (23569)------------------------------
% 5.22/2.26  % (23569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.22/2.26  % (23569)Termination reason: Unknown
% 5.22/2.26  % (23569)Termination phase: Property scanning
% 5.22/2.26  
% 5.22/2.26  % (23569)Memory used [KB]: 3582
% 5.22/2.26  % (23569)Time elapsed: 0.074 s
% 5.22/2.26  % (23569)Instructions burned: 128 (million)
% 5.22/2.26  % (23569)------------------------------
% 5.22/2.26  % (23569)------------------------------
% 5.22/2.26  % (23571)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_23404 for (2996ds/3Mi)
% 5.22/2.26  % (23571)Instruction limit reached!
% 5.22/2.26  % (23571)------------------------------
% 5.22/2.26  % (23571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.22/2.26  % (23571)Termination reason: Unknown
% 5.22/2.26  % (23571)Termination phase: shuffling
% 5.22/2.26  
% 5.22/2.26  % (23571)Memory used [KB]: 1535
% 5.22/2.26  % (23571)Time elapsed: 0.004 s
% 5.22/2.26  % (23571)Instructions burned: 4 (million)
% 5.22/2.26  % (23571)------------------------------
% 5.22/2.26  % (23571)------------------------------
% 5.22/2.27  % (23570)Instruction limit reached!
% 5.22/2.27  % (23570)------------------------------
% 5.22/2.27  % (23570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.22/2.27  % (23570)Termination reason: Unknown
% 5.22/2.27  % (23570)Termination phase: Property scanning
% 5.22/2.27  
% 5.22/2.27  % (23570)Memory used [KB]: 3198
% 5.22/2.27  % (23570)Time elapsed: 0.054 s
% 5.22/2.27  % (23570)Instructions burned: 100 (million)
% 5.22/2.27  % (23570)------------------------------
% 5.22/2.27  % (23570)------------------------------
% 5.22/2.28  % (23573)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_23404 for (2996ds/86Mi)
% 5.22/2.28  % (23572)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_23404 for (2996ds/20Mi)
% 5.22/2.29  % (23574)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_23404 for (2996ds/107Mi)
% 5.22/2.29  % (23572)Instruction limit reached!
% 5.22/2.29  % (23572)------------------------------
% 5.22/2.29  % (23572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.22/2.29  % (23572)Termination reason: Unknown
% 5.22/2.29  % (23572)Termination phase: shuffling
% 5.22/2.29  
% 5.22/2.29  % (23572)Memory used [KB]: 1918
% 5.22/2.29  % (23572)Time elapsed: 0.013 s
% 5.22/2.29  % (23572)Instructions burned: 20 (million)
% 5.22/2.29  % (23572)------------------------------
% 5.22/2.29  % (23572)------------------------------
% 5.77/2.31  % (23575)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_23404 for (2995ds/39Mi)
% 5.77/2.32  % (23573)Instruction limit reached!
% 5.77/2.32  % (23573)------------------------------
% 5.77/2.32  % (23573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.32  % (23573)Termination reason: Unknown
% 5.77/2.32  % (23573)Termination phase: Preprocessing 3
% 5.77/2.32  
% 5.77/2.32  % (23573)Memory used [KB]: 2814
% 5.77/2.32  % (23573)Time elapsed: 0.043 s
% 5.77/2.32  % (23573)Instructions burned: 87 (million)
% 5.77/2.32  % (23573)------------------------------
% 5.77/2.32  % (23573)------------------------------
% 5.77/2.33  % (23575)Instruction limit reached!
% 5.77/2.33  % (23575)------------------------------
% 5.77/2.33  % (23575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.33  % (23575)Termination reason: Unknown
% 5.77/2.33  % (23575)Termination phase: shuffling
% 5.77/2.33  
% 5.77/2.33  % (23575)Memory used [KB]: 2302
% 5.77/2.33  % (23575)Time elapsed: 0.023 s
% 5.77/2.33  % (23575)Instructions burned: 39 (million)
% 5.77/2.33  % (23575)------------------------------
% 5.77/2.33  % (23575)------------------------------
% 5.77/2.34  % (23576)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_23404 for (2995ds/448Mi)
% 5.77/2.35  % (23574)Instruction limit reached!
% 5.77/2.35  % (23574)------------------------------
% 5.77/2.35  % (23574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.35  % (23574)Termination reason: Unknown
% 5.77/2.35  % (23574)Termination phase: Preprocessing 3
% 5.77/2.35  
% 5.77/2.35  % (23574)Memory used [KB]: 3198
% 5.77/2.35  % (23574)Time elapsed: 0.061 s
% 5.77/2.35  % (23574)Instructions burned: 107 (million)
% 5.77/2.35  % (23574)------------------------------
% 5.77/2.35  % (23574)------------------------------
% 5.77/2.35  % (23577)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_23404 for (2995ds/46Mi)
% 5.77/2.37  % (23578)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_23404 for (2995ds/98Mi)
% 5.77/2.38  % (23577)Instruction limit reached!
% 5.77/2.38  % (23577)------------------------------
% 5.77/2.38  % (23577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.77/2.38  % (23577)Termination reason: Unknown
% 5.77/2.38  % (23577)Termination phase: Property scanning
% 5.77/2.38  
% 5.77/2.38  % (23577)Memory used [KB]: 2302
% 5.77/2.38  % (23577)Time elapsed: 0.028 s
% 5.77/2.38  % (23577)Instructions burned: 47 (million)
% 5.77/2.38  % (23577)------------------------------
% 5.77/2.38  % (23577)------------------------------
% 6.09/2.40  % (23579)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_23404 for (2994ds/507Mi)
% 6.09/2.42  % (23556)Instruction limit reached!
% 6.09/2.42  % (23556)------------------------------
% 6.09/2.42  % (23556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.42  % (23556)Termination reason: Unknown
% 6.09/2.42  % (23556)Termination phase: Saturation
% 6.09/2.42  
% 6.09/2.42  % (23556)Memory used [KB]: 8187
% 6.09/2.42  % (23556)Time elapsed: 0.402 s
% 6.09/2.42  % (23556)Instructions burned: 710 (million)
% 6.09/2.42  % (23556)------------------------------
% 6.09/2.42  % (23556)------------------------------
% 6.09/2.42  % (23578)Instruction limit reached!
% 6.09/2.42  % (23578)------------------------------
% 6.09/2.42  % (23578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.42  % (23578)Termination reason: Unknown
% 6.09/2.42  % (23578)Termination phase: Property scanning
% 6.09/2.42  
% 6.09/2.42  % (23578)Memory used [KB]: 3198
% 6.09/2.42  % (23578)Time elapsed: 0.054 s
% 6.09/2.42  % (23578)Instructions burned: 99 (million)
% 6.09/2.42  % (23578)------------------------------
% 6.09/2.42  % (23578)------------------------------
% 6.09/2.44  % (23580)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_23404 for (2994ds/149Mi)
% 6.09/2.44  % (23581)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23404 for (2994ds/39Mi)
% 6.09/2.46  % (23581)Instruction limit reached!
% 6.09/2.46  % (23581)------------------------------
% 6.09/2.46  % (23581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.46  % (23581)Termination reason: Unknown
% 6.09/2.46  % (23581)Termination phase: shuffling
% 6.09/2.46  
% 6.09/2.46  % (23581)Memory used [KB]: 2302
% 6.09/2.46  % (23581)Time elapsed: 0.023 s
% 6.09/2.46  % (23581)Instructions burned: 39 (million)
% 6.09/2.46  % (23581)------------------------------
% 6.09/2.46  % (23581)------------------------------
% 6.09/2.47  % (23563)Instruction limit reached!
% 6.09/2.47  % (23563)------------------------------
% 6.09/2.47  % (23563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.47  % (23563)Termination reason: Unknown
% 6.09/2.47  % (23563)Termination phase: Saturation
% 6.09/2.47  
% 6.09/2.47  % (23563)Memory used [KB]: 9083
% 6.09/2.47  % (23563)Time elapsed: 0.412 s
% 6.09/2.47  % (23563)Instructions burned: 780 (million)
% 6.09/2.47  % (23563)------------------------------
% 6.09/2.47  % (23563)------------------------------
% 6.09/2.49  % (23582)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23404 for (2994ds/6Mi)
% 6.09/2.49  % (23583)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_23404 for (2994ds/1087Mi)
% 6.09/2.49  % (23582)Instruction limit reached!
% 6.09/2.49  % (23582)------------------------------
% 6.09/2.49  % (23582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.49  % (23582)Termination reason: Unknown
% 6.09/2.49  % (23582)Termination phase: shuffling
% 6.09/2.49  
% 6.09/2.49  % (23582)Memory used [KB]: 1663
% 6.09/2.49  % (23582)Time elapsed: 0.006 s
% 6.09/2.49  % (23582)Instructions burned: 6 (million)
% 6.09/2.49  % (23582)------------------------------
% 6.09/2.49  % (23582)------------------------------
% 7.18/2.51  % (23584)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/47Mi)
% 7.18/2.52  % (23580)Instruction limit reached!
% 7.18/2.52  % (23580)------------------------------
% 7.18/2.52  % (23580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.52  % (23580)Termination reason: Unknown
% 7.18/2.52  % (23580)Termination phase: Property scanning
% 7.18/2.52  
% 7.18/2.52  % (23580)Memory used [KB]: 9338
% 7.18/2.52  % (23580)Time elapsed: 0.083 s
% 7.18/2.52  % (23580)Instructions burned: 149 (million)
% 7.18/2.52  % (23580)------------------------------
% 7.18/2.52  % (23580)------------------------------
% 7.18/2.54  % (23584)Instruction limit reached!
% 7.18/2.54  % (23584)------------------------------
% 7.18/2.54  % (23584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.54  % (23584)Termination reason: Unknown
% 7.18/2.54  % (23584)Termination phase: Property scanning
% 7.18/2.54  
% 7.18/2.54  % (23584)Memory used [KB]: 2302
% 7.18/2.54  % (23584)Time elapsed: 0.028 s
% 7.18/2.54  % (23584)Instructions burned: 48 (million)
% 7.18/2.54  % (23584)------------------------------
% 7.18/2.54  % (23584)------------------------------
% 7.18/2.54  % (23585)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/44Mi)
% 7.18/2.55  % (23565)Instruction limit reached!
% 7.18/2.55  % (23565)------------------------------
% 7.18/2.55  % (23565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.55  % (23565)Termination reason: Unknown
% 7.18/2.55  % (23565)Termination phase: Saturation
% 7.18/2.55  
% 7.18/2.55  % (23565)Memory used [KB]: 11257
% 7.18/2.55  % (23565)Time elapsed: 0.486 s
% 7.18/2.55  % (23565)Instructions burned: 879 (million)
% 7.18/2.55  % (23565)------------------------------
% 7.18/2.55  % (23565)------------------------------
% 7.18/2.55  % (23547)Instruction limit reached!
% 7.18/2.55  % (23547)------------------------------
% 7.18/2.55  % (23547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.55  % (23547)Termination reason: Unknown
% 7.18/2.55  % (23547)Termination phase: Saturation
% 7.18/2.55  
% 7.18/2.55  % (23547)Memory used [KB]: 10490
% 7.18/2.55  % (23547)Time elapsed: 0.595 s
% 7.18/2.55  % (23547)Instructions burned: 1041 (million)
% 7.18/2.55  % (23547)------------------------------
% 7.18/2.55  % (23547)------------------------------
% 7.18/2.56  % (23586)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/432Mi)
% 7.18/2.57  % (23585)Instruction limit reached!
% 7.18/2.57  % (23585)------------------------------
% 7.18/2.57  % (23585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.57  % (23585)Termination reason: Unknown
% 7.18/2.57  % (23585)Termination phase: shuffling
% 7.18/2.57  
% 7.18/2.57  % (23585)Memory used [KB]: 2430
% 7.18/2.57  % (23585)Time elapsed: 0.025 s
% 7.18/2.57  % (23585)Instructions burned: 44 (million)
% 7.18/2.57  % (23585)------------------------------
% 7.18/2.57  % (23585)------------------------------
% 7.18/2.57  % (23587)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/62Mi)
% 7.18/2.57  % (23576)Instruction limit reached!
% 7.18/2.57  % (23576)------------------------------
% 7.18/2.57  % (23576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.57  % (23576)Termination reason: Unknown
% 7.18/2.57  % (23576)Termination phase: Saturation
% 7.18/2.57  
% 7.18/2.57  % (23576)Memory used [KB]: 8699
% 7.18/2.57  % (23576)Time elapsed: 0.236 s
% 7.18/2.57  % (23576)Instructions burned: 449 (million)
% 7.18/2.57  % (23576)------------------------------
% 7.18/2.57  % (23576)------------------------------
% 7.18/2.58  % (23588)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/31Mi)
% 7.18/2.59  % (23589)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/96Mi)
% 7.18/2.59  % (23588)Instruction limit reached!
% 7.18/2.59  % (23588)------------------------------
% 7.18/2.59  % (23588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.59  % (23588)Termination reason: Unknown
% 7.18/2.59  % (23588)Termination phase: shuffling
% 7.18/2.59  
% 7.18/2.59  % (23588)Memory used [KB]: 2046
% 7.18/2.59  % (23588)Time elapsed: 0.019 s
% 7.18/2.59  % (23588)Instructions burned: 31 (million)
% 7.18/2.59  % (23588)------------------------------
% 7.18/2.59  % (23588)------------------------------
% 7.18/2.60  % (23590)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_23404 for (2993ds/453Mi)
% 8.24/2.60  % (23587)Instruction limit reached!
% 8.24/2.60  % (23587)------------------------------
% 8.24/2.60  % (23587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.60  % (23587)Termination reason: Unknown
% 8.24/2.60  % (23587)Termination phase: shuffling
% 8.24/2.60  
% 8.24/2.60  % (23587)Memory used [KB]: 2814
% 8.24/2.60  % (23587)Time elapsed: 0.035 s
% 8.24/2.60  % (23587)Instructions burned: 62 (million)
% 8.24/2.60  % (23587)------------------------------
% 8.24/2.60  % (23587)------------------------------
% 8.24/2.61  % (23591)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/71Mi)
% 8.24/2.62  % (23592)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/83Mi)
% 8.24/2.64  % (23589)Instruction limit reached!
% 8.24/2.64  % (23589)------------------------------
% 8.24/2.64  % (23589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.64  % (23589)Termination reason: Unknown
% 8.24/2.64  % (23589)Termination phase: Preprocessing 3
% 8.24/2.64  
% 8.24/2.64  % (23589)Memory used [KB]: 3070
% 8.24/2.64  % (23589)Time elapsed: 0.055 s
% 8.24/2.64  % (23589)Instructions burned: 96 (million)
% 8.24/2.64  % (23589)------------------------------
% 8.24/2.64  % (23589)------------------------------
% 8.24/2.65  % (23591)Instruction limit reached!
% 8.24/2.65  % (23591)------------------------------
% 8.24/2.65  % (23591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.65  % (23591)Termination reason: Unknown
% 8.24/2.65  % (23591)Termination phase: Preprocessing 1
% 8.24/2.65  
% 8.24/2.65  % (23591)Memory used [KB]: 2430
% 8.24/2.65  % (23591)Time elapsed: 0.041 s
% 8.24/2.65  % (23591)Instructions burned: 71 (million)
% 8.24/2.65  % (23591)------------------------------
% 8.24/2.65  % (23591)------------------------------
% 8.24/2.66  % (23593)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/11Mi)
% 8.24/2.67  % (23593)Instruction limit reached!
% 8.24/2.67  % (23593)------------------------------
% 8.24/2.67  % (23593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67  % (23593)Termination reason: Unknown
% 8.24/2.67  % (23593)Termination phase: shuffling
% 8.24/2.67  
% 8.24/2.67  % (23593)Memory used [KB]: 1791
% 8.24/2.67  % (23593)Time elapsed: 0.009 s
% 8.24/2.67  % (23593)Instructions burned: 12 (million)
% 8.24/2.67  % (23593)------------------------------
% 8.24/2.67  % (23593)------------------------------
% 8.24/2.67  % (23592)Instruction limit reached!
% 8.24/2.67  % (23592)------------------------------
% 8.24/2.67  % (23592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.67  % (23592)Termination reason: Unknown
% 8.24/2.67  % (23592)Termination phase: Preprocessing 1
% 8.24/2.67  
% 8.24/2.67  % (23592)Memory used [KB]: 2430
% 8.24/2.67  % (23592)Time elapsed: 0.049 s
% 8.24/2.67  % (23592)Instructions burned: 84 (million)
% 8.24/2.67  % (23592)------------------------------
% 8.24/2.67  % (23592)------------------------------
% 8.24/2.67  % (23594)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/41Mi)
% 8.24/2.69  % (23579)Instruction limit reached!
% 8.24/2.69  % (23579)------------------------------
% 8.24/2.69  % (23579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.69  % (23579)Termination reason: Unknown
% 8.24/2.69  % (23579)Termination phase: Saturation
% 8.24/2.69  
% 8.24/2.69  % (23579)Memory used [KB]: 10874
% 8.24/2.69  % (23579)Time elapsed: 0.288 s
% 8.24/2.69  % (23579)Instructions burned: 508 (million)
% 8.24/2.69  % (23579)------------------------------
% 8.24/2.69  % (23579)------------------------------
% 8.24/2.69  % (23595)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/6Mi)
% 8.24/2.69  % (23596)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23404 for (2992ds/150Mi)
% 8.24/2.69  % (23595)Instruction limit reached!
% 8.24/2.69  % (23595)------------------------------
% 8.24/2.69  % (23595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.69  % (23595)Termination reason: Unknown
% 8.24/2.69  % (23595)Termination phase: shuffling
% 8.24/2.69  
% 8.24/2.69  % (23595)Memory used [KB]: 1663
% 8.24/2.69  % (23595)Time elapsed: 0.006 s
% 8.24/2.69  % (23595)Instructions burned: 6 (million)
% 8.24/2.69  % (23595)------------------------------
% 8.24/2.69  % (23595)------------------------------
% 8.24/2.70  % (23594)Instruction limit reached!
% 8.24/2.70  % (23594)------------------------------
% 8.24/2.70  % (23594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.70  % (23594)Termination reason: Unknown
% 8.24/2.70  % (23594)Termination phase: shuffling
% 8.24/2.70  
% 8.24/2.70  % (23594)Memory used [KB]: 2302
% 8.24/2.70  % (23594)Time elapsed: 0.024 s
% 8.24/2.70  % (23594)Instructions burned: 41 (million)
% 8.24/2.70  % (23594)------------------------------
% 8.24/2.70  % (23594)------------------------------
% 8.89/2.71  % (23597)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23404 for (2991ds/343Mi)
% 8.89/2.71  % (23598)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_23404 for (2991ds/109Mi)
% 8.89/2.72  % (23599)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_23404 for (2991ds/253Mi)
% 8.89/2.77  % (23598)Instruction limit reached!
% 8.89/2.77  % (23598)------------------------------
% 8.89/2.77  % (23598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.77  % (23598)Termination reason: Unknown
% 8.89/2.77  % (23598)Termination phase: Preprocessing 3
% 8.89/2.77  
% 8.89/2.77  % (23598)Memory used [KB]: 3070
% 8.89/2.77  % (23598)Time elapsed: 0.062 s
% 8.89/2.77  % (23598)Instructions burned: 109 (million)
% 8.89/2.77  % (23598)------------------------------
% 8.89/2.77  % (23598)------------------------------
% 8.89/2.77  % (23596)Instruction limit reached!
% 8.89/2.77  % (23596)------------------------------
% 8.89/2.77  % (23596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.77  % (23596)Termination reason: Unknown
% 8.89/2.77  % (23596)Termination phase: Property scanning
% 8.89/2.77  
% 8.89/2.77  % (23596)Memory used [KB]: 3709
% 8.89/2.77  % (23596)Time elapsed: 0.085 s
% 8.89/2.77  % (23596)Instructions burned: 151 (million)
% 8.89/2.77  % (23596)------------------------------
% 8.89/2.77  % (23596)------------------------------
% 8.89/2.79  % (23586)Instruction limit reached!
% 8.89/2.79  % (23586)------------------------------
% 8.89/2.79  % (23586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.79  % (23586)Termination reason: Unknown
% 8.89/2.79  % (23586)Termination phase: Saturation
% 8.89/2.79  
% 8.89/2.79  % (23586)Memory used [KB]: 4477
% 8.89/2.79  % (23586)Time elapsed: 0.234 s
% 8.89/2.79  % (23586)Instructions burned: 433 (million)
% 8.89/2.79  % (23586)------------------------------
% 8.89/2.79  % (23586)------------------------------
% 8.89/2.80  % (23600)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23404 for (2991ds/140Mi)
% 8.89/2.80  % (23601)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_23404 for (2991ds/614Mi)
% 9.33/2.81  % (23602)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_23404 for (2990ds/202Mi)
% 9.33/2.84  % (23590)Instruction limit reached!
% 9.33/2.84  % (23590)------------------------------
% 9.33/2.84  % (23590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.84  % (23590)Termination reason: Unknown
% 9.33/2.84  % (23590)Termination phase: Saturation
% 9.33/2.84  
% 9.33/2.84  % (23590)Memory used [KB]: 9083
% 9.33/2.84  % (23590)Time elapsed: 0.246 s
% 9.33/2.84  % (23590)Instructions burned: 454 (million)
% 9.33/2.84  % (23590)------------------------------
% 9.33/2.84  % (23590)------------------------------
% 9.33/2.85  % (23599)Instruction limit reached!
% 9.33/2.85  % (23599)------------------------------
% 9.33/2.85  % (23599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.85  % (23599)Termination reason: Unknown
% 9.33/2.85  % (23599)Termination phase: Saturation
% 9.33/2.85  
% 9.33/2.85  % (23599)Memory used [KB]: 4733
% 9.33/2.85  % (23599)Time elapsed: 0.140 s
% 9.33/2.85  % (23599)Instructions burned: 254 (million)
% 9.33/2.85  % (23599)------------------------------
% 9.33/2.85  % (23599)------------------------------
% 9.33/2.86  % (23603)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_23404 for (2990ds/339Mi)
% 9.33/2.87  % (23600)Instruction limit reached!
% 9.33/2.87  % (23600)------------------------------
% 9.33/2.87  % (23600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.87  % (23600)Termination reason: Unknown
% 9.33/2.87  % (23600)Termination phase: Saturation
% 9.33/2.87  
% 9.33/2.87  % (23600)Memory used [KB]: 7291
% 9.33/2.87  % (23600)Time elapsed: 0.081 s
% 9.33/2.87  % (23600)Instructions burned: 140 (million)
% 9.33/2.87  % (23600)------------------------------
% 9.33/2.87  % (23600)------------------------------
% 9.33/2.88  % (23604)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_23404 for (2990ds/283Mi)
% 9.33/2.89  % (23602)Refutation not found, incomplete strategy
% 9.33/2.89  % (23602)------------------------------
% 9.33/2.89  % (23602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.89  % (23602)Termination reason: Refutation not found, incomplete strategy
% 9.33/2.89  
% 9.33/2.89  
% 9.33/2.89  % (23602)Memory used [KB]: 7675
% 9.33/2.89  % (23602)Time elapsed: 0.080 s
% 9.33/2.89  % (23602)Instructions burned: 138 (million)
% 9.33/2.89  % (23602)------------------------------
% 9.33/2.89  % (23602)------------------------------
% 9.33/2.90  % (23597)Instruction limit reached!
% 9.33/2.90  % (23597)------------------------------
% 9.33/2.90  % (23597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.90  % (23597)Termination reason: Unknown
% 9.33/2.90  % (23597)Termination phase: Saturation
% 9.33/2.90  
% 9.33/2.90  % (23597)Memory used [KB]: 8827
% 9.33/2.90  % (23597)Time elapsed: 0.189 s
% 9.33/2.90  % (23597)Instructions burned: 343 (million)
% 9.33/2.90  % (23597)------------------------------
% 9.33/2.90  % (23597)------------------------------
% 9.97/2.90  % (23605)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23404 for (2989ds/134Mi)
% 9.97/2.91  % (23606)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23404 for (2989ds/298Mi)
% 9.97/2.92  % (23607)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23404 for (2989ds/192Mi)
% 9.97/2.97  % (23605)Instruction limit reached!
% 9.97/2.97  % (23605)------------------------------
% 9.97/2.97  % (23605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.97  % (23605)Termination reason: Unknown
% 9.97/2.97  % (23605)Termination phase: Property scanning
% 9.97/2.97  
% 9.97/2.97  % (23605)Memory used [KB]: 3454
% 9.97/2.97  % (23605)Time elapsed: 0.074 s
% 9.97/2.97  % (23605)Instructions burned: 134 (million)
% 9.97/2.97  % (23605)------------------------------
% 9.97/2.97  % (23605)------------------------------
% 9.97/2.99  % (23608)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_23404 for (2988ds/258Mi)
% 9.97/3.02  % (23607)Instruction limit reached!
% 9.97/3.02  % (23607)------------------------------
% 9.97/3.02  % (23607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/3.02  % (23607)Termination reason: Unknown
% 9.97/3.02  % (23607)Termination phase: Property scanning
% 9.97/3.02  
% 9.97/3.02  % (23607)Memory used [KB]: 3582
% 9.97/3.02  % (23607)Time elapsed: 0.104 s
% 9.97/3.02  % (23607)Instructions burned: 192 (million)
% 9.97/3.02  % (23607)------------------------------
% 9.97/3.02  % (23607)------------------------------
% 9.97/3.02  % (23604)Instruction limit reached!
% 9.97/3.02  % (23604)------------------------------
% 9.97/3.02  % (23604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/3.02  % (23604)Termination reason: Unknown
% 9.97/3.02  % (23604)Termination phase: Saturation
% 9.97/3.02  
% 9.97/3.02  % (23604)Memory used [KB]: 7931
% 9.97/3.02  % (23604)Time elapsed: 0.148 s
% 9.97/3.02  % (23604)Instructions burned: 284 (million)
% 9.97/3.02  % (23604)------------------------------
% 9.97/3.02  % (23604)------------------------------
% 11.70/3.04  % (23609)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_23404 for (2988ds/90Mi)
% 11.70/3.04  % (23610)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_23404 for (2988ds/231Mi)
% 11.70/3.05  % (23603)Instruction limit reached!
% 11.70/3.05  % (23603)------------------------------
% 11.70/3.05  % (23603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.05  % (23603)Termination reason: Unknown
% 11.70/3.05  % (23603)Termination phase: Saturation
% 11.70/3.05  
% 11.70/3.05  % (23603)Memory used [KB]: 8443
% 11.70/3.05  % (23603)Time elapsed: 0.208 s
% 11.70/3.05  % (23603)Instructions burned: 339 (million)
% 11.70/3.05  % (23603)------------------------------
% 11.70/3.05  % (23603)------------------------------
% 11.70/3.07  % (23606)Instruction limit reached!
% 11.70/3.07  % (23606)------------------------------
% 11.70/3.07  % (23606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.07  % (23606)Termination reason: Unknown
% 11.70/3.07  % (23606)Termination phase: Saturation
% 11.70/3.07  
% 11.70/3.07  % (23606)Memory used [KB]: 7931
% 11.70/3.07  % (23606)Time elapsed: 0.156 s
% 11.70/3.07  % (23606)Instructions burned: 299 (million)
% 11.70/3.07  % (23606)------------------------------
% 11.70/3.07  % (23606)------------------------------
% 11.70/3.07  % (23611)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_23404 for (2988ds/458Mi)
% 11.70/3.09  % (23612)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23404 for (2988ds/31Mi)
% 11.70/3.09  % (23609)Instruction limit reached!
% 11.70/3.09  % (23609)------------------------------
% 11.70/3.09  % (23609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.09  % (23609)Termination reason: Unknown
% 11.70/3.09  % (23609)Termination phase: Preprocessing 3
% 11.70/3.09  
% 11.70/3.09  % (23609)Memory used [KB]: 2942
% 11.70/3.09  % (23609)Time elapsed: 0.052 s
% 11.70/3.09  % (23609)Instructions burned: 91 (million)
% 11.70/3.09  % (23609)------------------------------
% 11.70/3.09  % (23609)------------------------------
% 11.70/3.11  % (23612)Instruction limit reached!
% 11.70/3.11  % (23612)------------------------------
% 11.70/3.11  % (23612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.11  % (23612)Termination reason: Unknown
% 11.70/3.11  % (23612)Termination phase: shuffling
% 11.70/3.11  
% 11.70/3.11  % (23612)Memory used [KB]: 2046
% 11.70/3.11  % (23612)Time elapsed: 0.020 s
% 11.70/3.11  % (23612)Instructions burned: 31 (million)
% 11.70/3.11  % (23612)------------------------------
% 11.70/3.11  % (23612)------------------------------
% 11.70/3.11  % (23613)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/297Mi)
% 11.70/3.12  % (23583)Instruction limit reached!
% 11.70/3.12  % (23583)------------------------------
% 11.70/3.12  % (23583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.12  % (23583)Termination reason: Unknown
% 11.70/3.12  % (23583)Termination phase: Saturation
% 11.70/3.12  
% 11.70/3.12  % (23583)Memory used [KB]: 10490
% 11.70/3.12  % (23583)Time elapsed: 0.631 s
% 11.70/3.12  % (23583)Instructions burned: 1088 (million)
% 11.70/3.12  % (23583)------------------------------
% 11.70/3.12  % (23583)------------------------------
% 11.70/3.13  % (23608)Instruction limit reached!
% 11.70/3.13  % (23608)------------------------------
% 11.70/3.13  % (23608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.13  % (23608)Termination reason: Unknown
% 11.70/3.13  % (23608)Termination phase: Property scanning
% 11.70/3.13  
% 11.70/3.13  % (23608)Memory used [KB]: 9210
% 11.70/3.13  % (23608)Time elapsed: 0.136 s
% 11.70/3.13  % (23608)Instructions burned: 258 (million)
% 11.70/3.13  % (23608)------------------------------
% 11.70/3.13  % (23608)------------------------------
% 12.20/3.13  % (23614)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/987Mi)
% 12.20/3.13  % (23601)Instruction limit reached!
% 12.20/3.13  % (23601)------------------------------
% 12.20/3.13  % (23601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.20/3.13  % (23601)Termination reason: Unknown
% 12.20/3.13  % (23601)Termination phase: Saturation
% 12.20/3.13  
% 12.20/3.13  % (23601)Memory used [KB]: 10618
% 12.20/3.13  % (23601)Time elapsed: 0.359 s
% 12.20/3.13  % (23601)Instructions burned: 615 (million)
% 12.20/3.13  % (23601)------------------------------
% 12.20/3.13  % (23601)------------------------------
% 12.20/3.14  % (23615)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/182Mi)
% 12.20/3.15  % (23616)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/182Mi)
% 12.20/3.15  % (23617)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/154Mi)
% 12.20/3.16  % (23610)Instruction limit reached!
% 12.20/3.16  % (23610)------------------------------
% 12.20/3.16  % (23610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.20/3.16  % (23610)Termination reason: Unknown
% 12.20/3.16  % (23610)Termination phase: Property scanning
% 12.20/3.16  
% 12.20/3.16  % (23610)Memory used [KB]: 3326
% 12.20/3.16  % (23610)Time elapsed: 0.121 s
% 12.20/3.16  % (23610)Instructions burned: 231 (million)
% 12.20/3.16  % (23610)------------------------------
% 12.20/3.16  % (23610)------------------------------
% 12.20/3.19  % (23618)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_23404 for (2987ds/79Mi)
% 12.36/3.23  % (23618)Instruction limit reached!
% 12.36/3.23  % (23618)------------------------------
% 12.36/3.23  % (23618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.23  % (23618)Termination reason: Unknown
% 12.36/3.23  % (23618)Termination phase: Preprocessing 3
% 12.36/3.23  
% 12.36/3.23  % (23618)Memory used [KB]: 2686
% 12.36/3.23  % (23618)Time elapsed: 0.046 s
% 12.36/3.23  % (23618)Instructions burned: 80 (million)
% 12.36/3.23  % (23618)------------------------------
% 12.36/3.23  % (23618)------------------------------
% 12.36/3.23  % (23617)Instruction limit reached!
% 12.36/3.23  % (23617)------------------------------
% 12.36/3.23  % (23617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.23  % (23617)Termination reason: Unknown
% 12.36/3.23  % (23617)Termination phase: Property scanning
% 12.36/3.23  
% 12.36/3.23  % (23617)Memory used [KB]: 3198
% 12.36/3.23  % (23617)Time elapsed: 0.082 s
% 12.36/3.23  % (23617)Instructions burned: 155 (million)
% 12.36/3.23  % (23617)------------------------------
% 12.36/3.23  % (23617)------------------------------
% 12.36/3.24  % (23615)Instruction limit reached!
% 12.36/3.24  % (23615)------------------------------
% 12.36/3.24  % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.24  % (23615)Termination reason: Unknown
% 12.36/3.24  % (23615)Termination phase: Property scanning
% 12.36/3.24  
% 12.36/3.24  % (23615)Memory used [KB]: 9338
% 12.36/3.24  % (23615)Time elapsed: 0.098 s
% 12.36/3.24  % (23615)Instructions burned: 182 (million)
% 12.36/3.24  % (23615)------------------------------
% 12.36/3.24  % (23615)------------------------------
% 12.36/3.25  % (23616)Instruction limit reached!
% 12.36/3.25  % (23616)------------------------------
% 12.36/3.25  % (23616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.25  % (23616)Termination reason: Unknown
% 12.36/3.25  % (23616)Termination phase: Property scanning
% 12.36/3.25  
% 12.36/3.25  % (23616)Memory used [KB]: 3709
% 12.36/3.25  % (23616)Time elapsed: 0.100 s
% 12.36/3.25  % (23616)Instructions burned: 183 (million)
% 12.36/3.25  % (23616)------------------------------
% 12.36/3.25  % (23616)------------------------------
% 12.36/3.25  % (23619)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_23404 for (2986ds/216Mi)
% 12.36/3.25  % (23620)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23404 for (2986ds/114Mi)
% 12.36/3.26  % (23621)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_23404 for (2986ds/922Mi)
% 12.36/3.27  % (23613)Instruction limit reached!
% 12.36/3.27  % (23613)------------------------------
% 12.36/3.27  % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.27  % (23613)Termination reason: Unknown
% 12.36/3.27  % (23613)Termination phase: Saturation
% 12.36/3.27  
% 12.36/3.27  % (23613)Memory used [KB]: 7803
% 12.36/3.27  % (23613)Time elapsed: 0.157 s
% 12.36/3.27  % (23613)Instructions burned: 298 (million)
% 12.36/3.27  % (23613)------------------------------
% 12.36/3.27  % (23613)------------------------------
% 12.36/3.27  % (23622)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_23404 for (2986ds/182Mi)
% 12.36/3.29  % (23623)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_23404 for (2986ds/164Mi)
% 12.95/3.32  % (23620)Instruction limit reached!
% 12.95/3.32  % (23620)------------------------------
% 12.95/3.32  % (23620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.32  % (23620)Termination reason: Unknown
% 12.95/3.32  % (23620)Termination phase: Property scanning
% 12.95/3.32  
% 12.95/3.32  % (23620)Memory used [KB]: 3582
% 12.95/3.32  % (23620)Time elapsed: 0.065 s
% 12.95/3.32  % (23620)Instructions burned: 114 (million)
% 12.95/3.32  % (23620)------------------------------
% 12.95/3.32  % (23620)------------------------------
% 12.95/3.32  % (23611)Instruction limit reached!
% 12.95/3.32  % (23611)------------------------------
% 12.95/3.32  % (23611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.32  % (23611)Termination reason: Unknown
% 12.95/3.32  % (23611)Termination phase: Saturation
% 12.95/3.32  
% 12.95/3.32  % (23611)Memory used [KB]: 10106
% 12.95/3.32  % (23611)Time elapsed: 0.250 s
% 12.95/3.32  % (23611)Instructions burned: 458 (million)
% 12.95/3.32  % (23611)------------------------------
% 12.95/3.32  % (23611)------------------------------
% 12.95/3.34  % (23624)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/50Mi)
% 12.95/3.34  % (23625)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/368Mi)
% 12.95/3.35  % (23619)Instruction limit reached!
% 12.95/3.35  % (23619)------------------------------
% 12.95/3.35  % (23619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.35  % (23619)Termination reason: Unknown
% 12.95/3.35  % (23619)Termination phase: Property scanning
% 12.95/3.35  
% 12.95/3.35  % (23619)Memory used [KB]: 3198
% 12.95/3.35  % (23619)Time elapsed: 0.100 s
% 12.95/3.35  % (23619)Instructions burned: 217 (million)
% 12.95/3.35  % (23619)------------------------------
% 12.95/3.35  % (23619)------------------------------
% 12.95/3.36  % (23622)Instruction limit reached!
% 12.95/3.36  % (23622)------------------------------
% 12.95/3.36  % (23622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.36  % (23622)Termination reason: Unknown
% 12.95/3.36  % (23622)Termination phase: Property scanning
% 12.95/3.36  
% 12.95/3.36  % (23622)Memory used [KB]: 3198
% 12.95/3.36  % (23622)Time elapsed: 0.096 s
% 12.95/3.36  % (23622)Instructions burned: 183 (million)
% 12.95/3.36  % (23622)------------------------------
% 12.95/3.36  % (23622)------------------------------
% 12.95/3.37  % (23624)Instruction limit reached!
% 12.95/3.37  % (23624)------------------------------
% 12.95/3.37  % (23624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.37  % (23624)Termination reason: Unknown
% 12.95/3.37  % (23624)Termination phase: shuffling
% 12.95/3.37  
% 12.95/3.37  % (23624)Memory used [KB]: 2686
% 12.95/3.37  % (23624)Time elapsed: 0.029 s
% 12.95/3.37  % (23624)Instructions burned: 51 (million)
% 12.95/3.37  % (23624)------------------------------
% 12.95/3.37  % (23624)------------------------------
% 12.95/3.37  % (23626)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/1021Mi)
% 12.95/3.38  % (23623)Instruction limit reached!
% 12.95/3.38  % (23623)------------------------------
% 12.95/3.38  % (23623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.38  % (23623)Termination reason: Unknown
% 12.95/3.38  % (23623)Termination phase: SInE selection
% 12.95/3.38  
% 12.95/3.38  % (23623)Memory used [KB]: 3198
% 12.95/3.38  % (23623)Time elapsed: 0.089 s
% 12.95/3.38  % (23623)Instructions burned: 165 (million)
% 12.95/3.38  % (23623)------------------------------
% 12.95/3.38  % (23623)------------------------------
% 12.95/3.38  % (23628)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/204Mi)
% 12.95/3.38  % (23627)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/267Mi)
% 13.69/3.40  % (23629)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23404 for (2985ds/26Mi)
% 13.69/3.42  % (23629)Instruction limit reached!
% 13.69/3.42  % (23629)------------------------------
% 13.69/3.42  % (23629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.42  % (23629)Termination reason: Unknown
% 13.69/3.42  % (23629)Termination phase: shuffling
% 13.69/3.42  
% 13.69/3.42  % (23629)Memory used [KB]: 2174
% 13.69/3.42  % (23629)Time elapsed: 0.017 s
% 13.69/3.42  % (23629)Instructions burned: 26 (million)
% 13.69/3.42  % (23629)------------------------------
% 13.69/3.42  % (23629)------------------------------
% 13.69/3.44  % (23630)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_23404 for (2984ds/53Mi)
% 13.69/3.47  % (23630)Instruction limit reached!
% 13.69/3.47  % (23630)------------------------------
% 13.69/3.47  % (23630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.47  % (23630)Termination reason: Unknown
% 13.69/3.47  % (23630)Termination phase: shuffling
% 13.69/3.47  
% 13.69/3.47  % (23630)Memory used [KB]: 2686
% 13.69/3.47  % (23630)Time elapsed: 0.030 s
% 13.69/3.47  % (23630)Instructions burned: 53 (million)
% 13.69/3.47  % (23630)------------------------------
% 13.69/3.47  % (23630)------------------------------
% 13.69/3.49  % (23628)Instruction limit reached!
% 13.69/3.49  % (23628)------------------------------
% 13.69/3.49  % (23628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.49  % (23628)Termination reason: Unknown
% 13.69/3.49  % (23628)Termination phase: Property scanning
% 13.69/3.49  
% 13.69/3.49  % (23628)Memory used [KB]: 3582
% 13.69/3.49  % (23628)Time elapsed: 0.106 s
% 13.69/3.49  % (23628)Instructions burned: 205 (million)
% 13.69/3.49  % (23628)------------------------------
% 13.69/3.49  % (23628)------------------------------
% 13.69/3.49  % (23631)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_23404 for (2984ds/4436Mi)
% 13.89/3.51  % (23632)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_23404 for (2983ds/1539Mi)
% 13.89/3.52  % (23627)Instruction limit reached!
% 13.89/3.52  % (23627)------------------------------
% 13.89/3.52  % (23627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.89/3.52  % (23627)Termination reason: Unknown
% 13.89/3.52  % (23627)Termination phase: Saturation
% 13.89/3.52  
% 13.89/3.52  % (23627)Memory used [KB]: 7803
% 13.89/3.52  % (23627)Time elapsed: 0.140 s
% 13.89/3.52  % (23627)Instructions burned: 267 (million)
% 13.89/3.52  % (23627)------------------------------
% 13.89/3.52  % (23627)------------------------------
% 13.89/3.54  % (23625)Instruction limit reached!
% 13.89/3.54  % (23625)------------------------------
% 13.89/3.54  % (23625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.89/3.54  % (23625)Termination reason: Unknown
% 13.89/3.54  % (23625)Termination phase: Saturation
% 13.89/3.54  
% 13.89/3.54  % (23625)Memory used [KB]: 8955
% 13.89/3.54  % (23625)Time elapsed: 0.200 s
% 13.89/3.54  % (23625)Instructions burned: 369 (million)
% 13.89/3.54  % (23625)------------------------------
% 13.89/3.54  % (23625)------------------------------
% 13.89/3.54  % (23633)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_23404 for (2983ds/408Mi)
% 13.89/3.56  % (23634)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_23404 for (2983ds/5205Mi)
% 14.27/3.68  % (23614)Instruction limit reached!
% 14.27/3.68  % (23614)------------------------------
% 14.27/3.68  % (23614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/3.68  % (23614)Termination reason: Unknown
% 14.27/3.68  % (23614)Termination phase: Saturation
% 14.27/3.68  
% 14.27/3.68  % (23614)Memory used [KB]: 10234
% 14.27/3.68  % (23614)Time elapsed: 0.551 s
% 14.27/3.68  % (23614)Instructions burned: 988 (million)
% 14.27/3.68  % (23614)------------------------------
% 14.27/3.68  % (23614)------------------------------
% 14.85/3.70  % (23635)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_23404 for (2982ds/1913Mi)
% 14.85/3.77  % (23633)Instruction limit reached!
% 14.85/3.77  % (23633)------------------------------
% 14.85/3.77  % (23633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.77  % (23633)Termination reason: Unknown
% 14.85/3.77  % (23633)Termination phase: Saturation
% 14.85/3.77  
% 14.85/3.77  % (23633)Memory used [KB]: 10234
% 14.85/3.77  % (23633)Time elapsed: 0.253 s
% 14.85/3.77  % (23633)Instructions burned: 408 (million)
% 14.85/3.77  % (23633)------------------------------
% 14.85/3.77  % (23633)------------------------------
% 14.85/3.78  % (23621)Instruction limit reached!
% 14.85/3.78  % (23621)------------------------------
% 14.85/3.78  % (23621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.78  % (23621)Termination reason: Unknown
% 14.85/3.78  % (23621)Termination phase: Saturation
% 14.85/3.78  
% 14.85/3.78  % (23621)Memory used [KB]: 9850
% 14.85/3.78  % (23621)Time elapsed: 0.530 s
% 14.85/3.78  % (23621)Instructions burned: 922 (million)
% 14.85/3.78  % (23621)------------------------------
% 14.85/3.78  % (23621)------------------------------
% 15.66/3.80  % (23636)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_23404 for (2980ds/4350Mi)
% 15.66/3.81  % (23637)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_23404 for (2980ds/68Mi)
% 15.66/3.84  % (23637)Instruction limit reached!
% 15.66/3.84  % (23637)------------------------------
% 15.66/3.84  % (23637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.66/3.84  % (23637)Termination reason: Unknown
% 15.66/3.84  % (23637)Termination phase: SInE selection
% 15.66/3.84  
% 15.66/3.84  % (23637)Memory used [KB]: 2302
% 15.66/3.84  % (23637)Time elapsed: 0.040 s
% 15.66/3.84  % (23637)Instructions burned: 69 (million)
% 15.66/3.84  % (23637)------------------------------
% 15.66/3.84  % (23637)------------------------------
% 15.66/3.87  % (23638)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_23404 for (2980ds/358Mi)
% 15.72/3.95  % (23626)Instruction limit reached!
% 15.72/3.95  % (23626)------------------------------
% 15.72/3.95  % (23626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.72/3.95  % (23626)Termination reason: Unknown
% 15.72/3.95  % (23626)Termination phase: Saturation
% 15.72/3.95  
% 15.72/3.95  % (23626)Memory used [KB]: 10490
% 15.72/3.95  % (23626)Time elapsed: 0.578 s
% 15.72/3.95  % (23626)Instructions burned: 1022 (million)
% 15.72/3.95  % (23626)------------------------------
% 15.72/3.95  % (23626)------------------------------
% 15.72/3.97  % (23639)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23404 for (2979ds/31Mi)
% 15.72/3.99  % (23639)Instruction limit reached!
% 15.72/3.99  % (23639)------------------------------
% 15.72/3.99  % (23639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.72/3.99  % (23639)Termination reason: Unknown
% 15.72/3.99  % (23639)Termination phase: shuffling
% 15.72/3.99  
% 15.72/3.99  % (23639)Memory used [KB]: 2046
% 15.72/3.99  % (23639)Time elapsed: 0.020 s
% 15.72/3.99  % (23639)Instructions burned: 31 (million)
% 15.72/3.99  % (23639)------------------------------
% 15.72/3.99  % (23639)------------------------------
% 15.72/4.01  % (23640)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23404 for (2978ds/279Mi)
% 18.68/4.07  % (23638)Instruction limit reached!
% 18.68/4.07  % (23638)------------------------------
% 18.68/4.07  % (23638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/4.07  % (23638)Termination reason: Unknown
% 18.68/4.07  % (23638)Termination phase: Saturation
% 18.68/4.07  
% 18.68/4.07  % (23638)Memory used [KB]: 8443
% 18.68/4.07  % (23638)Time elapsed: 0.200 s
% 18.68/4.07  % (23638)Instructions burned: 358 (million)
% 18.68/4.07  % (23638)------------------------------
% 18.68/4.07  % (23638)------------------------------
% 18.68/4.09  % (23641)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23404 for (2978ds/258Mi)
% 19.34/4.16  % (23640)Instruction limit reached!
% 19.34/4.16  % (23640)------------------------------
% 19.34/4.16  % (23640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/4.16  % (23640)Termination reason: Unknown
% 19.34/4.16  % (23640)Termination phase: Saturation
% 19.34/4.16  
% 19.34/4.16  % (23640)Memory used [KB]: 3454
% 19.34/4.16  % (23640)Time elapsed: 0.146 s
% 19.34/4.16  % (23640)Instructions burned: 279 (million)
% 19.34/4.16  % (23640)------------------------------
% 19.34/4.16  % (23640)------------------------------
% 19.34/4.18  % (23642)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23404 for (2977ds/26Mi)
% 19.34/4.19  % (23642)Instruction limit reached!
% 19.34/4.19  % (23642)------------------------------
% 19.34/4.19  % (23642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/4.19  % (23642)Termination reason: Unknown
% 19.34/4.19  % (23642)Termination phase: shuffling
% 19.34/4.19  
% 19.34/4.19  % (23642)Memory used [KB]: 2174
% 19.34/4.19  % (23642)Time elapsed: 0.016 s
% 19.34/4.19  % (23642)Instructions burned: 27 (million)
% 19.34/4.19  % (23642)------------------------------
% 19.34/4.19  % (23642)------------------------------
% 19.75/4.22  % (23643)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_23404 for (2976ds/995Mi)
% 19.75/4.23  % (23641)Instruction limit reached!
% 19.75/4.23  % (23641)------------------------------
% 19.75/4.23  % (23641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.23  % (23641)Termination reason: Unknown
% 19.75/4.23  % (23641)Termination phase: Saturation
% 19.75/4.23  
% 19.75/4.23  % (23641)Memory used [KB]: 8443
% 19.75/4.23  % (23641)Time elapsed: 0.142 s
% 19.75/4.23  % (23641)Instructions burned: 259 (million)
% 19.75/4.23  % (23641)------------------------------
% 19.75/4.23  % (23641)------------------------------
% 19.75/4.25  % (23644)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_23404 for (2976ds/373Mi)
% 20.42/4.38  % (23632)Instruction limit reached!
% 20.42/4.38  % (23632)------------------------------
% 20.42/4.38  % (23632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.38  % (23632)Termination reason: Unknown
% 20.42/4.38  % (23632)Termination phase: Saturation
% 20.42/4.38  
% 20.42/4.38  % (23632)Memory used [KB]: 12920
% 20.42/4.38  % (23632)Time elapsed: 0.897 s
% 20.42/4.38  % (23632)Instructions burned: 1540 (million)
% 20.42/4.38  % (23632)------------------------------
% 20.42/4.38  % (23632)------------------------------
% 20.91/4.41  % (23645)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_23404 for (2974ds/253Mi)
% 20.91/4.46  % (23644)Instruction limit reached!
% 20.91/4.46  % (23644)------------------------------
% 20.91/4.46  % (23644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.91/4.46  % (23644)Termination reason: Unknown
% 20.91/4.46  % (23644)Termination phase: Saturation
% 20.91/4.46  
% 20.91/4.46  % (23644)Memory used [KB]: 9466
% 20.91/4.46  % (23644)Time elapsed: 0.208 s
% 20.91/4.46  % (23644)Instructions burned: 373 (million)
% 20.91/4.46  % (23644)------------------------------
% 20.91/4.46  % (23644)------------------------------
% 20.91/4.48  % (23646)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_23404 for (2974ds/832Mi)
% 21.54/4.54  % (23645)Instruction limit reached!
% 21.54/4.54  % (23645)------------------------------
% 21.54/4.54  % (23645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.54  % (23645)Termination reason: Unknown
% 21.54/4.54  % (23645)Termination phase: Saturation
% 21.54/4.54  
% 21.54/4.54  % (23645)Memory used [KB]: 3326
% 21.54/4.54  % (23645)Time elapsed: 0.133 s
% 21.54/4.54  % (23645)Instructions burned: 253 (million)
% 21.54/4.54  % (23645)------------------------------
% 21.54/4.54  % (23645)------------------------------
% 21.54/4.56  % (23647)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_23404 for (2973ds/668Mi)
% 22.08/4.66  % (23646)Refutation not found, incomplete strategy
% 22.08/4.66  % (23646)------------------------------
% 22.08/4.66  % (23646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.08/4.66  % (23646)Termination reason: Refutation not found, incomplete strategy
% 22.08/4.66  
% 22.08/4.66  
% 22.08/4.66  % (23646)Memory used [KB]: 9978
% 22.08/4.66  % (23646)Time elapsed: 0.182 s
% 22.08/4.66  % (23646)Instructions burned: 314 (million)
% 22.08/4.66  % (23646)------------------------------
% 22.08/4.66  % (23646)------------------------------
% 22.08/4.69  % (23648)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_23404 for (2972ds/40Mi)
% 22.69/4.71  % (23648)Instruction limit reached!
% 22.69/4.71  % (23648)------------------------------
% 22.69/4.71  % (23648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.69/4.71  % (23648)Termination reason: Unknown
% 22.69/4.71  % (23648)Termination phase: shuffling
% 22.69/4.71  
% 22.69/4.71  % (23648)Memory used [KB]: 2302
% 22.69/4.71  % (23648)Time elapsed: 0.024 s
% 22.69/4.71  % (23648)Instructions burned: 41 (million)
% 22.69/4.71  % (23648)------------------------------
% 22.69/4.71  % (23648)------------------------------
% 22.69/4.73  % (23649)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_23404 for (2971ds/294Mi)
% 22.69/4.74  % (23643)Instruction limit reached!
% 22.69/4.74  % (23643)------------------------------
% 22.69/4.74  % (23643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.69/4.74  % (23643)Termination reason: Unknown
% 22.69/4.74  % (23643)Termination phase: Saturation
% 22.69/4.74  
% 22.69/4.74  % (23643)Memory used [KB]: 9210
% 22.69/4.74  % (23643)Time elapsed: 0.523 s
% 22.69/4.74  % (23643)Instructions burned: 996 (million)
% 22.69/4.74  % (23643)------------------------------
% 22.69/4.74  % (23643)------------------------------
% 22.69/4.74  % (23635)Instruction limit reached!
% 22.69/4.74  % (23635)------------------------------
% 22.69/4.74  % (23635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.69/4.74  % (23635)Termination reason: Unknown
% 22.69/4.74  % (23635)Termination phase: Saturation
% 22.69/4.74  
% 22.69/4.74  % (23635)Memory used [KB]: 4989
% 22.69/4.74  % (23635)Time elapsed: 1.068 s
% 22.69/4.74  % (23635)Instructions burned: 1913 (million)
% 22.69/4.74  % (23635)------------------------------
% 22.69/4.74  % (23635)------------------------------
% 22.69/4.76  % (23650)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_23404 for (2971ds/187Mi)
% 22.69/4.77  % (23651)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23404 for (2971ds/371Mi)
% 23.64/4.85  % (23649)Refutation not found, incomplete strategy
% 23.64/4.85  % (23649)------------------------------
% 23.64/4.85  % (23649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.85  % (23649)Termination reason: Refutation not found, incomplete strategy
% 23.64/4.85  
% 23.64/4.85  
% 23.64/4.85  % (23649)Memory used [KB]: 7931
% 23.64/4.85  % (23649)Time elapsed: 0.121 s
% 23.64/4.85  % (23649)Instructions burned: 228 (million)
% 23.64/4.85  % (23649)------------------------------
% 23.64/4.85  % (23649)------------------------------
% 23.64/4.86  % (23650)Instruction limit reached!
% 23.64/4.86  % (23650)------------------------------
% 23.64/4.86  % (23650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.86  % (23650)Termination reason: Unknown
% 23.64/4.86  % (23650)Termination phase: Property scanning
% 23.64/4.86  
% 23.64/4.86  % (23650)Memory used [KB]: 3582
% 23.64/4.86  % (23650)Time elapsed: 0.102 s
% 23.64/4.86  % (23650)Instructions burned: 188 (million)
% 23.64/4.86  % (23650)------------------------------
% 23.64/4.86  % (23650)------------------------------
% 23.64/4.88  % (23652)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23404 for (2970ds/1827Mi)
% 23.64/4.88  % (23653)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_23404 for (2970ds/70Mi)
% 24.19/4.91  % (23647)Instruction limit reached!
% 24.19/4.91  % (23647)------------------------------
% 24.19/4.91  % (23647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.19/4.91  % (23647)Termination reason: Unknown
% 24.19/4.91  % (23647)Termination phase: Saturation
% 24.19/4.91  
% 24.19/4.91  % (23647)Memory used [KB]: 15607
% 24.19/4.91  % (23647)Time elapsed: 0.330 s
% 24.19/4.91  % (23647)Instructions burned: 670 (million)
% 24.19/4.91  % (23647)------------------------------
% 24.19/4.91  % (23647)------------------------------
% 24.19/4.92  % (23653)Instruction limit reached!
% 24.19/4.92  % (23653)------------------------------
% 24.19/4.92  % (23653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.19/4.92  % (23653)Termination reason: Unknown
% 24.19/4.92  % (23653)Termination phase: shuffling
% 24.19/4.92  
% 24.19/4.92  % (23653)Memory used [KB]: 2942
% 24.19/4.92  % (23653)Time elapsed: 0.039 s
% 24.19/4.92  % (23653)Instructions burned: 71 (million)
% 24.19/4.92  % (23653)------------------------------
% 24.19/4.92  % (23653)------------------------------
% 24.19/4.93  % (23654)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_23404 for (2969ds/316Mi)
% 24.19/4.94  % (23655)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_23404 for (2969ds/932Mi)
% 24.19/4.97  % (23651)Instruction limit reached!
% 24.19/4.97  % (23651)------------------------------
% 24.19/4.97  % (23651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.19/4.97  % (23651)Termination reason: Unknown
% 24.19/4.97  % (23651)Termination phase: Saturation
% 24.19/4.97  
% 24.19/4.97  % (23651)Memory used [KB]: 9338
% 24.19/4.97  % (23651)Time elapsed: 0.210 s
% 24.19/4.97  % (23651)Instructions burned: 371 (million)
% 24.19/4.97  % (23651)------------------------------
% 24.19/4.97  % (23651)------------------------------
% 24.19/5.00  % (23656)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_23404 for (2969ds/4714Mi)
% 25.61/5.09  % (23654)Instruction limit reached!
% 25.61/5.09  % (23654)------------------------------
% 25.61/5.09  % (23654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.61/5.09  % (23654)Termination reason: Unknown
% 25.61/5.09  % (23654)Termination phase: Saturation
% 25.61/5.09  
% 25.61/5.09  % (23654)Memory used [KB]: 3709
% 25.61/5.09  % (23654)Time elapsed: 0.166 s
% 25.61/5.09  % (23654)Instructions burned: 316 (million)
% 25.61/5.09  % (23654)------------------------------
% 25.61/5.09  % (23654)------------------------------
% 25.61/5.12  % (23657)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_23404 for (2967ds/8250Mi)
% 26.32/5.18  % (23656)Refutation not found, incomplete strategy
% 26.32/5.18  % (23656)------------------------------
% 26.32/5.18  % (23656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.32/5.18  % (23656)Termination reason: Refutation not found, incomplete strategy
% 26.32/5.18  
% 26.32/5.18  
% 26.32/5.18  % (23656)Memory used [KB]: 8955
% 26.32/5.18  % (23656)Time elapsed: 0.186 s
% 26.32/5.18  % (23656)Instructions burned: 345 (million)
% 26.32/5.18  % (23656)------------------------------
% 26.32/5.18  % (23656)------------------------------
% 26.72/5.21  % (23658)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_23404 for (2966ds/770Mi)
% 26.72/5.29  % (23658)Refutation not found, incomplete strategy
% 26.72/5.29  % (23658)------------------------------
% 26.72/5.29  % (23658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.72/5.29  % (23658)Termination reason: Refutation not found, incomplete strategy
% 26.72/5.29  
% 26.72/5.29  
% 26.72/5.29  % (23658)Memory used [KB]: 7419
% 26.72/5.29  % (23658)Time elapsed: 0.080 s
% 26.72/5.29  % (23658)Instructions burned: 136 (million)
% 26.72/5.29  % (23658)------------------------------
% 26.72/5.29  % (23658)------------------------------
% 27.32/5.31  % (23659)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23404 for (2965ds/794Mi)
% 27.82/5.43  % (23655)First to succeed.
% 27.82/5.44  % (23655)Refutation found. Thanks to Tanya!
% 27.82/5.44  % SZS status Theorem for DTF2THF_23404
% 27.82/5.44  % SZS output start Proof for DTF2THF_23404
% 27.82/5.44  thf(type_def_5, type, pi: $tType).
% 27.82/5.44  thf(type_def_7, type, name: $tType).
% 27.82/5.44  thf(type_def_8, type, late_freeRes: $tType).
% 27.82/5.44  thf(type_def_9, type, late_subject: $tType).
% 27.82/5.44  thf(type_def_10, type, late_residual: $tType).
% 27.82/5.44  thf(type_def_11, type, noption_name: $tType).
% 27.82/5.44  thf(type_def_12, type, noption_pi: $tType).
% 27.82/5.44  thf(type_def_13, type, noption_Late_freeRes: $tType).
% 27.82/5.44  thf(type_def_14, type, produc1141751126_pi_pi: $tType).
% 27.82/5.44  thf(type_def_15, type, noptio1575811931_pi_pi: $tType).
% 27.82/5.44  thf(type_def_16, type, produc1462499409ion_pi: $tType).
% 27.82/5.44  thf(type_def_17, type, produc405342261i_name: $tType).
% 27.82/5.44  thf(type_def_18, type, produc629157763_pi_pi: $tType).
% 27.82/5.44  thf(type_def_19, type, produc1834551554reeRes: $tType).
% 27.82/5.44  thf(type_def_20, type, produc53907987_pi_pi: $tType).
% 27.82/5.44  thf(type_def_21, type, produc367475239e_name: $tType).
% 27.82/5.44  thf(type_def_22, type, product_prod_name_pi: $tType).
% 27.82/5.44  thf(type_def_23, type, produc2008547984reeRes: $tType).
% 27.82/5.44  thf(type_def_24, type, product_prod_pi_name: $tType).
% 27.82/5.44  thf(type_def_25, type, product_prod_pi_pi: $tType).
% 27.82/5.44  thf(type_def_26, type, produc649380958reeRes: $tType).
% 27.82/5.44  thf(type_def_27, type, produc2052722628s_name: $tType).
% 27.82/5.44  thf(type_def_28, type, produc992857746Res_pi: $tType).
% 27.82/5.44  thf(type_def_29, type, produc1357834675reeRes: $tType).
% 27.82/5.44  thf(type_def_30, type, set_Pr1834926343_pi_pi: $tType).
% 27.82/5.44  thf(func_def_0, type, produc53907987_pi_pi: $tType).
% 27.82/5.44  thf(func_def_1, type, produc1462499409ion_pi: $tType).
% 27.82/5.44  thf(func_def_2, type, noptio1575811931_pi_pi: $tType).
% 27.82/5.44  thf(func_def_3, type, produc1834551554reeRes: $tType).
% 27.82/5.44  thf(func_def_4, type, produc405342261i_name: $tType).
% 27.82/5.44  thf(func_def_5, type, produc629157763_pi_pi: $tType).
% 27.82/5.44  thf(func_def_6, type, produc1141751126_pi_pi: $tType).
% 27.82/5.44  thf(func_def_7, type, produc1357834675reeRes: $tType).
% 27.82/5.44  thf(func_def_8, type, produc2052722628s_name: $tType).
% 27.82/5.44  thf(func_def_9, type, produc2008547984reeRes: $tType).
% 27.82/5.44  thf(func_def_10, type, produc992857746Res_pi: $tType).
% 27.82/5.44  thf(func_def_11, type, produc649380958reeRes: $tType).
% 27.82/5.44  thf(func_def_12, type, set_Pr1834926343_pi_pi: $tType).
% 27.82/5.44  thf(func_def_13, type, produc367475239e_name: $tType).
% 27.82/5.44  thf(func_def_14, type, product_prod_pi_name: $tType).
% 27.82/5.44  thf(func_def_15, type, product_prod_name_pi: $tType).
% 27.82/5.44  thf(func_def_16, type, product_prod_pi_pi: $tType).
% 27.82/5.44  thf(func_def_17, type, noption_Late_freeRes: $tType).
% 27.82/5.44  thf(func_def_18, type, noption_name: $tType).
% 27.82/5.44  thf(func_def_19, type, noption_pi: $tType).
% 27.82/5.44  thf(func_def_20, type, late_residual: $tType).
% 27.82/5.44  thf(func_def_21, type, late_subject: $tType).
% 27.82/5.44  thf(func_def_22, type, late_freeRes: $tType).
% 27.82/5.44  thf(func_def_23, type, name: $tType).
% 27.82/5.44  thf(func_def_24, type, pi: $tType).
% 27.82/5.44  thf(func_def_25, type, bang: pi > pi).
% 27.82/5.44  thf(func_def_26, type, input: name > name > pi > pi).
% 27.82/5.44  thf(func_def_27, type, match: name > name > pi > pi).
% 27.82/5.44  thf(func_def_28, type, mismatch: name > name > pi > pi).
% 27.82/5.44  thf(func_def_29, type, output: name > name > pi > pi).
% 27.82/5.44  thf(func_def_30, type, par: pi > pi > pi).
% 27.82/5.44  thf(func_def_31, type, piNil: pi).
% 27.82/5.44  thf(func_def_32, type, res: name > pi > pi).
% 27.82/5.44  thf(func_def_33, type, sum: pi > pi > pi).
% 27.82/5.44  thf(func_def_34, type, tau: pi > pi).
% 27.82/5.44  thf(func_def_35, type, subs: pi > name > name > pi).
% 27.82/5.44  thf(func_def_36, type, subst_name: name > name > name > name).
% 27.82/5.44  thf(func_def_37, type, if_name: $o > name > name > name).
% 27.82/5.44  thf(func_def_38, type, late_OutputR: name > name > late_freeRes).
% 27.82/5.44  thf(func_def_39, type, late_TauR: late_freeRes).
% 27.82/5.44  thf(func_def_40, type, late_BoundR: late_subject > name > pi > late_residual).
% 27.82/5.44  thf(func_def_41, type, late_FreeR: late_freeRes > pi > late_residual).
% 27.82/5.44  thf(func_def_42, type, late_BoundOutputS: name > late_subject).
% 27.82/5.44  thf(func_def_43, type, late_InputS: name > late_subject).
% 27.82/5.44  thf(func_def_44, type, late_transitions: pi > late_residual > $o).
% 27.82/5.44  thf(func_def_45, type, abs_fun_name_name: name > name > name > noption_name).
% 27.82/5.44  thf(func_def_46, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 27.82/5.44  thf(func_def_47, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 27.82/5.44  thf(func_def_48, type, abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi).
% 27.82/5.44  thf(func_def_49, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 27.82/5.44  thf(func_def_50, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 27.82/5.44  thf(func_def_51, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 27.82/5.44  thf(func_def_52, type, fresh_2065563522_pi_pi: name > (name > noptio1575811931_pi_pi) > $o).
% 27.82/5.44  thf(func_def_53, type, fresh_name_name: name > name > $o).
% 27.82/5.44  thf(func_def_54, type, fresh_name_pi: name > pi > $o).
% 27.82/5.44  thf(func_def_55, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 27.82/5.44  thf(func_def_56, type, fresh_81631222sidual: name > late_residual > $o).
% 27.82/5.44  thf(func_def_57, type, fresh_717452603ubject: name > late_subject > $o).
% 27.82/5.44  thf(func_def_58, type, fresh_225680151ion_pi: name > produc1462499409ion_pi > $o).
% 27.82/5.44  thf(func_def_59, type, fresh_453496559i_name: name > produc405342261i_name > $o).
% 27.82/5.44  thf(func_def_60, type, fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o).
% 27.82/5.44  thf(func_def_61, type, fresh_1711070152reeRes: name > produc1834551554reeRes > $o).
% 27.82/5.44  thf(func_def_62, type, fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o).
% 27.82/5.44  thf(func_def_63, type, fresh_441084397e_name: name > produc367475239e_name > $o).
% 27.82/5.44  thf(func_def_64, type, fresh_93646139ame_pi: name > product_prod_name_pi > $o).
% 27.82/5.44  thf(func_def_65, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 27.82/5.44  thf(func_def_66, type, fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o).
% 27.82/5.44  thf(func_def_67, type, fresh_261416607i_name: name > product_prod_pi_name > $o).
% 27.82/5.44  thf(func_def_68, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 27.82/5.44  thf(func_def_69, type, fresh_1504024600reeRes: name > produc649380958reeRes > $o).
% 27.82/5.44  thf(func_def_70, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 27.82/5.44  thf(func_def_71, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 27.82/5.44  thf(func_def_72, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 27.82/5.44  thf(func_def_73, type, produc1342893193ion_pi: (name > noption_pi) > (name > noption_pi) > produc1462499409ion_pi).
% 27.82/5.44  thf(func_def_74, type, produc540578151i_name: (name > noption_pi) > name > produc405342261i_name).
% 27.82/5.44  thf(func_def_75, type, produc1820286517_pi_pi: (name > noption_pi) > pi > produc629157763_pi_pi).
% 27.82/5.44  thf(func_def_76, type, produc1505598906reeRes: (name > noption_pi) > late_freeRes > produc1834551554reeRes).
% 27.82/5.44  thf(func_def_77, type, produc1275980869_pi_pi: (name > noption_pi) > produc1141751126_pi_pi > produc53907987_pi_pi).
% 27.82/5.44  thf(func_def_78, type, produc1570949143e_name: name > name > produc367475239e_name).
% 27.82/5.44  thf(func_def_79, type, product_Pair_name_pi: name > pi > product_prod_name_pi).
% 27.82/5.44  thf(func_def_80, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 27.82/5.44  thf(func_def_81, type, produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi).
% 27.82/5.44  thf(func_def_82, type, product_Pair_pi_name: pi > name > product_prod_pi_name).
% 27.82/5.44  thf(func_def_83, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 27.82/5.44  thf(func_def_84, type, produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes).
% 27.82/5.44  thf(func_def_85, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 27.82/5.44  thf(func_def_86, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 27.82/5.44  thf(func_def_87, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 27.82/5.44  thf(func_def_88, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 27.82/5.44  thf(func_def_89, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 27.82/5.44  thf(func_def_90, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 27.82/5.44  thf(func_def_91, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 27.82/5.44  thf(func_def_92, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 27.82/5.44  thf(func_def_93, type, p: pi).
% 27.82/5.44  thf(func_def_94, type, p2: pi).
% 27.82/5.44  thf(func_def_95, type, pxQ: pi).
% 27.82/5.44  thf(func_def_96, type, q: pi).
% 27.82/5.44  thf(func_def_97, type, rel: set_Pr1834926343_pi_pi).
% 27.82/5.44  thf(func_def_98, type, aa: late_subject).
% 27.82/5.44  thf(func_def_99, type, u: name).
% 27.82/5.44  thf(func_def_100, type, x: name).
% 27.82/5.44  thf(func_def_101, type, y: name).
% 27.82/5.44  thf(func_def_126, type, ph1: !>[X0: $tType]:(X0)).
% 27.82/5.44  thf(func_def_127, type, sK2: product_prod_pi_pi > pi).
% 27.82/5.44  thf(func_def_128, type, sK3: product_prod_pi_pi > pi).
% 27.82/5.44  thf(func_def_129, type, sK4: (product_prod_pi_pi > $o) > pi).
% 27.82/5.44  thf(func_def_130, type, sK5: name > name).
% 27.82/5.44  thf(func_def_131, type, sK6: (product_prod_pi_pi > $o) > pi).
% 27.82/5.44  thf(f2806,plain,(
% 27.82/5.44    $false),
% 27.82/5.44    inference(trivial_inequality_removal,[status(thm)],[f2805])).
% 27.82/5.44  thf(f2805,plain,(
% 27.82/5.44    ($false = $true)),
% 27.82/5.44    inference(boolean_simplification,[status(thm)],[f2804])).
% 27.82/5.44  thf(f2804,plain,(
% 27.82/5.44    ($true = (~ $true))),
% 27.82/5.44    inference(forward_demodulation,[status(thm)],[f2801,f1183])).
% 27.82/5.44  thf(f1183,plain,(
% 27.82/5.44    ((fresh_name_pi @ x @ (subs @ p2 @ y @ u)) = $true)),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f746])).
% 27.82/5.44  thf(f746,plain,(
% 27.82/5.44    ((fresh_name_pi @ x @ (subs @ p2 @ y @ u)) = $true)),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f745])).
% 27.82/5.44  thf(f745,plain,(
% 27.82/5.44    (fresh_name_pi @ x @ (subs @ p2 @ y @ u))),
% 27.82/5.44    inference(rectify,[status(thm)],[f4])).
% 27.82/5.44  thf(f4,axiom,(
% 27.82/5.44    (fresh_name_pi @ x @ (subs @ p2 @ y @ u))),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062)).
% 27.82/5.44  thf(f2801,plain,(
% 27.82/5.44    ($true = (~ (fresh_name_pi @ x @ (subs @ p2 @ y @ u))))),
% 27.82/5.44    inference(boolean_simplification,[status(thm)],[f2764])).
% 27.82/5.44  thf(f2764,plain,(
% 27.82/5.44    (((fresh_name_pi @ x @ (subs @ p2 @ y @ u)) => $false) = $true)),
% 27.82/5.44    inference(superposition,[status(thm)],[f2736,f1972])).
% 27.82/5.44  thf(f1972,plain,(
% 27.82/5.44    ($false = (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ x @ (par @ (subs @ p2 @ y @ u) @ q)) @ (par @ (subs @ p2 @ y @ u) @ (res @ x @ q))) @ rel))),
% 27.82/5.44    inference(forward_demodulation,[status(thm)],[f1963,f1961])).
% 27.82/5.44  thf(f1961,plain,(
% 27.82/5.44    ((subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) = (res @ x @ (par @ (subs @ p2 @ y @ u) @ q)))),
% 27.82/5.44    inference(backward_demodulation,[status(thm)],[f1066,f1949])).
% 27.82/5.44  thf(f1949,plain,(
% 27.82/5.44    ( ! [X0 : name] : ((q = (subs @ q @ y @ X0))) )),
% 27.82/5.44    inference(equality_proxy_clausification,[status(thm)],[f1912])).
% 27.82/5.44  thf(f1912,plain,(
% 27.82/5.44    ( ! [X0 : name] : (($true = ((subs @ q @ y @ X0) = q))) )),
% 27.82/5.44    inference(boolean_simplification,[status(thm)],[f1900])).
% 27.82/5.44  thf(f1900,plain,(
% 27.82/5.44    ( ! [X0 : name] : ((($true => ((subs @ q @ y @ X0) = q)) = $true)) )),
% 27.82/5.44    inference(superposition,[status(thm)],[f1880,f1150])).
% 27.82/5.44  thf(f1150,plain,(
% 27.82/5.44    ((fresh_name_pi @ y @ q) = $true)),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f449])).
% 27.82/5.44  thf(f449,plain,(
% 27.82/5.44    ((fresh_name_pi @ y @ q) = $true)),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f448])).
% 27.82/5.44  thf(f448,plain,(
% 27.82/5.44    (fresh_name_pi @ y @ q)),
% 27.82/5.44    inference(rectify,[status(thm)],[f7])).
% 27.82/5.44  thf(f7,axiom,(
% 27.82/5.44    (fresh_name_pi @ y @ q)),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062)).
% 27.82/5.44  thf(f1880,plain,(
% 27.82/5.44    ( ! [X2 : pi,X3 : name,X1 : name] : (($true = ((fresh_name_pi @ X3 @ X2) => ((subs @ X2 @ X3 @ X1) = X2)))) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f1877])).
% 27.82/5.44  thf(f1877,plain,(
% 27.82/5.44    ( ! [X2 : pi,X3 : name,X1 : name] : (($true = ((^[Y0 : name]: ((fresh_name_pi @ Y0 @ X2) => ((subs @ X2 @ Y0 @ X1) = X2))) @ X3))) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f1863])).
% 27.82/5.44  thf(f1863,plain,(
% 27.82/5.44    ( ! [X2 : pi,X1 : name] : (($true = (!! @ name @ (^[Y0 : name]: ((fresh_name_pi @ Y0 @ X2) => ((subs @ X2 @ Y0 @ X1) = X2)))))) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f1860])).
% 27.82/5.44  thf(f1860,plain,(
% 27.82/5.44    ( ! [X2 : pi,X1 : name] : ((((^[Y0 : pi]: (!! @ name @ (^[Y1 : name]: ((fresh_name_pi @ Y1 @ Y0) => ((subs @ Y0 @ Y1 @ X1) = Y0))))) @ X2) = $true)) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f1849])).
% 27.82/5.44  thf(f1849,plain,(
% 27.82/5.44    ( ! [X1 : name] : (((!! @ pi @ (^[Y0 : pi]: (!! @ name @ (^[Y1 : name]: ((fresh_name_pi @ Y1 @ Y0) => ((subs @ Y0 @ Y1 @ X1) = Y0)))))) = $true)) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f1844])).
% 27.82/5.44  thf(f1844,plain,(
% 27.82/5.44    ( ! [X1 : name] : (($true = ((^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ name @ (^[Y2 : name]: ((fresh_name_pi @ Y2 @ Y1) => ((subs @ Y1 @ Y2 @ Y0) = Y1))))))) @ X1))) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f1189])).
% 27.82/5.44  thf(f1189,plain,(
% 27.82/5.44    ((!! @ name @ (^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ name @ (^[Y2 : name]: ((fresh_name_pi @ Y2 @ Y1) => ((subs @ Y1 @ Y2 @ Y0) = Y1)))))))) = $true)),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f403])).
% 27.82/5.44  thf(f403,plain,(
% 27.82/5.44    ((!! @ name @ (^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ name @ (^[Y2 : name]: ((fresh_name_pi @ Y2 @ Y1) => ((subs @ Y1 @ Y2 @ Y0) = Y1)))))))) = $true)),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f402])).
% 27.82/5.44  thf(f402,plain,(
% 27.82/5.44    ! [X0 : name,X1 : pi,X2 : name] : ((fresh_name_pi @ X0 @ X1) => ((subs @ X1 @ X0 @ X2) = X1))),
% 27.82/5.44    inference(rectify,[status(thm)],[f48])).
% 27.82/5.44  thf(f48,axiom,(
% 27.82/5.44    ! [X9 : name,X4 : pi,X14 : name] : ((fresh_name_pi @ X9 @ X4) => ((subs @ X4 @ X9 @ X14) = X4))),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_47_forget)).
% 27.82/5.44  thf(f1066,plain,(
% 27.82/5.44    ((subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) = (res @ x @ (par @ (subs @ p2 @ y @ u) @ (subs @ q @ y @ u))))),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f876])).
% 27.82/5.44  thf(f876,plain,(
% 27.82/5.44    ((subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) = (res @ x @ (par @ (subs @ p2 @ y @ u) @ (subs @ q @ y @ u))))),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f6])).
% 27.82/5.44  thf(f6,axiom,(
% 27.82/5.44    ((subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) = (res @ x @ (par @ (subs @ p2 @ y @ u) @ (subs @ q @ y @ u))))),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062)).
% 27.82/5.44  thf(f1963,plain,(
% 27.82/5.44    ($false = (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (res @ x @ q))) @ rel))),
% 27.82/5.44    inference(backward_demodulation,[status(thm)],[f1465,f1949])).
% 27.82/5.44  thf(f1465,plain,(
% 27.82/5.44    ($false = (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (res @ x @ (subs @ q @ y @ u)))) @ rel))),
% 27.82/5.44    inference(not_proxy_clausification,[status(thm)],[f1464])).
% 27.82/5.44  thf(f1464,plain,(
% 27.82/5.44    ((~ (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (res @ x @ (subs @ q @ y @ u)))) @ rel)) = $true)),
% 27.82/5.44    inference(backward_demodulation,[status(thm)],[f1350,f1095])).
% 27.82/5.44  thf(f1095,plain,(
% 27.82/5.44    ((subs @ (res @ x @ q) @ y @ u) = (res @ x @ (subs @ q @ y @ u)))),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f720])).
% 27.82/5.44  thf(f720,plain,(
% 27.82/5.44    ((subs @ (res @ x @ q) @ y @ u) = (res @ x @ (subs @ q @ y @ u)))),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f2])).
% 27.82/5.44  thf(f2,axiom,(
% 27.82/5.44    ((subs @ (res @ x @ q) @ y @ u) = (res @ x @ (subs @ q @ y @ u)))),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062)).
% 27.82/5.44  thf(f1350,plain,(
% 27.82/5.44    ($true = (~ (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (subs @ (res @ x @ q) @ y @ u))) @ rel)))),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f740])).
% 27.82/5.44  thf(f740,plain,(
% 27.82/5.44    ($true = (~ (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (subs @ (res @ x @ q) @ y @ u))) @ rel)))),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f739])).
% 27.82/5.44  thf(f739,plain,(
% 27.82/5.44    ~(member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (subs @ (res @ x @ q) @ y @ u))) @ rel)),
% 27.82/5.44    inference(rectify,[status(thm)],[f340])).
% 27.82/5.44  thf(f340,negated_conjecture,(
% 27.82/5.44    ~(member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (subs @ (res @ x @ q) @ y @ u))) @ rel)),
% 27.82/5.44    inference(negated_conjecture,[status(cth)],[f339])).
% 27.82/5.44  thf(f339,conjecture,(
% 27.82/5.44    (member558706512_pi_pi @ (product_Pair_pi_pi @ (subs @ (res @ x @ (par @ p2 @ q)) @ y @ u) @ (par @ (subs @ p2 @ y @ u) @ (subs @ (res @ x @ q) @ y @ u))) @ rel)),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',conj_0)).
% 27.82/5.44  thf(f2736,plain,(
% 27.82/5.44    ( ! [X2 : pi,X3 : pi,X1 : name] : (($true = ((fresh_name_pi @ X1 @ X2) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X1 @ (par @ X2 @ X3)) @ (par @ X2 @ (res @ X1 @ X3))) @ rel)))) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f2731])).
% 27.82/5.44  thf(f2731,plain,(
% 27.82/5.44    ( ! [X2 : pi,X3 : pi,X1 : name] : ((((^[Y0 : pi]: ((fresh_name_pi @ X1 @ X2) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X1 @ (par @ X2 @ Y0)) @ (par @ X2 @ (res @ X1 @ Y0))) @ rel))) @ X3) = $true)) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f2692])).
% 27.82/5.44  thf(f2692,plain,(
% 27.82/5.44    ( ! [X2 : pi,X1 : name] : (((!! @ pi @ (^[Y0 : pi]: ((fresh_name_pi @ X1 @ X2) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X1 @ (par @ X2 @ Y0)) @ (par @ X2 @ (res @ X1 @ Y0))) @ rel)))) = $true)) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f2683])).
% 27.82/5.44  thf(f2683,plain,(
% 27.82/5.44    ( ! [X2 : pi,X1 : name] : ((((^[Y0 : pi]: (!! @ pi @ (^[Y1 : pi]: ((fresh_name_pi @ X1 @ Y0) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X1 @ (par @ Y0 @ Y1)) @ (par @ Y0 @ (res @ X1 @ Y1))) @ rel))))) @ X2) = $true)) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f2671])).
% 27.82/5.44  thf(f2671,plain,(
% 27.82/5.44    ( ! [X1 : name] : (((!! @ pi @ (^[Y0 : pi]: (!! @ pi @ (^[Y1 : pi]: ((fresh_name_pi @ X1 @ Y0) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X1 @ (par @ Y0 @ Y1)) @ (par @ Y0 @ (res @ X1 @ Y1))) @ rel)))))) = $true)) )),
% 27.82/5.44    inference(beta_eta_normalization,[status(thm)],[f2668])).
% 27.82/5.44  thf(f2668,plain,(
% 27.82/5.44    ( ! [X1 : name] : (($true = ((^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ pi @ (^[Y2 : pi]: ((fresh_name_pi @ Y0 @ Y1) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ Y0 @ (par @ Y1 @ Y2)) @ (par @ Y1 @ (res @ Y0 @ Y2))) @ rel))))))) @ X1))) )),
% 27.82/5.44    inference(pi_clausification,[status(thm)],[f1062])).
% 27.82/5.44  thf(f1062,plain,(
% 27.82/5.44    ($true = (!! @ name @ (^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ pi @ (^[Y2 : pi]: ((fresh_name_pi @ Y0 @ Y1) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ Y0 @ (par @ Y1 @ Y2)) @ (par @ Y1 @ (res @ Y0 @ Y2))) @ rel)))))))))),
% 27.82/5.44    inference(cnf_transformation,[status(thm)],[f995])).
% 27.82/5.44  thf(f995,plain,(
% 27.82/5.44    ($true = (!! @ name @ (^[Y0 : name]: (!! @ pi @ (^[Y1 : pi]: (!! @ pi @ (^[Y2 : pi]: ((fresh_name_pi @ Y0 @ Y1) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ Y0 @ (par @ Y1 @ Y2)) @ (par @ Y1 @ (res @ Y0 @ Y2))) @ rel)))))))))),
% 27.82/5.44    inference(fool_elimination,[status(thm)],[f994])).
% 27.82/5.44  thf(f994,plain,(
% 27.82/5.44    ! [X0 : pi,X1 : pi,X2 : name] : ((fresh_name_pi @ X2 @ X1) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X2 @ (par @ X1 @ X0)) @ (par @ X1 @ (res @ X2 @ X0))) @ rel))),
% 27.82/5.44    inference(rectify,[status(thm)],[f9])).
% 27.82/5.44  thf(f9,axiom,(
% 27.82/5.44    ! [X2 : pi,X1 : pi,X0 : name] : ((fresh_name_pi @ X0 @ X1) => (member558706512_pi_pi @ (product_Pair_pi_pi @ (res @ X0 @ (par @ X1 @ X2)) @ (par @ X1 @ (res @ X0 @ X2))) @ rel))),
% 27.82/5.44    file('/export/starexec/sandbox/tmp/tmp.73S2ZW1QB1/DTF2THF_23404.p',fact_8_Res)).
% 27.82/5.44  % SZS output end Proof for DTF2THF_23404
% 27.82/5.44  % (23655)------------------------------
% 27.82/5.44  % (23655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.82/5.44  % (23655)Termination reason: Refutation
% 27.82/5.44  
% 27.82/5.44  % (23655)Memory used [KB]: 10490
% 27.82/5.44  % (23655)Time elapsed: 0.495 s
% 27.82/5.44  % (23655)Instructions burned: 864 (million)
% 27.82/5.44  % (23655)------------------------------
% 27.82/5.44  % (23655)------------------------------
% 27.82/5.44  % (23534)Success in time 3.557 s
%------------------------------------------------------------------------------